Advances in the Bonded Composite Repair of Metallic Aircraft

Advances in the Bonded Composite Repair of Metallic Aircraft
Advances in the Bonded Composite
Repair o f Metallic Aircraft Structure
VOLUME 1
A
Edited by
Alan Baker
Francis Rose
Rhys Jones
ELSEVI ER
ADVANCES IN THE BONDED COMPOSITE
REPAIR OF METALLIC AIRCRAFT
STRUCTURE
Volume 1
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ADVANCES IN THE BONDED COMPOSITE
REPAIR OF METALLIC AIRCRAFT
STRUCTURE
Volume 1
Editors
A.A. Baker
Defence Science and Technology Organisation,
Air Vehicles Division,
Victoria, Australia
L.R.F. Rose
Department of Defince,
Dqfence Science and Technology Organisation,
Air Vehicles Division,
Victoria, Australia
R. Jones
Mechanical Engineering Department,
Monash University, Victoria, Australia
2002
ELSEVIER
Amsterdam Boston London - New York - Oxford Paris
San Diego San Francisco - Singapore - Sydney - Tokyo
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First Edition 2002
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Printed in The Netherlands.
Dr. Alan Baker
Dr. Alan Baker is Research Leader Aerospace Composite Structures, in Airframes
and Engines Division, Defence Science and Technology (DSTO), Aeronautical and
Maritime Research Laboratory and Technical Adviser to the Cooperative Research
Centre-Advanced Composite Structures, Melbourne Australia. He is a Fellow of
the Australian Academy of Technological Sciences and Engineering and an
Adjunct Professor in Department of Aerospace Engineering, Royal Melbourne
Institute of Technology. Dr. Baker is a member of the International Editorial
Boards of the Journals Composites Part A Applied Science and Manufacturing,
Applied Composites and International Journal of Adhesion and Adhesives.
He is recognised for pioneering research work on metal-matrix fibre composites
while at the Rolls Royce Advanced Research Laboratory. More recently, he is
recognised for pioneering work on bonded composite repair of metallic aircraft
components for which he has received several awards, including the 1990 Ministers
Award for Achievement in Defence Science.
Dr. Francis Rose
Dr. Francis Rose is the Research Leader for Fracture Mechanics in Airframes and
Engines Division, Defence Science and Technology (DSTO), Aeronautical and
Maritime Research Laboratory. He has made important research contributions in
fracture mechanics, non-destructive evaluation and applied mathematics. In
particular, his comprehensive design study of bonded repairs and related crackbridging models, and his contributions to the theory of transformation toughening
in partially stabilised zirconia, have received international acclaim. His analysis of
laser-generated ultrasound has become a standard reference in the emerging field of
laser ultrasonics, and he has made seminal contributions to the theory of eddycurrent detection of cracks, and early detection of multiple cracking.
He is the Regional Editor for the Znternational Journal of Fracture and a member
of the editorial board of Mechanics of Materials. He was made a Fellow of the
Institute of Mathematics and its Applications, UK, in 1987, and a Fellow of the
Institution of Engineers, Australia, in 1994. He is currently President of the
Australian Fracture Group, and has been involved in organising several local and
international conferences in the areas of fracture mechanics and engineering
mathematics. He currently serves on the Engineering Selection Panel of the
Australian Research Council and of several other committees and advisory bodies.
vi
Biographies
Professor Rhys Jones
Professor Rhys Jones joined Monash University in early 1993 and is currently
Professor of Mechanical Engineering, and Head of the Defence Science and
Technology Organisation Centre of Expertise on Structural Mechanics. Professor
Jones’ is best known for his in the fields of finite element analysis, composite repairs
and structural integrity assessment. Professor Jones is the Founding Professor of
both the BHP-Monash Railway Technology Institute and the BHP-Monash
Maintenance Technology Institute. He is heavily involved with both Australian
and overseas industry. In this context he ran the mechanical aspects of the
Australian Governments Royal Commission into the failure at the ESSO plant in
Victoria, and the Tubemakers-BHP investigation into the failure of the McArthur
River gas pipe line in the Northern Territory.
He is the recipient of numerous awards including the 1982 (Australian)
Engineering Excellence Award, for composite repairs to Mirage 111, the Institution
of Engineers Australia George Julius Medal, for contributions to failure analysis, a
TTCP Award, for contributions to Australian, US, UK, Canada and NZ Defence
Science in the field of composite structures, and a Rolls-Royce-Qantas Special
Commendation, for his work on F-111 aircraft. Since 1999 Professor Jones has
been Co-Chair of the International Conference (Series) on Composite Structures.
Acknowledgement
The editors are very pleased to acknowledge their appreciation of the great
assistance provided by Drs Stephen Galea and Chun Wang of the Defence Science
and Technology Organisation, Aeronautical and Maritime Research Laboratory,
who made important contributions, in the collation and editing of this book.
FOREWORD
The introduction of the technology for bonded composite repairs of metallic
airframe structures could not have come at a more opportune time. Today, many
countries are facing the challenge of aging aircraft in their inventories. These
airframes are degrading due to damage from fatigue cracking and corrosion.
Repair with dependable techniques to restore their structural integrity is
mandatory. The concept of using bonded composite materials as a means to
maintain aging metallic aircraft was instituted in Australia approximately thirty
years ago. Since that time it has been successfully applied in many situations
requiring repair. These applications have not been limited to Australia. Canada,
the United Kingdom, and the United States have also benefited from the use of this
technology. The application for the solution of the problem of cracking in the fuel
drain holes in wing of the C-141 is credited with maintaining the viability of this
fleet.
The concept for composite repair of metallic aircraft is simple. The bonded repair
reduces stresses in the cracked region and keeps the crack from opening and
therefore from growing. This is easy to demonstrate in a laboratory environment. It
is another thing to do this in the operational environment where many factors exist
that could adversely affect the repair reliability. The researchers at the Aeronautical
and Maritime Research Laboratory in Australian realized there were many
obstacles to overcome to achieve the desired reliability of the process. They also
realized that failures of the repair on operational aircraft would mean loss of
confidence and consequently enthusiasm for the process. They proceeded slowly.
Their deliberate approach paid off in that they developed a process that could be
transitioned to aircraft use by engineers and technicians. The essential ingredient
for application of this technology is discipline. When the applicator of this process
maintains the discipline required for the process and stays within the bounds of
appropriate applications, then the repair will be successful.
This book, edited by Drs A.A. Baker, L.R.F. Rose and R. Jones, includes the
essential aspects of the technology for composite repairs. The editors have chosen
some of the most knowledgeable researchers in the field of bonded repairs to
discuss the issues with the many aspects of this technology. Included are discussions
on materials and processes, design of repairs, certification, and application
considerations. These discussions are sufficiently in-depth to acquaint the reader
with an adequate understanding of the essential ingredients of the procedure. The
application case histories are especially useful in showing the breadth of the
possible uses of the technology.
vii
viii
Foreword
It is easy to be excited about the future of composite repairs to metallic
airframes. It has all the ingredients for success. Today’s applications have shown
that it is reliable, there is typically a significant return on the investment, and it can
be transitioned to potential users. Additional research will open up possible new
applications.
This book is intended to provide the reader with a good understanding of the
basic elements of this important technology. It fulfills that purpose.
John W. Lincoln
Technical Adviser for Aircraft Structural Integrity
United States Air Force
DEDICATION
The Editors would like to dedicate these volumes to Dr J.W Lincoln who passed
away a few months after he wrote this foreword. Jack's outstanding contributions
to the many fields related to the structural airworthiness of aircraft are legend and
need not be repeated here. He was very supportive of the work on bonded repair
technology, as indicated in the foreword, and, indeed, was the Chairman of an
international group addressing certification issues. This report is referenced in
Chapter 1.
It is rare to find in science and engineering, such a giant in the field who was so
modest, approachable and friendly. Jack was regarded both as a supportive father
figure and the expert to be convinced on all airworthiness issues, particularly as
related to the USAF.
ix
DEFAULT NOMENCLATURE
Boron/epoxy
Shear modulus (also used for
strain energy release rate)
Characteristic crack length
Stress intensity
Cycles
Paris Coefficient
Shear stress
Shear strain
Thickness
Length
Width
Elastic shear strain exponent
Inclusion factor
Stress Ratio
Angle
blep
G
I
K
N
A
?
Y
t
L
W
B
B
R
e
graphite/epoxy
Young’s modulus
Poissons ratio
Crack length
Disbond length
Paris Exponent
Stress
Strain
Displacement
Thickness
Applied load
Force per unit width
Stiffness ratio
Thermal expansion coefficient
Temperature range
PIeP
E
Y
a
b
n
d
e
u
or S
t
P
F
S
a
AT
SUBSCRIPTS/SUPERSCRIPTS
Panel
Elastic condition
Ultimate value
Adhesive
Temperature
Value at infinity
Critical value
Reinforcement
xi
P
e
U
A
T
m
e
R
Plastic condition
Maximum value
Minimum value
Outer adherend
Inner adherend
Allowable value
P
max
min
0
I
*
CONTENTS
Biographies
V
Foreword
vii
Dedication
ix
Volume I
Chapter 1. Introduction and Overview
A.A. Baker
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
1.9.
1.10.
Aim of book
Classification of aircraft structures for inspection and repair
Design and certification of airframe structures
1.2.1.
Problems with ageing metallic airframe components
1.2.2.
Repair requirements
I .3.1.
Repair levels
Repair procedures
The case for adhesively bonded repairs
Composite versus metallic patches
Scope of applications
Some experimental comparisons of bonding versus bolting
R&D requirements
Conclusion
References
1
1
2
2
3
5
h
6
7
9
10
11
14
17
17
Chapter 2. Materials Selection and Engineering
R. Chester
19
2.1.
19
20
21
21
24
26
28
28
29
30
32
34
35
35
36
38
2.2.
2.3.
2.4.
2.5.
2.6.
xiii
Introduction
2.1.1.
Factors affecting adhesion
Materials for patches and reinforcements
2.2.1.
Metallic materials
2.2.2.
Non-metallic materials
2.2.3.
Patch material selection
Adhesive systems
2.3.1.
Adhesive types
2.3.2.
Adhesive properties
2.3.3.
Adhesive selection
Primers and coupling agents
Adhesive and composite test procedures
Materials engineering considerations
2.6.1.
Residual stresses
2.6.2.
Cure pressure and voids
2.6.3.
Spew fillet
Composites offer the possibility of embedded strain sensors to
2.6.4.
form “SMART” repairs
References
39
39
xiv
Contents
Chapter 3. Surface Treatment and Repair Bonding
D. Amott, A. Rider and J. Mazza
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.10.
3.11.
3.12.
Introduction
3.1.1.
Surface energy and wetting
3.1.2.
Bondline pressurisation and adhesive cure
3.1.3.
Adhesive bond performance
3.1.4.
Standards and environments for adhesive bonding
Mechanical tests
3.2.1.
Loading and failure modes
Qualification of bonding procedures and performance
3.2.2.
Standard tests
3.3.1.
Wedge durability test
3.3.2.
Fracture mechanics and the cleavage specimen
Fundamentals of durable bonding
3.4.1.
Surface roughness and bond durability
Surface hydration and bond durability
3.4.2.
3.4.3.
Surface contamination and bond durability
Bond durability model
3.4.4.
Requirements of surface preparation
3.5.1.
Degreasing
3.5.2.
Abrasion, grit-blasting or etching
3.5.3.
Creation of a high energy surface oxide
3.5.4.
Coupling agent
3.5.5.
Adhesive primer
3.5.6.
Drying
Adhesive application
3.6.1.
Factors controlling bondline thickness
3.6.2.
Void formation and minimisation
Surface treatment quality control
3.7.1.
Waterbreak Test
3.7.2.
Surface work function methods
3.7.3.
Fourier transform infrared spectroscopy
3.7.4.
Optical reflectivity
Process control coupons (traveller or witness specimens)
3.7.5.
3.7.6.
Practitioner education, skill and standards
Surface preparations for aluminium adherends
3.8.1.
Factory processes
On-aircraft acid anodisation and acid etch processes
3.8.2.
Surface preparations for titanium adherends
3.9.1.
Factory processes
3.9.2.
On-aircraft processes
Surface preparations for steel adherends
3.10.1. Factory processes
3.10.2. On-aircraft processes
Surface preparations for thermosetting-matrix composites
3.1 1.1. Precured patches
Recent surface preparation research
3.12.1. Sol-Gel technology for adhesive bonding
3.12.2. Hot solution treatment for adhesive bonding
References
41
41
41
42
43
44
45
45
46
47
47
48
48
49
50
51
53
56
57
58
60
61
63
63
64
65
65
66
66
67
67
68
68
68
69
69
72
74
74
76
77
77
78
78
80
80
80
81
82
Contents
xv
Chapter 4. Adhesives Characterisation and Data Base
P. Chalkley and A.A. Baker
87
4. I.
4.2.
87
88
89
94
94
95
95
96
96
98
98
99
99
4.3.
4.4.
4.5.
Introduction
Common ASTM and MIL tests
4.2.1.
Stress-strain allowables
Fatigue loading
Fracture-mechanics allowables
4.4.1.
Static loading
4.4.2.
Mode I
Mode I1 and mixed mode
4.4.3.
4.4.4.
Fatigue loading
FM73 database
In situ shear stress-strain allowables
4.5.1
4.5.2.
Yield criterion
4.5.3.
The glass transition temperature
Fickean diffusion coefficients for moisture absorption
4.5.4.
4.5.5.
Mode I fracture toughness
References
100
100
101
Chapter 5. Fatigue Testing of Generic Bonded Joints
P.D. Chalkley, C.H. Wang and A.A. Baker
103
5.1.
103
103
104
104
106
108
109
1 I4
115
120
123
124
125
5.2.
5.3.
5.4.
Introduction
Damage-tolerance regions in a bonded repair
5.1.1.
The generic design and certification process
5.1.2.
The DOFS
5.2.1.
Stress state in the DOFS
5.2.2.
Experimental method
5.2.3.
Experimental results
The skin doubler specimen
Stress state in the skin doubler specimen
5.3.1.
5.3.2.
Experimental method and results
5.3.3.
Fracture mechanics approach
Discussion
References
Chapter 6. Evaluating Environmental Effects on Bonded Repair Systems
Using Fracture Mechanics
L.M. Butkus, R.V. Valentin and W.S. Johnson
6.1.
6.2.
6.3.
6.4.
6.5.
6.6.
Introduction
Materials and specimens
Bonded material system and fabrication
6.2.1.
Experimental procedures
6.3. I.
Pre-test environmental conditioning
6.3.2.
Testing procedures
Analysis
Results and discussion
6.5.1.
Fracture toughness
6.5.2.
Fatigue behavior
Summary and conclusions
References
127
127
128
128
129
129
129
131
132
131
134
135
135
XVi
Contents
Chapter 7. Analytical Methods for Designing Composite Repairs
L.R.F. Rose and C.H. Wang
137
7.1.
7.2.
7.3.
7.4.
137
139
141
144
144
147
149
150
154
155
157
157
162
163
167
168
170
171
173
173
I 74
7.5.
7.6.
7.7.
Introduction
Formulation and notation
Load transfer of bonded reinforcement
Symmetric repairs
7.4.1.
Stage I: Inclusion analogy
7.4.2.
Stage 11: Stress intensity factor
7.4.3.
Plastic adhesive
7.4.4.
Finite crack size
7.4.5.
Finite element validation
Shear mode
One-sided repairs
7.6.1.
Geometrically linear analysis
7.6.2.
Crack bridging model
7.6.3.
Geometrically non-linear analysis
Residual thermal stress due to adhesive curing
7.7.1.
Temperature distribution
7.7.2.
Residual stress due localised heating
7.7.3.
Residual stresses after cooling from cure
7.7.4.
Thermal stress due to uniform temperature change
7.7.5.
Validation
References
Chapter 8. Recent Expansions in the Capabilities of Rose’s Closed-form
Analyses for Bonded Crack-patching
L.J. Hart-Smith
8.1.
8.2.
8.3.
8.4.
8.5.
8.6.
8.7.
8.8.
8.9.
8.10.
8.11.
8.11.
8.12.
8.13.
Introduction
8.1.1.
Rose’s use of the inclusion model to establish stress fields
8.1.2.
Rose’s solution for stress-intensity factor K at the crack tips
Universal efficiency charts for isotropic patches
Equivalence between octagonal and elliptical patch shapes
Effects of patch tapering on the adhesive stresses
Universal charts for the effects of corrosion
Design of patches to compensate for corrosion damage
Analysis of patches over cracks in stiffened panels
Designing to avoid crack initiation
Universal efficiency charts for orthotropic patches
Effects of residual thermal stresses on bonded repairs
Effects of adhesive non-linearity and disbonds on crack-tip stress-intensity
factors
Out-of-plane bending effects with one-sided patches
Remaining challenges involving closed-form analyses
Concluding remarks
References
177
177
178
180
183
184
186
189
191
192
194
196
197
200
202
204
204
205
Chapter 9. Numerical Analysis and Design
R. Jones
207
9.1.
9.2.
207
208
210
Analysis and design
The 2D finite element formulation
9.2.1.
Element stiffness matrix
9.3.
9.4.
9.5.
9.6.
9.7.
9.8.
9.9.
9.10.
9.11.
9.12.
Contents
xvii
9.2.2.
Repair of cracks in aircraft wing skin
Initial design guidelines
Comparison with experimental results for non rib stiffened panels
Repair of thick sections
9.5.1.
Experimental results
Repair of cracked holes in primary structures
Repair of cracked lugs
9.7.1.
Numerical analysis
9.7.2.
Experimental test
9.7.3.
Discussion
Repairs to interacting surface flaws
Material nonlinearities
9.9.1.
Governing differential equations for bonded joints/repairs
Effect of variable adhesive thickness
9.10.1. The effect of variable adhesive thickness and material non-linearity
Repairs to cracked holes under bi-axial loading
Findings relevant to thick section repair
9.12.1. Comparison of commercial finite element programs for the 3D
analysis of repairs
References
212
215
227
229
23 I
233
236
238
240
24 1
242
243
245
25 1
256
258
262
264
266
Chapter 10. Shape Optimisation for Bonded Repairs
M. Heller and R. Kaye
269
10.1.
269
270
27 1
27 1
272
272
273
274
275
276
10.2.
10.3.
10.4.
10.5.
10.6.
Introduction
10.1.1. Context for finite element based shape optimisation
10.1.2. Finite element modelling considerations
10.1.3. Outline of chapter
Analytical formulation for improved stepping in patch taper region
10.2.1. General configuration for symmetric stepped patches
10.2.2. Analysis for single step case
10.2.3. Analysis for patch with multiple steps
10.2.4. Estimate for optimal first step length
10.2.5. Minimum bound for peak shear strain due to patch length
10.2.6. Minimum bound for peak shear strain due to stiffness of first
step
10.2.7. Numerical examples
10.2.8. Discussion
FE analysis for adhesive stress and plate stress concentration
10.3.1. Configuration and finite element analysis method
10.3.2. Results for no-fillet case
10.3.3. Results for fillet case
10.3.4. Discussion of results
Gradientless FE method for optimal through-thickness shaping
10.4.1. Optimal adherend taper profile at the end of a bonded joint
Sensitivity FE method for optimal joint through-thickness shaping
10.5.1
Initial geometry, materials and loading arrangement
10.5.2. Optimisation method
10.5.3. Analysis for symmetric crack repair with aluminium patch
10.5.4. Analysis for non-symmetric crack repair with boron/epoxy patch
Optimal through-thickness shaping for F/A-18 bulkhead reinforcement
10.6.1. Initial geometry, materials and loading arrangement
10.6.2. Parameters for reinforcement optimisation analyses
10.6.3. Stress results for optimal reinforcement designs
277
277
280
28 1
28 I
283
283
285
286
288
289
289
292
294
297
297
298
300
xviii
10.7.
10.8.
10.9.
Contents
10.6.4. Discussion
Optimisation for F/A-18 aileron hinge reinforcement
10.7.1. Initial geometry, materials and loading arrangement
10.7.2. Shape optimisation before reinforcement
10.7.3. Iterative reinforcement design
10.7.4. Discussion
In-plane shaping effects
10.8.1. Geometry, loading and modelling considerations
10.8.2. Determination of Kt from FEA output
10.8.3. Uniaxial loading and patches with aspect ratios of 2:l
10.8.4. Uniaxial loading and other patch aspect ratios
10.8.5. Analogy with hole-in-a-plate problem.
10.8.6. Stress reduction at the centre of the patch for uniaxially loaded
plate
10.8.7. Summary of results and discussion
Conclusions
References
300
300
303
303
305
308
308
308
309
310
310
31 1
312
312
313
314
Chapter 11. Thermal Stress Analysis
R.J. Callinan
317
I 1.1.
317
318
324
328
330
332
333
335
337
339
341
343
346
349
350
350
351
11.2.
11.3.
11.4.
11.5.
11.6.
Introduction
Analytical expression for initial stresses in a circular plate due to heating
11.2.1. Comparison of F.E. and analytic results
11.2.2. Orthotropic solution
11.2.3. Thermal stresses in a one-dimensional strip
11.2.4. Peel stresses
11.2.5. Coefficients of thermal expansion of a laminate
Finite element thermal stress analysis
1 1.3.1. Two-dimensional strip joints
1 1.3.2. Three-dimensional strip joints
Application of analysis to large repairs of aircraft wings
1 1.4.1. F.E. analysis
11.4.2. Edge restraint factor
Conclusions
Acknowledgment
References
Appendix
Chapter 12. Fatigue Crack Growth Analysis a Repaire Structures
C.H. Wang
353
12.1.
12.2.
353
354
354
357
12.3.
12.4.
12.5.
Introduction
Crack-closure analysis of repaired cracks
12.2.1. Small-scale yielding
12.2.2. Large-scale $elding solution for a stationary crack
12.2.3. Plasticity induced crack closure under large-scale yielding
solutions
Overload effect and validation using finite element method
Thermal residual stresses and comparison with experimental results
12.4.1. Thermal residual stresses
12.4.2. Experimental results under spectrum loading
Conclusions
References
361
361
365
365
367
372
373
Contents
Chapter 13, Boronlepoxy Patching Efficiency Studies
A.A. Baker
13.1.
13.2.
13.3.
13.4.
13.5.
Introduction
Stress intensity analysis of patched cracks
13.2.1. Model for estimating stress intensity
13.2.2. Use of model to estimate crack growth
13.2.3. Extension of the model for growth of disbond damage
Experimental approach
Fatigue studies
13.4.1. Disbond damage in the patch system
13.4.2. Influence of stress range
13.4.3. lnfluence of patch thickness
13.4.4. Influence of R ratio
13.4.5. Influence of temperature
13.4.6. Influence of panel thickness variation
13.4.7. Residual strength of patched panels
An approach to b/ep patch design
13.5.1. Cyclic loading
13.5.2. Spectrum loading
13.5.3. Check on residual strength
References
Chapter 14. Glare Patching Efficiency Studies
R. Fredell and C. Guijt
14.1
14.2.
14.3.
14.4.
14.5.
Introduction
14.1.1. Overview and background of fibre metal laminates
Parametric studies of various patch materials
Experimental results
Discussion
Summary and conclusions
References
Chapter 15. Graphitelepoxy Patching Efficiency Studies
P. Poole
15.1.
15.2.
15.3.
15.4.
15.5.
15.6.
15.7.
15.8.
15.9.
15.10.
15.11
Introduction
Repair of thin skin components
Repair of thick sections
Graphitelepoxy versus boron/epoxy
Effect of bondline defects
Effect of impact damage
Effect of service temperature
Effect of exposure to hot-wet environments
Repair of battle damage
Future work
Acknowledgements
References
Chapter 16. Repair of Multi-site Damage
R. Jones and L. Molent
16.1.
16.2.
Introduction
Specimen and loading
xix
375
375
376
376
378
379
379
381
38 1
383
384
384
386
387
389
392
392
394
396
396
399
399
399
400
408
410
412
413
415
415
416
418
424
427
433
435
436
438
440
440
441
443
443
444
xx
Contents
16.2.1.
16.2.2.
16.3.
Boeing lap joints
Airbus lap joints
Repairs
Repair philosophy
Repair details
Stress analyses
16.4.1. Thermo-elastic analysis
16.4.2. Finite element analyses
Specimen fatigue test results
16.5.1. Unreinforced baseline fuselage lap joint specimens
16.5.2. Reinforced baseline fuselage lap joint specimens
16.5.3. Environmental evaluation of repairs
16.5.4. Hot/wet
16.5.5. NaCl aqueous
Damage tolerant evaluation of specimens
16.6.1.
Adhesive disbonds
16.6.2. Impact damage
16.6.3. Tension testing
Full scale repair demonstrators
16.7.1. Airbus A330/A340 fatigue test article
16.7.2. Boeing 727, 747 and 767 in-flight demonstrators
16.7.3. Doubler inspections
16.7.4. Demonstrator summary
Conclusions
References
16.3.1.
16.3.2.
16.4.
16.5.
16.6.
16.7.
16.8,
Chapter 17. Damage Tolerance Assessment of Bonded Composite Doubler
Repairs for Commercial Aircraft Applications
D. Roach
17.1.
17.2.
17.3.
17.4.
17.5.
Introduction
17.1.1. Damage tolerance and fracture control plan
17.1.2. Damage tolerance establishes fracture control plan
Composite doubler damage tolerance tests
Conformity inspection and FAA oversight
Test results
17.4.1. Fatigue tests
17.4.2. Strain field measurements
Conclusions
References
Chapter 18. Validation of Stress Intensity Estimations in Patched Panels
B. Aktepe and A.A. Baker
18.1.
18.2.
18.3.
18.4.
18.5.
Introduction
The K-gauge
18.2.1. K-gauge equations
Theory of KI measurement using strain gauges
18.3.1. Westergaard equations
18.3.2. Rose’s inclusion model for stress intensity
18.3.3. Wang’s crack-bridging model
Experimental procedure
Strain surveys
18.5.1. Unpatched specimen
444
449
450
45 1
452
453
453
456
459
459
464
464
465
466
468
468
469
472
474
474
477
479
480
480
482
485
485
486
488
49 1
492
500
500
506
514
515
517
517
518
518
519
519
52 1
52 1
522
524
524
Contents
18.6.
18.7.
18.8.
18.9.
18.5.2. Patched specimen
Crack length
Time-dependent behaviour
Conclusions
Nomenclature
References
xxi
525
526
527
529
529
530
Volume 2
Chapter 19. Bonded Repair of Acoustic Fatigue Cracking
R.J. Callinan and S.C. Galea
531
19.1.
19.2.
Introduction
Cracking history
19.2.1. Inlet nacelle
19.2.2. Aft fuselage cracking
19.3. Sound pressure levels
19.3.1. Inlet nacelle
19.3.2. Aft fuselage
19.3.3. Power spectral density
19.4. Random response analysis
19.5. Stress intensity factors
19.6. FEA of cracked nacelle inlet
19.6.1. Crack growth study
19.6.2. Summary of repair failure investigation
19.7. Highly damped repairs for cracked panels
19.7.1. Design of highly damped patch
19.7.2. Damping of highly damped patch
19.7.3. Analysis of repaired cracked plate
19.7.4. Results and discussion
19.8. Aft fuselage finite element model
19.8.1. Modes and frequencies
19.8.2. Acoustic fatigue crack growth data
19.8.3. Residual thermal stresses
19.8.4. Damping data
19.8.5. Adhesive data
19.9. Thermal environment for F/A-18
19.10. Analytical results
19.11. Experimental work
19.12. Conclusions for aft fuselage repair
References
531
533
533
536
536
536
536
537
537
538
539
540
546
546
547
547
55 1
55 1
557
558
559
560
56 1
56 1
562
563
566
568
568
Chapter 20. Smart Patch Systems
S.C. Galea
57 1
20.1.
20.2.
20.3.
57 1
573
578
578
588
20.4.
Introduction
Smart patch approach
Damage detection studies
20.3.1. Load transfer (strain) technique
20.3.2. Residual strain technique
20.3.3. Electro-mechanical impedance, transfer function and stress wave
technique
20.3.4. Adhesive bond degradation sensors - active sensing technique
Laboratory smart patch conceptional demonstrators
593
597
599
xxii
20.5.
20.6.
Contents
In-flight demonstrator
20.5.1. Finite element analysis - damage sensing technique
20.5.2. Health monitoring systems
Conclusions
References
Chapter 21. Adhesively Bonded Repairs: Meeting the Safety Requirements
Implied within Existing Aviation Industry Certification Regulations
D. Bond
21.1.
21.2.
21.3.
21.4.
21.5.
21.6.
21.7.
21.8.
Introduction
Certification of an adhesively bonded repair
21.2.1. The need to certify a repair
21.2.2. Adhesively bonded repairs
21.2.3. Regulatory deficiencies
Repair design information
21.3.1. Existing requirements
21.3.2. Additional guidance
Analysis and development testing
21.4.1. Design allowables
21.4.2. Static analysis
21.4.3. Fatigue and damage tolerance analysis
21.4.4. Development testing
Full scale testing
21.5.1. Existing requirements
In-service management and inspection
21.6.1. Existing requirements
21.6.2. Additional guidance
Future approaches to bonded repair certification
Conclusions
References
604
604
607
61 1
612
615
615
617
617
617
618
619
619
62 1
62 1
62 1
626
630
635
637
637
637
637
637
638
638
639
Chapter 22. Certification Issues for Critical Repairs
A.A. Baker
643
22.1.
22.2.
Current limitations of crack patching
Justifying credit for patching efficiency fatigue concerns
22.2.1. Influence of fatigue on patching efficiency
22.2.2. Obtaining patch system fatigue allowables
22.2.3. Validation of patching analysis
Justifying credit for patching efficiency environmental durability concerns
22.3.1. Assurance of patch system environmental durability
22.3.2. Australian experience on service durability
Justifying credit for patching efficiency - the Smart Patch approach
Discussion
Conclusions
References
643
644
645
646
648
648
650
653
654
655
656
656
Chapter 23. Nondestructive Evaluation and Quality Control for Bonded Composite
Repair of Metallic Aircraft Structures
D.P. Roach and C.M. ScaIa
659
22.3.
22.4.
22.5.
22.6.
23.1.
~
~
Introduction
23.1.1. NDI needs and damage tolerance
659
660
Contents
23.2.
23.3.
23.4.
23.5.
23.6.
23.1.2. NDI assessments
Inspection for delaminations, disbonds and adhesion failure
23.2.1. Pulse-echo ultrasonics
23.2.2. Through-transmission ultrasonics
23.2.3. Guided waves
23.2.4. Resonance test inspection method
23.2.5. Thermography
23.2.6. Other techniques
Inspections for cracks in parent material beneath composite doublers
23.3.1. Eddy-current inspections
23.3.2. X-radiographic inspections
23.3.3. Challenges in crack monitoring
Quality control issues in service
23.4.1. Quality assurance
23.4.2. Use of realistic calibration standards
Conclusions
Acknowledgements
References
xxiii
663
664
665
679
680
683
685
689
694
694
70 1
703
714
714
715
719
723
724
Chapter 24. Practical Application
Technology for Adhesive Bonded Repairs
~.
M. Davis
727
24.1.
727
730
730
73 1
732
742
748
750
75 1
752
752
752
752
754
755
755
757
757
24.2.
24.3.
24.4.
24.5.
24.6.
24.7.
24.8.
Introduction
24. I. 1. Management of repair technology
Repair application technology
24.2.1. Materials selection
24.2.2. Surface preparation
24.2.3. Heating procedures for on-aircraft repairs
24.2.4. Repair pressurisation
Occupational health and safety (OHS)
24.3. I. Solvents
24.3.2. Grit
24.3.3. Fibres
24.3.4. Risks to aircraft
Quality management
Facilities
Training and certification
Deficient repair concepts
Conclusion
References
Chapter 25. Rapid Application Technology: Aircraft Battle Damage Repairs
R. Bartholomeusz, P. Pearce and R. Vodicka
76 1
25.1.
25.2.
76 1
762
762
763
764
25.3.
Introduction
Aircraft battle damage repair
25.2.1. Battle damage
25.2.2. ABDR criteria
25.2.3. Types of ABDR
Comparison of metallic mechanically fastened repairs to bonded composite
repairs for ABDR
25.3.1. Adaptation of bonded composite repairs for battle damage
25.3.2. The composite laminating resin and adhesive
25.3.3. Fibre
765
766
766
767
xxiv
25.4.
25.5.
25.6.
Contents
25.3.4. Simplified design methods for ABDR
25.3.5. Surface treatment
25.3.6. Forming the bonded composite patch
25.3.7. Mechanically fastened, metallic repair
25.3.8. Fatigue and static testing of specimens
25.3.9. Comparison of test results
Development of a bonded composite ABDR system
25.4.1. Resin development
25.4.2. Repair durability, strength and surface treatment
25.4.3. Mechanical properties
Application of the DSTO/ABDR system
25.5.1. Resin measurement, mixing and dispensing
25.5.2. Pre-bonding surface treatment procedures
25.5.3. Repair consolidation and application
25.5.4. Heating procedures
25.5.5. Vacuum moulding tool
Conclusions
References
Chapter 26. Standardized Training
- and Certification for Bonded Repair
Specialists
Marty A. Smith
26.1.
26.2.
26.3.
26.4.
26.5.
26.6.
26.7.
Introduction
26.1.1. Benefits of improved training and process control - an example
The task at hand - a uniform approach
26.2.1. Advantages of standardization
26.2.2. Building a database of reliable repairs - “We’re all in this
together”
Current approaches to training and certification
Formalized trade structure
26.4.1. The purpose of a trade structure
26.4.2. A four-tiered trade structure - the ARTI model
The ARTI model for training of bonded repair specialists
Certification of bonded repair specialists
26.6.1. The Boeing wedge test (BWT) - an accepted standard
26.6.2. Administration of certification tests
Conclusion
References
767
768
768
769
769
769
77 1
772
773
774
776
776
777
777
777
778
779
779
783
783
783
784
784
785
785
786
786
786
787
79 I
79 1
793
795
795
Chapter 27. Case History: F-111 Lower Wing Skin Repair Substantiation
K.F. Walker and L.R.F. Rose
797
27.1.
27.2.
27.3.
797
798
800
800
801
80 I
802
802
803
805
805
27.4.
27.5.
27.6.
27.7.
Introduction
Crack location and residual strength
Repair substantiation requirements
27.3.1. Design load cases
27.3.2. Fatigue loading
Validation strategy
Design validation (finite element analysis)
27.5.1. Uncracked, unpatched wing model
Cracked, patched model including thermal effects
Repair substantiation (representative specimen testing)
27.7.1. Representative bonded joints
Contents
xxv
27.7.2. Panel specimens
27.8. Box specimens
27.9. Repair history
27.10. Conclusion
References
807
809
809
811
81 1
Chapter 28. Case History: Composite Doubler Installation on an L-1011
Commercial Aircraft
D. Roach
813
28.1.
28.2.
28.3.
28.4.
28.5.
28.6.
28.7.
Introduction
Fuselage door surround structure tests
28.2.1. Full-scale structural testing philosophy
28.2.2. L-1011 fuselage structure
28.2.3. Repair of fuselage test article with a composite doubler
28.2.4. Biaxial test facility description
Fuselage door surround structure test results
28.3.1. Structural tests before composite doubler installation
28.3.2. Structural tests after composite doubler installation
28.3.4. Validation of finite element model analytical results
28.3.5. Nondestructive inspection
Component level tests: door corner specimen
28.4.1. Door corner test overview
28.4.2. Subsize door corner test results
L-1011 composite doubler installation
28.5.1. Composite doubler repair of L-1011 aircraft passenger door
28.5.2. Non-destructive inspection of door surround structure and
composite doubler
28.5.3. Inspection intervals for L-1011 aircraft
28.5.4. Quality assurance measures
FAA and industry approvals
Conclusions
References
Chapter 29. Case History: F-111 Wing Pivot Fitting Reinforcement
R. Chester
29.1.
29.2.
29.3.
29.4.
29.5.
29.6.
29.7.
29.8.
Introduction
Reinforcement design
Selection and evaluation of materials
Selection and evaluation of the reinforcement
29.4.1. Mechanical test evaluation
29.4.2. Cure characterisation and formability studies
29.4.3. Selection and evaluation of candidate adhesives
29.4.4. Selection and evaluation of surface treatment procedures
29.4.5. Modifications to doubler system
29.4.6. Residual stress minimisation
Doubler application technology
29.5.1. Temperature
29.5.2. Pressure
Doubler fitment
Fitment to fleet aircraft
Conclusions
References
813
814
814
815
815
817
819
819
820
825
826
826
826
828
832
832
836
839
839
840
841
842
845
845
846
849
850
851
851
852
853
853
853
854
854
854
855
856
857
858
xxvi
Contents
Chapter 30. Case History: Bonded Composite Reinforcement of
the F/A-18 Y470.5 Centre Fuselage Bulkhead
R.A. Bartholomeusz and A. Sear1
30.1.
30.2.
30.3.
30.4.
30.5.
30.6.
30.7.
30.8.
Introduction
30.1.1. Background
FE analysis of bulkhead and reinforcement
30.2.1. Results of the bulkhead FE analysis
30.2.2. Measurement of adhesive through-thickness stresses
FE design of representative specimen (curved beam specimen)
Experimental test program
30.4.1. Static testing of curved beam specimen
30.4.2. Durability testing of the curved beam specimen
30.4.3. Residual strength after fatigue
Trial installation of reinforcement to full-scale fatigue test article
Discussion
30.6.1. Pre ECP reinforcement
30.6.2. Post ECP reinforcement
Conclusions
Acknowledgments
References
Chapter 31. C-5A Fuselage Crown Cracking
C. Guijt and S. Verhoeven
31.1.
3 1.2.
31.3.
3 1.4.
31.5.
3 1.6.
Introduction
Damage tolerance analysis
Repair options
Design of the bonded repair
FEM model of the patched crack
Conclusions
References
Chapter 32. Case History: F-16 Fuel Vent-hole Repairs
C. Guijt and J . Mazza
859
859
860
860
862
862
864
864
864
865
866
866
867
867
868
869
869
869
871
871
872
874
875
879
883
884
885
Introduction
Damage tolerance analysis
Repair options
32.3.1. Mechanically fastened aluminum patch
Design of the bonded repair
32.4.1. Operating temperatures
32.4.2. Maximum operating temperature
32.4.3. Cumulative temperatures
Testing
32.5.1. Fatigue analysis of the aluminum doubler
Bonded repairs
32.6.1. Repair installation procedures
Conclusions
References
885
885
887
888
889
890
890
89 1
892
892
892
894
895
895
Chapter 33. Reinforcement of the F/A-18 Inboard Aileron Hinge
R. Chester
897
32.1.
32.2.
32.3.
32.4.
32.5.
32.6.
32.7.
33.1.
Introduction
897
Contents
33.2.
33.3.
33.4.
33.5.
33.6.
Load cases
Design and stress analysis
Static testing and repair validation
Certification and implementation to aircraft
Conclusions
References
xxvii
898
899
903
905
906
906
Chapter 34. UK Applications
P. Poole
907
34.1.
34.2.
34.3.
907
908
909
909
91 1
912
913
918
918
34.4.
34.5.
Introduction
Design studies
Repairs to RAF aircraft
34.3.1. Secondary structure repairs
34.3.2. Primary structure repairs
34.3.3. Birdstrike protection
Repairs to EHlOl development airframe full scale fatigue test specimen
Acknowledgements
References
Chapter 35. Case History: Repair Applications On
DC-lO/MD-ll Aircraft
D. Roach
35. I.
35.2.
35.3.
35.4.
35.5.
35.6.
Introduction
Repair development and validation tasks to support on-aircraft
installation
35.2.1. Repair design
Repair analysis
Repair design validation
Nondestructive inspection
Current status of DC-lO/MD-11 commercial aircraft repairs
919
919
92 1
92 1
92 1
926
933
934
Chapter 36. Case History: CF-116 Upper Wing Skin Fatigue Enhancement Boron
Doubler
D. Raizenne
937
Introduction
Background
36.2.1. Compression induced fatigue cracking
36.3. Repair considerations
36.4. Bonded composite doublers
36.5. Doubler design and analysis
36.6. Doubler manufacturing and installation procedures
36.6.1. Doubler qualification testing
36.7. Doubler fractographic analysis
36.8. Fleet experience
36.9. Discussion
36.10. Conclusions
36.1 1. Composite repair lessons learned
36.12. Acknowledgements
References
Appendix A
Material properties
937
937
939
940
941
94 1
946
947
949
95 1
954
954
955
956
956
957
957
36.1.
36.2.
xxviii
Contents
Chapter 37. In-service Durability of Bonded Composite Repairs - Commercial
Demonstrator Programs
R.A. Bartholomeusz and R.C. Geddes
37.1.
37.2.
37.3.
37.4.
37.5.
37.6.
37.7.
Introduction
Demonstrator doublers
37.2.1. QANTAS demonstrator program
37.2.2. Ansett keel beam reinforcement
In-service environment and repair location
37.3.1. Temperature
37.3.2. Foreign object damage.
37.3.3. Airtlow and erosion
37.3.4. Aircraft fuels, hydraulics and lubricants
37.3.5. Miscellaneous
Bond durability and surface treatment
Case study results
37.5.1. QANTAS program
37.5.2. Ansett keel beam demonstrator reinforcement
Discussion and lessons learnt
37.6.1. Erosion protection by the use of shields
37.6.2. Repair location and design
37.6.3. Applicability of demonstrator programs
Conclusions
References
Chapter 38. Case History: Bonded Composite Repair of A CH-47 Cargo Hook
Beam
B.J. Harkless, A.P. Kerr and M.A. Shupick
38.1.
38.2.
38.3.
38.4.
38.5.
38.6.
Introduction
Defect description
Justification of approach
38.3.1. Loads analysis
38.3.2. Design loads
38.3.3. Static strength analysis
38.3.4. Fatigue analysis
38.3.5. Proof testing
Patch system and environmental protection
Repair procedure
Continuing ainvorthiness/inspection
References
Chapter 39.
39.1.
39.2.
39.3.
Case History: Application of Bonded Repair Technology to Large
Areas
B. Harkless and A. Kerr
Background
Examples of applicability to large areas
39.2.1. Full length rotor blade doublers
39.2.2. Large scale wing reinforcement
39.2.3. Large scale fuselage reinforcement
Current state of the technology
39.3.1. Critical features of the bonding process
39.3.2. Grit blast/silane process steps
959
959
960
960
962
962
962
963
964
964
964
964
965
965
968
970
97 1
97 1
97 1
972
972
973
973
973
974
975
975
975
977
977
978
978
979
979
983
983
984
984
984
894
985
985
986
Contents
39.4.
39.5.
39.6.
Process areas requiring adaptation
39.4.1. Solvent scrubbing step
39.4.2. Grit blast step
39.4.3. Heating methods
Large area repairs in a production environment
Conclusions
References
mix
987
987
988
988
989
994
995
Chapter 40. Case History: Composite Patch Reinforcement of T-38 Lower Wing
Skin
M.M. Ratwani, J. Helbling, B. Heimerdinger and N.M. Ratwani
997
Introduction
Validation testing
40.2.1.
Test specimen description
40.2.2. Composite reinforcement fabrication and bonding
40.2.3. Strain gage installation
40.2.4. Test spectrum and equipment
Test results
40.3.1.
Strain gage results
40.3.2. Crack growth results
Comparison between test results and analytical predictions
Application of composite reinforcement to a full scale wing test
Conclusions
References
997
999
999
1000
1000
1001
1001
1001
1003
1005
1007
1007
1008
Chapter 41. Case Historis: Advanced Composite Repairs of USAF C-141 and
C-130 Aircraft
W.H. Schweinberg and J.W. Fiebig
1009
40.1.
40.2.
40.3.
40.4.
40.5.
40.6.
41.1.
41.2.
41.3.
41.4.
41.5.
41.6.
41.7.
41.8.
41.9.
41.10.
Background
Repair design
Installation development
Industrialization and repair
Success and failures
Other applications
Cost savings
Additional research
Lessons learned
Summary
References
Chapter 42. Case History: Bonded Composite Reinforcement of Ship Structures
I. Grabovac
42.1.
42.2.
42.3.
42.4.
42.5.
42.6.
42.7.
42.8.
Introduction
Materials development and characterisation
Installation of composite reinforcement
Reinforcement efficiency assessment
Service. performance
Technology improvement
The current status - year 2000
Conclusion
1009
1012
1016
1014
1017
1020
1024
1025
1029
1032
1032
1035
1035
1038
1042
1044
1046
1047
1048
1048
Contents
xxx
42.9.
Index
Acknowledgement
References
1049
1049
1051
Chapter 1
INTRODUCTION AND OVERVIEW
A.A. BAKER
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
1.1. Aim of book
In 1988 the book “Bonded Repair of Aircraft Structures” [l] was published. This
book described the status of the technology, in the late 198Os, on bonded composite
repair of conventional metallic, adhesively bonded metallic and fibre-composite
airframe components. Because over the last fourteen years the technology has
progressed considerably and become widely exploited, a decision was made to
produce this follow-up book “Advances in Bonded Composite Repairs of Metallic
Airframe Structure”.
This aim of this book is to provide a comprehensive coverage of the current
research and technology highlighting advances in capabilities, and case histories of
recent applications. It is intended to be useful both to researchers in the field and to
practicing aerospace engineers.
Contributions to the book are largely drawn from the Defence Science and
Technology Organisation, Australia, where this technology was pioneered in
the early 1970s. Significant contributions are also provided by the USA Air
Force (USAF), Sandia Laboratories of the USA, Defence Evaluation and
Research Agency UK and the National Aeronautical Laboratory of Canada,
reflecting the worldwide interest in this technology. As may be expected with
ongoing R&D, these contributions often differ in technical approach and
conclusions.
The purpose of this chapter is to set the scene for this book. To this end, a brief
background is provided on structural problems in ageing aircraft and on the
requirements for repairs. A case is then made for use of adhesively bonded
composite (fibre-reinforced plastic or metal-laminate) reinforcements for repairs as
compared to standard mechanical procedures, based on mechanically fastened
1
Baker, A.A., Rose, L.R.F. and Jones, R. (eds.).
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright Q 2002 Published by Elsevier Science Ltd. All rights reserved.
2
Advances in ihe bonded composite repair of metallic aircrafi structure
metallic patches. The requirements for future research and development are then
discussed, based, in part, on a recent USAF study on ageing aircraft [2].
Before introducing repair issues, some brief background is provided in the next
section on the key issues and terminology associated with the design and
maintenance of airframe structures.
1.2. Classification of aircraft structures for inspection and repair
For the purpose of engineering management (including repairs) aircraft
structures are generally classified as follows:
0 Primary structure: a structure that is critical to the safety of the aircraft;
0 Secondary structure: a structure that, if it were to fail, would affect the operation
of the aircraft but not lead to its loss;
0 Tertiary structure: a structure in which failure would not significantly affect
operation of the aircraft.
Inspection, damage assessment, and repair requirements differ significantly
between these classified structures. Even within a single component, the allowable
damage type and size (and consequently acceptable repair actions) may vary
according to the criticality of the damaged region. The component is generally
zoned by the original equipment manufacturer (OEM) in the structural repair
manual (SRM) to indicate these regions. Mainly, the SRM addresses repairs to
non-primary structure or non-critical repairs to primary structure. Repairs outside
the scope of the SRM, particularly repair of critical damage in primary structure,
require engineering design and approval by the OEM (or its delegate).
1.2.1. Design and certification of airframe structures
Certification of airframe structure generally requires that the structure (by test
and/or analysis) demonstrates the following capabilities:
a Static strength:
Design limit load (DLL) no failure or unacceptable deformations;
Design ultimate load (DUL) no failure, although permanent deformation is
acceptable; DUL = DLL x 1.5 (generally).
0 Fatigue strength:
- Safe life approach - No cracking should occur in the life of the airframe that
could lead to failure. This approach was used in design of most of the older
fighter aircraft, and is still used for US Navy fighter aircraft, such as the F-18
and helicopters.
Or
- Fail safe approach - The structure is damage tolerant in that cracking may
occur but will not reduce strength below acceptable level before being detected.
This requirement is generally met by multi-load-path design where should one
load path fail the remaining load paths can continue to provide the required
Chapter 1. Introduction and overview
3
level of residual strength until the damage is detected. This approach is
generally used in the structure of large transport (and civil) aircraft.
Or
Slow crack growth approach - The structure is damage tolerant in that cracking
may occur but cracks will grow slowly and will not cause failure for the full life
of the structure or before detection by planned inspection (safety by inspection).
This approach can be applied to single-load-path structure, where failure would
be catastrophic. Damage tolerant design for single-load-path structure is based
on the assumed presence of flaws at critical locations. This is the design
approach adopted for USAF fighter aircraft, such as F-16.
0 Damage tolerance general requirement:
- The strength will not fall below an acceptable level (typically 1.2 x DLL) due to
representative damage to the structure, e.g. caused by fatigue cracking, or
corrosion or accidental mechanical contact before being detected. Critical
damage must be of a size that can be detected with a high degree of probability.
Durability, economic requirement:
- For the life of the airframe, damage requiring costly repairs will not occur for
example, due to fatigue or corrosion.
Essentially, certification of a repair requires demonstration [3,4] that the repaired
structure is as flight-worthy as the original structure, possibly allowing for life
already consumed. According to the latest civil regulations, FAR 25.571, this
demonstration must include damage-tolerant behaviour of the repaired structure,
even if the original structure was designed on a safe-life basis.
-
1.2.2. Problems with ageing metallic airframe components
To minimise weight, metallic airframes are predominantly made of high-strength
aluminium alloys. Steel and titanium alloys are also used but only where higher
strength or temperature capabilities are required and the weight penalty can be
accepted.
All metallic structures are prone to degradation by cracking and corrosion in
service, particularly when design, manufacture or environmental protection is
inadequate to meet actual serviced usage. In military aircraft fatigue cracking may
be more of a problem than originally envisaged because of exposure to more severe
usage (higher loading) than originally anticipated. Corrosion is a problem with
older aircraft because of the use of susceptible alloys and inadequate corrosionprotective processes.
Because of limited budgets and escalating replacement costs, many military
aircraft are being maintained in service well past their planned life. Thus these
degradation problems are becoming a major operational and economic issue. For
example, Australia is planning to maintain the F-1 11 in service until the year 2020,
when it will be over 50 years old. Several aircraft in the USAF fleet, for example
C-141 and B-52, are currently over 30 years old, most with no plans for
replacement within the next 10-20 years.
4
Advances in the bonded composite repair of metallic aircraft structure
Corrosion imposes a very high maintenance cost burden [2] for ageing airframes
since many man-hours can go into its detection, treatment and eradication.
Consequently corrosion, although generally not as critical structurally as fatigue
cracking, may determine the economic life of the airframe.
Unfortunately, management of corrosion by the setting of inspection intervals is
not always effective since the location of corrosion and its rate of growth are hard
to predict. Management problems can be reduced when a history of occurrence for
a particular airframe is obtained. Hidden corrosion in joints and faying surfaces is
particularly difficult to detect and very costly to treat.
Damage caused by corrosion includes uniform section loss, pitting, exfoliation
(grain boundary attack) and cracking. Other than stress-corrosion cracking,
considered later, exfoliation and pitting are the most damaging to structural
capability since they can result in extensive local loss of section and can initiate
fatigue cracking. The implication of corrosion damage on structural integrity [SI
is usually difficult to assess. In the absence of this capability, there is a tendency
to remove excessive amounts of metal including much sound material. The
current approach [6] is to quantify the corrosion damage (pitting) as an
equivalent initial flaw, then use conventional fracture mechanics to predict its
growth.
Cracks can arise from repeated loading (fatigue) or stress-corrosion. Stresscorrosion cracks arise in susceptible alloys (particularly thick 7000 series T6
forgings and machined, integrally stiffened plate) in the short-transverse grain
direction from the combination of stress and adverse environment. The stresses can
be internal arising during forming or externally caused, for example by forced fit or
excessive use of oversized fasteners. Stresses caused by corrosion product trapped
between layers can also result in stress-corrosion cracking. Fortunately, stresscorrosion cracks often lie parallel to the grain direction and thus the loading
direction so may not constitute a major threat to structural integrity unless they
initiate transverse fatigue cracks.
Fatigue cracks arise from highly localised cyclic plastic deformation caused by
fluctuating service loads. These cracks pose the greatest threat to structural
integrity since they grow perpendicularly to the applied load direction and
eventually severing the load path.
Low-cycle fatigue cracks, caused by manoeuvre and gust loads, generally initiate
from local regions of high surface stresses. These high stresses occur due to faulty
design, materials defects (including voids and inclusions) or poor manufacturing
procedures, including notches and scratches.
Fatigue crack growth from known “hot spots”, such as highly loaded fastener
holes, can be managed by basing inspection intervals of these regions on
conservative estimates of the rate of crack growth. The USAF damage-tolerance
approach based on slow crack growth is to assume the presence of a crack typically
just at the limits of easy detectability in each critical region.
This inspection approach, called safety by inspection, may not be feasible in
some of the older aircraft. In these aircraft the tendency was to choose high
strength alloys to maximise the safe life, which have long (nominal) crack initiation
Chapter 1. Introduction and overview
5
lives at the expense of poor fracture toughness and therefore small critical crack
size and relatively high rates of crack growth.
The presence of an aggressive environment can also markedly increase the rate of
crack growth, making inspection intervals very difficult to estimate, or too short to
be economic. In this case management on a safe-life basis is the only option,
possibly following a rework of the area to remove small cracks and reduce stress
concentrations.
Planning of the inspection intervals and locations is much more difficult when
cracks can initiate at random points in the structure, e.g. from pitting corrosion or
large inclusions. This is particularly a problem in structures with enhanced fatigue
resistance, for example with “fatigue-resistant holes” - produced by cold expansion
or by using interference-fit fasteners.
Widespread damage, viz, extensive minor cracking in multi-load-path structure, is
a significant concern with ageing aircraft [2]. This is because of loss of the ability of
the structure to maintain the required level of residual strength (above DLL) in case
of failure of one of the loading paths. Multiple-site damage, viz, extensive local
minor cracking in a single-load-path structure (or in an element of multi-load-path
structure), is a related problem that can result in an abnormally fast crack growth as
the cracks link up to form a large crack, again compromising residual strength.
High-cycle fatigue is caused by high-frequency aerodynamic or acoustic
excitation of the structure. It differs from low-cycle fatigue in that the high
numbers of cycles imposed on the structure can result in crack initiation and
growth, even in unflawed structure. Crack growth is generally very rapid on a
service time basis, making management by standard damage tolerance [7]
approaches infeasible.
1.3. Repair requirements
When significant structural degradation is detected, a decision must be made on
the need for a repair. Essentially [SI one of the following decisions is required:
1. No-repair action is required.
2. Cosmetic or sealing repair is required to correct minor damage.
3. Structural repair is required (if feasible), because strength has been reduced
below the design limits or has the potential to be reduced in subsequent service.
4. Repair is not economical and the component must be replaced.
Generally, the repair scheme employed for structural restoration should be the
simplest and least intrusive to the structure that can restore structural capability to
the required level. The repair must be able to be implemented in the repair
environment, without compromising other functions of the component or
structure, such as clearance on moving parts, aerodynamic smoothness and
balance (control surfaces).
Important additional requirements are that implementation of the repair should:
0 Require minimal down-time of the aircraft
0 Use readily available and easily storable materials
6
0
0
0
Advances in the banded composite repair of metallic aircraft structure
Remove as little sound material as possible
Minimise degradation or damage to the surrounding region
Require only simple procedures or tooling.
I .3.I . Repair levels
A major consideration in the choice of repairs is the level at which the repair can
be implemented. Repair activities on military aircraft are performed at one of the
following levels:
0 Field level: Undertaken directly on the aircraft in a situation where skilled
personnel and/or adequate facilities are unavailable. Such activities will generally
be limited to fairly minor repairs to non-primary structure or non-critical repairs
to primary structure. However, aircraft battle-damage repairs (ABDR) to
primary structure may be undertaken very rapidly to make the aircraft
operational or to ferry it back to base. Since battle damage repairs will
subsequently be replaced with permanent repairs, they must cause minimum
damage to the airframe. ABDR can strongly influence aircraft availability and so
can prove to be a decisive factor in times of conflict.
0 Depot level: Undertaken in a situation where skilled personnel and facilities are
available (up to factory capability in some cases). However, if the component is
too large or difficult to remove from the aircraft, repairs are implemented
directly on the aircraft.
1.4. Repair procedures
Repairs can be broadly divided into non-patch procedures for minor damage and
patch (or reinforcement) procedures to restore structural capability.
Patch repairs restore the load path weakened or removed by damage or cracking,
ideally without significantly changing the original load distribution. Reinforcements or doublers are used to replace lost strength or stiffness (for example after
removal of corrosion damage), correct design errors, or to improve performance.
The patch repair approach recommended in the OEM’s SRM is generally based on
the use of bolted or riveted metal plates, generally of a similar alloy to the parent
material - often one gauge thicker.
Non-patch repair of corrosion types such as pitting or exfoliation in aircraft
aluminium alloy structure generally involves the removal of visible damage by
grinding usually followed by an extra confidence cut to ensure that all the corrosion
is removed. The region is then treated, primed and painted. In the case of severe
corrosion, panel thickness may be reduced below the allowable thickness
(according to the SRM) and must be reinforced to make it airworthy.
Simple non-patch repair of cracking involves stop drilling the crack tip. This is
only a temporary and relatively ineffective measure, since it is difficult to find the tip
of the crack. Even if the tip is found, cracking resumes very shortly after stop drilling
because of the high stress concentration associated with the shank of the crack.
Chapter 1. Introduction and overview
I
A much superior approach is to stop drill and then expand the stop-drilled hole,
usually with a special sleeve to develop favourable compressive stresses that reduce
or prevent crack opening. While this approach is often highly effective in stopping
crack growth it is not damage tolerant, because when the crack does eventually
grow through the compressive zone, growth is unrestrained and will be rapid.
1.5. The case for adhesively bonded repairs
Repairs based on mechanically fastened metallic patches are currently the
recommended SRM approach, however, compared to adhesively bonded patches
they are less efficient and more problem prone for the reasons described in this
section. To illustrate the reinforcing efficiency of mechanical fastening versus
bonding, a simple comparison is made by modelling the repairs as equivalent
overlap joints as shown in Figures 1.1 and 1.2. These diagrams depict joints
representing patch repairs to a cracked parent structure where the crack is
represented by the gap in the lower joint member.
In mechanical joints, referring to Figure 1.1, loads are transferred between the
joint elements primarily by compression on the internal faces of the fastener holes,
resulting in high local stress concentrations. A smaller component of load is
transmitted by shear on the outer faces of the elements through friction, depending
on the stress level on the joint surface produced by clamp-up as the fastener is
applied. The mechanical joint is generally fairly compliant or flexible for several
reasons, including:
(a) The requirement for a finite edge distance (generally 2-3 x (hole diameter) for
fasteners results in a long fastener-free zone spanning the gap (simulating the
crack).
(b) Large hole tolerances, as may be expected in a repair, allow movement and
rotation of fasteners [9].
(c) The high stresses at the fasteners and fastener holes result in significant local
displacements.
(d) The frictional shear component can relax under cyclic loading or due to the
lubricating effect of water-displacing compounds and other aircraft fluids.
Long Spring - Flexible
i
Fig. 1.1. Schematic of a joint representing a region of the patch spanning the crack. This joint may be
relatively flexible because of the high local stresses, the large span needed to provide a reasonable edge
distance for the fasteners and the tendency of the fasteners to rotate or move to take up any tolerances.
8
Advances in the bonded composite repair of metallic aircraft structure
Short Spring
- Stiff
Crack in Shucture Under
Bonded Repair
Fig. 1.2. Schematic of a bonded joint representing a section through the repaired region. This is
relatively stiff because loading is distributed over the whole surface of the joint, the span over the gap is
very short and there is no tolerance take-up to allow movement.
The low stiffness and therefore patching efficiency of the mechanically fastened
joint is illustrated by the long spring in Figure 1.1.
As a result of the relatively low reinforcing efficiency in mechanical repairs,
components with cracks generally cannot be satisfactorily reinforced. Thus, the
cracked region must be removed prior to application of the repair and the resulting
hole filled with an insert before covering with the reinforcing patch. In relatively
thick-skinned components crack removal is a costly, time-consuming requirement
and may be impractical in many repair situations. Furthermore, in situ drilling of
new fastener holes can cause internal damage (e.g. to hydraulic lines, electrical
wires or optical fibres) as well as introducing swarf into the structure.
Mechanical repairs are generally designed simply to restore static strength. Swift
[lo] shows that these repairs, if not well designed, can significantly reduce fatigue
life. The main concern is the danger of initiation of a crack from a fastener hole
(usually in the first row where stresses are highest). The crack may initiate at quite
low stresses because of high stress concentrations (usually at the first row of
fasteners) or because of poor quality hole drilling or riveting - common problems
under field conditions. There is also the danger of cracks initiating from hidden
corrosion which can develop under a poorly sealed mechanical repair. Additionally, there is concern with the difficulty of detecting the crack by standard nondestructive inspection (NDI) procedures, until it emerges from under the repair when growth may be very rapid because of low reinforcing efficiency. Thus,
mechanical repairs are inherently not damage tolerant.
By contrast, loads in bonded joints are transferred by shear over the surface area
of the elements. Because of the large area for load transfer, which extends right up
to the gap (crack), the bonded joint is intrinsically much stiffer than the mechanical
joint. This is despite the low stiffness of the adhesive compared to the metal
fasteners. The transfer length determines the rate of load transfer from the cracked
region into the composite adherends, which is a function of the joint geometry and
mechanical properties. A low transfer length equates to high joint stiffness. The
transfer length increases as a (square-root) function of the adhesive thickness and
shear compliance and is strongly dependent on its shear yield strength.
Chapter 1. Introduction and overview
9
Relative stiffness for the bonded joint is further increased compared to the
mechanical joint (unless it has interference-fit fasteners) since there are no slacks to
be taken up.
Thus, as illustrated by the short spring in Figure 1.1, bonded joints provide a
very stiff and therefore very efficient reinforcement. This minimises the gap opening
and therefore the stress intensity in the case of a patched crack. It then becomes
feasible to successfully patch live cracks.
Finally, in a well-designed joint, one with optimally tapered ends, there are only
minor local regions of high deformation in the adhesive at the ends of the joint and
thus no major stress concentrations in the joint elements where the patch
terminates.
1.6. Composite versus metallic patches
The advantages of high performance fibre composite graphite/epoxy (gr/ep) and
boron/epoxy (b/ep) materials for patches when compared with metallic alloys
include:
0 High directional stiffness, which allows use of thin patches (important for
external repairs) and allows reinforcement to be applied only in desired
directions;
0 High failure strain and durability under cyclic loading, which minimises danger
of patch failure at even quite high elastic strain levels in the parent metal
structure;
0 Low density, an important advantage where changes in the balance of a control
surface must be minimised; and
0 Excellent formability that allows low-cost manufacture of patches with complex
contours.
Another important advantage of composites is that the pre-bonding surface
treatment of composite patches (with thermosetting matrices) for adhesive bonding
is less demanding than for metals. This is because mechanical abrasion to produce a
high-energy uncontaminated surface is all that is required. Alternatively, the
composite patch can be cocured on the metallic component with the adhesive,
which obviates the need for any surface treatment of the patch and simplifies the
patch fabrication procedure. The choice of material type for bonded patches or
reinforcements is considered in more detail in Chapter 2.
In most repair applications use of unidirectional patches (all 0" plies) is optimal
since this provides the highest reinforcement efficiency in the loading direction, and
minimises undesirable stiffening in other directions. However, in some applications
with high biaxial stress components, or where there is concern that the crack may
change orientation, it may be desirable to provide transverse and/or shear
reinforcement. This can be achieved by using a laminate with the appropriate
number of k45" and 90" plies.
The main disadvantage of using gr/ep or b/ep results from a mismatch in thermal
expansion coefficient between the composite and the metal [l], and Chapter 2.
10
Advances in the bonded composite repair of metallic aircraft structure
Residual stresses are tensile in the metal and compressive in the composite. These
stresses are particularly severe when elevated-temperature-curing adhesives are
used to bond the patch and when operating temperatures are very low, typically
-10 to -50°C. The tensile residual stress could be expected, for example, to
increase the growth rate of the patched crack by increasing the stress ratio R,
reducing patching efficiency.Further, thermal cycling of the patched region causes
cyclic stresses that could result in crack growth, independent of external stressing.
The desire to avoid the residual stress problem is the major reason why Fredel as
described in Chapter 14 and [l 11 developed the use of GLARE patches for repairs
to thin-skin fuselage structure. GLARE is a glass-fibre/epoxy-reinforced aluminium alloy laminate, the epoxy matrix also acts as an adhesive which bonds the
aluminium alloy layers. GLARE has a similar expansion coefficient to aluminium
alloys and excellent fatigue crack growth resistance compared to normal aluminium
alloy materials; the glass fibres bridge any fatigue crack which may develop in the
metal layers.
GLARE is less suited for repair of thick structures since it has a lower modulus
then aluminium alloys and has limited formability (similar to that of sheet
aluminium alloy), compared with fibre composites. ARALL (Aramid Reinforced
Aluminium Laminate) is a similar concept using higher modulus aramid fibres
instead of glass. Although ARALL has a higher stiffness, it has somewhat inferior
fatigue properties to those of GLARE.
Despite the residual stress concerns, the composites b/ep and gr/ep offer excellent
properties for patches or reinforcements. However, b/ep is generally considered to
be the superior because of its:
0 Superior combination of strength and stiffness which provides the highest
efficiency reinforcement;
0 Higher coefficient of thermal expansion, which reduces the severity of the
residual stress problem;
0 Low electrical conductivity, which:
- avoids the danger associated with gr/ep of inducing galvanic corrosion of the
metal, and
- allows optimal use of eddy-current NDI to detect and monitor cracks under the
patch.
However, gr/ep is chosen if patches with low radii of curvature (less than 30mm)
are required or if b/ep cost (which is very much higher than gr/ep) or availability is
a concern.
1.7. Scope of applications
Bonded composite repairs can be regarded as a versatile cost-effective method of
repairing, strengthening or upgrading inadequate metallic structures. The
reinforcements or patches are ideally implemented in situ, avoiding the need for
costly disassembly of built-up structures.
Chapter 1. Introduction and overview
11
Potential applications can be summarised as follows:
(a) Reduce stress intensity:
- in regions with fatigue cracks
- in regions with stress-corrosion cracks
to increase damage tolerance (provide slow crack-growth characteristics) in
safe-life structure or structure with multi-site damage
(b) Restore strength and stiffness:
after removal of corrosion damage to below allowable SRM limits
- after removal of flaws
- after re-shaping to minimise stress concentrations
- after heat damage
after failure of a load path in multi-load-path structure
(c) Stiffen under-designed regions:
- to reduce strain at stress concentrations
- to reduce secondary bending
- to reduce vibration and prevent acoustic damage.
1.8. Some experimental comparisons of bonding versus bolting
Experiments to compare the effective stiffness of bonded or bolted joints were
made using the double overlap joint specimen illustrated schematically in Figure
1.3. The double overlap joint represents a slice through a two-sided repair over the
cracked region. The ability of the joint to restrict "crack" opening was measured
using a clip gauge, as shown. In each joint the nominal stiffness of the outer
adherends are similar on the basis of modulus x thickness. This work was
conducted as part of an early study on joints representing repairs [12].
The results, Figure 1.4, show the much superior stiffness of a joint (a) bonded
with the 120 "C curing epoxy-nitrile structural film adhesive over the bolted joint
(c), confirming the much higher reinforcing efficiency of bonded over traditional
mechanically fastened repairs.
Joint (b), bonded with the relatively soft modified epoxy-paste adhesive, had
intermediate stiffness, which is what would be expected of the joint bonded with the
120 "C curing epoxy-nitrile adhesive at temperatures above 70 "C or so.
Note also the marked viscoelastic behaviour of the joint bonded with this
adhesive as indicated by the open hysteresis loops and the time-dependent recovery.
Even joint (a) exhibits small viscoelastic effects as indicated by the reduction in
hysteresis and increase in stiffness with increasing rates of loading.
To highlight the advantages of the use of bonded composite repairs for crack
repair (known as "Crack Patching"), fatigue tests were performed on patched edgenotched panels, shown inset in Figure 1.5. The total thickness of the aluminium
patches, both sides, was equal to the panel for metal patches and 1/3 of this for the
WpIt is seen from Figure 1.6 that the mechanically attached metallic patch provides
rather poor reinforcing efficiency since there is only a very slight reduction in crack
growth rate; it is also seen from the figure that the crack once it emerges from under
12
Advances in the bonded composite repair of metallic aircraft structure
Specimen (a, b)
Strain gauge centers
.I::
I ,
I
I
=109mm
7
' +'?
E
z
Clip gauge
Specimen (c)
L 2 0 2 4 T3
L 2 0 2 L T3
ir"="""
5mm Dia.
clip gauge-/
Fig. 1.3. Double-overlap joints with 2024 T3 inner member showing the position of clip gauge and strain
gauges. Specimen (a) boron/epoxy patch bonded with an epoxy-nitrilestructural film adhesive (AF126)
and (b) bonded with a relatively soft modified epoxy paste adhesive (EC2216). Specimen (c) has an
outer member 2024 T3 of nominally similar stiffness to the boron/epoxy mechanically fastened with
M5 high-strength steel bolts, torque 11 N-m.
the patch grows very rapidly. The metallic patch can appear to be effective in some
cases if the crack arrests temporarily at a fastener hole. In contrast, the adhesively
bonded b/ep patch is shown to greatly reduce the growth rate, even when the crack
emerges from under the patch. The growth rate of the emerging crack with the b/ep
patch is similar to that expected for a crack of the emerged length, indicating that
the patch is still operating very effectively in restraining crack opening.
Based on these observations and the previous discussion, the advantages of
bonded composite repairs for fatigue crack are summarised in Figure 1.6.
Chapter 1. Introduction and overview
13
4
Displacement
6 (mrn x 10')
Fig. 1.4. Stress-displacement plots from the clip-gauge measurements for the (a), (b) and (c) specimens
from Fig. 1.3. Note the relatively low stiffness of the mechanical joint and to a lesser extent specimen (b)
compared with specimen (a). Also note the time-dependent behaviour of specimen (b).
14
Advances in the bonded composite repair of metallic aircraft structure
80
70
60
50
40
30
20
10
0
0
1
2
3
4
0
Cycles x 10‘
1
2
cycles x
3
4
io’
(b)
Fig. 1.5. Comparison of crack growth performance of patching efficiency between a) a mechanically
fastened mechanical repair and b) an adhesively bonded composite repair.
e
e
e
e
Stress concentrationsat fastener holes
Difficult to detect cracks under patch
Low patching efficiency,cannot patch cracks
Rapid crack growth on exit from patch
Danger of corrosion under patch
No damage to structure or hidden componenets
Minimises stress concentrations
e Slow crack growth even on exit from patch
High reinforceing efficiency, can repair cracks
0
Can detect crack growth under patch
No corrosion problems, sealed interface
e
e
Fig. 1.6. (a) Some disadvantages of standard mechanically fastened repairs and (b) advantages of
bonded composite repairs.
1.9. R&D requirements
At the time of writing of the first book [I] bonded composite repair technology
had advanced to the stage that repairs and reinforcements could be applied with
some confidence to non-flight critical components. Since then technological
capabilities have improved and long-term experience has been accumulated such
that the scope and range of applications can be extended with some confidence.
The challenges (as viewed in Australia) are to push the boundaries for
application of bonded composite repairs to increasingly demanding situations;
for example, to repair critical damage in primary structure. A recent example [ 131 is
the development of a repair of a crack in the lower wing skin of Australian F-1 1 1
aircraft. This crack had reduced the residual strength of the wing below DLL. Such
a repair would probably not be accepted by UK or US military airworthiness
authorities; indeed a very lengthy and costly program was required to have it
accepted in Australia, which may not be cost effective in many applications.
Currently most airworthiness authorities will only accept bonded repairs to
critical structure on the basis that a margin on DLL is retained in case of complete
Chapter 1. Introduction and overview
15
failure of the repair. Essentially this implies that no credit is permitted for the patch
in improving residual strength and slowing crack growth [4,14]. However, it is
possible this limitation will be overcome by the “Smart Patch” approach. R&D on
this topic is described in Chapter 20. The smart patch is a patch (or reinforcement)
capable of monitoring and reporting its own structural integrity and, if required,
that of the damaged structure.
Recently, three major reviews were undertaken to define the general R&D needs
for further development of bonded composite repair technology. These reviews
were by the Committee on Aging of US Airforce Aircraft in 1997, the technical
cooperation program (TTCP) Aeronautical Vehicles Action Group on Certification
on Bonded Structure in 1999 and an Australian Defence Science and Technology
(DSTO) in 1998.
The USAF review [2] formed part of a major study on aging USAF aircraft,
undertaken by a select US committee. In this review, the capability of bonded
composite repairs to prolong the life of ageing aircraft was recognised. They state
that:
“The primary emphasis is on the maturation of bonded composite repairs,
especially for metallic structures. The committee believes that the focus on
optimisation of materials and processes, repair criteria and analysis tools for
bonded composite repair of metallic structure is appropriate”.
TTCP is a program for collaboration in (non-nuclear) defence science involving
UK, US, Canada, New Zealand and Australia. The Air Vehicles Sub Group in
TTCP established an Action Group (AER 13) to review issues related to the
certification of bonded structures for military aircraft structures [15].
In the Terms of Reference for the study it was stated that “one of the primary
applications of bonded structures is the application of composite patching of
metallic structures. The benefits from this application are the cost savings over
other types of repairs and the aircraft availability improvement through reducing
need for procurement of long lead items. Even wider use of this application would
achieve these benefits, while maintaining flight safety, through the development of
suitable certification procedures”.
The third study was an in-house strategic review conducted in 1998 in the
author’s organisation DSTO with input from the Royal Australian Air Force. The
aim was to establish the needs, topics and aims for future work on bonded
composite repairs.
In addition to these reviews, the author in references [4,14] address certification
R&D issues for bonded composite repairs to primary aircraft structure.
Table 1.1 lists recommendations from these reviews. Those related to
certification issues are listed under the major headings of (a) Acquisition of Design
Data, (b) Validation of Procedures, (c) Assessment of Bond Environmental
Durability. Those related to improved technology are listed under the major
headings of (d) Improved Design Capability and (e) Improved Materials and
Processing and (f) Improved NDI. To fit more clearly under these headings some of
the recommendations have been edited, without significantly changing the aim or
meaning.
16
Advances in the bonded composite repair of meiallic aireraft structure
Table 1.1
R&D requirements from various studies on bonded repairs.
A . Acquire design dota
Acquisition of data on static
and fatigue stresses
patch/reinforcement
system properties
Parent structure properties
Methods to acquire design stresses and usage spectra by analysis or by
direct measurement [DSTO]
Develop damage criteria that correctly predict observed patch system
static and fatigue failure modes [TTCP]
Obtain materials allowables and knockdown factors for the relevant
failure modes, including degradation caused by moisture and other
service environments [TTCP]
Determine influence of patch application procedure, including residual
stresses on parent allowables [DSTO]
B. Validate design procedures
Design models
Validation of analysis techniques to evaluate continuing damage growth
beneath repairs [USAF, TTCP]
Validation of models for single-sided repairs and complex geometries
FCPI
Check ability of models to allow for variables, including R ratio, holds,
temperature-residual stress, spectrum loading and environment [TTCP,
DSTO]
C. Assess bond environmental durability
Quality assurance
Self-assessment
Correlate accelerated tests such as the Boeing Wedge Test with actual
service performance F C P , DSTO]
Develop methods for risk assessment of bonded repairs W C P , DSTO]
Develop smart patch approach to patch system self-health assessment
[TTCP, DSTO]
D. Improve design capability
Increased scope
Design aids
Optimisation
Develop design procedures able to minimise stress concentrations in
parent structure and patch system [DSTO]
Develop analytical methods for complex and curved structures [USAF]
Develop design guidelines for dynamically loaded structures [USAF]
Develop design methodology for corrosion damage [DSTO]
Develop models which include effects of thermal mismatch, bending and
disbonding V C P ]
Simplified approaches to be programmed into notebook PCs [rrCP]
Develop Expert system to aid assessment of repair, the need for repair
and design analysis of repairs [USAF]
Optimisation procedures for patch geometry to minimise stresses in
adhesive bond layer and parent structure [TTCP]
Chapter 1. Introduction and overview
17
Table 1.1
Continued
E. Improve materials and processes
Screening
Bonding
Patch systems
Develop rapid screening tests for new adhesives, composites and
processes suitable for repair applications [DSTO]
Develop/evaluateimproved pre-bonding surface treatments if required
[TTCP]
Establish processing window for existing and new systems VTCP]
Develop composites with tougher surface layer matrices to improve
fatigue resistance [DSTO]
F. Improve NDI
Pre-bond NDI
Post-bond NDI
Develop pre-bond NDI capability [TTCP, DSTO]
Determine adhesive bond quality, degradation, accept/reject standards
[USAFl
Capability for detecting cracks under patches in complex geometries
[DSTO]
1.10. Conclusion
While simple in concept and often in application, bonded composite repair
technology can be challenging from both the scientific and engineering viewpoint,
particularly for the repair of primary structures. This is because it involves
interdisciplinary inputs from several fields, including aerodynamic loading, stress
analysis, fibre composites, structural adhesive bonding, linear-elastic fracture
mechanics and fatigue. The technologies of non-destructive inspection and, more
recently smart materials, must also to be included. Operational issues are equally
critical, including airworthiness certification, application technology (including
health and safety issues) and training.
It is hoped that the material provided in this book will provide at least partial
answers to many of the R&D issues and promote the required degree of
interactions between experts in the various fields mentioned.
References
1. Baker, A.A. and Jones, R. (1988). Bonded Repair of Aircraft Structures. Martinus Nijhoff.
2. Aging of US.Airforce Aircraf?. Publication NMAB-488-2 National Academy Press, Washington
D.C. 1997.
3. Baker, A.A. (1994). Bonded Composite Repair of Metallic Aircraft Components, Paper 1 in
AGARD-CP-550 Composite Repair of Military Aircraft Structures.
4. Baker, A.A. (1997). On the certification of bonded composite repairs to primary aircraft structures.
Proc. 11th Int. Con$ on Comp. Mat. (ICCM-II), Gold Coast, Australia, volume 1, pp. 1-24.
5. Simpson, D.L. and Brooks, C.L. (1999). Tailoring the structural integrity process to meet the
challenges of aging aircraft. Int. J. of Fatigue, 21, S1-S14.
18
Advances in the bonded composite repair of metallic aircraft structure
6. Clark, G. (1999). Corrosion and the management of structural integrity. In Structural Integrity for
the Next Millennium (J.L. Rudd, ed.) EMAS, Warley.
7. Nicholas, T. (1997). Critical issues in high cycle fatigue. Int. J. of Fatigue, 21, S221-231.
8. Baker, A.A. (1997). Joining and repair of aircraft composite structures. Chapter 14 in Composite
Engineering Handbook (P.K. Mallick, ed.) Marcel Dekker, Inc.
9. Hart-Smith, L.J. (1989). The Design of Efficient Bolted and Riveted Fibrous Composite Structures.
Douglas Paper 8335, July.
10. Swift, T. (1990). Repairs to damage tolerant aircraft. Proc. Int. Symp. on Structural Integrity of
Aging Airplanes, FAA-AIR-01.
11. Fredell, R.S., van Barnveld, W. and Vlot, A. (1994). Analysis of composite crack patching of
fuselage structures: High patch modulus isn’t the whole story. SAMPE Int. Symp. 39, April.
12. Baker, A.A., Roberts, J.D. and Rose, L.R.F. (1981). Use of joint parameters in estimating the K
reduction due to crack patching. Proc. of an Int. Workshop on Defence Applications for Advanced
Repair Technology for Metal and Composite Structure, Naval Research Labs., Washington.
13. Baker, A.A., Rose, L.R.F., Walker, K.F., et al. (1999). Repair substantiation for a bonded
composite repair to an F-l 11 lower wing skin. Applied Composites, 6, 251-256.
14. Baker, A.A. (1999). Issues in the certification of bonded composite patch repairs for cracked metallic
aircraft structures. Proc. Int. Conf. on Aircraft Fatigue, Seattle.
15. Certification of Bonded Structures Action Group 13 Report of the Technical Co-operation
Program, Feb. 2001.
Chapter 2
MATERIALS SELECTION AND ENGINEERING
R. CHESTER
Air Vehicles Division, Defence Science and Technology Organisation, Fisherrnans
Bend, Victoria 3207, Australia
2.1. Introduction
The three critical steps in implementing a bonded repair are design, choice of
materials and application. In this chapter the various considerations associated
with the selection of materials will be discussed along with some of the various
materials engineering issues associated with repair application [ 11.
A well-designed repair can only be effective if it is strongly bonded to the parent
adherend and therefore the issues of adhesive bond strength and bond durability
are absolutely crucial for a fully successful repair. These issues will be introduced in
this chapter and explored in more detail in Chapter 3. The material selected for the
patch will almost always be either metallic or composite and within these classes are
many different materials with different advantages and disadvantages associated
with their use. These issues will be considered together with those of adhesive
selection where two of the important factors are the operating temperature and
nature of the applied loads.
The use of chemicals to modify the adherend surface prior to bonding is an
essential step in the repair process and needs careful consideration as the
inappropriate use of some of these chemicals can cause further damage to the
structure, as in the case of acids for example. The selection of chemicals which
reduce the likelihood of such damage while retaining high levels of effectiveness will
be discussed. Various mechanical tests will be described which may be required for
either quality assurance reasons or for generation of design allowables for the patch
materials or adhesives. It is common to find that data suitable for design is not
available from the material manufacturer (especially for adhesives), and the only
alternative is to perform the appropriate tests to generate the data.
19
Baker, A.A., Rose, L.R.F. and Jones, R. (eds.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 02002 Published by Elsevier Science Ltd. All rights reserved.
20
Advances in the bonded composite repair of metallic aircraft struelure
Finally, the application of an adhesively bonded repair to a structure creates a
number of materials engineering design issues which may be important depending
on the repair circumstances. An example is the development of residual stresses
when an elevated temperature adhesive is used to bond a repair patch to a substrate
with a different coefficient of thermal expansion. Issues such as these will be raised
and discussed in the final section.
2.1.1. Factors affecting adhesion
Although there are many theories of adhesion, it is generally considered that
strong adhesion can only take place when the adhesive is in sufficiently intimate
contact with the adherends to enable the development of chemical or physical
bonds. These surface attachments are the mechanism by which the load is
transferred into the repair and is uniformly distributed across the interface. TO
achieve the required level of intimate contact, the adhesive needs to behave as a
liquid in order to wet the adherend surface. When a strong bond is achieved, it is
important to maintain that level of strength over time and such strength retention
in the operating environment is termed durability in this book. Adhesive bond
durability is not solely a function of the adhesive type but also depends critically on
the other components of the joint such as the adherends, and any interfacial layers
between the adherends and the adhesive.
Wetting of the adherend by the adhesive is an essential part of the bonding
process. Adhesives used for Bonded Repairs are either in the form of pastes or films
and these two categories will be discussed further in Section 2.3.1. Regardless of the
initial form of the adhesive, it is important that at some stage of the cure cycle, the
viscosity of the adhesive should be sufficiently low so as to enable the adhesive to
flow and wet the adherend. Adhesives cured at room temperature are often already
in the form of a liquid or paste, however, higher temperature curing adhesives may
initially be in the form of a film or sheet which softens significantly as the
temperature is increased. Any factor which inhibits the ability of the adhesive to
flow and wet the adherend will potentially reduce the adhesion strength.
Three important factors which can influence the flow characteristics of an
adhesive are temperature, contaminants and adhesive age. If the correct temperature
during the cure is not reached at the correct time, the adhesive may not reach the
right level of viscosity. For example if the cure temperature increases slightly and is
then held for some time, the adhesive may not have dropped sufficiently in viscosity
but may be beginning to cure and develop cross links. If the temperature is then
raised again, the crosslinking will have increased the viscosity of the adhesive and
proper flow will not take place. At the end of the cure cycle, the adhesive may be fully
cured (crosslinked) but as proper wetting did not take place the adhesion strength
may be low. Contaminants such as absorbed water may change the chemical
characteristics of the adhesive and inhibit the proper level of flow. Adhesive that has
passed it’s storage date may also be incapable of achieving the correct level of
viscosity. This is because the adhesive will have been slowly crosslinking during
storage and then during the cure cycle, the crosslinks prevent proper flow in the same
Chapter 2. Materials selection and engineering
21
way as the improper cure cycle described above. Tests described in Section 2.5 can be
used to determine if the adhesive is in an acceptable state for use.
Although wetting is a necessary condition for the development of strong bonds,
it is not a sufficient condition. An adhesive can wet an adherend surface but still
have low adhesive strength because of the presence of contamination or weak
surface layers on the adherend. On aluminium surfaces for example, the adhesive
can form a strong bond to old, thick (hydrated) oxide layers on the surface which
themselves have relatively low cohesive strength. Under the action of structural
loads the joint can subsequently fail through these weak layers. Other forms of
organic contamination on the surface can have much the same effect. A clean
contaminant-free surface is therefore an essential requirement for the development
of a strong adhesive bond. Producing such a surface is known as surface
preparation.
While attention to these factors will permit the development of good initial bond
strength, they will not provide any guarantee of good bond durability. The
durability of an adhesive bond is dependent on the adherend materials, the
adhesive and the interfacial layers between the adhesive and adherends. The
presence of water is by far the most serious cause of bond degradation, and metallic
adherend surfaces are commonly affected. Water can degrade the bond strength to
a metallic surface by causing the surface to either oxidise (steel) or hydrate
(aluminium). In both cases the new interfacial layer formed has poor cohesive
strength and the adhesive no longer adheres to the metallic adherend. An essential
requirement then for the production of durable adhesive bonds to metallic surfaces,
is the production of a bonding layer on the adherend which is resistant to
degradation mechanisms by moisture such as oxidation or hydration. Producing
such a layer is known as surface treatment.
Composite or polymeric surfaces are not susceptible to these degradation
mechanisms and therefore the preparation of composite patches for bonding
generally only requires the use of surface preparation methods (Chapter 3). For
metallic adherends, however, it is essential to use both surface preparation and
surface treatment methods
2.2. Materials for patches and reinforcements
The two main categories of materials for patches or reinforcements are metals
and composites. More recently, laminated metallic materials such as ARALL and
GLARE have been developed and are being used successfully for Bonded Repairs.
These new materials will be discussed together with the conventional metallic
materials. The main points are summarised in Table 2.1.
2.2.1. Metallic materials
The usual objective of a Bonded Repair is to restore the damaged structure back
to its original condition in terms of strength and stiffness. For this reason, perhaps
22
Advances in the bonded composite repair of metallic aircraft structure
Table 2.1
Summary of the advantages and disadvantages of metallic and composite materials for bonded repairs.
Material type
Advantages
Metallic
0
0
0
0
Long shelf life
Properties well known
Isotropic properties
High coefficient of thermal expansion
Disadvantages
0
0
0
0
Composite
0
0
0
0
0
0
Lightweight
Corrosion and fatigue resistant
High specific stiffness
Easy to form strong durable bond (if
thermoset)
Comparativelyeasy to inspect
substructure
Excellent formability to curved
surfaces
0
0
Requires careful surface treatment
Susceptible to corrosion and fatigue
Inspections of underlying structure can
be difficult
Difficult to form to curved surfaces
Low Coefficient of thermal expansion
Comparativelyshort shelf life (in
uncured state)
the most obvious choice of repair material is that which the structure is already
made from. For aircraft this is commonly an aluminium alloy from either the 2000
or 7000 series. The other common materials are steel and titanium. These three
materials can usually be successfully treated to produce durable bonds and
therefore can be considered as potential repair materials. Magnesium on the other
hand is difficult to bond to, and while some Bonded Repairs have been carried out
to magnesium components, it would not generally be considered as a repair
material.
The use of the original materials for design of the repair may help to simplify the
design process, however, there are also very good reasons to consider the use of an
alternate material; composites make exceptionally good repair materials due to
their resistance to fatigue stresses and corrosion as well as many other advantages
which are discussed later.
Metallic repair materials are often readily available and of course, compared
with uncured composites have an infinite shelf life. Compared with composites,
metals have isotropic properties that may be important if there is concern about
unusual stress states. A metallic repair may be better able to withstand multi-axial
loads and perhaps high levels of through-thickness stresses. On the other hand,
many repairs are required on relatively flat structure where the loads causing
cracking are in one direction and here the use of unidirectional composites can
produce a much more efficient repair. For the same level of repair efficiency, a
metallic repair in this situation would be thicker and heavier and this may be
a problem where balance or aerodynamic smoothness is required. Metals have a
higher coefficient of thermal expansion than composites and this can be an
advantage where elevated temperature curing adhesives are used. This topic is
discussed further in Section 2.6.
Chapter 2. Materials selection and engineering
23
If the problem causing the need for the repair was fatigue or corrosion, it may
be more appropriate to use a composite for the repair as these materials are
effectively immune to these problems (composite repair layups generally have fibre
dominated properties which are immune to fatigue whereas layups with matrix
dominated properties may be susceptible to fatigue). The repair material chosen
can also be important where subsequent inspections are required and in many
cases the use of boron/epoxy composites is advantageous as eddy current methods
can be used to readily detect the crack underneath the repair. This is usually more
difficult if a metallic or graphite fibre patch is used due to the fact that these
materials are electrically conducting. Metallic materials will require the use of
stringent surface preparation and surface treatment processes to obtain a durable
bond, however, if a corrosion inhibiting primer is used, these processes could be
conducted elsewhere and the patch stored prior to use. Composite repairs using
thermosetting matrices such as epoxies are comparatively easier to prepare for
bonding, although the processes required are still important [2]. Thermoplastic
composites are in general harder to bond to than the more commonly used
thermoset composites. Finally metals lend themselves best to relatively flat repair
locations due to the difficulty in accurately forming a metallic sheet to a curved
profile. This is one of the strengths of composites where the desired shape can be
formed into the repair during cure.
Further considerations for the selection of a metallic material may include
corrosion and patch thickness. To avoid galvanic corrosion problems between
dissimilar metals, a sensible choice would be to use the original material for the
repair material as well. Where this is not possible, a check should be made to ensure
that different repair materials would not be susceptible to corrosion. For example,
repairs to a graphite/epoxy component will often be performed with a graphite/
epoxy material as well. Use of an aluminium material in this situation would be
unusual as the aluminium will readily corrode if in galvanic contact with the
graphite fibres. The adhesive should serve as an electrically insulating layer,
however, the more usual alternative to a graphite patch in this situation would be
titanium which will not corrode should the insulation break down.
In situations where the thickness of the repair is critical (on an aerodynamic
surface for example) consideration may be given to either steel or titanium to repair
aluminium. The greater stiffness of these materials should permit the design of a
thinner patch than would be possible with aluminium. Again consideration should
be given to possible galvanic coupling and potential corrosion problems in this
situation and it is possible that the choice of a composite may be preferable.
Laminated metallic materials have been developed in the Netherlands which
consist of layers of composite sandwiched between thin aluminium alloy sheets [3].
Where the composite used is kevlar (or aramid) the laminate is referred to as
ARALL (aramid reinforced aluminium laminate) and if the composite used is glass
fibre, the laminate is referred to as GLARE (Chapter 14). The fundamental idea
behind the development of these materials is to combine the traditional advantages
of both metals and composites. The composite component confers increased fatigue
strength and damage tolerance to the structure, while the aluminium allows the use
24
Advances in the bonded composite repair of metallic aircraft structure
of conventional metallic forming, fastening and manufacturing processes for
reduced cost.
GLARE has been proposed as a possible material for use in bonded repairs and
in particular has been used as a material for the repair of damage to the fuselages of
transport aircraft. The principal advantage of GLARE in this situation is the high
coefficient of thermal expansion. Work by Fredell et al. [4] and Chapter 14, has
shown that for repairs to thin fuselage skins which will mostly see pressurisation
loads at cruising altitudes (-55 "C), the higher coefficient of thermal expansion of
GLARE provides structural advantages compared with composite alternatives (see
Section 2.6 for further discussion). On the other hand the low specific stiffness of
GLARE results in a much thicker patch than for a high modulus composite
material, and this needs to be carefully considered in the design to ensure that
bending effects due to neutral axis offset are not excessive and that high stresses at
the ends of the patch are alleviated by tapering for example.
Finally, it may be possible to use nickel as a repair material in some specific
circumstances for example where geometry is complex. The repair of a crack in the
comer of a bulkhead pocket is a good example. Nickel can be electroformed to
replicate the surface of a mould with very high precision, and therefore it should be
possible to produce an electroformed nickel patch which will fit precisely into the
pocket. As mentioned above, the isotropic nature of the nickel would be an
advantage in this situation, although care needs to be made to ensure that the
electroforming process does not produce planes of weakness within the electroform. Work is underway to evaluate this method as a repair option for a damaged
army gun support structure [5]. In situations such as this where a certain degree of
rough handling can be expected, the hard, damage resistant surface of the nickel
provides another important advantage over a fibre composite repair.
2.2.2. Non-metallic materials
The two main non-metallic materials used are boron/epoxy and graphite/epoxy
composites. Glass fibre composites are not used due to their low stiffness and
kevlar composites while strong and stiff in tension have relatively poor
compression performance.
Boron fibres were first reported in 1959 and were the original high modulus fibre
before the development of graphite fibres in the 1960s. Boron composites were used
to produce aircraft components such as the skins of the horizontal stabilisers on the
F-14 and the horizontal and vertical stabilisers and rudders on the F-15. The use of
boron composites in large-scale aircraft manufacturing has largely stopped now
due to the development of more cost-effective graphite fibres. The production
process for boron fibres is time consuming and does not lend itself to mass
production in the same way as modem methods for producing graphite fibres. For
this reason the price of boron fibres has not dropped as significantly as that of
graphite fibres which are now at around I/lOth the cost. Boron fibres are
manufactured individually by chemically vapour depositing boron onto a heated
tungsten wire substrate from boron trichloride gas in a reactor. The fibres are
Chapter 2. Materials selection and engineering
25
available from Textron Speciality Materials in 100 and 140 micron diameters and
commercial pre-pregs are available with either 120°C or 175°C curing epoxies. The
fibre diameter is significantly larger than normal graphite fibres due to the presence
of the tungsten core. Attempts have been made in the past to use a carbon filament
precursor to reduce the production costs, however, these boron-carbon filaments
have generally not had the high level of strength that can be produced with the
tungsten filament precursor.
Boron fibre is an extremely hard material with a Knoop value of 3200 which is
harder than tungsten carbide and titanium nitride (1800-1880) and second only to
diamond (7000). Cured boron composites can be cut, drilled and machined with
diamond tipped tools and the pre-pregs are readily cut with conventional steel
knives. In practice the knives cannot actually cut the hard fibres, however, gentle
pressure fractures the fibres with one or two passes. “Snap-off’ knife blades are
commonly used as the cutting edge is rapidly worn by the hard fibres. Although it is
possible to cut complex shapes with the use of templates, laser cutting has been
shown to be the most efficient way to cut a large amount of non-rectangular boron
plies. Circular patches, for example, are readily cut using a laser cutter with the prepreg supported on a backing material such as Masonite.
The combination of very high compressive stiffness, large fibre diameter and high
hardness means that boron fibres can readily penetrate skin and care must be
exercised in handling boron pre-preg to reduce the chance of splinter-type injuries.
If a fibre does enter the skin, it should be removed very carefully with h e tweezers.
Trying to squeeze the fibre out must be avoided as the fibre may fracture into
smaller segments.
The stiffness and diameter of boron fibres also restricts their use in small radius
corners. The 100 micron diameter fibre can be formed into a radius of 30 mm, but
this is about the limit than can be comfortably achieved. The smaller diameter of
graphite fibres makes it the choice for smaller radii situations. In most other
aspects, boron pre-pregs handle and process in a similar fashion to the more
common graphite pre-preg materials.
As a repair material, boron/epoxy composites have a number of advantages [1,6]
including;
0 an intermediate coefficient of thermal expansion which helps to minimise the
level of thermally induced residual stress which results from an elevated
temperature cure. This contrasts with graphite fibres mentioned below.
0 relatively simple NDI is possible using eddy currents through the repair patch to
detect the extent of the defect. This is possible due to the non-conducting nature
of the fibres.
0 no galvanic corrosion problems when bonded to common airframe materials.
0 a good combination of high compressive and tensile strength and stiffness (the
compressive strength of a unidirectional B/EP composite is 2930 MPa compared
with 1020MPa for HMS GR/EP)
Graphite fibres are now available in a very wide range of properties and forms and
improvements in manufacturing processes has seen the cost of the fibres reduce
over the past 25 years. Although the fibres are not as hard as boron, the cured
26
Advances in the bonded composite repair of metallic aircraft structure
composites are very abrasive and diamond tipped tools are normally used for
cutting or machining. The fine graphite laden dust from such operations is believed
to be a health hazard and so measures to control this hazard must be taken. This
electrically conducting dust can also cause problems with electrical equipment if it
is not removed and filtered from the room air. Graphite pre-pregs are commonly
available as 120°C and 175°C curing systems and lower temperature cure resins are
also available now for use in repair situations.
Graphite fibre is an unusual material in that it has a slightly negative coefficient
of thermal expansion, which means that the fibres contract slightly in the axial
direction when heated. This results in relatively high levels of thermally induced
residual stress if the cured composite is bonded to the structure with an elevated
temperature curing adhesive. As well, the fibres are electrically conducting and will
cause galvanic corrosion of aluminium if the two are in electrical contact. Due to
the electrical conductivity it is more difficult to use eddy-current NDI methods with
these materials to check the position of a crack under the patch for example.
Graphite composites are significantly cheaper than boron composites and are
available from a very wide range of suppliers. They offer a wide range of properties
for design and with epoxy resin matrices are readily processed and can be cured to
complex shapes to suit the damaged structure. If a repair is required to a tight
comer with a small radius, graphite fibres would be preferred to boron as
mentioned above.
Repairs to aircraft are usually weight critical and so the specific properties of the
various repair materials are therefore of interest. Table 2.2 compares the mechanical
and thermal properties of some candidate patch or reinforcing materials. This
comparison includes boron/epoxy (b/ep) and graphite/epoxy (gr/ep), the metal/
composite laminates GLARE and ARALL and typical high-strength aluminium
and titanium alloys - which also represent the metals to be repaired.
2.2.3. Patch material selection
Many of the criteria for selection of a successful repair material have been
discussed in the above two sections. The reader is referred to Sections 2.1 and 2.2
for a complete discussion of the issues and in this section a summary of the main
points is given referring to the four main repair materials and some of the main
design issues that are commonly faced.
0 Patching efficiency: High tensile stiffness is required to minimise the crack
opening displacement after repair and therefore keep the stress intensity and
crack growth down. The fibre composite materials are naturally more efficient
than either the conventional or laminated metallic materials (refer Table 2.2 for
specific stiffness i.e. modulus divided by destiny).
0 Operating temperature: For sustained high temperature operation over 1 50"C, a
titanium patch may prove to be the best solution. Conventional aluminium
alloys and the laminated metals would need to be carefully investigated as there
are a range of upper temperature limits depending on the alloy and heat
treatment involved. In general, most aluminium alloys could withstand extended
Chapter 2. Materials selection and engineering
21
Table 2.2
Relevant materials mechanical and physical properties for component and patch materials.
Material
Aluminium alloy
1015 T6
Aluminium alloy
2025 T3
Titanium alloy 6
A1/4V
Boron/epoxy b/ep
(unidirectional)
Graphite/epoxy gr/
ep (unidirectional)
Aluminium laminate
GLARE 2
Aluminium laminate
ARALL 3
Electroformed
Nickel
Modulus
GPa
Shear
modulus
GPa
Critical
strain
x 10-~
Fatigue
Strain
x 10-~
Density
(g/cm3)
Thermal
expansion
coefficient
x
oc
12
21
6.5
3.3
2.8
23
12
21
4.5
3.3
2.8
23
110
41
8.8
6.8
4.5
9
1
7.3
1.0
2.0
12.0
1.6
208 max
20 min
148 max
12 min
65
IOP
4.5 min
na
5.2
3.3
2.5
23 max
- 0.3 min
28 max
15
68
na
8.9
3.3
2.3
-
201
16
1.7-3.4
5
13
na
-
16
... 13
-9
Notes: (a) Maximum modulus and minimum expansion coefficient are in the fibre direction, other values
are for the transverse direction, (b) shear modulus values for the composite are for through-thickness
deformation, (c) critical strain refers to failing strain for the composites and yield strain for the metals,
(d) fatigue strain refers to approximate strain for crack initiation at lo6 cycles, R 0.
-
0
0
0
periods at 120°C, which is slightly higher than the normal operating temperature
of 105°C for a 175°C curing composite pre-preg. Higher temperature curing
resins are available for composites, although the availability is not as high and
depending on the system involved, processability may be reduced.
Residual stress: If a repair (cured at elevated temperature) is likely to see
extended service at low temperatures (for example a fuselage repair to a transport
aircraft - [4]), the best choice may be either a conventional or laminated metallic
material where the coefficient of thermal expansion is more nearly matched to
the structure. In this situation, graphite/epoxy repairs and to a lesser extent
boron/epoxy repairs will result in higher levels of thermally induced residual
stress [7].
Cost: Although not usually a major driver, conventional metallic materials
would offer the lowest material costs, followed by the laminated metals, graphite
composites and the boron fibre composites are the most expensive. Analysis of
repair costs need to be done carefully as often a composite repair may prove to
be cheaper than a metallic repair despite greater material costs. This is largely
due to the excellent formability of composites and the reduced time required to
form the repair patch to the desired shape.
Inspections: If full use is made of the benefits of bonded repair technology and
the defect is left in the structure under the repair, it is likely that future non-
28
0
Advances in the bonded composite repair of metallic aircraft siructure
destructive inspections will be required to confirm that the defect has not grown
significantly in size. Boron composites are well suited to such circumstances, as
the routine use of eddy currents will detect the presence of fatigue cracks for
example under the patch. The detection of defects with eddy currents under
highly curved boron repairs is more difficult as is the detection of defects under
any sort of graphite repair due to the conductivity of the fibres. Detection of
defects under bonded metallic repairs can be difficult and may involve the use of
X-rays or ultrasonics.
Weight: If the repair is to be made to a weight critical component such as a flight
control surface, materials with the highest specific properties are desirable. The
composite materials will enable repairs with greatly reduced weight compared
with the metallic materials. This same point is also of relevance where
aerodynamic smoothness is important. Composite repairs will typically be onethird the thickness of an aluminium repair and so will provide significantly less
drag.
2.3. Adhesive systems
Adhesive technology has undergone rapid growth over the past 50 years and
adhesives are now widely used in markets such as automotive, aerospace,
construction, packaging and consumer appliances. Most common adhesives can
be usefully categorised as belonging to one or more of the following classes;
structural, hot melt, water-based or pressure sensitive. Of these only the structural
class is of interest in this book. Structural adhesives are defined as those adhesives
capable of withstanding significant loads and capable of bonding together
adherends also capable of carrying significant loads. For the purposes of this
book, shear strengths of 10MPa would be seen as the minimum requirement.
2.3.1. Adhesive types
Within the structural adhesive class are a number of adhesive types based on
chemistry. The most important are epoxies, modified acrylics, polyurethanes,
cyanoacrylates, anaerobics, phenolics and polyimides. Anaerobics cure in the
absence of oxygen by free radical polymerisation and are widely used in threaded
assemblies to prevent loosening of nuts. They can develop high shear strengths but
generally have limited temperature capability and are not used for Bonded Repairs.
Cyanoacrylates cure due to the presence of water molecules on the adherends which
act as initiation sites for polymerisation. They have excellent shear strength but are
comparatively brittle with poor peel strength, are not suitable for filling gaps and
are degraded by moisture. Relatively high shrinkage stresses on cure also mitigate
against their use in Bonded Repairs. Polyurethanes have good toughness and
flexibility, but tend not to have the high shear strength and temperature capabilities
that are required for bonded repairs. Phenolic adhesives were the original structural
adhesives used in aircraft construction but tended to be very brittle until the
Chapter 2. Materials selection and engineering
29
introduction of modified phenolics (the “Redux” adhesives) which had higher peel
strength. Phenolic adhesives exhibit excellent bond durability and the modern
nitrile modified phenolics are widely used in a range of demanding applications. In
general, however, they require high cure temperatures and pressures which may be
difficult to accommodate in a repair situation. The other main structural adhesives
are those capable of very high temperature operation such as the polyimide (PI) or
bismaleimide (BMI) adhesives. These could be considered in specialised repair
applications, however, compared with epoxies or acrylics they tend to be difficult to
cure.
The two adhesive types used most successfully for Bonded Repairs are the
epoxies and modified acrylics. The properties of these adhesives are discussed in
greater detail in the next section. Acrylics are normally produced in paste form,
however, epoxies are commonly available in both paste and film versions. Film
adhesives have the resin and curing agents pre-mixed at the factory and are then
coated onto a thin carrier cloth or scrim in the form of a thin film. The advantages
of this are that mistakes can’t be made in mixing the correct ratio of hardener, the
film makes it easy to achieve uniform thickness bondlines and film adhesives are
much easier to apply and handle than pastes. Disadvantages are increased cost and
the resin is effectively curing as soon as the hardener is mixed and therefore film
adhesives must be refrigerated to provide a reasonable shelf life.
2.3.2. Adhesive properties
Epoxies come in a very wide range of formulations and types but are generally
characterised by high levels of strength, good temperature capability, low shrinkage
stresses on cure and the ability to form durable bonds. Epoxies are normally
considered to be the most expensive of the common adhesive types (although are
not as expensive as the high temperature polyimides). The ability to form durable
bonds is highly dependent on the level of surface treatment that is applied to
metallic adherends in contrast to the behaviour of acrylic adhesives. The
temperature capability of the adhesive is dependent on the cure temperature and
so for repairs to structure that sees high temperatures, an elevated temperature cure
is required. Room temperature curing epoxies are commonly available in paste
form (usually two components) and these adhesives can often provide moderate
temperature capability with a post cure to above the operating temperature. Some
pastes can also provide higher temperature capability, however, for service at
100°C or higher, film adhesives are commonly used. Unmodified epoxies are
inherently brittle materials like phenolics and so most commercial systems are
modified with the addition of the toughening agent which is commonly an
elastomer.
Modified acrylics or second generation acrylics were developed during the 1960s
from the original acrylics which were too brittle to be of practical use in structural
joints. The rubber toughened acrylics have good shear and peel strengths although
the shear strengths are generally not as high as those of the epoxies. They usually
cure rapidly at room temperature, in some cases within 1 to 2min, and they have
30
Advances in the bonded composite repair of metallic aircraft structure
the ability to readily bond a range of different adherend materials. The ability of
these adhesives to develop good adhesion strengths with limited surface treatment
is due to the acrylic monomer which is a free flowing liquid of low surface tension.
Modern acrylics are able to produce strong, durable bonds to unprepared
aluminium and steel surfaces; epoxy adhesives are unable to achieve this.
Commercially available systems now do not require mixing of two components
but instead can use an activator applied to one adherend and the adhesive to the
other which simplifies the use compared with two-part epoxies. Disadvantages
include an odour that some people find objectionable, limited temperature
capability and limited pot life which can be a problem for larger repairs. Acrylics
are widely used in industrial applications where the ability to rapidly bond poorly
prepared steel sheet is an important advantage and is able to replace the use of spot
welding or riveting.
2.3.3. Adhesive selection
The designer of a bonded repair has a very wide range of adhesives to choose
from, although in practice the selection is usually made from those adhesives that
are readily available to the company. The two most important selection criteria are
temperature and load carrying capability. A conservative approach is to use an
adhesive for the repair of equal temperature capability to the original structure.
This is typically 120 "C cure for commercial (subsonic) aircraft and 175 "C cure for
military (supersonic) aircraft. However, the use of a 175 "C curing adhesive during
manufacture does not necessarily mean the structure will be exposed to such high
temperatures. Often a 175"Cadhesive is used in manufacture to be compatible with
the 175°C curing pre-preg so that the part can be cured and bonded in one
autoclave cycle. If the actual operating temperature of the component can be
shown to be 60°C for example, it is possible to produce a sound repair with a
120 "C curing adhesive.
It should be noted that the use of 175 "C curing adhesives for repair has in itself
caused significant problems when the structure to be repaired contains honeycomb
core and water is present within the core. At around 140 "C, the pressure generated
inside the core by the air and water exceeds the flat-wise tension strength of the skin
to core adhesive and the skin can be disbonded by the pressure. The risk of such
damage occurring is greatly reduced at 120°C and at least one adhesive
manufacturer has developed a 120°C version of the standard 175°C adhesive
system for use during repair to honeycomb structure.
Bond durability (particularly for epoxies) is generally related to cure temperature
and it is common to find excellent bond durability for 175°C systems, good
durability at 120"C but only fair to good durability for room temperature curing
adhesives. The improvement in durability for the 175 "C cure, however, needs to be
weighed up against the other problems which can develop such as blown skin to
honeycomb core bonds and increased thermally-induced residual stresses.
The required load carrying capacity of the adhesive needs to be carefully
considered. Some manufacturers of structural adhesives are now beginning to
Chapter 2. Maierials selection and engineering
31
provide design data in the form of shear stress/shear strain data. The more common
lap shear strength is not suitable for use in a bonded repair and is generally only
useful in comparing one adhesive to another. Details of the data that is required for
design based on adhesive properties is given in Chapter 4, and if it is necessary to
generate this data, appropriate test methods are described in Section 2.5 and
Chapter 4.Two key parameters are the shear strength and plastic strain to failure.
The adhesive needs to have sufficient shear strength so as not to yield excessively
under the design loads, and care should be taken in designing with relatively brittle
adhesives which cannot provide a soft, yielding type of failure under high loads.
Less well understood is the ability of the adhesive to withstand through-thickness
stresses, i.e. those perpendicular to the plane of the joint. Conventional design
wisdom with adhesive joints is to eliminate such stresses by the use of different
design techniques. In many cases it is possible to eliminate or greatly reduce the
magnitude of these stresses simply by the use of sensible design features such as
tapering of the end of the repair. In some circumstances, however, it is not possible
to reduce these stresses and some examples are given in Chapters 30 and 33. In
repairs to structure involving a high degree of curvature, the question then becomes
one of determining the capacity of the adhesive to withstand the through-thickness
or peel stresses that are present. There is currently no generally agreed test method
to generate design data for this situation, although a novel test specimen has been
proposed which may be suitable for this purpose [8,9]. Any repair design where
high levels of peel stress are likely to be present needs to be very carefully
considered and would be expected to require extensive analysis and experimental
validation for certification. The work described in [8] is aimed at increasing the
understanding of the performance of adhesives under peel stresses, however, while
this may lead to some easing of certification requirements, the sound engineering
practice will continue to be to design peel stresses out of an adhesive joint where
ever possible.
Other criteria which may be important in the selection of a repair adhesive could
be availability and the ability to cure at low temperatures. Availability and the
requirement for refrigerated storage could be important at some forward Air Force
bases for example, where only a very limited range of adhesives may be available at
short notice. When rapid repairs have to be made in primitive conditions, for
example to battle damage, it may not be possible to provide refrigerated storage
and therefore only two-part adhesives would be available. As described in Section
2.6, thermally-induced residual stresses are produced when the repair material has a
different coefficient of thermal expansion to the substrate and an elevated
temperature cure is necessary. The obvious way of reducing the level of such
stresses is by reducing the cure temperature of the adhesive as much as possible.
Some adhesives are able to cure at temperatures lower than their advertised cure
temperature although this is not always the case [lo]. Film adhesives are often sold
as either 120 "C or 175"C curing systems (partly for compatibility with other prepregs etc.), however, a careful examination of the thermodynamics of cure can
indicate that the optimum cure temperature is different from these advertised
temperatures. Considerable care must be taken if a decision is made to cure at
32
Advances in the bonded composite repair of metallic aircraft strucmre
temperatures other than those advertised to ensure that other properties are not
compromised.
The ability of the adhesive to remain durable in the operating environment is
normally of critical importance and consideration may need to be given to the
influence of solvents or chemicals which the adhesive may be exposed to. For
example some repairs have been applied inside aircraft fuel tanks or in regions
where the adhesive is exposed to hydraulic oil. Most epoxies and acrylics have very
good resistance to solvents and chemicals and so these types of exposures have not
been of major concern to date, but do need to be checked on an individual basis
v11Where possible it is recommended that repairs are cured under positive (as
compared to vacuum) pressure and further details are given in Chapter 25. When
the use of vacuum bag pressure is the only alternative, consideration may need to
be given to the void content in the cured adhesive bondline (Section 6.2). Some
adhesives do not cure well under vacuum and heavily voided bondlines can result.
There is some evidence to suggest that moderate amounts of voids do not adversely
affect fatigue strength, however, in general significant void contents in structural
adhesive bondlines are to be avoided.
2.4. Primers and coupling agents
A range of different chemicals may be required for effective surface preparation
and a detailed scientific discussion of these is given in Chapter 3. This section will
look at some of these chemicals from a materials engineering perspective and
consider some of the common factors that may be need to be considered in the
overall design of the repair.
From Section 2.1 it is clear that significant attention must be paid to the surface
treatment of metallic adherends prior to bonding if a strong, durable adhesive bond
is to be produced. There are two major types of treatments for aluminium alloys
that for historical reasons have developed in Europe and North America. In
Europe, the preferred treatment is the use of a chromic acid etch to produce a
hydration resistant oxide, whereas in North America the use of phosphoric acid is
preferred. Both treatments have been used successfully in aircraft manufacturing
and are capable of producing highly durable bonds. Components are dipped into
tanks of acids and other chemicals in the factory to produce the required oxide
structure for bonding. The difficulty comes in transferring this technology to a
repair situation. For example when acids are used on an assembled aircraft
structure, care must be taken to completely remove the acids or corrosion may
result. Boeing in particular have developed procedures whereby the same
technology as used in manufacturing can be applied to some repairs. The
phosphoric acid containment system (PACS) uses vacuum bags over the repair site
to transport the acid across the surface. This contains the acids to minimise health
and safety concerns and permits a final flush with water to remove the acid from the
aircraft surface. The anodisation is carried out under the bag as well. This
Chapter 2. Materials selection and engineering
33
procedure can produce bonds with durabilities close to the best factory treatment
such as a full phosphoric acid anodisation (PAA). While this process can be highly
effective, it requires specialised equipment, it is relatively complicated to perform
and cannot be used in many repair situations.
A common requirement in repair situations is for a surface treatment method
which is simple to use, preferably does not require use of anodisation (the electrical
voltage of which can create a hazard inside wing tanks for example) and does not
use chemicals that could cause harm to either the operator or aircraft. In some
situations a repair must be applied to two different materials at the same time and
so the ability to treat both metals at the same time can be an advantage. The use of
silane coupling agents can meet all of these requirements. Silanes are well known as
adhesion promoters and are bi-functional molecules containing polar silanol
groups and organofunctional groups capable of reacting with the chosen adhesive.
The silanol group forms a strong bond with the oxide surface that is hydrolytically
stable, and the organofunctional group forms a strong bond with the adhesive. It is
of course important to choose a silane that is compatible with the adhesive being
used. Silanes are available for both epoxy and acrylic adhesives.
The use of silanes as a coupling agent is advantageous in a repair situation for
several reasons. Silanes do not cause any damage to the surrounding structure if
they are not completely removed following application. They are very simple to
apply requiring only hydrolysation prior to use and can be applied simply with no
special equipment required. They are relatively safe to use, although care must be
taken to avoid ingestion and contact with the eyes. Silanes can effectively treat a
range of different materials thereby greatly reducing the complexity of the repair
application. Finally they are very effective as coupling agents and can produce
adhesive bonds with durabilities close to that produced by the factory PAA
treatments.
Further improvement in the bond durability can be achieved with the use of a
corrosion inhibiting primer after the application of the silane or other surface
treatment. Primers are normally dilute polymeric solutions which are usually
sprayed onto the bonding surface and are able to easily wet the surface. If the
surface has been roughened by abrasion, the primer is able to flow easily over the
surface irregularities to provide a thin polymeric layer in intimate contact with
and having strong bonds with the surface. The polymer is chosen to readily bond
to the repair adhesive and is often the same type of polymer. Primers commonly
require a period after spraying to enable volatiles to evaporate before the primer
is cured at elevated temperature. A surface primed in this way can be stored for
several months prior to bonding, requiring only a careful solvent wipe to remove
surface contamination prior to bonding. The primer will often contain fine
chromate particles which help to prevent the hydration of the adjacent metal
oxide layer. The chromate particles are however toxic and care must be taken in
the use of such primers. The thickness of chromated primer layers for use in an
adhesively bonded joint is also important and care must be taken to follow the
manufacturers’ directions and not to build up too much thickness in the sprayed
layer.
34
Advances in the bonded composite repair of metallic aircraji structure
2.5. Adhesive and composite test procedures
There are a wide range of test procedures that are directly applicable to adhesives
and composites and these range from quality assurance type tests to chemical and
physical tests to measure adhesive properties to static and fatigue tests aimed at
generating mechanical design data. Mechanical tests are covered in Chapter 4,
where the use of the thick-adherend lap shear test is described to generate adhesive
shear stress and shear strain data. Also in this section is a description of the skin
doubler specimen for fatigue testing and the double cantilever beam specimen for
Mode 1 fracture toughness.
An important test for quality assurance is the flow test that measures the ability
of the adhesive to flow when heat and pressure are applied. This is particularly
important for film adhesives where the catalyst and resin are pre-mixed in the
factory and so the adhesive is effectively curing all the time. As described in Section
2.3.1, iilm adhesives require refrigeration to ensure the curing reaction is reduced to
a level where the adhesive has a reasonable shelf life. When stored under the
appropriate conditions, the shelf life of the adhesive should be as specified by the
manufacturer. If there is any doubt as to whether the adhesive may have cured or
“advanced” too far to be of use, a flow test can be performed. There are many
forms of flow tests in existence and a typical example is that specified in [12]. In this
test, discs of film adhesive are punched from the film and subjected to heat and
pressure in a controlled manner. The adhesive flows and cures and the degree of
flow is measured as a function of the increase in perimeter or area. Flow of an
adhesive drops rapidly as the adhesive crosslinks and it is possible to set flow
criteria beyond which the adhesive is deemed to be no longer useable. As described
in Section 2.1.1, it is essential for the adhesive to flow during the cure to adequately
wet the adherends and produce high bond strengths. The advantage of the flow test
is that it is relatively simple to perform and does not require particularly
sophisticated equipment. A similar result can be obtained from chemical tests such
Differential Scanning Calorimetry in which the amount of unreacted epoxide is
measured. Tests such as these are perhaps more precise than a flow test, but require
sophisticated equipment and skilled operators to perform the tests. Although
simple mechanical tests such as lap shear strength have been used to determine
whether an adhesive is still in life, this property is not very sensitive to overageing
and so the much more sensitive flow measurement is to be preferred.
When film adhesive is used for a repair, there are often good reasons to
deliberately advance or “B-stage” the adhesive prior to cure (see Section 2.6.2 for
details). Where this is done it is very important to ensure that the adhesive is not Bstaged to the extent that flow is compromised. A flow test can be used to confirm
that sufficient flow remains in the adhesive after the B-staging process. Using this
method, a B-staging time of 45 min at 80 “C has been proposed for use with fresh
FM73 adhesive 1131. Note that the B-staging conditions will change as the adhesive
stock ages. B-staging for 45 min at 80 “Cwill not be appropriate for FM73 adhesive
which exhibits only marginal flow in the un B-staged condition. One way of
managing film adhesives (for repair situations) is to always use the adhesive in
Chapter 2. Materials selection and engineering
35
the same flow condition. When the adhesive stock is fresh, the adhesive may require
considerable B-staging prior to use, but the amount of B-staging will reduce
progressively as the stock ages, until the flow limit is reached. At this time the
adhesive could be used without B-staging, but any further ageing of the stock
would take it over the flow limit and would require that stock to be scrapped.
If a composite material is being used for the patch, a simple test to confirm that it
is within life and is suitable for use is the interlaminar shear (ILS) test or short
beam shear (SBS) test. One form of this test is described in ASTM D2344. As for
the flow test, the test is relatively simple to perform and only requires a small
amount of material and mechanical testing equipment. This test measures the
interlaminar shear strength of a small sample of the material, and this strength is a
resin dominated property. If the resin in the pre-preg is too advanced, the pre-preg
will not flow adequately during cure and high shear strengths between the laminae
of the composite will not be developed. In this test, the critical factor is the correct
ratio of the support span to specimen thickness. For the 5521/4 B/Ep composite, an
ILS value of 97 MPa or above, indicates the material is in good condition.
An advantage of the use of metallic materials for repair patches is their infinite
shelf life. No testing is required before use, other than to confirm that the alloy and
heat treatment are correct.
2.6. Materials engineering considerations
2.6.1. Residual stresses
An adhesively bonded repair may experience high levels of residual stress [11.
These stresses are thermally induced and generally arise from the different
coefficients of thermal expansion of the repair substrate and repair material
respectively. The influence of these stresses can be readily seen in a coupon
specimen as shown in Figure 2.1. Note that in a real repair, the restraint from the
Fig. 2.1. Photograph of a 3mm thick 2024 aluminium specimen with a 0.6mm thick boron patch. The
curvature results from the 121 "C cure temperature used to cure the FM73 adhesive.
36
Advances in the bonded composite repair of metallic aircraft structure
substructure will minimise any actual bending, however, the residual stresses will
still be present. Often, if an elevated-temperature curing adhesive is used, residual
stresses will exist when the repair has cooled to ambient temperature. On the other
hand if an ambient-temperature curing adhesive is used with different repair
materials, residual stresses can be induced if the repair has to operate at
temperatures significantly different from that at which the cured was achieved.
The level of stress is highest when the difference between the coefficients of thermal
expansion (a)are greatest. The use of a unidirectional gr/ep repair patch (which has
an a of -0.3 OC-') will create a large residual stress when bonded to aluminium
(a= 23.5 OC-').
If the repair material is different to the substrate, the level of residual stress
should be calculated during the design process. Procedures for analysing the
residual stress level are given in Chapter 11. In extreme cases, the level of thermally
induced residual stress can be large enough to fail the joint, although this is not
usual. Residual stresses will influence the stress intensity at the defect site after
repair and possibly the static and fatigue strength of the repair and therefore it is
important that they be carefully considered during the repair design.
There are several ways in which the level of residual stress in an adhesivejoint can
be minimised. Clearly choosing the repair material to be the same as the substrate is
the easiest, however, this may often not be the optimum choice. Usually the benefits
of using a fibre reinforced composite as the repair material outweigh the
disadvantage of increased residual stress levels. Secondly, it may be possible to
reduce the temperature of cure so as to keep the residual stress levels as low as
possible and the factors to consider in such a situation have been discussed in Section
2.3.3. Thirdly, if the extent of the structure to be heated is minimised, this will act to
keep the residual stresses low. For example, when an aluminium skin of an aircraft is
heated, the skin is not able to expand in an unconstrained manner. The structure
surrounding the heated zone will be cooler, will not expand as much and will
therefore act as a constraint to the expansion of the repair zone. For this reason,
when it is important to minimise residual stresses, consideration can be given to
heating the smallest possible repair zone so as to maximise the constraint. Analytical
considerations for constrained expansion are discussed in Chapter 11. Of course care
must be taken to ensure that the adhesive is uniformly heated and that the edges of
the repair are not under cured (Chapter 24). Finally, it may be possible to apply a
pre-load to the structure to off-set the expected thermal expansion. This has been
done successfully during an important reinforcement to the F-111 Wing Pivot
Fitting [lo]. An upload was applied to the wing, prior to the repair, placing the upper
wing skin in compression. Normally the metallic substrate is left in a state of tension
following the elevated temperature cure. By releasing the compressivepre-load after
the repair, the extent of the tensile residual stress was substantially reduced.
2.6.2. Cure pressure and voids
Voids within the adhesive bondline are generated during the cure from either
entrapped air or from gases generated from the adhesive or adherends. The gas will
Chapter 2. Materials selection and engineering
(a)
31
(b)
Fig. 2.2. Micrographs showing fractured adhesive surfaces containing voids. The void concentration
seen in (b) resulted from the aluminium substrate being heavily grit blasted before application of the
silane solution. The only different process applied to (a) was a drying period at 110°C in an oven after
the application of the silane.
typically form a bubble within the liquid adhesive and when the adhesive has crosslinked and solidified, the bubble remains as a void as shown in Figure 2.2. Gases
that are commonly involved in this process are water vapour present on the
adherends [13], water or other chemicals generated during the curing reaction, or
solvents such as MEK or acetone present within the adhesive that are liberated
during the cure. The gases themselves are not normally of any concern, however,
the voids that are created by the gases can act as stress concentration sites within
the adhesive. If the void concentration is sufficiently high, there could be a
reduction in the mechanical properties of the joint. In extreme cases the void
content can be more than 50% of the joint area, and at these levels significant
reductions in strength can be expected. A preliminary study into the influence of
voids on fatigue strength indicated that for FM300 adhesive, a void content of
more than 30% was required before there was a noticeable drop in fatigue
performance. A possible reason for this was that the scrim cloth inside the adhesive
acts as a site for fatigue initiation and occupies approximately 30% of the joint
area. It is not until the void content exceeds this level that there is a marked
reduction in fatigue life.
Void contents less than 5% should be readily achievable in adhesive bondlines
during repair procedures. Keeping void contents low is a matter of recognising
the origins of the voids and ensuring that appropriate procedures are used. If the
38
Advances in the bonded composite repair of metallic aircrafr structure
voids arise from adsorbed water vapour on the adherends, the bonding surfaces
should be dried prior to bonding [13]. Entrapped air can be minimised by correct
procedures such as avoiding blending air into paste adhesives during mixing, and
avoiding applying film adhesives to adherends at too high a temperature where
they become too tacky. Voids generated from volatiles within the adhesive are
perhaps the most common reason for voids in film adhesives and can be
minimised in several ways. Before using the adhesive, it may be possible to “Bstage” the adhesive film by gently heating in an oven. This permits the volatiles to
be released and partially cures the adhesive. This partial cross-linking prior to the
full cure helps to prevent the expansion of voids. Care needs to be taken during a
B-staging operation to ensure the adhesive is not advanced too far so that flow is
restricted. Pressure applied to the joint during the cure helps to restrict the
expansion of the volatile gases within the voids. In this regard the use of positive
pressure is much preferred to the use of a vacuum bag, as the negative pressure
within the bag can allow the expansion of the voids at some locations such as
around the edges or where the bag is unable to transmit the atmospheric pressure.
With either type of pressure application, it is difficult to generate the high
pressure desired in the interior of the joint if the joint is too narrow [13]. Figure
2.2 illustrates the improvements in void contents that are possible by using
improved processes and with a fully optimised bond procedure, negligible void
contents should be readily achievable.
2.6.3. Spew jillet
For structurally loaded joints, it is well known [I41that the adhesive spew fillet
that forms around the edge of the joint is beneficial. This spew is formed as some of
the adhesive flows out from under the repair patch during the cure and the resulting
fillet acts to soften the stress concentration at the edge of the repair patch. The
presence of the fillet can reduce the magnitude of the shear stresses at the end of the
joint by around 30%. It is thus very important that this adhesive fillet is not
removed during the final clean up procedure.
The condition of the fillet can also be an important point to visually check after
the repair has been completed. Some information about the quality of the
adhesive bond can be gained by this visual inspection. The absence of a well
formed, smooth fillet would indicate poor flow of the adhesive and this may have
been due to inadequate pressurisation, out of life adhesive or perhaps the heat up
rate being too slow. An extremely high void content in the fillet could be an
indication of an excessively high volatile content within the adhesive or perhaps
the use of poor pressurisation procedures involving a vacuum bag. A large
amount of adhesive in the fillet may indicate that the bond has been subjected to
excessive pressure and that the bondline around the edge of the joint may be
starved of adhesive due to excessive flow. If the spew is not fully hardened, it
would indicate that the cure is not complete and either the required time or
temperature has not been reached.
Chapter 2. Materials selection and engineering
39
2.6.4. Composites offer the possibility of embedded strain sensors to form “SMART”
repairs
There are a number of materials engineering advantages when a composite
material is used to form the repair patch rather than a metallic material. One of
these is that the patch can be readily formed to match the complex curvatures that
are often found on aircraft surfaces. Another is that by virtue of the way in which
composite materials are produced, it is comparatively easy to include small sensors
within the patch material. In the short term this is unlikely to be cost effective for
routine repairs as the additional costs involved will be high, however, this is
expected to change as the costs of sensors and associated instrumentation reduce.
For critical repairs to primary structure, these extra costs are less important and
repairs are being developed for such applications with inbuilt sensing mechanisms.
These patches will have the ability to detect strain transfer into the patch and
therefore will be able to determine if the patch is disbonding. When combined with
the ability to transfer the data collected by remote means (infra red or high
frequency communication for example), the “Smart” repair will be able to inform
the maintenance crew if there is any important structural problem. This topic is
covered in more detail in Chapter 20, where some examples are given of the way in
which the technology can be used.
References
1. Baker, A.A. and Jones, R. (eds.) (1988). Bonded Repair of Aircraft Structures, Martinus Nijhoff
Publishers, Dordrecht.
2. Hart-Smith, L.J., Brown, D. and Wong, S. (1993). Surface Preparations for ensuring that the Glue
will stick in Bonded Composite Structures, 10th DoD/NASA/FAA Conference on Fibrous
Composites in Structural Design, Hilton Head Is, SC.
3. Vlot, A., Vogelesang, L.B.and de Vries, T.J. (1999). Towards application of fibre metal laminates in
large aircraft. Aircraft Engineering and Aerospace Technology, 71(6), pp. 558-570.
4. Fredell, R., van Barneveld,W. and Vogelesang, L.B. (1994). Design and testing of bonded GLARE
patches in the repair of fuselage fatigue cracks in large transport aircraft. Proceedings of the 39th
International SAMPE Symposium, 11-14 April, pp. 624-638.
5. Solly, R.K., Chester, R.J. and Baker, A.A. Bonded Repair of a Damaged Army Field Gun, Using
Electroformed Nickel Patches, in preparation.
6. Chester, R.J., Clark, G., Hinton, B.R.W., et al. (1993). Research into materials aspects of aircraft
maintenance and life extension. Aircraft Engineering, Part 1, 65(1) pp. 2-5, Part 2, 65(2) pp. 2-5,
Part 3, 65(3), pp. 2-6.
7. Fredell, R., van Barneveld,W. and Vlot, A. (1994). Analysis of composite crack patching of fuselage
structures: High patch elastic modulus isn’t the whole story. Proceedings of the 39th International
SAMPE Symposium, 11-14 April, pp. 61M23.
8. Bartholomeusz, R.A., Baker, A.A., Chester, R.J., et al. (1999). Bonded joints with through thickness
adhesive stresses - reinforcing the F/A-18 Y470.5 Bulkhead. Int. J. of Adhesion and Adhesives, 19,
pp. 173-180.
9. Chester, R.J., Chalkley, P.D. and Walker, K.F. (1999). Adhesively bonded repairs to primary
aircraft structure. Int. J. of Adhesion and Adhesives, 19, pp. 1-8.
10. Baker, A.A., Chester, R.J., Davis, M.J., et al. (1993). Reinforcement of the F-111 wing pivot fitting
with a boron/epoxy doubler system - materials engineering aspects. Composites, 24, pp. 511-521.
40
Advances in the bonded composite repair of metallic aircraft structure
1 1 . Chalkley, P.D. and Geddes, R. (1999). Fatigue testing of bonded joints representative of the F-Ill
WPF Upper Plate Doublers. DSTO - TR - 0920, December.
12. Boeing System Support Standard BSS 7240 Adhesive Flow Test.
13. Chester, R.J. and Roberts, J.D. (1989). Void minimisation in adhesive joints. Int. J. ofAdhesion and
Adhesives, 9, p. 129.
14. Adams, R.D. and Peppiatt, N.A. (1974). Stress analysis of adhesive-bonded lap joints. J. Strain
AnaIysis, 9, pp. 185-196.
Chapter 3
SURFACE TREATMENT AND REPAIR BONDING
D. ARNO'IT,A. RIDERand J. MAZZA*
Defence Science and Technology Organisation, Air Vehicles Division, Australia
*Materials and Manufacturing Directorate, US.Air Force Research Laboratory
(AFRLIMLSA), Australia
3.1. Introduction
Adhesion can be seen as the force or energy of attraction between two materials
or phases in contact with each other [I]. In order to achieve intimate contact, one
phase called the adhesive must behave as a liquid at some stage and wet the second
phase called the adherend. It may be necessary to apply heat or pressure for the
adhesive to behave as a liquid. Once formed, the adhesive bond is expected to carry
loads throughout the life of the joint. Although many substances can act as an
adhesive, the discussion here is restricted to toughened epoxy adhesives used to
bond metallic aircraft structure. Discussion of adherends will also be restricted to
metals and composites.
This chapter focuses on prebonding surface treatments and bonding procedures
leading to the development of durable void-free adhesive bonds for repair
applications. It describes both fundamental aspects, including some current
research work, and practical procedures. A basic understanding is required to
avoid some of the many pitfalls that can lead to inadequate bonding. It is
complimentary to Chapter 24 which deals also with practical bonding.
There is no doubt that the reproducible development of durable bonds is a key
issue for bonded repair technology [2].
3.1.1. Surface energy and wetting
The complex interface between an adhesive and a metal adherend is best
described as an interphase in which critical dimensions are measured in
nanometres. Although there is controversy over the exact nature of the interactions
between epoxy polymers and metal oxides on the adherend [3], it is generally
believed that the predominant forces involve hydrogen bonds in which the hydroxyl
41
Baker, A.A.. Rose, L.R.F. and Jones, R. (e&.).
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 02002 Published by Elsevier Science Ltd. All rights reserved.
42
Advances in the bonded composite repair of metallic aircraft structure
groups on the metal oxide interact with hydroxyl groups in the polymer [4].
However, it is very likely that a variety of chemical bonds and interaction forces are
involved as well.
The interactions between an adhesive and an adherend are often described in
thermodynamic terms with expressions derived for the case of a liquid drop
adsorbed on a flat, homogeneous substrate in the presence of vapour [5]. The
balance of forces between the liquid drop and the solid substrate in equilibrium
with vapour (Figure 3.1) can be expressed in terms of the Young equation [6]:
where y represents the relevant surface tensions at the three-phase contact point
(i.e. solid-vapour (sv), solid-liquid (sl) and liquid-vapour (Iv)) and 8 is the
equilibrium contact angle. Low values of 8 suggest strong attractive interfacial
forces between the liquid and the adherend or a tendency to wet the substrate and
to establish intimate atomic contact with the solid. Contaminant present on the
solid can lead to a weakening of the attractive forces with the liquid phase and
hence to a change in the contact angle.
The issues of wetting are complex, particularly in response to chemical
inhomogeneity [6], rough surfaces [1,7], capillary forces [SI and the dynamic
spreading of viscous liquids [SI. Theoretical considerations indicate that external
pressure to assist the capillary driving pressure and heat (or solvent) to lower the
viscosity of the adhesive will aid wetting and penetration [9,10]. Adherend surface
preparation plays a pivotal role in the formation of a strong and durable adhesive
bond.
nV
Fig. 3.1. Balance of surface tensions for a liquid drop on a solid surface.
3.I.2. Bondline pressurisation and adhesive cure
The structural film adhesives are cured thermally using controlled heating rates.
During heating, the adherends are pressurised either mechanically or hydrostatically. As the temperature is ramped up, the viscosity of the adhesive initially
decreases, then it increases as the polymer crosslinks [l 11. In a pressurised sandwich
of 2 metal plates separated by a film adhesive, the adhesive will flow during the low
viscosity phase and the plate separation will decrease (Figure 3.2). A quadratic
pressure profile is developed within the adhesive [l 11. The local pressure in the
adhesive at the centre of the sandwich is higher than the applied load on the plate
Chapter 3. Surface treatment and repair bonding
43
10’
1o8
lo7
I
5
IO6
k
.3 io5
In
io4
1000
100
10
t
I
I
0
20
40
I
I
I
I
I
60
80
100
120
140
0.01
Temperature (“C)
Fig. 3.2. Pressurised sandwich panel showing viscosity changes with temperature and consequent
calculated plate separation for a typical thermoset epoxy film adhesive.
and can lead to deformation of thin adherend plates loaded by hydrostatic
pressure. The thickness of the bondline at the plate edges can be less than at the
centre for cures conducted using vacuum bag procedures. The pressure profile also
applies a hydrostatic constraint to bubble development in the adhesive and it is not
uncommon for voids to develop at the periphery of a repair when using a vacuum
bag for bond pressurisation. It must be kept in mind that almost all structural film
adhesives are designed for a positive pressure constraint on volatile gases to
minimise bubble development.
3.1.3. Adhesive bond performance
A strong adhesive bond does not imply a long-lasting or durable bond. Water is
the environment most commonly assessed in the literature, although other fluids
such as fuel and hydraulic fluid may degrade a bond. This chapter will focus on the
critical role of adherend surface treatment on the durability of a stressed adhesive
bond exposed to a humid atmosphere [12].
Whilst much has been written on the subject of adhesive bonding, knowledge is
still inadequate, and the engineering tools available for the through-life management of adhesively bonded structure are primitive. The books by Kinloch [13] and
Minford [ 141 are, respectively, an excellent introduction to adhesion and adhesives
and a compendium for adhesion with aluminium alloys. It is not the intent of the
authors to reproduce a summary of these works here. The focus will be on surface
treatments for repair bonding, giving consideration to the atomic nature of the
bond interface and the relationship between microscopic behaviour and macroscopic mechanical properties. It cannot be over emphasised that a strong adhesive
44
Advances in the bonded composite repair of metallic aircraft structure
bond does not imply a durable bond. The influence of adherend surface treatment
on bond durability is therefore a key issue.
3.1.4. Standards and environments for adhesive bonding
The facilities, environment, conditions, skills and techniques available for
adhesive bonding vary widely. However, it must be emphasised that the quality and
long-term performance of an adhesive bond relies on attention to standards and the
skill of the technician, together with controls over processes and procedures for all
bonding situations.
3.1.4.1. Bond integrity and standards
Adhesively bonded components are manufactured, and bonded repairs are
conducted, without the benefit of a comprehensive set of effective nondestructive
process control tests or techniques to fully assess the through-life integrity of the
bonded product. Nondestructively inspected (NDI) techniques may be able to
detect physical defects leading to voids or airgaps in bondlines but they cannot
detect weak bonds or bonds that may potentially weaken in service. The quality
and integrity of the bonded component, thus, relies upon a fully qualified bonding
procedure, together with the assurance that the process was carried out correctly.
The Aloha Airlines Boeing 737 incident in April 1988, where the aircraft lost part
of the cabin roof in an explosive decompression [15,16], illustrates the importance
of bond durability and more importantly, the ease with which this issue was
overlooked.
In the repair environment, experience has shown that some bonded repair
designs and application procedures have little chance of success and can, in some
cases, decrease the service lives of components [17]. A survey of defect reports
conducted at one Royal Australian Air Force (RAAF) Unit [17-191 indicated that
53% of defects outside structural repair manual limits were related to adhesive
bond failure. In addressing the standards applied to adhesively bonded repairs, the
RAAF [20] have established a substantial improvement in the credibility of bonded
repair technology.
3.1.4.2. Adhesive bonding environments
The performance of an adhesive bond is sensitive to the adherend surface
treatment and the environmental conditions under which the bond is prepared.
Facilities located adjacent to operational airbases or in industrial environmentsneed
to have concern for the effect of hydrocarbon contamination. Facilities in tropical
locations need special consideration for the effect of heat and high humidity.
Factory manufacture uses specialised facilities and staff. The facilities will
include vapour degreasing or alkaline cleaning, etching tanks, anodising tanks, jigs,
autoclaves and appropriate environmental controls. Adhesives will be stored in
freezers, and monitoring procedures will be in place. There is a well trained
workforce with skills maintained through production volumes, and highly
developed inspection procedures are available.
Chapter 3. Surface treatment and repair bonding
45
At the other extreme, field repairs are generally conducted with relatively
unsophisticated facilities, minimal surface treatments, vacuum bag or reacted force
pressurisation and little or no environmental control. Staff multiskilling and
rotation influence the currency of experience and hence the quality and
performance of adhesive bonds [21]. The requirement for environmental controls,
the attention to bonding procedure detail and the need for staff training and
supervision is of particular concern.
Depot-level repairs are conducted with facilities and staff skills that vary
considerably. Some depots have almost factory-level facilities and high level of staff
skill. Other depots are capable of only low-level bonded repairs and are little
removed from a field repair capability.
Laboratory experiments are designed to establish knowledge and principles. It is
easy to overlook important detail from factory or field experience since most
laboratories are held to close environmental tolerances and do not resemble the
workshop environment.
3.1.4.3. Constraints for on-uircruft repairs
On-aircraft repairs impose additional constraints on processes and procedures.
The considerations include: accessibility of the area, limitations in the use of
corrosive chemicals, adequacy of environmental controls and constraints on the
tools for pressurisation and heating of the bond during cure. Safety, health and
environmental issues are more demanding for on-aircraft bonding since it is harder
to control, contain and clean-up hazardous chemicals. Constraints on the use of
electrical power on fuelled aircraft, or those with inadequately purged fuel tanks,
can restrict the range of treatment and bonding methods available. The
surrounding aircraft structure imposes constraints on the choice of surface
preparation, heating arrangements and pressurisation tools.
3.2. Mechanical tests
3.2.1. Loading and failure modes
The most common method used to assess the relative performance of an
adherend surface pretreatment involves loading an adhesive joint asymmetrically in
tension, as shown in Figure 3.3, described as mode I opening. The stresses leading
to failure are localised in a region adjacent to the crack tip. The extent of this region
depends on the stiffness of the adherends, the toughness of the adhesive and,
importantly, the effectiveness of the adherend surface treatment.
The mechanical performance of a bond should be accompanied by an inspection
of the fracture surface. Visual inspection assisted with optical microscopy will
provide macroscopic information concerning the locus of fracture and the presence
of voids or defects. The term cohesional failure describes fracture totally within the
adhesive, leaving adhesive on both separated adherends. The term adhesional
failure describes a fracture at one interface with the adherend, resulting in one face
46
Advances in the bonded composite repair of metallic aircraft structure
Fig. 3.3. Asymmetric tension or mode I opening of an adhesive joint.
having the visual appearance of the adherend material and the mating face with the
appearance of the adhesive. Visual inspection alone does not convey the complete
picture. Because an adhesive bond is formed as a result of atomic interactions,
closer inspection of adhesional failures with surface composition analysis
techniques can provide detailed insight into the material leading to the weakness
at the fracture site.
3.2.2. Qualification of bonding procedures and performance
An adhesive bond represents a complex system of materials, treatments and
processing steps. The issue of qualification of the adhesive system is complex since
specific requirements depend on the application. The focus must be on mechanical
performance and durability because the bonded joint is expected to transfer load
for the service life. For structural joints, strength is typically evaluated using shear
tests (for static properties and fatigue) and toughness with cleavage tests. For
honeycomb structure, properties are typically evaluated with flatwise tension and
peel tests. Tests are conducted at representative temperatures experienced
throughout the service environment, including the operating extremes. Tests are
also conducted using moisture-conditioned specimens to evaluate durability
performance. Other conditioning may include exposure to salt fog, SO2, hydraulic
fluids, fuels, de-icers and more. Subcomponent or component testing normally
follows coupon testing.
The failure modes of test specimens are as important as the strength or toughness
values obtained. Failure modes at interfaces between the treated metal surface and
the adhesive or primer are generally not acceptable. The primary objective is for the
mechanical properties of joint to be limited by the properties of the cured adhesive,
not the surface treatment.
Qualification of the adherend surface treatment procedure is of particular
importance. Many surface preparations can provide adequate initial bond strength,
however, maintaining this strength for the life of a system in its operating
environment is a more difficult challenge. Moisture durability is of primary
concern. However, for certain titanium applications, long-term durability at
elevated temperature is important.
Chapter 3. Surfnee treatment and repair bonding
41
3.3. Standard tests
3.3.1. Wedge durability test
The ASTM D 3762 wedge test is often called the Boeing wedge durability test.
A crack is initiated in a bonded joint through insertion of a wedge into the
bondline (Figure 3.3). The test specimen is then exposed to hot/wet conditioning
and crack growth is monitored. The initial pre-exposure fracture is expected be
cohesive within the adhesive layer, and the equilibrium crack length is therefore
expected to reflect the toughness of the adhesive system under dry conditions. An
excessive initial crack length accompanied by interfacial failure, even before
environmental exposure, reflects a poor surface treatment. The specimen failure
mode is a critical piece of information. Cracks that remain within the adhesive
are desirable since they indicate that the surface preparation is not the weak link
in the bonded joint. Poor surface preparations readily lead to interfacial failures
accompanied by substantial crack growth. The wedge test is properly employed to
compare a surface preparation against a control, provided all aspects of specimen
configuration and conditioning are held constant as the surface treatment is
varied.
The wedge test is widely misused because ASTM D 3762 is not fully prescriptive.
Difficulties in the comparison of published data occur because pass/fail criteria,
conditioning environment, time of conditioning, and limits on adhesive systems are
not fully specified. By way of illustration, the US Services mostly condition wedge
specimens at 60 "C and 95% relative humidity (RH),whereas the Australian
counterpart test in condensing humidity at 50 "C. As a second illustration, the high
fracture energy characteristics of tough adhesives place higher demands on the
performance of the surface treatment than do brittle adhesives. The testing of tough
adhesives introduces the essential requirement to conduct a simple calculation to
ensure that the adherends will not plastically deform in cases where fracture energy
measurements are made [22]. However, bonded joints that strain significantly when
exposed to hot/wet environment may provide a less rigorous test and, generally, the
wedge test is not used to provide quantitative data.
The wedge test is a severe test, since the adhesive is at its breaking stress at the
crack tip while directly exposed to the conditioning environment. For this reason,
surface preparations that allow limited interfacial failures may be satisfactory. The
RAAF Engineering Standard C5033 [20] uses crack growth criteria and allows
some interfacial failure in relation to one particular tough adhesive based on service
histories of RAAF aircraft. However as a general rule, without service experience
to correlate with test results, the safe approach is to insist on a cohesional failure
mode, where the adhesive, rather than the surface treatment, limits the mechanical
properties of the adhesive bond.
There is ongoing pressure to establish a relationship between service life and the
performance of an accelerated durability test. Although the wedge test has been
correlated to adhesive bond service life for limited applications, similar durability
performance for new treatments does not imply similar service lives [23]. With
Advances in the bonded composite repair of metallic aircraft structure
48
current understanding and the complexity of the bonded joint, there is no reliable
way to accelerate nature to obtain a quantitative correlation [24].
3.3.2. Fracture mechanics and the cleavage specimen
Fracture mechanics has been applied to the cleavage specimen in an attempt to
quantify the test. The elastic energy release rate, GI, is the energy delivered from
the stressed cantilevers to create a unit area of fresh fracture surface. For the
double cantilever beam specimen [22,25-271:
where h and E are the thickness and modulus of the adherends respectively, w is the
load point displacement and a is the effective crack length. Corrections can be
made to the measured crack length to improve precision of the effective crack
length 128,291. A small fraction of GI is dissipated in breaking atomic bonds whilst
the remainder is dissipated as thermal energy as a result of deformation processes in
the stressed polymer. Equation (3.2) shows that for a plane double cantilever beam
bonded specimen, GI decreases as the crack grows since the stress intensity at the
crack tip decreases. It is thus common practice to assess a critical elastic energy
release rate, GI,,at some arbitrarily long time where the crack velocity is small.
It is now becoming more common practice to use longer and thicker adherends
for durability tests [30],primarily to avoid plastic bending of the adherends. Longer
adherends allow a choice of a longer initial crack length and hence the change in GI
with crack length is less pronounced and much closer to GI,. To avoid adherend
bending, the adherend thickness must exceed a critical value, hcritgiven by [22]:
hdt =
3.Gl.E
>
(3.3)
0;
where cyis the yield stress of the cantilevers.
3.4. Fundamentals of durable bonding
The employment of complex surface treatments to prepare high-energy surfaces
(such as metals) prior to bonding is primarily conducted to ensure adequate service
life of the joint when it is exposed to aqueous environments. Moisture will always
eventually gain access to a bonded joint. The surface preparation must ensure that:
(1) the adhesion forces between the substrate and the adhesive are stable in the
presence of moisture and (2) the surface regions of the substrate will not weaken
and form an in-situ weak boundary layer as can occur when an oxide layer
hydrates. The choice of the surface treatment must follow a “systems” approach
since consideration must be given to the nature of the substrate and its initial
49
Chapter 3. Surface treatment and repair bonding
condition, the type of adhesive to be used and the intended service environment
r311.
Surface treatments modify both the physical and the chemical properties of the
adherend. In general, the relative contribution of the physical roughness and the
chemical character of the adherend to bond strength and durability is not known as
it is quite difficult to design experiments to separate these effects. A review of
experiments to highlight the relative effect of physical and chemical properties of
the adherend on bond durability is described below.
3.4.1. Surface roughness and bond durability
The surface roughness profile has a dramatic effect on the fracture toughness of
an adhesive bond when the bond is degraded by exposure to a humid environment
132-341. Wedge durability tests conducted with aluminium adherends, surface
prepared using an ultramilling method, showed that the elastic energy release rate at
the slow crack velocities in a humid environment, Glscc, depended strongly on the
adherend surface profile angle (a) (Figure 3.4). The ultramilling method created
either a flat adherend surface with a 0" profiIe angle, or sawtooth profile angles of
either 30" or 60" and a peak to valley depth of 10 pm. The surface relief on the 0"
ultramilled terraces was less than 5 nm (Figure 3.5) indicating that mechanical
1000
10
0
0.5
1
1.5
2
tan (a)
Fig. 3.4. Equilibrium elastic energy release rate for a degraded adhesive bond (GlSw),determined using
crack-length data measured from wedge tests conducted in 95% relative humidity at 50°C showing the
effect of surface roughness profile angle (a.). The adherends were 2024 clad aluminium alloy surface
prepared with an ultramilling or grit-blast (GB) treatment. The ultramilled adherends had either ultraflat
surfaces (0") or sawtooth profiles with angles of a= 30" or 60" and peak to valley depths of 10pm. The
adhesive used was Cytec FM 73.
50
Advances in the bonded composite repair of metallic aircraft structure
(a) Ultramilled (a=Oo)
(b) Gritblast
nm
140
:h
40
/Jn
1.5-
40
0
0 40
40
lm
20
Pm
PJn
O 0
Fig. 3.5. Atomic force micrographs of (a) ultramilled (180") and (b) grit-blasted surfaces. The
micrographs show that the relief on the terraces of the ultramilled surface is less than 5 nm.
d
peel component
Fig. 3.6. The interfacial peel and shear components of interfacial loading for (a) 0" ultraflat surface and
(b) 60" sawtooth surface.
interlocking between the adhesive and the adherend was not significantly
contributing to the durability performance of the joint. The flat 0" ultramill surface
provided a baseline for bond durability in the absence of mechanical effects. In this
case, load transfer depends primarily on basic chemical interactions occurring at the
interface between the adhesive and the flat aluminium adherend. These experiments
suggested that surface roughness may introduce an interfacial shear component
(Figure 3.6) at the adhesive to adherend interface, that contributes to improvements
in fracture toughness in humid environments. Introducing surface roughness is a
critical aspect of producing a durable adhesive bond.
3.4.2. Surface hydration and bond durability
Epoxy resins have a high polarity which provide strong hydrogen bonding
attraction between epoxy molecules and metal oxides [35]. DeBruyn [4] showed that
the nominal breaking stress of an aluminium epoxy single lap joint depended
strongly on the hydroxyl content of the epoxy. This observation leads to the
expectation that the interfacial strength of an adhesive bond would similarly
depend on the hydroxyl content of the surface oxides on the adherend. Plasma
oxidation experiments were conducted on ultramilled aluminium adherends [34] to
systematically change the hydroxyl concentration of planar y-alumina films from
very low levels to concentrations expected for pseudoboehmite-type hydrated
oxides. These experiments demonstrated that the initial strength and the durability
Chapter 3. Surface treatment and repair bonding
51
of the adhesive bond were both independent of the oxide hydroxyl concentration.
This led to the conclusion that the hydroxyl content on the metal oxide was
sufficient to form an adequate density of linkages between the adhesive and the
metal oxide for the adhesive itself to be the fracture-limiting material in dry
conditions. It was also concluded that changes in adhesive bond durability were
controlled more by the surface microtopography and hydrophobic contaminant
than by the hydration state of the oxide.
It is important that the surface oxide is cohesively strong i.e. the oxide should not
fail or separate from the metal surface. It is well known that hydration and growth
of the oxide in water can lead to weakness of the oxide structure and that these
conditions should be avoided. In the plasma experiments, planar cohesive yalumina films were formed and the contributions of a weak oxide were avoided [34].
3.4.3. Surface Contamination and bond durability
It is universally acknowledged that an unprepared surface covered with thick
layers of hydrophobic contamination leads to a weak adhesive bond with very poor
long-term durability. Reduction of the contaminant concentration will ultimately
lead to adequate initial bond strength, limited by fracture in the adhesive, but the
long-term durability may still be poor due to the overriding influence of
environment-induced failure at the adhesive to adherend interface. The adhesive
bond durability is very sensitive to the presence of hydrophobic contaminant on the
adherend, but the dependence involves a complex combination of the nature, the
concentration and the distribution of the contaminant.
Studies of bond durability with one epoxy film adhesive following deliberate
contamination of prepared aluminium adherends showed sensitivity to the nature
of the hydrocarbon contaminant [36]. The durability was remarkably tolerant to
contamination with aviation kerosene and a homologous series of alkanes of lower
chain length than C16. This suggested that the adhesive was capable of displacing
sufficient area of some surface contaminants for the adhesive to make good
bonding attachment with the adherend. It is expected that the durability response
to the nature of the contaminant will be adhesive specific as it is well known that
some adhesives are formulated for application to grossly soiled surfaces [37].
In some surface treatments, an aqueous organosilane coupling agent is applied to
improve bond durability performance [36]. The ability of this organosilane
coupling agent solution to wet an adherend surface is very sensitive to the presence
of contaminant. Aviation fuel contamination before organosilane application leads
to a marked reduction in adhesive bond durability, whereas, contamination after
the organosilane is dried has minimal effect on durability (Figure 3.7) [38].
Hydrocarbon contaminants are not uniformly distributed over the surface.
Angle resolved X-ray photoelectron spectroscopy (XPS) studies show that
hydrocarbon is distributed as islands on the surface [38]. Some surface treatments
will accentuate the island distribution of residual contaminant, whereas, others will
lead to a more uniform distribution.
52
Advances in the bonded composite repair of metallic aircraft structure
Time (hrs)
1m1
.-.
0
25
100
I
I
I
90 -
400
I
I
GB + Avtur dip + SCA
I
I
80 -
60 50 40 30 20 70
SB + wipe(MEK)+ SCA
I
SB + wipe(water)+SCA
Root Time (hrs”’)
Fig. 3.7. Crack growth rate curves from wedge tests conducted in condensing humidity at 50°C for clad
2024 aluminium adherends and FM 73 adhesive showing the effect of abrasive surface treatments and
the introduction of aviation kerosene. Labels indicated on the plot correspond to the following:
SB +wipe (MEK) SCA = Scotch-Brite abrade then wipe with MEK soaked tissues then organosilane
coupling agent application
SB +wipe (water) + SCA = Scotch-Brite abrade then wipe with water soaked tissues then organosilane
coupling agent application
GB SCA = grit-blast then organosilane coupling agent application
GB Avtur SCA = grit-blast then contaminate with aviation kerosene then organosilane coupling
agent application
GB SCA + Avtur = grit-blast then organosilane coupling agent then contaminate with aviation
kerosene
GB = grit-blast.
+
+
+
+
+
Abrasion and grit-blasting processes roughen the surface, but an estimated 5 to
10 atomic layers of residual contaminant remain on the surface, distributed
nonuniformly [12,381. By contrast, wiping the surface with a solvent-soaked cloth
or tissue will spread solvent containing dissolved organic material uniformly across
the surface. The solvent evaporates leaving the surface uniformly covered with
hydrophobic contaminant. A contact angle experiment conducted on polished
aluminium, as shown in Figure 3.8, illustrates the importance of considering the
solvent, and the tool used to apply it, as a source of unwanted contamination [39].
Fig. 3.8. Contact angle between a 5 p1 water droplet and a polished aluminium surface ultrasonically
degreased in (a) high purity MEK and (b) MEK containing tissue residues.
Chapter 3. Surface treatment and repair bonding
25
120
3
Time (hours)
100
53
400
100
E
v
2
80
ii
5
60
5
40
_20_
0
5
10
15
20
25
Root Time (hrs'")
Fig. 3.9. Crack growth rate curves from wedge durability tests conducted in condensing humidity at
50 "C for clad 2024 aluminium adherends and FM 73 adhesive, showing the effect of abrasive surface
treatments. The treatments are (a) Scotch-Brite abrade plus wipe with MEK soaked tissues (SB wipe
(MEK), (b) Scotch-Brite abrade plus wipe with water soaked tissues (SB + wipe (water)), (c) Scotch-Brite
abrade plus wipe with water soaked tissues + grit-blast (GB) (d) forest products laboratory etch followed
by phosphoric acid anodisation (FPL + PAA representing a factory benchmark treatment) [40] and (e)
the grit-blast then organosilane coupling agent application (GB SCA).
+
+
The contamination deposited by the solvent can have a dramatic effect on bond
durability, as illustrated in Figure 3.9. Here, clad 2024 aluminium alloy was surface
prepared by abrasion with Scotch-Brite followed by debris removal, or grit-blast,
then bonded with FM73 adhesive. The debris removal with aerospace wipes
soaked in methyl ethyl ketone (MEK) leads to very poor durability, whereas, the
debris removal with wipes soaked in water lead to durability approaching that of
the grit-blast. Composition analysis of the failure surface (Figure 3.10) shows that
the very poor durability of the solvent-wiped adherend is associated with weakness
at the adhesive to metal oxide interface due to the contaminant. The water-wiped
and grit-blasted surfaces failed within the oxide film.
3.4.4. Bond durability model
A stress based diffusion model (Figure 3.11) was developed to describe the rates
of bond degradation and modes of fracture for a series of aluminium/epoxy wedge
test specimens exposed to humid environments [34,41,42]. Large interfacial cavities
were observed along the bondline of wedge test specimens exposed to humid
environments [43]. Observations by other workers [44] and scanning electron
microscopy (SEM) micrographs (Figure 3.12), indicate that microcavities exist at
the interface in the crack tip region for stressed wedge test samples. Under stress,
the size and distribution of these microcavities could be determined by variations in
bond strength along the interface induced by the distribution of contaminant or by
inhomogeneous stress distributions induced by surface roughness.
54
Advances in the bonded composite repair of metallic aircraft structure
SB+wipe
SB +wipe
(water)
(MEW
n
s
80
60
i
Q
v
E
40
ti
20
3
0
8
20
0
i
9
8
d
2
m
40
60
Fig. 3.10. Surface composition of both fracture faces measured with XPS for the treatments (a) ScotchBrite abrade plus wipe with MEK soaked tissues (SB +wipe (MEK)) and (b) Scotch-Brite abrade plus
wipe with water soaked tissues (SB wipe (water)).
+
Firstly, all practical adherends will have several atomic layers of residual
contaminant distributed nonuniformIy on the surface [38]. During cure, adhesive
bonds will form more efficientIy in the uncontaminated surface regions. Increased
concentrations of contaminant may lead to less effective bonding. This has the
capacity to explain a variation in cavity size with changes in contaminant levels.
Secondly, inhomogeneous stress distributions induced by surface roughness have
been used by several workers to describe adhesive joint fracture [45,46]. At a
microscopic Ievel, surface roughness may introduce a surface shear component to
the existing surface peel component in a normally stressed bond and thereby would
change the effectiveness of the interfacial transfer of load. This may potentially
influence the size of microcavity formation.
Microcavities represent paths for moisture ingress. The size and distribution of
microcavities will determine the ease of moisture access and the fractions of the
adherend surface subjected to rapid bond degradation. At these localised sites of
Chapter 3. Surface treatment and repair bonding
(a)
moisture
ingress
55
polymer
hydrolysis
polymer
desorption
oxide
degradation
I
region
1
Strong bond
region
Fig. 3.11. Stress based diffusion model that describes moisture ingress to the adhesive metal interface
and three degradation reactions. The magnitude of microcavities ahead of the crack tip would control
the rate of moisture diffusion and the dominant degradation reaction path would determine the position
of bond weakening and the dominant locus of failure.
moisture ingress, the adhesive bond can degrade by any one of three reaction paths
as shown in Figure 3.1 l(a): polymer degradation, polymer desorption or oxide
degradation. With time, the sites of adhesive bond degradation expand and
coalesce, leading to a reduction in the fracture strength and crack propagation [32341. Moisture in contact with the metal oxide at the bond interface will lead to oxide
growth and hydration. The presence of localised sites of oxide growth some
hundreds of microns ahead of the crack tip is illustrated by the Scanning Auger
Micrographs of the fracture surface of a forcibly opened wedge test specimen with
ultramilled adherends (Figure 3.13). This supports the concept that bond
degradation occurs in advance of the crack tip. Mechanical strength may be
sustained by stress sharing networks in the polymer bridging load across the
degraded regions of the interface.
The stress based diffusion model has the potential to be developed to describe a
more comprehensive view of adhesive bond durability and its dependence upon
interfacial stress, contaminant concentration, surface roughness, coupling agent
performance and other relevant influences. An opportunity exists for modelling the
micromechanics of the bondline and moisture diffusion behaviour. Microscale
finite element modelling may aid progress in the development of a quantitative
bond degradation model.
56
Advances in the bonded composite repair of metallic aircraft structure
I
voids at the stressed
interface just ahead of
the crack tip
Fig. 3.12. SEM micrographs showing the presence of microcavities in the stressed regions just ahead of
the crack tip of a wedge test specimen exposed to condensing humidity at 50°C.
3.5. Requirements of surface preparation
Adherend preparation typically involves a series of steps, each with an important
purpose. Whilst the surface preparation affects the initial bond strength, it is the
influence of surface preparation on the long-term environmental durability of
bonded structures that is of particular concern.
Chapter 3. Surface treatment and repair bonding
51
Direction of Crack
Crack till
Metal Failure Surface
Infront of Tip
Kinetic Energy(eV)
Kinetic Energy(eV)
Fig. 3.13. Scanning auger microprobe (SAM) analysis of the crack tip region of a failed wedge sample
pre-treated with a 180" ultramill. The SAM maps indicate the distribution of metallic aluminium at
positions ahead of the crack tip and the spectra show the relative concentrations of aluminium oxide and
aluminium metal at the locations indicated.
3.5.1. Degreasing
Degreasing is conducted to remove gross organic contamination. Greases and
oils are usually present on alloys received from the manufacturer. After prolonged
service, components are expected to have a wide variety of organic contaminants,
with some so aged and firmly adsorbed that they are resistant to solvents.
Degreasing is used to decrease the concentration these organic contaminants on the
adherend surface prior to subsequent preparation steps.
Factory facilities often use vapour degreasing to reduce the concentration of
organic contaminant on components to be bonded. A solvent such as
trichloroethylene is evaporated in a closed space then allowed to condense and
drip from the soiled components. Organic contaminants are slowly dissolved in the
58
Advances in the bonded composite repair of metallic aircrafi structure
liquid phase whilst it is in contact with the component and are transported to the
solvent reservoir under gravity. In many cases, tank based cleaning using alkaline
aqueous solutions has replaced vapour degreasing due to environmental and safety
concerns. Degreasing is typically the only surface preparation used for aluminium
honeycomb.
In the repair environment, degreasing is frequently conducted with solventsoaked tissues or cloths. Common solvents used are MEK and acetone. Again, the
solvent dissolves the organic contaminant on the soiled component, but it is
important to ensure that sufficient solvent volume is swept over the component to
ensure a solvation gradient. A unidirectional sweep to the edge of the region is
important to ensure that the dissolved organic contaminant is adequately flushed
from the zone undergoing the degreasing process. None-the-less, a volatile solvent
will evaporate and can leave a thin film of organic contaminant uniformly spread
over the adherend surface. Further, the solvent can dissolve polymers and residual
greases from the tissue or cloth and deposit these on the adherend surface as the
solvent evaporates (Figure 3.9) [39].
The waterbreak test is widely used to assess the presence of contaminant on an
adherend surface. However, the waterbreak test must be treated with caution
because contaminants such as water-displacing fluids yield low contact angles [39].
3.5.2. Abrasion, grit-blasting or etching
Abrasion, grit-blasting or etching is conducted to remove loosely adherent
oxides, to prepare a contaminant-free active surface and to generate a rough
surface topography. Abrasion physically removes metal by the action of hard
particles bonded to a carrier cloth or pad. This creates a surface with furrows and
leaves residual metal debris on the surface.
The practice of removing debris from an abraded aluminium alloy adherend
using clean tissues must be approached with caution. Debris removal with tissues
soaked in MEK led to poorer bond durability than removal using tissues soaked in
water (Figure 3.9) [39]. The reason is that the MEK solvent can dissolve organic
material from certain tissues and leaves the contaminant distributed across the
surface as the solvent evaporates. This contaminant then interferes with the bond
between the adhesive and the metal surface allowing moisture to diffuse into the
stressed bondline at a faster rate than for a bondline where there is better
attachment between the adhesive and the metal surface [36].
The grit-blast process uses fine abrasive particles carried in a high velocity stream
of clean, dry air or nitrogen to impact the adherend surface. Plastic deformation of
the metal surface is more dominant than metal removal and crater formation in the
surface is evident [47] (Figure 3.14). Pre-existing debris is consolidated into the
surface during impact deformation of the metal surface.
The grit-blast treatment improves the hydrophilic wetting of the surface (Figure
3.15) [36] and the durability of the bond (Figure 3.9) over that of the abraded
surface. Some of the improvement in wetting can be attributed to a decrease in the
concentration of hydrophobic contaminant and some to the roughening of the
Chapter 3 . Surface treatment and repair bonding
59
Fig. 3.14. Micrograph cross sections showing (i) no grit-blast, (ii) single impact grit-blast and (iii) double
impact grit-blast. The micrograph of the double impact grit-blast shows the degree of overfolding and
cavities formed on the surface (iv).
90
80
70
h
Ei
2
E
60
50
2
M
40
4*
30
U
2
5
u
20
10
0
Fig. 3.15. The contact angle for clad 2024 aluminium following degreasing (MEK wipe), abrasion with
Scotch-Brite plus debris removal with water soaked tissues (SB + wipe (water)), dry at 110"C, grit-blast
(GB), recontamination with either exposure to burnt aviation kerosene or a laboratory environment.
surface. Measurements with XPS show that hydrocarbon concentrations are
decreased by solvent degreasing and further reduced by abrasion [36].Curve fitting
of the Cls peak in XPS spectra of solvent degreased and grit-blasted surfaces shows
the reduction of a species containing a C=O bond, which could be attributed to the
removal of residual MEK solvent.
The severity of grit-blast must be controlled. Insufficient grit-blasting leads to
ineffective preparation of a contaminant-free active surface. The threshold
60
Advances in the bonded composite repair of metallic aircraft structure
grit-blast density for 50 micron alumina grit to achieve full surface coverage is
0.5 g ~ m [48].
- ~ It is recommended that 1gem-* should be used to ensure complete
surface impact and contamination removal. Excessive grit-blasting does not
improve the durability performance of the adhesive bond, although additional
deformation of the surface has occurred. This additional surface deformation gives
rise to subsurface cavities in the adherend which become sites for the entrapment of
moisture and other volatile materials. During cure of the adhesive at elevated
temperatures, these volatile materials form bubbles in the adhesive leading to voids
in the cured bond [I 1,49,SO]. Void formation will be discussed in Section 3.6.2
Chemical etching dissoIves metal from the surface in a complex process involving
dissolution and regrowth of the oxide film. Aluminium alloys immersed in chromic
acid etches develop a relatively flaw-free oxide due to the absence of contaminants
[51]. The chemical dynamics of the etching process leads to a microporous structure
[52] on the metal surface which leads to similar bond durability performance to that
of the grit-blast treatment 1471.
3.5.3. Creation of a high energy surface oxide
Creation of a high energy surface oxide implies the optimisation of surface
wetting. It may be an automatic result of abrasion, grit-blasting or etching
processes. Alternatively, processes such as anodising may be employed to create
hydrophilic surface oxides. The creation of a high energy surface oxide implies that
steps to minimise the readsorption of hydrophobic contamination have been taken.
Surface oxides form rapidly on almost all metal and alloy surfaces. Abrasion and
chemical surface treatments are conducted to reduce contaminant, to remove preexisting loose oxides, to generate compact mechanically robust surface oxides and
to produce an hydroxylated oxide surface on the metal which will bond to the
hydroxylated moieties in the adhesive. Most surface treatments are optimised by
trial and error with very little fundamental understanding of properties at the
nanometre scale. The oxides formed on structural metals such as aluminium, steel
and titanium will be sufficiently hydroxylated to form strong bonds [34]. However,
the possibility of forming a weak oxide on the adherend must be considered.
Extended etching of a nickel surface in a nitric acid solution produced an
appropriately rough surface, but the smut and thickened oxide produced a weak
bond interface [S3]. The presence of residual contaminant or the possibility of
reintroduction of contaminant is of concern.
Anodising is a process involving electrolytic treatment of metals in which a
stable, porous oxide is intentionally grown on the surface of the metal 154,551. This
oxide is mechanically cohesive and tenaciously adheres to the metal surface. In a
typical anodising bath, the metal alloy is connected as the anode in an electric
circuit, is immersed in an oxidising electrolyte of usually low pH and a positive dc
(direct current) potential is applied [%I. Whilst most anodising baths use acidic
electrolytes and dc potentials, some use alkaline electrolytes and some use
alternating current. The oxide is formed on the metal surface as a result of
controlled chemical dissolution of the metal and electrochemical oxidation of the
Chapter 3. Surfnee treatment and repair bonding
61
surface [57]. The microtopography of the outer oxide is very sensitive to bath
composition, anodising parameters, alloy composition and the surface finish on the
metal. Since the best durability performance is generally obtained with a high
degree of microroughness of the metal oxide surface, it is not surprising that
attention to details of the bath and alloy is essential to obtain optimum surface
oxide film properties. There is extensive literature on factory anodising [57].
In field repair applications, tank anodisation is often not practical. The
electrolyte is either formed into a self-supporting gel or special approaches for
the containment of circulating electrolyte over the treatment region are used. The
use of anodisation for on-aircraft repairs needs to consider issues including the
potential for unwanted corrosion, the potential for hydrogen embrittlement of
fasteners, difficulties with the removal of the electrolyte, difficulties with the use of
electrical equipment in the vicinity of flammable vapours and the potential for
damaging the oxide film with the post-anodising processes.
3.5.4. Coupling agent
The purpose of the coupling agent is to enhance the effectiveness of the hydroxyl
(OH) terminations on the metal oxide in linking with the adhesive. In the case of
the organosilane coupling agents, the organic head group is chosen for crosslink
compatibility with the adhesive polymers and the silanol groups formed during
hydrolysis (Figure 3.16) either react chemically with the hydroxyl groups on the
metal oxide surface to form oxirane bonds (M-0-Si)
or form hydrogen bonds
with these hydroxy groups (M-OH . ..HO-Si) [58]. The exact nature of the
interaction remains speculative. The organosilane forms strong polysiloxane
networks which play a significant role in interfacial durability enhancement [%I.
Characteristics of a good coupling agent are the crosslinking with the adhesive
and hydrolytic stability to water, which can hydrate the oxide film. Both are
essential, but the crosslink connection into the adhesive and increased load sharing
appears to be most important. Nitrilotris methylene phosphonic acid (NTMP) is an
outstanding hydration inhibitor and was reported by Venables to improve bond
durability [59]. However other research [42] suggests that the inability of NTMP
molecules to crosslink through primary chemical interactions prevents a cohesively
strong film forming and leads to ineffective performance as a durability improver.
Mazza et al. [60] conducted a detailed investigation of “the Australian Silane
Surface Treatment” [61] by varying the process parameters. This work identifies the
optimum organosilane concentration, silane hydrolysis time, application time,
drying time and drying temperature. This data supports the defined processes in the
Royal Australian Air Force Engineering Standard (3033 [20]. Whilst Mazza
initially reported that the optimum temperature for drying organosilane coupling
agent was 93 “C for 90min, other work suggests that higher temperatures may be
required for void minimisation [50]. Later work by Mazza et al. also supports the
use of a higher drying temperature [62].
The presence of contaminant on the metal surface plays a significant role in the
ability of the organosilane coupling agent to attach to the hydroxyl groups on the
62
Advances in the bonded composite repair of metallic aircraft structure
CH,O
'
V
R .
y-glycidoxy propyl tnmethoxy
(Y- G W
RSi(OMe),
HYDROLYSIS
RSi(OH)3
RSi(OH)3+ RSi(OH),
1-H.ll
R
R
R
I
I
I
HYDROGEN
BONDING
RI
COVALENT
BOND
FORMATION
Af20
I
RI
Fig. 3.16. Organosilane coupling agent y-glycidoxypropyltrimethoxy silane showing the hydrolysis,
condensation and surface reactions.
metal oxide. This is illustrated in Figure 3.7 where it is shown that the durability
enhancement afforded by the organosilane coupling depends strongly on the
surface treatment prior to the application of the coupling agent. Analysis of the
failure surface with XPS indicates that as the durability improves, fracture shifts
from the oxide film toward the interface between the coupling agent and the metal
oxide [36]. The effectiveness of the coupling between the organosilane and the metal
oxide has an influence on the ability of water to diffuse to the interface between the
adhesive and the metal adherend together with the hydrolytic stability of the metal
oxide. In practical terms, it is essential to ensure that the surface treatment has
produced a hydrophilic surface and to ensure that contamination is avoided before
Chapter 3. Surface treatment and repair bonding
63
the application of the organosilane coupling agent [39]. Brushes or tissues used to
apply organosilane can transfer organic contaminant to the prepared metal surface
leading to deterioration in bond durability performance [39].
3.5.5. Adhesive primer
Most adhesive suppliers recommend a primer for metal bonding. Primers protect
the adherend surface from contamination or chemical changes between surface
preparation and the bonding process. Since they are low-viscosity fluids, primers
can readily penetrate surface roughness and microporosity developed by the
surface preparation and better wet the adherend surface. Primers also help protect
the bonded adherend from moisture attack in order to improve long-term
durability. For this reason, adhesive primers often contain corrosion inhibitors [63].
Popular adhesive primers are epoxy-phenolic based and contain chromate
inhibitors. Whilst hexavalent chromium ions provide the best protection to the
metal oxide surface, these materials are toxic to the environment, are known
carcinogens and as a result there is pressure to find alternative inhibiting agents.
Application of a corrosion-inhibiting adhesive primer to enhance bond durability
for on-aircraft repair is as desirable as it is for factory and depot processes.
However, priming on aircraft is more difficult to control both from the application
and the environmental hazard point of view. Wipe-on or brush application of the
primer is frequently substituted for spray application used in off-aircraft bonding.
It is important to recognise that improperly applied primer, especially if it is too
thick, can lead to inadequate initial bond strengths.
Primer thickness may be measured by eddy current thickness gauges. Primers
also may have pigments added as an aid to visual thickness control, particularly in
the case of sprayed application. However, this optical method limits thickness
control to fractions of a micron and the choice of the pigment can influence the
visual sensitivity. The performance on thickness control is very dependent on
operator skill and ability. The RAAF Engineering Standard (25033 [20] does not
include a primer specification. This follows concern over the ability of technicians
to adequately control primer thickness and cure properties in a repair environment.
The elimination of primer usually results in some reduction in wedge test
performance, but RAAF service experience has indicated good performance using
only the grit-blast /silane treatment.
3.5.6. Drying
Drying the surface thoroughly following any treatment involving solvents or
water is absolutely essential to minimise the evolution of volatile materials
responsible for void formation during the cure phase of the adhesive. Measurements of water evolution from a grit-blasted aluminium alloy surface indicate that
sufficient steam can be generated by a poorly dried surface to eject most of the
adhesive from the bondline [l 1). Some of the water on the adherend is physisorbed
and some is bound in the hydrated surface oxide film (Figure 3.17). Curing an
64
Advances in the bonded composite repair of metallic aircraft structure
temperature 20°C
0.3
0 25
Q)
0.2
Q
a
0.15
LI
a
0.1
0.05
0
0
10
20
30
40
50
60
70
Time (min)
Fig. 3.17. FTIR water evolution profile for grit-blasted clad 2024 aluminium alloy illustrating the
chemical affinity of the adsorbed water with the aluminium oxide surface and the effect of drying for 1 h
at a range of temperatures.
adhesive bond at elevated temperature will release even the chemically bound water
as steam [50].Experiments have shown that drying at 110 "C for at least an hour is
essential to minimise void formation in some epoxy adhesives where cure is
conducted using vacuum bag pressurisation. Conducting the bonding process in
low humidity to avoid readsorption of moisture is also essential (Figure 3.17).
3.6. Adhesive application
Adhesives (and primers) have a limited shelf life, and refrigerated storage in
sealed containers is essential for most. Repacking of application lots of film
adhesives in sealed polyethylene bags must be conducted in controlled atmospheric
conditions to minimise moisture absorption. Quality assurance requires careful
documentation of histories and conditions of storage. The quality of the bonding
process relies on the flow of adhesive and the curing conditions. Process control of
the temperature ramp rate and final temperature is essential. Aircraft structure has
differential heat sinks leading to a requirement for zoned heating and looped
control to avoid local over-temperature and under-temperature regions. Experience
has shown that there is a general lack of care with ensuring that temperaturesensing devices are properly located and properly calibrated to ensure that the
temperature sensed reflects the temperature in the curing adhesive.
Chapter 3. Surface treaiment and repair bonding
65
Trivial mistakes such as leaving the peel plies or separator sheets on the adhesive
are committed even by the most experienced technicians. Fortunately, the
consequences are quite apparent. However, the use of peel plies and other
materials containing a silicone release agent is a more insidious error of judgement.
The RAAF has taken steps to ban these materials from all bonding operations.
3.6.1. Factors controlling bondline thickness
The mechanical properties of an adhesive joint are influenced by the thickness of
the bondline [64,65]. Many film adhesives contain a supporting scrim, which
exercises some control over bondline thickness. The scrim may also act as a
strength-limiting defect, or can toughen the bond, or can provide a path for
moisture ingress into the bond.
3.6.2. Void formation and minimisation
Periodically, high levels of void formation in the bond have been observed for
repairs conducted at tropical airbases [66]. Calculations show that the water
content of the bondline in which the adhesive and the adherend are both exposed to
humid, tropical conditions can be sufficient to produce enough steam during an
elevated temperature cure to eject most of the adhesive from the bondline (Figure
3.18) [l 11. The resultant degradation in mechanical properties has airworthiness
implications and, therefore, must be addressed.
The volatile gases present in the bond have three potential sources [49]:
Firstly, the adhesive supplied from the manufacturer may contain solvents with
their concentration limits defined by a specification designed for positive pressure
cure. There will be batch-to-batch variations in the concentration of these volatile
materials [49].
Secondly, the adhesive can quickly absorb water [49] if exposed to hot, humid
tropical conditions. The equilibrium concentration of moisture depends strongly on
the relative humidity of the atmosphere.
Thirdly, moisture is readily adsorbed by the rough overfolded surface (Figure
3.14) of the abraded and grit-blasted aluminium alloy adherend, [49,67]. This
moisture is both physisorbed and chemisorbed by the aluminium alloy surface
(Figure 3.17).
Whilst each source of volatile gases on its own may be relatively innocuous, the
combined effect of all three sources can lead to a level of voiding which will affect
mechanical properties (Figure 3.18) [50].
Void minimisation strategies are generally centred on minimising the moisture
content of the bondline or by constraining the volatile gases using hydrostatic
pressure. The most effective strategies are to conduct bonding in a temperature
controlled, dehumidified atmosphere and to use positive pressurisation of the
bondline with an autoclave, press or pressurised bladder.
66
Advances in the bonded composite repair of metallic aircraft structure
1 mm
(b)
Fig. 3.18. Void formation in Cytec FM 300 epoxy film adhesive where both the adhesive and adherend
were exposed to (a) temperate (50% RH at 20 “C) and (b) tropical (70% RH at 30 “C), conditions.
3.7. Surface treatment quality control
Tools to assist with quality control during the production of an adhesive bond
and nondestructive evaluation of the bonded joint are very limited and not
particularly reliable. The production of a strong and durable adhesive joint
depends critically on the skill and the integrity of qualified personnel manufacturing the bonded joint. Strict adherence to a qualified procedure is essential. A
benchmarking activity conducted for the RAAF [211 indicates that adherence to
well-defined qualified procedures, underpinning standards, staff training, regular
reviews of staff qualification and continuity of experience were of utmost
importance to achieving acceptable bond durability performance in the repair
environment.
3.7.1. Waterbreak Test
The aerospace industry routinely uses the tendency of clean water to “bead” or
“break” as an indication of the presence of hydrophobic contaminant on an
adherend during surface preparation. In practice, the waterbreak test relies on the
Chapter 3. Surface treatment and repair bonding
61
skill and experience of the technician and is not necessarily reliable. Surface
roughness has a significant influence on the outcome. Some contaminants have
hydrophilic characteristics and therefore lead to a waterbreak free indication.
Examples of hydrophilic contaminants commonly encountered are water-displacing fluids used in aircraft maintenance.
3.7.2. Surface work function methods
The electron work function of a metal surface is very sensitive to its chemical
state. A number of methods based on work function are in use to assess
contaminated surfaces [68-701. However, the work function methods have
difficulty in discriminating between oxide growth, contaminant concentration
and surface roughness.
The Fokker surface contamination tester is based on the Kelvin vibrating
capacitor surface potential difference method [68]. The physical size of the
measurement area, the sensitivity to interelectrode spacing and potential
contamination of the gold reference electrode are limitations.
The optically stimulated electron emission (OSEE) method is also commercially
available [71]. The method is based on the emission of photoelectrons with energies
of less than 6.7 eV, stimulated by ultraviolet radiation from a mercury vapour
source. The photocurrent is measured in air using an electrically biased plate
located 1 to 6mm from the sample surface [70]. Aluminium metal with a work
function of 4.08 eV [72] will emit photoelectrons whereas aluminium oxide with a
work function greater than 6.7 eV will not [70]. It was found [73] that the principal
impediments to quality control in the base repair environment is the absence of a
suitable simple reference calibration and the convoluted response to contaminant
concentration, oxide growth and surface roughness.
3.7.3. Fourier transform infrared spectroscopy
Advances in fourier transform infrared (FTIR) spectroscopy have led to some
promise as a technique to evaluate contaminants on a rough metal surface.
However, the complexity of infrared spectroscopy leads to the requirement for a
skilled analyst to interpret the data, and it may be some time for expert systems to
be developed to the point where semiskilled technicians can routinely apply
infrared spectroscopy to quality control in the field. Commercial instrument
manufacturers [74] have developed infrared spectroscopic systems for noncontact
evaluation of surfaces. It should, however, be clearly understood that the depth
discrimination of infrared spectroscopy is typically in the hundreds of nanometres
range and that special grazing incidence techniques are required to bring the
sensitivity down to monolayer coverage levels.
68
Advances in the bonded composite repair of metallic aircraft structure
3.1.4. Optical reflectivity
Inspection of the quality of a grit-blasted surface is performed visually and, for
aluminium surfaces prepared with fine grit, optical reflectance characteristics are a
good indicator of the severity of grit-blast impact [48,73].
Commercial reflectance colourimeters have been used to quantitatively assess the
reflectivity of aluminium alloys and show a exponential dependence on the density
of impact of fine 50 micron alumina particles [48,73]. A very simple hand-held
instrument has been shown to adequately monitor grit-blast severity on aluminium
alloys and is currently being used as a training and qualification tool by the RAAF.
The polarisation response of reflected polarised light is used as a quality control
tool for phosphoric acid anodised surfaces. The method indicates defects in the
thickness and maturity of the porous anodised film [75].
3.7.5. Process control coupons (traveller or witness specimens)
In the absence of a comprehensive array of quantitative quality control tools, it is
common practice for process control coupons, also known as traveller or witness
specimens, to be prepared in parallel to the production or repair task. Whilst these
provide a form of quality assurance, there is no guarantee that the surface
treatment or the bonding conditions were identical to those on the real component.
The potential exists for the technician to apply undue care with the traveller
specimen or to prepare the traveller specimen at a different time to the bonded
component. The RAAF Engineering Standard C5033 [20] places emphasis on
quality control through a strategy of qualification of processes, procedures and
personnel.
3.7.6. Practitioner education, skill and standards
Quality control in the manufacture and repair of bonded components relies on a
strategy of qualification of processes, procedures and personnel [17]. It is essential
for the procedures to include a quality assurance trail to ensure that the task was
performed in strict accordance with the qualified specification. It is to be noted that
the regulatory framework used to manage the structural integrity of bonded
components is currently not capable of identifying bonded components which are
susceptible to time-dependent bond degradation [161. There is much work to be
done toward developing regulations addressing preproduction validation tests to
eliminate practices which lead to bond degradation. The lack of reliable
nondestructive evaluation tools has led to a reluctance by many engineers to
accept the engineering risks involved in an adhesively-bonded joint, particularly for
primary load-bearing structure [2].
Chapter 3 . Surface treatment and repair bonding
69
3.8. Surface preparations for aluminium adherends
The overwhelming majority of failures in aluminium adhesive joints in aircraft
have been initiated by moisture [76]. Thus, the employment of complex chemical
treatments ensures adequate service life of the joint when it is exposed to aqueous
environments. In general, the surface preparation of aluminium is designed to
remove weak boundary layers (oxide scale and organic contaminants) and to form
stable layers that adhere well to the base metal and are chemically and physically
compatible with the adhesive or primer [54,77]. This is required of both factory and
field surface preparation processes, including on-aircraft treatments. The extent of
the surface treatment depends upon the demands of the application.
3.8.1. Factory processes
Considerable research has been conducted regarding preparation of aluminium
for adhesive bonding, particularly for 2000 and 7000 series alloys since they are
most used in aerospace applications. Most factory processes for aluminium surface
preparation involve etching in acid solutions or electrochemical anodisation or
both. These treatments are intended to produce a stable oxide layer that tenaciously
adheres to the metal surface. The best durability performance is generally obtained
with a high degree of microroughness on the surface. Durability is further increased
when the adherend surface is also chemically compatible with the adhesive or
primer [54].
3.8.1.1. Phosphoric acid anodise (PAA)
Phosphoric acid anodise (PAA) is currently the most widely used anodisation for
aluminium prebond treatment [55]. This is largely due to the superior performance
the treatment demonstrated during the United States Air Force’s Primary
Adhesively Bonded Structure Technology (PABST) program [78,79]. PAA is
characterised by its simple chemistry, room-temperature requirements, low
electrical needs, relatively good environmental acceptability and fairly wide
tolerances for process parameters [80]. The PAA process produces an approximately 400 nm thick amorphous aluminium oxide characterised by a thin inner
barrier layer, an outer porous layer, external whiskers and a phosphate rich surface
[76]. In relation to alternative anodise processes, the PAA oxide will not hydrate or
“seal”, is much thinner and has the largest pore sizes [56].
Anodisation is carried out in 10%aqueous H3P04 (by weight) at 10 V. The exact
details of the procedure vary slightly between using organisations [31,81,821. The
best durability performance is obtained by employing an acid etch prior to
anodising [83]. Both Forest Products Laboratory and P2 etch [83] have been
employed in this way. In order to obtain repeatable durability results, key process
variables, such as tank make-up and rinse water, must be controlled.
The microporous PAA oxide is fragile and must be primed or bonded as soon as
practical. A low-viscosity primer can penetrate the pores, stabilise the oxide layer
and protect the adherend surface from corrosion, given that the thin PAA oxide
70
Advances in the bonded composite repair of metallic aircraft structure
provides little inherent corrosion protection. Although the use of a few rubbercontaining 177 "C curing adhesive primers led to suboptimal bond strengths when
used with PAA, most primers are compatible with PAA oxides [84-861. PAAprimer systems yield good bond strengths and are generally considered to provide
the best long-term durability performance for joints made with typical aerospace
aluminium alloys and epoxy adhesives [313,871.
3.8.1.2. Chromic acid anodise (CAA)
Chromic acid anodise (CAA) is the other common, high-performance anodise
for aluminum alloys. The overall oxide thickness is nearly four times that of PAA
(approximately 1500nm). This thicker, denser oxide is less fragile than the PAA
oxide and provides greater corrosion protection to the base alloy. Although the
CAA oxide provides less developed porosity than does the PAA oxide, primers
have been shown to penetrate the pores.
Anodisation is conducted in 5% aqueous CrO3 (by weight) at a temperature in
the range of 32 "C to 42 "C with the potential gradually raised to 40-5OV. The
oxide morphology can be altered by varying the process parameters [81]. Cleaning
and deoxidizing steps are similar to those for PAA. The pretreatment acid etch step
for the CAA process influences the porosity of the outer surface of the oxide [76].
The CAA treatment is optimal when preceded by a chromic-sulphuric acid etch
[881Corrosion protection provided by CAA can be enhanced by sealing the oxide
with hot water or dichromate solution [89], but sealing fills the pores and decreases
adhesion. Although sealed CAA has performed well in some applications [90], the
process is generally not recommended for adhesive bonding applications [31,881.
The unsealed oxide may be primed with a corrosion-inhibiting adhesive primer
or an organosilane coupling agent. The CAA-primer systems yield good initial
bond strengths and durability. Performance in moist environments is slightly
inferior to PAA [31,55,91] when tested with toughened epoxy adhesives. In actual
service with vinyl-phenolic adhesives, CAA-treated aluminium joints have an
outstanding durability record. The CAA process has recently become less popular
as environmental and safety concerns regarding hexavalent chromium are making
it more expensive and difficult to use.
Recently, boric-sulfuric acid anodise (BSAA) has been developed to produce an
oxide similar to the CAA oxide without the use of chromium. Although the
treatment was intended originally for paint adhesion applications, a variant called
sulphuric boric acid anodise (SBAA) was optimised for aluminium adhesive
bonding [92].
3.8.1.3. Optimised Forest Products Laboratory (FPL) etch
The optimised forest products laboratory (FPL) etch produces a 40 nm thick
amorphous A1203 film [93] with an outer network of shallow pores and whiskerlike protrusions on top of a thin barrier layer. This microroughness is less
pronounced than that of the PAA oxide.
Chapter 3. Surface treatment and repair bonding
71
The optimised FPL etch is 5% by weight Na2Cr207 2H20, 26.7% H2SO4 and
68.3% water with a small quantity of 2024 aluminium to seed the bath [Sl]. Etching
is conducted for 10 min at a temperature of about 65 “C. Pretreatment steps include
solvent degreasing and/or alkaline cleaning. As with the other chemical processes,
rinse steps are important. The FPL etch variables must be carefully controlled. The
etched aluminium surface is usually primed with a corrosion-inhibiting adhesive
primer prior to adhesive bonding.
The FPL etch process is less expensive and time-consuming than the anodise
procedures. It yields good initial bond strengths, but inferior moisture durability
compared to the CAA or PAA anodises [55,31,91,93,94].
3.8.1.4. P2 etch
The P2 etch uses ferric sulphate in place of the toxic sodium dichromate as the
oxidiser (15% by weight FeS04, 37% H2S04 and 48% water [81]) and produces an
oxide with a similar morphology to those obtained using the various chromicsulphuric etches [54]. The P2 etch produces similar initial bond strengths and
durability to those of FPL etch. Its performance as an anodisation pretreatment is
comparable to FPL etch [54,83,95].
Three factory aluminium surface preparations are compared on the basis of
wedge test data, indicated in Figure 3.19, for Cytec BR 127-primed A1-7075-T6
alloy bonded with Loctite Hysol EA 9628 adhesive [83]. The failure modes are
indicated on the plot, where “Adhesive” failure represents interfacial failure
between the adhesive and the metal surfaces and “Cohesive” failure represents
failure within the adhesive layer.
40
h
E
E
36
W
c
5
C
s
u
32
E
0
28
0
2
4
6
8
10
12
14
Root time (hrs”5)
Fig. 3.19. Wedge test data comparing the relative durability performance of the PAA, FPL and P2
factory based surface pretreatment processes for BR 127-primed A1-7075-T6 alloy bonded to EA 9628
adhesive and tested at 50 OC/95% RH [83].
12
Advances in the bonded composite repair of metallic aircrafi structure
3.8.2. On-aircraft acid anodisation and acid etch processes
The limitations imposed by the on-aircraft environment lead to a demand for
simple surface preparations. Solvent degreasing and manual abrasion alone lead to
extremely poor long-term durability [3 1,871.
Adaptations of factory acid etch and anodisation processes have been made to
enable their use on aircraft to obtain adequate bond performance. Care must be
exercised with the use of acids since these can cause either corrosion in joints and
around fasteners or embrittlement of high-strength steel fasteners [96].
Some aircraft structural repair manuals specify primer application with
cheesecloth [87]. Inadequate control over primer thickness, often encountered
during aircraft repairs, such as with wipe-on or brush applications, can lead to poor
initial bond strength. The elimination of the primer can decrease the long-term
bond durability. Decisions regarding priming and the entire surface preparation
process must often be made on a case-by-case basis for on-aircraft repair.
3.8.2.1. On-aircraft phosphoric acid anodise
PAA has been adapted to on-aircraft use. Pretreatment steps involve the removal
of organic coatings, solvent degreasing, manual abrasion and dry-wipe removal of
abrasives and debris. Two anodising approaches have been developed:
The phosphoric acid non-tank anodise (PANTA) process uses phosphoric acid,
thickened with fumed silica, in a gauze sandwich with a stainless steel mesh cathode
[97]. Precautions to keep the gel moist and to avoid trapping hydrogen gas are
essential during anodisation. After anodisation, the acid must be removed quickly
and without damaging the fragile oxide surface. The surface is then dried prior to
priming [87].
The phosphoric acid containment system (PACS) contains the phosphoric acid
under a double vacuum bag [98,99]. For the PACS process, the steel cathode screen
is placed on top of a nylon breather material. Vacuum is used to pull phosphoric
acid through the bag, and anodising is conducted for 25 min with a continual flow
of acid over the repair area. Rinsing is accomplished by drawing clean water
through the vacuum bag. Final rinsing is conducted after removing the vacuum
bag, breather and cathode screen. The surface is then dried and primed prior to
bonding.
The advantages of the PACS process over PANTA include acid containment, the
ability to more conveniently conduct overhead applications, the avoidance of
electrolyte drying and the minimisation of trapped gas against the repair area.
However, limited access to the repair area or leaking fasteners under the
containment bag could prevent the use of PACS in some applications.
Morphology studies of PANTA and PACS oxides created under controlled
laboratory conditions indicate they are similar to those obtained with the factory
PAA process. Mechanical testing shows initial bond strength and durability
comparable with the tank PAA process [87,97,99].
Both the PANTA and PACS preparations should be followed by application of a
corrosion-inhibiting adhesive primer to protect the anodised surface.
Chapter 3. Surface treatment and repair bonding
73
3.8.2.2. Acid paste etching processes
The popular chromic-sulphuric acid etches have also been adapted for onaircraft application using fumed silica, barium sulphate or other suitable material
to thicken the acid. Ambient-temperature etching increases the application time.
Typical pretreatment steps include a solvent degrease and manual deoxidisation by
abrasion or grit-blasting. The paste etches can be difficult to apply or rinse. They
generally provide good initial bond strengths but poorer durability than the factory
etch processes.
Pasa-Jell 105 ([email protected] Division of PRC-DeSoto International) is an
inorganically thickened blend of acids, activators and inhibitors that is specified in
many aircraft repair manuals. Durability results obtained using Pasa-Jell 105 are
much better than the simple hand cleaning approaches but are inferior to those
obtained using the factory optimised FPL etch and PAA processes as well as
PANTA [87].
The P2 paste etch uses a thickened version of the factory P2 solution and delivers
performance similar to that obtained with the chromic-sulphuric etches. Ideally, a
corrosion-inhibiting adhesive primer is applied after rinsing and drying the repair
surface.
3.8.2.3. Chromate conversion coatings
Certain conversion coating processes that are primarily intended to promote the
adhesion of paint to aluminium have been used as prebond treatments. In general,
conversion coatings should not be used where good adhesive bond durability [loo]
and cohesive failure modes [loll are desired. The best results employ a 2%
hydrofluoric acid etch prior to conversion coating within 15min of the etch [loll.
Durability results show the process can be superior to Pasa-Jell 105 but inferior to
factory processes and PANTA. Although the 2% hydrofluoric acid method has
been included in aircraft repair manuals, it is really no longer a viable on-aircraft
surface preparation due to the hazardous chemicals involved.
3.8.2.4. Silane surface preparation
The application of y-glycidoxypropyltrimethoxysilane coupling agent following
grit-blast produces very good durability results [60-62]. The silane coupling agent is
applied from a dilute aqueous solution which deposits an ultrathin layer that
dramatically improves the durability of adhesive bonds formed with a grit-blasted
aluminium surface (Figure 3.7). The fundamental chemistry that explains the
mechanism of the silane layer is explained in Section 3.5.4. Versions of the gritblast/silane surface preparation, known as the “Australian Silane Surface
Treatment”, are popular for aluminium treatment for repair bonding applications
worldwide. The primary reason for the use of the silane treatment is the ability to
achieve high-performance bond strength and durability without the use of acids
that can be problematic for on-aircraft processing. Application of BR 127
chromate-containing primer after the silane surface treatment can offer improved
durability in applications where harsher environmental conditions may be
experienced.
Advances in the bonded composite repair of metallic aircraft structure
74
n
E
E
4E
100% Adhesive
-
EI
v
Pasa-Jell 105
60
~~~0~~
Silane
-
x . .. - - - - -. - - -
0
V
40
L
-
l&e~.
-0
100% Cohesive
20 L
0
5
10
15
20
Root time (hrs"')
Fig. 3.20. Wedge test data comparing the relative durability performance of the PANTA, Pasa-Jell 105
[lo21 and Silane on-aircraft [62] surface treatment processesfor BR 127-primed A1-7075-T6 alloy bonded
with FM 73 adhesive and tested at 50°C/95% RH.
The relative performance of PANTA, Pasa-Jell 105 and silane on-aircraft
aluminium surface preparations are indicated by the wedge test data shown in
Figure 3.20 for BR 127-primed A1-7075-T6 alloy bonded to FM73 adhesive
[62,102]. The failure modes for each treatment are also indicated on the plot.
3.9. Surface preparations for titanium adherends
Titanium alloys are found in specialised aerospace applications due to their high
strength-to-weight ratios, retention of mechanical properties at elevated temperatures (exceeding 400 "C),excellent fracture toughness and corrosion resistance
[1031. The most widely-used aerospace titanium alloy, Ti-6A1-4V, will be the focus
of this discussion.
As with aluminium, moisture is the environment of primary concern, limiting the
long-term durability of the bonded joint. Long-term exposure to high temperatures
is also a durability concern for titanium bonded joints.
3.9.1. Factory processes
Most factory processes for titanium surface preparation involve etching or
electrochemical anodisation in acidic or alkaline baths. The best durability
performance is obtained when the treatment creates microroughness, moderate to
good durability is obtained with treatments generating macroroughness and poor
durability performance is generally obtained with smooth titanium surfaces [1031.
Plasma spray is one potential nonetching factory treatment, driven by the need to
find a surface preparation for titanium that can withstand long-term exposure to
Chapter 3. Surface treatment and repair bonding
75
elevated temperatures. Good durability results have been obtained when Ti-6A1-4V
powder was sprayed on the same alloy. A microscopically rough metallic film is
deposited. Its morphology is more random than those obtained with the chemical
treatments, having deep pores and many knob-like protrusions [104].
3.9.1.1. Chromic acid anodise (CAA)
The CAA process is a widely utilised and accepted process for prebond treatment
of titanium, particularly Ti-6A1-4V. CAA leaves a durable, porous layer of
amorphous Ti02 that is microrough to increase surface area for physical and
chemical bonding [103]. Both 5-volt and 10-volt CAA processes exist. These differ
from the CAA procedures used for aluminium preparation since they contain
hydrofluoric acid. A study conducted by the U.S. Navy in 1982 found the 5-volt
CAA process to provide the best overall moisture durability as determined by the
wedge test (ASTM D 3762) with conditioning at 60°C and 100% (condensing)
relative humidity. Four epoxy film adhesives, 121 "C-curing and 177 "C-curing,
were used. For the study, various organisations provided treated titanium panels to
the U.S. Navy for testing. The 10-volt process also provided very good durability
[105]. Although there is regulatory pressure in many areas to eliminate the use of
hexavalent chromium, the CAA process is still popular. Its use will likely decline
when a high-performance alternative is identified.
3.9.1.2. Phosphate fluoride
Several phosphate fluoride procedures have been developed. Although phosphate fluoride treatments are still used for titanium prebond surface preparation,
long-term durability is generally not good. These processes ranked at the bottom of
the 1982 U.S. Navy study, with markedly poorer wedge test results than the other
processes evaluated [105].
3.9.1.3. Pasa-Jell 107-M
Pasa-Jell 107-M is a proprietary ([email protected] Products Division of PRC-DeSoto
International) blend of mineral acids (nitric and chromic), activators and inhibitors
that is specifically formulated for treatment of titanium. It is intended to clean and
chemically activate the titanium surface to improve chemical bonding of the adhesive
or primer. The process, including rinsing, is conducted at ambient temperature (less
than 38 "C) [1061. Pretreatment steps include degreasing and mechanically abrading
the titanium surface. Solvents or alkaline cleaners can be used for the former. Dry or
wet abrasive blasting with aluminium oxide grit is recommended for the latter. In the
1982U.S. Navy evaluation, the Pasa-Jell107 process, preceded by a liquid hone step,
provided very good wedge test durability, refer to Figure 3.21. This treatment ranked
just behind the 10-volt CAA process [105]. The dry blasting step prior to Pasa-Jell
107 treatment produced poorer durability.
3.9.1.4. [email protected] 5578
[email protected] ([email protected] Division of Henkel Surface Technologies)
is an alkaline etchant containing sodium hydroxide. The process, including rinsing,
E
B
W
/
90 :
SOL
d
P*'
-.-
4- -0-
01
/
-
-- 100% Adhesive
- CAA(5V)
+- Phosphate Flouride
Root time (hrsoe5)
Fig. 3.21. Wedge test data comparing the relative durability performance of the CAA, Phosphate
Fluoride, Pasa-Jell 107M and TURCOR 5578 factory-based surface treatment processes for Ti-6AI-4V
alloy primed with BR 127, bonded with FM 300K adhesive and tested at 6O0C/1O0% RH (1051.
is conducted at elevated temperature (80-95 "C). [email protected] 5578 can be used to
remove contaminants and evenly etch titanium surfaces. It does not contain
chromates, phenol or hydrofluoric acid [107]. The [email protected]5578 process does not
etch titanium as quickly as the common acid etchants and it is slightly more
difficult to maintain in the process tank, however, it does not cause the hydrogen
embrittlement that can be a concern with acid etchants. Although the [email protected]
5578 process was not found to produce a great deal of microroughness on the
treated titanium surface [103], the US Navy showed that it provided very good
wedge test durability, similar to the two CAA processes [105].
Five factory titanium surface preparations are compared on the basis of wedge
test data indicated in Figure 3.21 for BR 127-primed Ti-6A1-4V alloy bonded with
FM 300K adhesive [105]. The failure modes for each surface treatment are
indicated in the plot.
3.9.2. On-aircraft processes
Due to restrictions imposed by the on-aircraft environment, there are fewer
titanium treatment options. The key on-aircraft challenges are the inability to use
an elevated-temperature process, the difficulty in containing and rinsing the highly
acidic or alkaline etchants and controlling hazardous materials. Although onaircraft CAA could be conducted in a manner similar to on-aircraft PAA for
aluminium, this does not appear to be common. The viable options for on-aircraft
repair include grit-blasting, Pasa-Jell 107 (a thickened version of the tank etchant)
and grit-blast/silane identical to the process used for aluminium (Section 3.8.2.4).
Chapter 3. Suqace treatment and repair bonding
11
3.9.2.1. Grit-blasting
Grit-blasting is often used as a stand-alone titanium prebond treatment [108]. In
contrast to the case for aluminium, grit-blasting treatment of titanium is one of the
best procedures for obtaining good initial joint strength. For this reason and the
fact it is relatively easy and nonhazardous, grit-blasting is often used for on-aircraft
titanium treatment. However, although adequate joint durability can often be
obtained, long service life in moisture or other aggressive environments requires
alternate approaches [31]. It is best to use grit-blasting as a pretreatment step for
Pasa-Jell 107 or the silane process.
3.9.2.2. Pasa-Jell107
The paste version of Pasa-Jell 107 (inorganically thickened Pasa-Jell 107-M)
can
be used to treat titanium on aircraft since it is an ambient-temperature process.
Pretreatment via grit-blasting with aluminium oxide is required for best durability
performance. Care must be taken to contain the acid and properly rinse the aircraft
components after etching.
3.10. Surface preparations for steel adherends
Surface preparations for steels, particularly chemical treatments, are greatly
influenced by the nature of the substrate and its initial condition. The large number
of steels makes the objective of achieving a universal treatment difficult [108]. The
approach of intentionally forming a coherent, adherent oxide with fine
microroughness on the surface of steel is not an effective strategy for good
adhesion [108].
In general, the important factors for steel surface preparation are cleanliness and
descaling or rust and oxide removal, and passivation for stainless steels [109]. Care
must be taken during the preparation process, since many steel alloys rapidly form
surface oxides. For instance, drying cycles after treatment can be critical. Also,
alcohol is often found in treatment solutions, and alcohol rinses may be used after
water rinses. Primers are also desirable to help protect the bonded joint from
moisture attack [I lo].
3.10.1. Factory processes
For surface preparation, three general approaches exist: mechanical abrasion,
chemical etching and conversion coating.
3.10.1 . I . Grit-blasting
The formation of a macro-rough surface using grit-blasting is a very common
surface treatment for steels. Angular alumina grit is often used for this process.
This approach can readily yield good, reproducible initial bond strengths [3 13 and
adequate durability may be realised for many applications. However, to obtain the
longest service life, additional treatment is usually required [3 1,1081.
78
Advances in the bonded composite repair of metallic aircraft structure
3.10.1.2. Acid etches
The morphologies produced on acid-etched steel surfaces are a function of the
steel microstructures. Acid etchants can create surface roughness by attacking the
grain boundaries of the metal. Some of these processes include the following: nitricphosphoric acid, phosphoric acid-alcohol, chromic acid, nitric-hydrofluoric acid,
sulphuric acid-sodium dichromate, sulphuric acid-sodium bisulphate, oxalicsulphuric acid and hydrochloric acid-ferric chloride [108,110,111]. Many of the
acid etches leave a deposit of carbon, known as smut, on the steel surface.
Therefore, a desmutting step, typically using another acid, must also be conducted.
It has been suggested that chemical etches for steels, other than stainless, are not
desirable. The many different etches investigated do not tend to outperform gritblasting, even in durability testing. The ultimate performance for stainless steel
bondedjoints is obtained when the steel is chemically treated, although little is known
about the mechanisms that lead to this improved performance [31]. Furthermore,
there is no consensus regarding which treatment is best for a particular alloy.
3.10.1.3. Conversion coatings
Corrosion-resistant conversion coatings are available for steel and are used as
treatments prior to painting. Several of these have also been evaluated for adhesive
bonding applications. Wegman found the conventional phosphate coatings for
steel did not provide adequate bond durability and were adversely affected by
elevated-temperature adhesive cure cycles [1113. Improved results are obtained
when the phosphating process is closely controlled [108,lllJ.
3.10.2. Omaircraft processes
Preparation of steel is even more difficult for on-aircraft adhesive bonding. Most
of the factory processes are impractical since they rely on strong acids, typically
used at elevated temperatures. Grit-blasting is a viable option for on-aircraft repair
of steel as it was for titanium. In order to improve environmental durability, a
corrosion-inhibiting adhesive primer should be applied.
The silane surface preparation successfully employed for numerous aluminium
repair applications can also be used to treat many steel substrates. The process is
the same as that used on aluminium. It can also be used as a factory treatment for
steel. The silane surface treatment has been applied successfully to prepare D6AC
steel wing skin surfaces for bonded repair using boron/epoxy patches bonded with
epoxy adhesive [1121.
3.1 1. Surface preparations for thermosetting-matrix composites
Many types of composite materials exist and, as with metals, the nature of the
adherend to be bonded determines the best surface preparation. The types of
composites used in structural applications in the aerospace industry are typically
fibre-reinforced thermosetting resins. The fibres contribute strength and stiffness to
Chapter 3 . Surface treatment and repair bonding
19
the composite while the resin matrix transfers loads. This discussion concentrates
on epoxy matrices reinforced with graphite or boron fibres and bonded with epoxy
adhesives.
While most people realise adhesive bonding of metal structures requires strict
adherence to proper processes, many pay little attention to the need for proper
processing for adhesive bonding of composite adherends [113]. Obviously, surface
preparation of composites is critical since, impact damage aside, the only in-service
failures of bonded composite structures have been interfacial and most relate to
durability problems. The durability issue primarily concerns marginal surface
preparations that typically result in some surface contamination [3 11. Weak initial
bonds cannot be nondestructively tested, and in-service loading may lead to bond
failure [1131.
Two main techniques are used to prepare thermosetting matrix composites for
bonding: (1) the peel-ply method and (2) solvent cleaning and abrasion, often
conducted after a peel-ply surface has been exposed [114].
Solvent cleaning followed by mechanical abrasion is the primary means to remove
contamination from a composite surface. For badly contaminated surfaces, a
solvent-soak process using reagent-gradeacetone has been recommended [115].If the
condition of the surface is poor, Scotch-Brite abrasion may be employed. Pumice has
also been used as an abrasive. Deionised water should be used, especially for the final
rinsing, to prevent surface contamination [115]. The standard waterbreak test can be
used to verify cleanliness of the composite surface [113].
Grit-blasting should be conducted after abrasive scrubbing and/or solvent
degreasing procedures. A light grit-blast with aluminium oxide results in optimal
bond strengths with a minimum of variability [115]. Practice is essential, and
limiting the blast pressure is critical to preventing surface damage. Very little
material should be removed, and the blasted surface should have a dull or matt
finish [115]. A pressure of 140 kPa has been recommended using No. 280 dry
alumina grit [1151.
Manual abrasion with 80-120 grit aluminium oxide paper can be employed as an
inferior alternative to grit-blasting. If the composite surface ply is unidirectional,
sanding should be in parallel with the fibres to minimise damage [114].
Removal of the grit and other debris can be achieved by a pressurised jet of
clean, dry nitrogen or air, or wiping. Dry-wiping is preferred given the potential for
solvent wiping to recontaminate the surface (refer to Section 3.4.3). Hart-Smith et
al. [115] suggest a final cleaning operation with isopropyl alcohol since it is more
miscible in water than the stronger solvents and can be removed by rinsing with
deionised water, then waterbreak tested. The present authors recommend dry
removal of blasting residue followed by a waterbreak test using deionised water.
Composite surfaces must be dry as well as cleaned prior to bonding. After the
waterbreak test, the surface should be dried at 120°C [113]. However, the real
moisture problems result from environmental moisture absorbed by the matrix
resin. Drying times depend on the laminate thickness. For example, laminates
6.3 mm thick require 24 h of drying at 135 "C to enable the moisture to migrate out.
It is most important to dry laminates slowly and thoroughly prior to bonding at
80
Advances in the bonded composite repair of metallic aircraft structure
elevated temperature. Special care should be taken if honeycomb or foam core is
present since any moisture in the cells could convert to steam and destroy the
component. Drying temperatures should be limited to 70 "Cin these cases [115].
Following surface preparation and drying, composite substrates are sometimes
primed prior to bonding to take advantage of flow and wetting properties of the
primer [1151. However, priming does not necessarily improve bond performance.
3.11.1. Precured patches
Precured patch preparation typically involves peel ply removal prior to bonding.
Debate continues as to the type of peel ply that should be used and whether
additional treatment is needed after peel ply removal [3 1,113,1161.
The peel ply can prevent gross contamination of the patch surface up to the time
it is removed. In principle, the peel ply should tear a very thin layer of resin from
the composite to create a fresh clean surface. However, peel plies, particularly
nylon [1161and those using release agents, have the potential to transfer material to
the composite surface. Peel plies containing silicone release agents must be avoided.
Although polyester peel plies seem to be better than nylon, the best approach for
patch preparation is a light grit-blasting step [I 161.
3.12. Recent surface preparation research
Few advances in metal prebond surface preparation technology were made during
the 15 years following the aluminium treatment work conducted in the late 1970sas
part of the United States Air Force PABST program. Acid etch and anodisation
processes continued to form the basis for durable bonded joints. A notable
exception were the silane surface preparations developed for on-aircraft repair
bonding by the Defence Science and Technology Organisation (DSTO) in Australia.
In the 1990s, the need to develop environmentally friendly processes and better
methods for high-temperature titanium bonding spurred new interest in the area.
In 1993, the Materials and Manufacturing Directorate of the United States Air
Force Research Laboratory (AFRL/ML) became active in metal surface
preparation research and funded multiple efforts through 1997. The technologies
investigated included excimer laser, plasma polymerisation, ion beam enhanced
deposition (IBED), plasma spray and sol-gel [117]. The focus was on structural
adhesive bonding of aluminium, titanium and stainless steel alloys using epoxy
adhesives. The sol-gel work clearly showed the greatest potential for application
due to its performance as well as scale-up potential. For this reason, AFRL focused
its efforts on optimising sol-gel technologies.
3.12.1. Sol-Gel technology for adhesive bonding
The area of sol-gel chemistry represents a branch of polymer science that, beyond
silicones, has only recently been exploited for aerospace applications [118]. The
Chapter 3 . Surface treatment and repair bonding
81
term “sol-gel’’ is a contraction for solution-gelation and refers to a series of
reactions where soluble precursors (typically metal alkoxides, substituted metal
alkoxides or metal salts) undergo hydrolysis and condensation to form a sol and
then crosslink to become a gel. This crosslinked structure can be deposited as a
coating and consolidated by dehydration. Many different metal atoms can be used
to produce films with a wide variety of properties. Organic functionalities can be
attached to the hybrid metal-oxygen framework to create organometallic polymer
systems with even more diversity.
Sol-gel technology has the potential to revolutionise metal adhesive bonding by
providing an environmentally compliant, high-performance, simple and inexpensive approach for surface preparation [118]. One of the big advantages to sol-gel
chemistry is its versatility and the ability to be tailored for specific applications.
Solution chemistry can be controlled to vary deposited film density, porosity and
microstructure. Ideally, adhesion is via direct chemical bonding at the coating/
substrate interface as well as the coating/adhesive interface [1191.
Several sol-gel chemistries are under development by a number of organisations
[120,121]. AFRL has focused its efforts on technology that leads to a surface
preparation similar to the existing silane processes while using a more reactive
water-based silicon-zirconium chemistry [118,122,1231. This approach is intended
to improve performance while eliminating the need for grit-blasting pretreatment
and elevated temperature cures [124].
As with the silane preparations, sol-gel chemistry investigated by AFRL
eliminates the dependency on strong acids and bases. Also, there are no power
requirements as required for anodisation, and wastewater is greatly reduced over
conventional wet chemistry approaches since rinsing is not required. There is no
need for hexavalent chromium in the sol-gel process, and it may be possible to
eliminate chromates from the priming step. Formulations that contain both the solgel and primer constituents in one solution that can be applied via spraying or
brushing, after pretreatment consisting of degreasing and manual abrasion, are
being developed and evaluated [1251. Simple on-aircraft repair versions intended
for use in repair bonding of noncritical structure are being evaluated, without
adhesive primer, and show promise with both film and paste epoxy adhesives [126].
Sol-gel methodologies are being evaluated for adhesive bonding applications for
factory, rework and on-aircraft applications. In limited situations, the technology
has already been implemented for several applications, primarily to treat titanium.
Repair demonstrations conducted on several aircraft included the treatment of
aluminium, titanium and steel.
3.12.2. Hot solution treatment for adhesive bonding
A process termed the “Hot Solution” treatment has been developed at DSTO
also in response to the need for environmentally friendly surface treatments. The
process involves immersion of aluminium alloys in boiling water followed by
immersion in a 1% solution of epoxy silane. Wedge test experiments indicate that
82
Advances in the bonded composite repair of metallic aircraft structure
the durability of this treatment may perform as well as phosphoric acid anodisation
for some aluminium alloy and epoxy adhesive combinations [127].
Fundamental research has identified that optimum durability is achieved for
immersion of the aluminium between 4min and 1 h in the distilled water heated to
between 80 "C and 100 "C.These conditions enable a platelet structure to grow in
the outer film region, which, combined with the formation of hydrolytically stable
adhesive bonds made to the epoxy silane, appears to be critical in the development
of the excellent bond durability [127].
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123. Ma=, J., Gaskin, G., DePiero, W., et al. (2000). Faster durable bonded repairs using sol-gel
surface treatment. Proc. the 4th Joint DoDIFAAINASA Con$ on Aging Aircraft, St. Louis MO,
May.
124. McCray, D.B. and Mazza, J.J. (2000). Optimization of sol-gel surface preparations for repair
bonding of aluminum alloys. Proc. 45th Int. SAMPE Symp. and Exhibition, Long Beach CA, May,
pp. 53-54.
125. Blohowiak, K.Y., Osborne, J.H., Krienke, K.A., et al. (1997). DODIFAAINASA Conf. on Aging
Aircraft Proc., July 8-10, Ogden UT.
126. McCray, D.B., et af.(2001). An ambient-temperatureadhesive bonded repair process for aluminum
alloys. Proc. 46th In?. SAMPE Symp. and Exhibition, Long Beach CA, May, pp. 1135-1 147.
127. Rider, A.N. and Arnott, D.R. (2000). Int. J. Adhes. and Adhes., 20, p. 209.
Chapter 4
ADHESIVES CHARACTERISATION AND DATABASE
P. CHALKLEY
and A.A. BAKER
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
4.1. Introduction
The design of a bonded repair is often more demanding than the ab initio design
of a bonded structure. For example, secondary bending in the repair, often induced
by the repair patch itself, can lead to the development of detrimental peel stresses in
the adhesive. Such stresses can be avoided or at least minimised in the early design
stages of a bonded panel so that the adhesive is mainly loaded in shear. For bonded
repair then, assuming the adhesive determines patch performance, a greater range
of allowables data is needed for the adhesive from pure shear through shear/peel
combinations to pure peel.
However, while the stress-strain properties of the adhesive largely determine the
efficiency of load transfer into the patch, there are several possible modes of failure
of the bond system, including:
0 The adhesive
0 The adhesive to metal or composite interface
0 The adhesive to primer interface
0 The surface matrix resin of the composite
0 The near-surface plies of the composite.
Obviously the failure mode that occurs will be the one requiring the lowest driving
force under the applied loading. Where more than two or more modes have similar
driving forces then mixed mode failure will result.
In this chapter it is assumed that the primary failure mode is cohesive failure of
the adhesive layer. This is a reasonable assumption for static loading for wellbonded metallic adherends, in this case with a metallic patch. However, for
composites, such as boronlepoxy or graphitelepoxy, failure at low and ambient
temperature is often in the surface resin layer of the composite. The tendency for
87
Baker, A.A., Rose, L.R.F. and Jones, R. (eds.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 0 2002 Published by Elsevier Science Ltd. All rights reserved.
88
Advances in the bonded composite repair of metallic aircraft structure
this mode of failure to occur will increase with low adhesive thickness, the presence
of peel stresses, low temperatures and under cyclic loading [l].
At high temperature and particularly under hot/wet conditions, the mode may be
expected to change to one of cohesive failure in the adhesive, even with composite
adherends since the matrix of the one of composite is generally more temperature
resistant than the adhesive.
Thus the test methods outlined here to determine the static properties of the
adhesive should provide useable design allowables for static strength of
representative repair joints with metallic patches and in some circumstances with
composite patches. The methods are also required for determining the stressstrain
properties of the adhesive and thus the reinforcing efficiency of the patch prior to
failure.
Stress-strain and fracture mechanics type allowables are considered. Having
identified which design allowables are needed, typical manufacturers’ data,
including results from the more common ASTM tests, are examined for their
suitability (or lack of) for providing useful design allowables. Such data is often
found wanting and more suitable test methods for obtaining allowables are
suggested. Finally, a data set of some design allowables for one of the more
commonly used repair adhesives is tabulated.
The best approach for fatigue and other complex loading conditions is to obtain
the design allowables from representative joints, as discussed in Chapter 5.
4.2. Common ASTM and MIL tests
Manufacturers’ data sheets often report a variety of ASTM, MIL and other
standard test results. ASTM and MIL test specimens and methods cover the full
spectrum of stress states and loading regimes that can occur in adhesively bonded
joints, but most suffer from severe stress concentrations and combined stress states.
Consequently, while useful for ranking the performance of adhesives, this data
cannot be used for bonded repair design because it contains little or no
fundamental strain-to-failure or fracture mechanics information.
For example, the data sheet for the Cytec adhesive FM300-2 contains results
obtained from tests performed according to US Military Specification MIL-A25463B and US Federal Specification MMM-A-132A (now superseded by MMMA-132B). Tests include single-lap shear, T-peel, fatigue strength and creep rupture.
For honeycomb structure applications, tests include sandwich peel, flatwise tensile,
flexural strength and creep detection. The test results reported are useful for
ranking adhesives but do not provide adhesive allowables. For example, stress
analyses of the single-lapjoint [2], reveal pronounced stress concentrations near the
ends of the joint and shear and peel stresses. The “shear strength” value that is
obtained by dividing the failure load of the single-lap joint by its bond area is
something of a misnomer in that failure is caused by a combination of peel and
shear stresses. Also, these stresses are far from uniform over the area of the bond.
Other standard ASTM and MIL-A-25463B tests have similar limitations.
Chapter 4. Adhesives characterisation and data base
89
A useful set of test data now provided by many manufacturers and which is
provided with the adhesive FM300-2 is shear stress-strain data. This data is usually
obtained from the testing of thick-adherend lap shear specimens and the techniques
used are now the subject of an ASTM standard: ASTM D5656. This test is
described in the next section.
4.2.1. Stress-strain allowables
h situ test data for the adhesive (data obtained from testing bonded joints) is
required for the generation of adhesive material allowables because of the highly
constrained state of the adhesive in a joint. Neat tests, in which the adhesive is free
to undergo Poisson’s contraction, may yield inaccurate allowables for the
performance of an adhesive in a joint, particularly on strain-to-failure. Pure shear
test data is most commonly used to design adhesive joints, whereas most practical
joints experience both triaxial direct stressing and shear.
4.2.1.1. Static loading
Pure shear
Test specimen types most commonly used to obtain pure shear stress-strain data
include:
0 Napkin ring (ASTM E229)
0 Iosipescu [3]
0 Thick-adherend (ASTM D5656).
The thick-adherend test, Figure 4.1, is most widely used because of its ease of
manufacture and testing. Stress concentrations present in this specimen [2] are
limited in range and alleviated by plastic yielding of the adhesive. Consequently, a
more uniform stress field conducive to obtaining material property allowables is
obtained. Allowables and design data such as strain-to-failure, ultimate shear
strength, yield stress and shear modulus can be obtained from this test. The
manufacturer may also provide data from tests performed at various temperatures
and after saturation of the adhesive with moisture.
However, the test may not suitable for brittle adhesives because of the stress
concentrations near the ends of the bondline [4]. For most structural adhesives,
however, especially those that are rubber-toughened, the thick-adherend test is
more than adequate [5,6]. This technique has been adapted to provide data on the
strain rate sensitivity of adhesives [7].
An international standard similar to ASTM D5656 is I S 0 11003-2 “Adhesives Determination of Shear Behaviour of Structural Bonds, Part 2: Thick-Adherend
Tensile-Test Method”. The I S 0 standard advises the use of extensometers similar
to those recommended in ASTM D5656. The major difference between the two
standards is in the geometry of the specimen. The specimen in I S 0 11003-2 has a
shorter overlap length and thinner adherends than the specimen in ASTM D565695. The types of design allowables that can be obtained from shear stress-strain
testing depend on the design method followed. If the Hart-Smith design
methodology [8] is used the adhesive is idealised as elastic/perfectly plastic. The
Advances in the bonded composite repair of metallic aircraft structure
90
T
7
30;
20 -
10-
0-
I
I
0.0
,
I
0.2
0.1
I
0.3
I
0.4
t
Fig. 4.1. Schematic diagram of the thick-adherend test and shear stress-shear strain curves for adhesive
FM 73 at two temperatures obtained using this specimen, taken from reference [9].
advantage of this technique is that relatively simple design formulae result and that
the ability of the adhesive to undergo considerable plastic flow and thus lead to
higher joint strengths is incorporated. Since, as Hart-Smith argues [SI, the
maximum potential bond strength is determined by the ultimate adhesive strain
energy in shear per unit bond area (area under the shear stress/shear strain curve),
the type of idealisation is not as important as the value of the ultimate shear energy
(provided this is preserved in the idealisation). The type of design allowables
obtainable using this method are listed in Table 4.1.
These allowables and their relationship to an actual stress-strain curve are shown
in Figure 4.2.
Table 4.1
Hart-Smith’s stressstrain design allowables.
Design allowable
Symbol
“elastic” shear strain limit
plastic shear strain
plastic shear stress (MPa)
modulus in shear (MPa)
Ye
YP
2,
G
Chapter 4. Adhesives characterisation and data base
91
1 fLI
I I
/i
/
liL
actual stress
strain curve
Hart-Smith elastidperfectly
plastic idealisation
I /
Y
Fig. 4.2. Hart-Smith [8] type idealisation of an adhesive stress-strain curve
Pure tension
Obtaining in situ measurements of the stress-strain behaviour of adhesives in
bonded joints is problematic because of the triaxial stresses developed at the joint
edges [lo]. The stress concentration at the edges of butt joints renders the data
obtained invalid for design purposes. Data can be obtained from neat adhesive
specimens but care must be taken in its use. Such data can be used only in the
context of a material deformation model that accounts for the highly constrained
nature of the adhesive in a bonded joint (see the next section) and the strain rate.
Figure 4.3 shows some neat stress-strain data obtained at two different strain rates.
Similar data can be found in other work [ll].
Combined shear-tensionlcompression
The actual stress state of the adhesive in a bonded repair is most likely to be one
of combined shear and tension/compression. Repairs to curved surfaces can
develop large through-thickness tensile stresses in the adhesive layer as well as shear
stresses, Chapter 7. However, even repairs to flat surfaces will develop these stresses
though to a lesser extent. Also, the relatively low modulus adhesive is constrained
92
Advances in the bonded composite repair of metaNic aircraft structure
IS
rate
--A-- ~ O - ~ strain
-0-
10% strain rate
h
---A
u
o
;
:A l l "
m
a
30-
u)
20 -
E.
!??
-Y
u)
10 -
0-
-0.005 0.000 0.005 0.010 0.015 0.020 0.025 0 30
strain
Fig. 4.3. FM73 adhesive tensile test results (specimens not taken to failure).
by stiff adherends and this imparts a triaxial constraint on the adhesive leading to
the development of hydrostatic stresses within the adhesive.
The adhesives used in bonded repairs are often required to carry a high level of
stress and may suffer yielding. Since the yield behaviour of many polymers is
known to be sensitive to hydrostatic pressure, it is no surprise that the yield
behaviour of the Cytec adhesive FM73 is also pressure sensitive. Clearly, a yield
criterion that can properly account for the effect of hydrostatic stresses is needed
for bonded repair studies. A recent study [12] of the in situ yield behaviour of the
adhesive FM73 subject to combined shear-tension/compression showed that the
modified Drucker-Prager/Cap Plasticity model correlated best with measured data
for the adhesive FM73. The Drucker-Prager/Cap Plasticity model is more
commonly associated with geological materials but performed better than more
conventional models modified to include pressure sensitivity such as the modified
von Mises and the modified Tresca models. The specimen used in this study was a
modified Iosipescu specimen [131, which was capable of applying combined shear
and peel stresses. Yield data from a range of shear and peel stress combinations
were obtained. Various yield criteria, some such as von Mises and Tresca modified
to include pressure-dependent yield, have been proposed [14,151 for adhesives. The
Drucker-Prager criterion has also been proposed [16]. However, as shown in
Figures 4.4 and 4.5 (from reference [12]), the modified Drucker-Prager/Cap
Plasticity works best for the rubber-modified structural epoxy adhesive FM73 (the
modified Tresca is very similar to the modified von Mises plot).
Thus for design of bonded repairs that are subject to complex loading, the
multiaxial material model used should be the modified Drucker-Prager/Cap
Plasticity model. This type of yield criterion can be implemented in a finite element
code such as ABAQUS [17]. The parameters (for details on the physical meaning of
these parameters see references [12,17]) needed for this criterion are given in Table
4.2.
Chapter 4. Adhesives characterisation and data base
1
3 40a .
I
'
I
~
z. 35- i
I
'
l
.
l
f
shear
compression
$ . neat
6 30- compression
v)
a , pure shear
% 25-
rm
c
s
151
.$
10-
m
u
W
.
l
93
.
l
t
hear tension
neat tension
r,
= 38.6 + 1 . 1 3 " ~
constrained tension
.
-.-
-
Hydrostaticpressure (negative value of), -p, (MPa)
Fig. 4.4. Modified von Mises yield criterion curve fit.
80
X
Neat tension
Neat compression
Constrained tension
Constrained shear-compression
Constrained shear-tension
Constrainedsimple shear
Linear Drucker-Prager surface
Transition yield surface
Compressionyield surface
"
-3 0
-1 5
0
15
30
Hydrostatic pressure p (MPa)
Fig. 4.5. Modified Drucker-Prager/Cap Plasticity curve fit.
Although yield stress data does exist, there is little strain-to-failure data under
complex loading for adhesives. Current design practice is to knockdown pure shear
data by a factor as much as one half. This is clearly an area that needs further
development but is complicated by the triaxial stress states that develop in bonded
joints when any stress state other than pure shear is applied.
94
Advances in the bonded composite repair of metallic aircraft structure
Table 4.2
Modified Drucker-Prager/Cap plasticity parameters for FM73.
0.778
69.3
86.5
8.0
1.0
0.18
4.3. Fatigue loading
Fatigue data ideally should be gathered from a bonded joint that is
representative of the repair under design, and this approach for composite
adherends is discussed in Chapter 5. However, simple endurance testing of
adhesives is often undertaken using the single-overlap shear specimen. Although
ASTM D3 166 describes a test method using a metal-to-metal single-lap joint for
investigating the fatigue strength of adhesives in shear, the actual stress state of
the specimen is one of combined peel and shear and the length of the overlap is
too short to properly reproduce the large strain gradients present in bonded
repairs.
For the model joints (which are designed to have uniform shear in the adhesive)
repeated cyclic stressing to high plastic strain levels can result in creep failure of the
joint after a relatively small number of cycles [18]. This is because cyclic shear
strains are cumulative. (If the cycle rate is high, full strain recovery cannot occur
during the unloading cycle.) The result is an accelerated creep failure of the
adhesive by a strain ratcheting mechanism. In practical lap joints this situation is
avoided by maintaining a sufficiently long overlap, so that much of the adhesive
remains elastic. The elastic region on unloading acts as an elastic reservoir to
restore the joint to its unstrained state preventing the damaging strain
accumulation. Fracture mechanics approaches to measuring fatigue properties
can also be taken as described in Section 4.4.3.
4.4. Fraeture-mechanics allowables
At present the use of fracture mechanics to evaluate the strength and durability
of adhesive joints is not highly developed. Its application is complicated by factors
such as geometric non-linearity in test specimens and mixed failure loci (cohesive
failure of the adhesive mixed with interfacial failure). Nevertheless, high loads may
induce static propagation of the disbond and similarly repeated loading can cause
fatigue. Consequently fracture mechanics design allowables may become useful.
The types of specimens useful for fracture mechanics studies of adhesive are shown
in Figure 4.6.
Chapter 4. Adhesives characterisation and data base
95
CLS
-L-Lh2
w
s
-
1
-
w
(0
a
STRAIN GAUGE
Y
w
K
>
W
Z
(0
k
W
0
0
s
MODE If STRAIN ENERGY RELEASE RATE
Fig. 4.6. Types of specimen used for measurement of fracture properties in laminated composites and
bondedjoints, showing the percentage of mode 1; adapted from reference [19]. DCB = double cantilever
beam, CLS = cracked Shear specimen, MMF = mixed mode flexural, ENF = edge notced flexural.
4.4.1. Static loading
If a disbond is present in a bonded repair then it is typically subject to mixed
mode loading (usually a combination of Mode I and Mode I1 and sometimes Mode
111). However, test standards only exist for Mode I loading. Since adhesives used in
repair are usually very tough (GIc > 2W/m2) static crack propagation in the
adhesive is unlikely for most repairs to composites where G I <~ 150J/mz.
4.4.2. Mode I
ASTM standard D3433 covers the measurement of Mode I fracture toughness.
Either flat or tapered adherend double-cantilever beam specimens can be used to
measure toughness. For toughened adhesives such as FM73 the value of toughness
varies with bondline thickness as shown in Figure 4.7 (tapered cantilever beam
results).
6
2000-
3
Q)
c
E
1500-
8
2E
1000-
$
C
500-
* .**.
n-
*
---
0.1 mm adhesive thickness
0.4 mm adhesive thickness
-
Q)
.-
C
E
0-
4-
ln
Fig. 4.7. Mode I fracture toughness of FM73 from a cantilever beam specimen (cure 8 h at 80 "C).
4.4.3. Mode I1 and mixed mode
Fracture mechanics testing of adhesives, from pure Mode I through mixed Mode
I/Mode I1 through to pure Mode I1 can be performed using the test specimen and
loading rig developed by Fernlund and Spelt [20]. Mode I1 tests, however, are
difficult to perform for most toughened adhesives as yield of metallic adherends
often occurs before the adhesive undergoes crack propagation.
4.4.4. Fatigue loading
Data on fatigue damage threshholds and crack propagation under fatigue
loading are most usually obtained from the fracture mechanics-type lap-joint tests
using an edge-notched flexural specimen [21] for Mode 11, the double-cantilever
beam specimen for Mode I and cracked lap-shear specimen for mixed mode (see
Figure 4.6). In these tests the rate of crack propagation in the adhesive is usually
plotted as a function of the strain-energy-release-rate range. The empirical
relationship between the range of strain-energy-release rate and the crack growth
rate is of the form:
da
-=AAG"
dN
,
where a is the disbond or crack length in the adhesive, N the number of fatigue
cycles, and AG the range of strain energy release rate for the relevant mode. The
parameters A and n are empirically determined constants. In the mixed-mode
specimens, Figure 4.8, it was found that the better correlation is with the total
strain energy range AGT, showing that Modes I and I1 contribute to damage
growth. Figure 4.8 shows a typical result for the adhesive FM 300.
Chapter 4. Adhesives characterisation and data base
97
loA -
IOd
-m
a
da
(I)
dN
0)
W
w
k-
mlcycle
10"
o-9
10-'O
-1
u
\I
8 150 - %..-...
5
W7
200
FM300
;
~
a.
DEBOND
G,,,= 87 j I m 2
NO DEBO"
w
98
Advances in the bonded composite repair of metallic aircraft structure
A G T was
~ taken as the strain-energyrelease range for a disbond propagation rate of
10-9m/cycle. For FM300 the value of AGTh was found to be 87J/m2 at this
propagation rate.
Generally, as shown in Figure 4.8(b), the correlation was very good between the
predicted and observed cyclic stress levels for disbond growth for the various taper
angles, indicating the potential of this approach for fatigue-critical joints having a
significant Mode I (peel) component. Sensitivity to adhesive thickness and other
joint parameters remains to be demonstrated.
4.5. FM73 database
4.5.1 In situ shear stressstrain allowables
To reduce thermal residual stresses in bonded repairs or to ease application
problems, a cure of 8h at 80°C of FM73 is often used in contrast to the
manufacturer's recommended 1 h at 120 "C.Thus in the test specimen this was the
cure temperature used and the pressure applied during cure was 100kPa also to
simulate in-field repairs. The surface treatment used was the standard solvent clean,
grit blast and application of aqueous silane-coupling agent [9]. The data from
testing 30 test specimens [9] at each test condition (-40 "Cdry, 24 "C dry and 80 "C
wet) is shown below in Table 4.3. It is reported in both the form recommended in
ASTM 5656 and in the form advocated by Hart-Smith (elastic-perfectly plastic
idealisation) - the latter being the more useful for design purposes. The standard
deviation is shown for the value reported.
Hart-Smith [8] type design allowables are shown in Table 4.4.
Table 4.3
FM73 stressstrain data [9] and standard deviations for three test conditions (8 h at S O T , lOOkPa
pressure cure condition).
Linear limit shear stress (MPa)
Linear limit shear strain
Shear modulus (MPa)
Knee value of shear stress (MPa)
Knee value of shear strain
Knee shear modulus (MPa)
Ultimate shear stress (MPa)
Ultimate shear strain
RT dry
-40 "C dry
80 "Cwet
27.34 f 1.21
0.0364 0.0022
805.47 f 38.84
39.22 f 0.96
0.0739 f 0.0028
530.7 f 23.9
39.14 f 1.76
0.5774 & 0.0475
27.23 f4.72
0.0302 f 0.0068
959 f 150
50.27 f 2.45
0.0688 f 0.0079
730.7 f 91.1
55.71 & 2.14
0.1870 f 0.0415
5.97 f 2.95
0.0207 f 0.0054
278 f 134
8.95 3.1 1
0.0546 f 0.0121
163.9 f 67.6
21.85 f 3.83
0.8630 0.1013
+
Chapter 4. Adhesives characterbation and data base
99
Table 4.4
Hart-Smith type design allowables for FM73 cured at 80 "C for 8 h.
Elastic shear strain
Shear modulus (MPa)
Yield stress (MPa)
Plastic shear strain
RT, dry
-4O"C, dry
80°C, wet
0.0804 k 0.0151
503 f 88
41.52 k 0.97
0.4970 k 0.0468
0.0723 f 0.0082
791 f 107
56.46 f 2.15
0.1192 f 0.0261
0.6616 f 0.1214
34.8 f 13.9
21.88 f 3.46
0.2014 & 0.1035
4.5.2. Yield criterion
A report by Wang and Chalkley [12] details an investigation of the yield
behaviour of FM73 (1 h at 120"Ccure). An experimental investigation, using the
modified Iosipescu specimen loaded at various angles and various neat adhesive
tests was undertaken. Yield criteria investigated include modified Tresca, modified
von Mises, modified Mohr-Coloumb, modified Drucker-Prager and modified
Drucker-Prager with cap plasticity. The last criterion was found to best fit the data
and the resulting yield parameters are shown in Table 4.5.
4.5.3. The glass transition temperature
Studies at AMRL using dynamic mechanical thermal analysis (DMTA) have given
the following estimates for the glass transition temperature of FM73 (Table 4.6).
Table 4.5
Modified Drucker-Prager/cap plasticity parameters for FM73.
K
fl (degrees)
d(MPa)
pa (MPa)
R
a
0,778
69.3
86.5
8.0
1.0
0.18
Table 4.6
Glass transition temperature data for FM73.
FM73 - 1h at 120°C cure
FM73 - 8 h at 80°C cure
99.7 "C
108.5 "C
Advances in the bonded composite repair of metallic aircraft structure
100
4.5.4. Fickean diffusion coeflcients for moisture absorption
Althof [24] gives the following data for the diffusion coefficients of FM73 (Table
4.7).
Althof's bulk adhesive film specimens had dimensions 1 mm x 60 mm x 10mm.
This size of specimen conforms to DIN 53445 (torsion-vibration tests). The
aluminium plate specimens had dimensions 5mm x 100mm, lOmm x 100mm,
20mm x IOOmm, and 30mm x 100mm. The number of specimens per data point
is not reported. Althof's data is also reported by Comyn [25], which an easier
reference to obtain.
Jurf and Vinson also give data for the adhesive FM73-M (FM73 having a matt
scrim) and their data is given in Table 4.8.
4.5.5. Mode I fracture toughness
Fracture toughness data for the 8 h at 80 "C-cure condition (24 "C test
temperature) is presented in Table 4.9.
Table 4.10 presents the fracture toughness measured for the 1 h at 120°C cure
condition.
Note that the 8 h at 80 "C cure of the adhesive results in a more brittle adhesive.
Table 4.7
Althof's [24] Fickean moisture diffusion coefficients for FM73.
(a)
Max.
moisture
content (%)
Diffusion coefficients
obtained from water
absorption by adhesive film
experiments (m's-')
Diffusion coefficients
obtained from in situ
absorption between
aluminium plates
experiments (rn's-')
70
95
70
95
95
95
1.1
2.0
1.2
2.5
2.5
1 0"
2.8
1.7
8.1
4.2
11.6
-
3.6
3.9
10.3
41.7
15.2
33.3
Relative
humidity
Temp
( "C)
20
20
40
40
50
70
10-l~
10-l~
10-l~
10-13
10-l3
10-13
10~3
10-13
10-1~
10-1~
10-l~
"Althof reports this value as an abnormal increase in moisture.
Table 4.8
Jurf and Vinson's [26] moisture diffusion coefficients for FM73-M.
Temperature
( "C)
Relative
humidity (%)
(rn's-I)
Diffusion coefficient
Saturation moisture
content (a)
38
49
60
71
95
95
95
95
6.2 x io-"
8.0 1 0 - l ~
8.7 10-13
9.8 10-13
1.55
2.05
2.20
2.30
Chapter 4. Adhesives characterisation and data base
101
Table 4.9
Author's mode I fracture toughness data for FM73 cured for 8 h at 80 "C.
Adhesive
thickness (mm)
Minimum fracture
toughness (J/m')
Maximum fracture
toughness (J/m2)
Average fracture
toughness (J/m2)
0.1
0.4
0.9
1113
1502
1906
1230
1790
2903
1172
1646
2405
Table 4.10
Mode I fracture toughness data for FM73 [27] (1 h at 120°C cure).
Temperature ("C)
21
-40
Mode I fracture toughness (J/m*)
3000
2700
References
1 . Chalkley, P.D. and Baker, A. (1999). Development of a generic repair joint for the certification of
bonded repairs. Int. J. of Adhesion and Adhesives 19, 121-132.
2. Anderson, G.P. (1984). Evaluation of adhesive test methods. In Adhesive Joinfs - Formation,
Characteristics and Testing (K.L. Mittal, ed.) Plenum Press, New York.
3. Wycherley, G.W., Mestan, S.A. and Grabovac, I. (1990). A Method for Uniform Shear StressStrain Analysis of Adhesives, ASTM JOTE, May.
4. Grabovac, I. and Morns, C.E.M. (1991). The application of the Iosipescu shear test to structural
adhesives. J. of Applied Polymer Science, 43, 2033-2042.
5. Renton, W.J. (1976). The symmetric lap-shear test - What good is it? Experimental Mechanics, Nov.
pp. 409415.
6. Tsai, M.Y.,Morton, J., Krieger, R.B., et al. (1996). Experimental investigation of the thickadherend lap shear test. J. of Advanced Materials, April, pp. 28-36.
7. Chalkley, P.D. and Chiu, W.K. (1993). An improved method for testing the shear stress-strain
behaviour of adhesives. Int. J. of Adhesion and Adhesives, 13(4), October.
8 . Hart-Smith, L.J. (1973). Adhesive-Bonded Double-lap Joints, NASA CR 112235, Douglas Aircraft
Company, McDonnell Douglas Corporation, Long Beach, California, USA.
9. Chalkley, P.D. and van den Berg, J. (1997). On Obtaining Design Allowables for Adhesives used in
the Bonded-composite Repair of Aircraft, DSTO-TR-0608, Defence Science and Technology
Organisation, Melbourne.
10. Adams, R.D., Coppendale, J. and Peppiatt, N.A. (1978). Stress analysis of axisymmetric butt joints
loaded in torsion and tension. J. of Strain Analysis, 13(1).
1 1 . Butkus, L.M. (1997). Environmental Durability of Adhesively Bonded Joints, Ph.D. Thesis, Georgia
Institute of Technology, September.
12. Wang, C.H. and Chalkley, P.D. (2000). Plastic yielding of a film adhesive under multiaxial stress.
Int. J. offdhesion and Adhesives, 20(2), April, pp. 155-164.
13. Broughton, W.R. (1 989). Shear Properties of Unidirectional Carbon Fibre Composites, Ph.D.
Thesis, Darwin College, Cambridge.
14. Haward, R.N. (1973). The Physics of G h s y Polymers, Applied Science Publishers Pty. Ltd.,
London.
15. Bowden, P.B. and Jukes, J.A. (1972). The plastic flow of isotropic polymers. J. of Materiais Science,
7, pp. 52-63.
102
Advances in the bonded composite repair of metallic aircraft structure
16. Chiang, M.Y.M. and Chai, H. (1972). Plastic deformation analysis of cracked adhesive bonds
loaded in shear. Int. J. of Soli& and Structures, 31,2477-2490.
17. ABAQUS (1997). Theory Manual, Version 6.5. Hibbitt, Karlsson & Sorensen Inc., U S A .
18. Hart-Smith, L.J. (1981). Difference Between Adhesive Behaviour in Test Coupons and Structural
Joints, Douglas Paper 7066, presented to ASTM Adhesives Committee, Phoenix.
19. Russell, A.J. and Street, K.N. (1985). Moisture and temperature effects on the mixed mode
delamination fracture of unidirectional graphitelepoxy. Delamination and Disbonding of Materials
( W . S . Johnson, ed.) ASTM STP 876.
20. Fernlund, G. and Spelt, J.K. (1994). Mixed-mode fracture characterisation of adhesive joints.
Composites Science and Technology, 50, pp. 4 4 4 4 9 .
21. Russell, A.J. Fatigue crack growth in adhesively bonded graphite/epoxyjoints under shear loading.
ASME Symposium on Advances in Adhesively Bonded Joints 1988, MD 6 (S. Mall, K.M. Liechti and
J.R. Vinson, eds.) (Book No G00485).
22. Lin, C. and Liechti, K.M. (1987). Similarity concepts in the fatigue fracture of adhesively bonded
joints. J. of Adhesion, 21, pp. 1-24.
23. Johnson, K.W.S. and Dillard, D.A. (1987). Experimentally determined strength of adhesively
bonded joints in joining fibre reinforced plastics (F.L. Mathews, ed.) Elsevier Applied Science
pp. 105-183.
24. Althof, W. (1980). The Diffusion of Water Vapour in Humid Air into the Adhesive Layer of Bonded
Metal Joints, DFVLR-FB 79-06, 1979 - RAE translation into English no. 2038, February.
25. Comyn, J. (1981). Joint durability and water diffusion. In Developments in Adhesives - 2 (A.J.
Kinloch, ed.) Applied Science Publishers, London.
26. Jurf, R.A. and Vinson, J.R. (1985). Effect of moisture on the static and viscoelastic properties of
epoxy adhesives. J. of Materials Science 20, pp. 2979-2989.
27. Baker, A.A., Chester, R.J., Davis, M.J., et al. (1993). Reinforcementof the F-111 wing pivot fitting
with a boron/epoxy doubler system - Materials engineeringaspects. Composites 24(6), pp. 51 1-521.
Chapter 5
FATIGUE TESTING OF GENERIC BONDED JOINTS
P.D. CHALKLEY, C.H. WANG and A.A. BAKER
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
5.1. Introduction
A certification process has been proposed El] (see also Chapter 22) based largely
on a generic approach to patch design, validation and the acquisition of materials
allowables. This approach includes testing of joints representing the repaired
region. This chapter reports on the development of and preliminary results for two
such generic bonded joints to be used in the validation process: the double overlapjoint fatigue specimen (DOFS)and the skin doubler specimen (SDS). These two
joints are selected to represent parts of the bonded repair with widely differing
damage-tolerance requirements as discussed later in this chapter.
The layout of this chapter is as follows. The role of the two representative joints
within the generic design and certification process is established. Then the damagetolerance requirement for the structure that each joint represents is discussed. The
specimen preparation and manufacture are outlined for each joint in turn. The
stress-state of the specimen is analysed. The experimental method and test results
are reported and the suitability of various fatigue-correlation parameters is
discussed. Finally the suitability/limitations of the specimens for generic design and
certification is discussed and further work is suggested before concluding.
5.1.1. Damage-tolerance regions in a bonded repair
Figure 5.1 shows a schematic of a bonded repair to a cracked plate for which
Baker [I] proposed that two distinctly different regions exist in terms of structural
integrity requirement.
The central damage-tolerant region is the zone where a significant disbond
between the patch and plate can be tolerated. This is because small disbonds reduce
103
Baker, A.A., Rose, L.R.F. and Jones, R. (eds.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 0 2002 Published by Elsevier Science Ltd. All rights reserved.
,
104
Advances in the bonded composite repair of metallic aircraft structure
I
Fig. 5.1. Damage-tolerant and safe-life zones in a bonded repair.
the repair effectiveness only slightly and disbond growth under repeated loading is
slow and stable. The ends of the patch are stepped, thinning down to one ply of
fibre composite at the edges. In this zone disbonds cannot be tolerated because as
the disbond grows it moves into a region of increasing patch thickness and
consequently greater driving force for disbond growth. The result may be rapid
disbond growth resulting in patch separation.
To represent these two regions testing of two types of generic joint was proposed:
0 The double overlap-joint fatigue specimen (DOFS), which represents the
damage-tolerance region where the patch spans the crack
0 The skin doubler specimen (SDS), which represents the safe-life region at the
termination of the patch.
Both specimens have fibre-composite outer adherends on both sides of an
aluminium inner adherend to represent bonded repairs to aircraft structural plate
where there is substantial out-of-plane restraint from substructure such as stringers,
stiffeners or honeycomb core.
5.1.2. The generic design and certification process
Table 5.1 places the two generic repair joints, the DOFS and the SDS, in the
context of the certification process.
5.2. The DOFS
Details on the materials and geometry of the DOFS are provided in Figure 5.2.
The DOFS were manufactured by bonding the outer composite adherends to the
aluminium inner adherends with adhesive FM73 and then cutting into three
individual specimens. The inner adherends were made from aluminium alloy 2024T3 (bare). Surface treatment of the aluminium plates, prior to adhesive bonding,
was the solvent clean, grit blast, silane treatment described in Chapter 3. The
boron/epoxy (120°C cure system) outer adherends were cocured with a layer of
Chapter 5. Fatigue testing of generic bonded joints
105
Table 5.1
Generic joint test program to obtain repair system allowables, taken from reference [l].
Requirement
Approach
To find joint static and fatigue strain allowables
and confirm validity of failure criteria based on
coupon test data.
The failure damage criteria must hold for similar
geometrical configurations, e.g. adherend thickness
and stiffness and adhesive thickness.
Undertake static strength tests to:
check strength against predictions based on
coupon data
0 Undertake fatigue tests to:
- obtain B-basis threshold for fatigue disbond
growth
- determine disbond growth rates under constant
amplitude and spectrum loading
0 Find knockdown factors for:
- hot/wet conditions
- non-optimum manufacture
- typical damage
- more representative loading conditions
I
I
Double overlap-joint fatigue specimen (DOFS)
representing cracked region
a
$
\
d
0
-
Skin doubler specimen (SDS), representing patch
termination
A
ti=6.4mm
aluminium
alloy inner
adherend
t0=1.17 mm
teflon film
starter crack
length 30 mm
knife edges
structural
flim
adhesive
such as M73
-
t
nine plies of
borodepoxy
outer adherend
Fig. 5.2. The double-overlap-joint fatigue specimen (DOFS).
106
Advances in the bonded composite repair of metallic aircraft structure
FM73 at 120 "C then grit blasted and bonded to the aluminium plates at 80 "C with
another layer of FM73. The cocured adhesive layer is used to prevent damage to
the boron/epoxy during the grit-blasting process and to toughen the matrix surface
layer of the composite. All bonding was done in an autoclave.
5.2.1. Stress state in the DOFS
A finite element (FE) analysis of the DOFS 121 showed, as expected, that the joint
is essentially in a state of shear plus transverse compression (to the plane of the
adhesive), referring to Figure 5.3. The FE results were obtained based on the
assumed material properties listed in Table 5.2.
I
DOFS
Lines: spring-beam theory
20
-Shear
stress
Or-
-10
-20 [
0
5
10
15
1
20
Distance from centre of joint (mm)
Fig. 5.3. Plot of shear and peel stresses along the mid-plane of the adhesive layer in DOFS; load/unit
width = 1 kN/mm. (neglecting thermal residual stresses).
Table 5.2
Material properties used in the DOFS and SDS analyses.
Adhesive
Aluminium
Boron/Epoxy
GR= 800 MPa
VA = 0.35
aA = 66 x IOp6 (per "C)
Ei=71GPa
vi = 0.33
ai= 24 x
E, = 193GPa
EZ2= 19.6 GPa
G12 = 5.5GPa
v,2=0.21
v21= 0.021
(per°C)
a1,=4.3 x
a22= 15.6 x
(per "C)
t A = 0.4
ti
mm
= 6.4
(per "C)
~lllll
to = 1.1 mm
Chapter 5 . Fatigue testing of generic bonded joints
107
In the case of elastic deformation only, the maximum adhesive shear stress in a
DOFS can be determined using beam-spring theories for adhesive joint [3]:
with
where and E; = Ei/(l - v:) and E
A = E O / ( l- v;). The parameter P denotes the
total load applied to the specimen. In the present study, the specimen width W is
approximately 20mm for all the specimens tested. For the problem depicted in
Figure 5.3 with material properties being given in Table 5.2, Eq. (5.1) yields a
maximum shear stress of approximately 33.3 MPa, which compares well with the
finite element solution of 32MPa as shown in Figure 5.3. The distribution of the
shear stress is given by [3]:
Although the above solutions have been derived for isotropic reinforcement, the
comparison shown in Figure 5.3 suggests that these solutions can also be applied to
orthotropic patch with low shear modulus, indicating that the effect of shear lag is
quite small and can be ignored.
Also shown in Figure 5.3 are the results of the peel stress. It is noted that near the
centre of the joint, the peel stress is compressive. According to the conventional
beam-spring theories, the peel stress distribution is given by the following
expression [4]:
with
where E> = E A / (1 - V A - 2vi) to account for the effect of triaxial stresses within
the adhesive layer [5]. It can be seen that the simple beam-spring theory would overpredict the magnitude of the peel stress, which is mainly due to the non-uniformity
of the stress in the thickness of the reinforcement, and cannot be captured by the
simple beam-spring model.
108
Advances in the bonded composite repair of metallic aircraft structure
5.2.2. Experimental method
Since the DOFS represents a section through the disbond/damage-tolerant
central region of a bonded repair, disbond propagation data are required. To this
end, a Teflon starter disbond was included during specimen manufacture to ensure
rapid crack initiation. As discussed in the reference [2] a compliance technique was
used to measure the disbond length. Essentially the compliance technique measures
the relative displacement between the two inner adherends at the centre of the joint,
with the aid of a crack-opening displacement (COD) gauge attached to the inner
adherends as shown in Figure 5.2. Opening of the inner adherends is directly
related to the disbond length via the following expression:
6 = 2Y,,,t~
+ 2bso
,
(5.6)
where ymax is the nominal adhesive shear strain (assuming the shear strain is
uniform through the adhesive layer, i.e. ignoring the effect of crack-tip singularity),
tA is the thickness of the adhesive layer, the parameter b is the effective disbond
length and E,, which is equal to P/2wEot,, is the normal strain in the outer
adherend. Equation (5.1) can be rewritten as:
The ratio 6/2% is calculated from the measured displacement-force pairs and is
effectively the normalised compliance of the specimen. Calibration of the
compliance using various lengths of Teflon starter crack gave the result shown in
Figure 5.4,confirming that the compliance method provides a very good means of
directly measuring the disbond length.
The slope of the fitted line shown in Figure 5.4 is 0.96, which compares well with
the factor of 1.0 (coefficient of b) predicted in Eq. (5.2). It is important to note that
2 0 ) .
14
,
16
,
.
,
20
22
disbond length (mm)
.
,
18
.
.
J
24
Fig. 5.4. Validation of the compliance-to-disbondlength relationship.
Chapter 5 . Fatigue testing of generic bonded joints
109
the first term on the right-hand side of Eq. (5.2) does not change with crack length,
consequently the rate of disbond growth at a given cycle db/dN, can be determined
by taking the derivative of Eq. (5.2) with respect to N
db d(6/2&,)
dNdN
--
(5.8)
The disbond growth rates presented in this chapter have been determined using this
technique.
Since the length of the initial Teflon starter disbond is known, the nominal shear
strain y can be determined via Eq. (5.2) from the measured opening displacement.
Alternatively, the adhesive shear strain can be determined using adhesive joint
theory discussed earlier. Provided the adhesive does not undergo cyclic plastic
deformation, Le. the cyclic shear-strain range is less than the following value,
Ayv = ~ T Y / G=A0.08, where the subscript Y denotes the shear strain at the onset
of plastic yielding, and for FM73 adhesive the shear yield stress z y at room
temperature is approximately equal to 32MPa [6]. In the case of elastic
deformation, the adhesive shear stress in a double-overlap joint specimen can be
determined using Eq. (5.1).
Fatigue testing was carried out in an Instron testing machine at room
temperature at a frequency of about 3 Hz. The load ratio (minimum value divided
by the maximum value) for all cyclic loads was kept approximately zero. Damage
growth in the adhesive due to the cyclic loads was measured using the above
outlined compliance technique every 1000 cycles.
5.2.3. Experimental remIts
Two fatigue-damage criteria (correlation parameters) were investigated: the
shear-strain range in the adhesive, A?, and the “global” strain energy release rate
range, AJ. The shear-strain range was taken directly from the COD gauge
measurements and the global strain energy release rate range was calculated from
the load applied and constituent-material elastic properties and thicknesses. The
shear-strain range was found to best correlate disbond growth rates in different
specimens. Table 5.3 lists the details of the specimens. It is noted that the adhesive
in specimen 2 was cured at a lower temperature than the adhesive in the other
specimens and hence different adhesive material properties may have contributed
to the discrepancy shown later.
Disbond growth rates for specimens 4, 5 and 6 in Table 5.3 were obtained from
three structural detail specimens. Each specimen was tested under constant
amplitude loading. At the end of testing the boron patches were removed and the
extent of adhesive disbond measured. The disbond rate was determined by dividing
the length of the disbond by the number of cycles. In all cases, for both the joints
and crack-patch specimen the disbond was found to propagate along the interfaces
between the first ply of the boron fibre and the cocured adhesive layer [2]. This
Advances in the bonded composite repair of metallic aircraft structure
110
Table 5.3
DOFS and structural details.
Specimen no.
Spec. type
Adhesive
Adhesive
thickness (mm)
1
DOFS
DOFS
DOFS
Crack patch specimen [7]
Crack patch specimen [7]
Crack patch specimen [;1
FM73'
FM73b
FM73a
FM73a
FM73'
FM73*
0.38
0.30
0.54
0.48
0.55
0.28
2
3
4
5
6
a
1 h at 120°C cure.
8 h at 80 "C cure.
failure process involves separation of the epoxy from the boron fibres and fracture
of the resin between fibres, referring to Figure 5.5.
The experimental results are plotted in Figure 5.6(a) versus the measured shearstrain range Aymax for various DOFS and crack-patching specimens. It can be seen
that for a given shear-strain range, specimen 2 exhibited faster growth rates than
other specimens. This is possibly due to the lower cure temperature (80°C
compared with 120°C for the rest of the specimens; see Table 5.3) resulting in a
bondline having a lower resistance to fatigue crack growth, even though crack
growth was not through the adhesive. The same experimental results, excluding
those of specimen 2, are re-plotted in Figure 5.6(b) against the calculated shearstrain range using Eq. (5.1). The shear-strain ranges for all the specimens are below
the cyclic plastic limit, verifying the validity of the elastic solution. It can be seen in
Figure 5.6(b) that all the experimental results now lie within a narrow band of
k 100% of growth rates. The experimental results can be well correlated by the
following equation:
with C = 37154.0 (m/cycle) and m = 10.1. Similarly, the results of the 80 "C cured
specimen (number 2) can be correlated by the same relation with the following
constants: C =
and m = 14.2.
However, the above correlating parameter seems to contradict the conventional
fracture mechanics approach [&lo], where disbond growth rates ought to be
correlated by the strain-energy release rate or the J-integral [I 1,121. In particular, it
has been reported that under tensile mode (Mode I), disbond growth rates
pertaining to different adhesive thicknesses could be well correlated by the Jintegral [l 11. Furthermore, the applied load ratio has been found to have negligible
effect on growth rates when the cyclic strain-energy release rate is chosen as the
correlating parameter [131. To examine the applicability of the strain-energy release
rate as a suitable correlating parameter for shear-dominated growth, the disbond
Chapter 5 . Fatigue testing of generic bonded joints
111
Direction of
crack growth
End of composite
adherend
(b)
Fig. 5.5. SEM micrographs of (a) fracture surface on the boron/epoxy adherend and (b) on the adhesive
surface showing imprint of fibres.
112
Advances in the bonded eomposite repair of metallic aireraft structure
0.08
0.06
0.04
0.10
Measured shear strain range AYmm
(a)
1 0-'
Load ratio R =O
E-
.-
1 O4
1 o-?
lo4
o-~
1
1o-'O
0.04
0.06
0.08
0.10
Calculated shear strain range Arm,
(b)
Fig. 5.6. Comparison of DOFS and generic structural detail specimen disbond growth rates versus (a)
the measured shear strain range and (b) the calculated shear strain range.
growth rates are plotted against the strain-energy release rate, which is given by
[12]:
(5.10)
where GA denotes the shear modulus of the adhesive layer. It can be shown that in
the case of DOFS, the strain-energy release rate can be expressed in terms of the
Chapter 5. Fatigue testing of generic bonded joints
0
v
v
A
Specimen 1 (tA=0.38mm)
Specimen 3 (tz4=0.54mm)
Specimen 4 (tA=0.48 mm)
Specimen 5 (tA=0.55mm) o
Specimen 6 (tA=0.28mm)
A
113
V
D
0
V
0
V
V
V
V
0
100
200
500
1000
2000
Range of strain-energy release rate AG (J/m')
Fig. 5.7. Comparison of DOFS and generic structural detail specimen disbond growth rates using the
strain energy release rate.
load applied to the specimen, noting Eqs (5.1) and (5.2):
(5.11)
It is clear that, for a given applied load, the strain-energy release rate is independent of
the adhesive thickness. Figure 5.7 shows the plot of disbond growth rates versus the
above calculated strain-energy release rate, indicating that for the same strain-energy
release rate, disbond growth rates can differ by more than a factor of ten. Therefore,
for shear-dominated disbond growth, the maximum adhesive shear strain provides a
better correlating parameter than the strain-energy release rate, The shear-strain
range over the central region can be readily calculated in the design stage, so the data
shown here are directly applicable to design. Further work needs to be done to
quantify the effects of environment and temperature on disbond growth rate.
Although the strain range criterion for the adhesive appears to be of practical
value as a fatigue-damage parameter, it is not yet clear why it should be relevant for
the boron/epoxy specimens where, as previously noted, fatigue failure occurs
largely by separation of the epoxy matrix from the fibres in the interface ply,
implying that the strain-energy release rate ought to be a more suitable correlating
parameter. Nevertheless, there is evidence in the literature lending support to the
use of shear-strain range. Russell [14] in his work on the fatigue of adhesively
bonded end-notched flexural specimens (Mode 11), postulated that the magnitude
of the adhesive shear modulus determines the locus of failure in graphite/epoxy
joints bonded with the adhesive FM300. Presumably this is because the shear
modulus and shear strain in the adhesive determine the shear stress experienced at
the interface on the adhesive and surface matrix of the composite. Chai and Chiang
[I51 in their work on static shear fracture showed for a compression-side interface
114
Advances in the bonded composite repair of metallic aircraft structure
crack in an adhesively-bonded end-notched flexural specimen (a stress state similar
to that of the DOFS) that micro-disbond initiation ahead of the crack was
controlled by the value of the maximum through-thickness stress (or bond-normal
stress). The through-thickness stress changes from compression to tension ahead of
the crack tip and reaches a maximum at a location that depends on the average
shear strain in the crack tip region. Furthermore, the value of the maximum
through-thickness stress depends solely on the average shear strain in the crack tip
region. Clearly, the adhesive shear strain strongly influences the fracture of such
joints and may influence fatigue behaviour also if the fatigue mechanism is microdisbond initiation ahead of the crack tip. The mechanism may be a recurring microdisbond initiation in the adhesive near the interface followed by subsequent growth
into the first ply of the laminate.
5.3. The skin doubler specimen
The skin doubler specimen, which represents the ends of a repair patch, is
depicted in Figure 5.8.
The materials and surface treatment used in the manufacture of the SDSs were
identical to those for the DOFS. Since disbond initiation data was sought from
these specimens, no Teflon starter was used. Four end-step geometries, shown in
detail in Figure 5.9, were investigated.
Note that specimen type I1 in Figure 5.9 has ply drop-offs occurring on both the
inside patch surface and the outside patch surface, i.e. two plies are added every
4-mm step. Therefore, while the step length in joint I11 is shorter at 3mm, the
effective taper angle is lower since only one ply is added per step. The adhesive
6.2 mm thick 2024
T3 bare inner
FM73 adhesive:
8 h 80°C cure
Stepped
ends of
patches
(see Fig. 5.8)
~ ~1
Specimen width: 20 mm
1111
11 PlY
borodepoxy
outer. One layer
of cocured
FM73 on
bonding
surface.
Fig. 5.8. Schematic of the skin doubler specimen (not to scale).
Chapter 5. Fatigue testing of generic bonded joints
(a) No end-stepping
115
steps inside and outside
steps inside
steps outside
(b) 4 mm steps
(c) 3 mm steps
(d) thick adhesive
Fig. 5.9. The end step geometries investigated: (a) type I, (b) type 11, (c) type 111, and (d) type IV.
thickness, t A , at the end of the overlap was typically 0.4 mm for joints I, 11, and 111,
and 3.0mm for joint IV.
5.3.1. Stress state in the skin doubler specimen
5.3.1.1. Block-end (no taper)
The most significant difference between the SDS and the DOFS is that the
transverse stress (peel stress) in the adhesive at the patch ends is positive, as
opposed to compressive in the DOFS, when the joint is subjected to tensile load. In
the case of square end (no tapering at patch end) without adhesive fillet, the
adhesive shear stress near the patch end is given by [3]:
(5.12)
It is worth noting that the above formula is different from Eq. (5.1). However, in the
case of the balanced repair (Eiti = 2Eit,), Eqs (5.1) and (5.13) become the same. For
unbalanced repair, the shear stress at the centre of double overlap joint is different
from that at the end of the joint. The maximum peel stress can be expressed in terms
of the maximum adhesive shear stress, according to Eqs (5.4) and (5.5),
(5.13)
To verify these simple solutions, a FE analysis was carried out under plane-strain
conditions. The material properties used in the FE analysis are listed in Table 5.2.
The FE mesh employed near the patch end is shown in Figure 5.10.
A comparison between the FE results and the predictions of the above beamspring theory is shown in Figure 5.11, indicating a good agreement.
The mismatch in the coefficients of thermal expansion for the metallic adherend
and the composite patch gave rise to thermal residual stresses after the specimens
116
Advances in the bonded composite repair of metallic aircraft structure
I I t I I I I I I I I I I I I
V
I
I
I
I
I
\
\-
Fig. 5.10. Finite element mesh near the end of a block-end patch.
30
n
6
A
Symbols: FE results (blockend)
Lines: spring-beam theory
20
a
E
e,
v1
2
2 10
2
0
.
0
.
.
.
.
.
5
.
.
.
.
.
.
10
.
.
.
.
.
.
.
15
.
20
Distance from end of patch (mm)
Fig. 5.1 1. Stress state in a SDS with block end; load/unit width = 1 kN/mm
had been cooled to the room temperature after curing at 80 "C.The peak residual
shear stress at the end of the adhesive layer can be determined [3]:
(5.14)
where the material properties are listed in Table 5.2. The minus sign indicates that
the residual shear stress at the end of patch is opposite to the shear stress induced
by remote tension. For specimens cured at 80 "C,the temperature drop AT equals
to 60 "C,which leads to a thermal residual shear stress of -17.8 MPa. This estimate
compares well with the finite element solution shown in Figure 5.12, i.e. -21 MPa.
Chapter 5 . Fatigue testing of generic bonded joints
5
"
"
~
"
"
'
'
"
~
"
'
~
Pee) stress
117
'
0
g
-5
E
-10
h
v)
s
(
I
I
2
Symbols: FE results
Lines: beam-spring theory
5 j -15
-20
Thermal residual stress near block-end
-25
0
5
10
15
Distance from end of joint (mm)
20
Fig. 5.12. Thermal residual stress in a SDS with block end subjected to a 60°C temperature drop.
However, the beam-spring solution considerably underestimates the magnitude of
the peel stress. The reason for this discrepancy is not clear. Further study is
required to develop an improved solution for the residual peel stress.
5.3.1.2. Tapered end
In practice, to enhance the fatigue resistance, patches are normally tapered at the
ends so as to reduce the maximum adhesive shear and peel stresses, as illustrated in
Figure 5.9(b) and Figure 5.9(c). To examine the effect of tapering on the adhesive
stresses, a detailed FE analysis of the type I1 joint was carried out for both
mechanical load and thermal load. The properties of the orthotropic reinforcement,
the adhesive, and the metallic plate are given in Table 5.2. The FE mesh is shown in
Figure 5.13. The adhesive bondline thicknesses for these specimens were quite large
Fig. 5.13. FE mesh of half-model of type I1 SDS (see Fig. 5.9(b))
118
Advances in the bonded composite repair of metallic aircraft structure
Full height block end
2
B
20
0
5
10
15
20
Distance from end of patch (mm)
t"""""""""""
10
0
0
1
2
3
4
Distance from end of patch (mm)
Fig. 5.14. Stress state in a tapered SDS; load/unit width= 1 kN/mm.
because effectively two layers of adhesive were present in each bondline: one cocured with the patch and one used to secondarily bond the patch to the aluminium
strips. Consequently the adhesive was thick enough for significant variations in
stress to exist across the bondline width. To this end, the adhesive layer was
modelled by at least four elements in the thickness direction.
Figure 5.14 shows the stresses along the mid-plane of the adhesive layer in a
tapered repair (type 11) subjected to an external loading, together with the
estimated shear stress that would exist in a joint with a single-ply patch
( t = 0.1 mm). The magnitude of the peak shear stress seems to be well
approximated, but not the transfer distance. The actual shear stress decays more
slowly than that in a single-ply patch. Perhaps the more striking finding is that
Chapter 5. Fatigue testing of generic honded,joints
119
51
*}.
!2
Open symbols: no fillet
Closed symbols: with fillet
-15
AT=-60 "C
-
0
8
4
Distance from end of patch (mm)
Fig. 5.15. Residual thermal stresses in a tapered SDS (AT = -60 "C)
maximum peel stress is nearly equal to the maximum shear stress. Comparison with
the results shown in Figure 5.11 suggest that tapering has reduced the maximum
shear stress and the maximum peel stress by respectively 52% and 43%.
For a thermal loading of AT = -60 "C, which corresponds to cooling the cured
specimens from the curing temperature of 80 "C down to the testing temperature of
20 "C, the residual thermal stresses as determined using the F E method are shown
in Figure 5.15. Comparison with the thermal residual stress for a block-end patch
as shown in Figure 5.12 suggests that tapering the patch has reduced the maximum
residual shear stress by 53%, similar to the reduction in the maximum shear stress
induced by applied load. However, the maximum peel stress has been reduced only
by 23%, much less than the reduction in the peel stress due to applied mechanical
load.
Table 5.4 lists the results for the adhesive displacements at the joint ends for the
four joint types shown in Figure 5.9. Note that the residual stresses due to thermal
mismatch between the composite and metal inner adherends are negative. This is
Table 5.4
Maximum stresses for the four joints shown in Fig. 5.9.
Joint type I
(tA=0.4mm)
v u e 10
applied load
Shear stress
(MPa)
Peel stress
Residual
stress (60 "C
drop from
cure temp)
Shear stress
(MPa)
Peel stress
(MPa)
-
.
Joint type I1
(tA=0.4mm)
Joint type I11
(tA=0.4mm)
Joint type IV
(tA=3.0mm)
26.5
12.7
12.0
6.0
20.6
11.7
11.0
4.32
20.9
- 9.8
10.0
- 2.57
- 24.7
- 19.0
- 20.6
0.48
~
-
Advances in the bonded composite repair of metallic aircraft strueture
120
highly beneficial in offsetting the positive stresses caused by the external stresses. It
is also clear that the square end joint, type (a), has the highest stresses for a given
applied load and temperature change.
5.3.2. Experimental method and results
The SDS represents a section through the safe-life region of a bonded repair.
Therefore the emphasis here is to obtain disbond initiation data. The technique
used to determine disbond initiation load was adopted from reference [16].
Essentially it involves bonding strain gauges to the very tips of the boronlepoxy
patches and monitoring strain response as a function of time as cyclic loads are
applied. Disbond initiation was defined to have occurred when the amplitude of the
output of one of the strain gauges dropped by 10% (see Figure 5.16). Constant
amplitude loading at 3 Hertz was applied at various load ratios (ratio of maximum
to minimum load). An initiation level was recorded for each load ratio. The
sequence of events, starting from the small value of applied load amplitude, was
1. Select load ratio.
2. Apply 50000 cycles at a certain load amplitude and monitor strain gauge
measurement every 100 cycles.
3. If one of the strain gauge amplitudes does not drop by more than 10% then
increase amplitude of cyclic load and go to step 2, otherwise go to step 4.
4. Crack initiation has occurred. Terminate test.
Figure 5.16 shows some typical strain gauge outputs for the cyclic strain response
to various cyclic loads for one of the strain gauges. The initiation load for this
specimen was 24.2kN using the definition above. Since the strain gauge was
installed very close to the end of patch, as illustrated in Figure 5.17, the drop in the
strain gauge reading is nearly proportional to the disbond length. Therefore a 10%
2500h
!!
v
22.0 kN
W
-0
3
c
.-
19.8 kN
a
6
2000-
*
17.6 kN
15.4 kN
1500
0
10000 20000 30000 40000 50000 60000
cycle number
Fig. 5.16. Strain amplitude versus cycle number (dry, load ratio = -0.1) for a type II specimen,
Chapter 5. Fatigue testing of generic bonded joints
Strain gauge
121
t
+
.
+
+
e
e
e
e
Fig. 5.17. Strain-gauge technique to detect disbond growth, showing sign conventions for positive
stresses.
drop in the measured strain implies that the length of disbond would be equal to
approximately 0.3 mm, considering that the strain gauge length is about 3 mm.
Consequently, once disbond has been detected, the average disbond growth rate
would be at least 6 x lop9m/cycle. This growth rate is about an order of magnitude
higher than the growth rate used to define the conventional fatigue threshold.
A series of fatigue tests were conducted using type I1 specimens at various load
ratios ranging from -0.4 to 0.4. Using the results given in Table 5.4, the adhesive
stresses are obtained by converting the applied load and the results are shown in
Table 5.5, where the sign convention shown in Figure 5.17 is employed.
Table 5.5
Disbond initiation stresses for joint 11.
Load ratio
(min/max)
- 0.4
- 0.2
- 0.2
-0.1
-0.1
0
0
0
0
0.1
0.1
0.2
0.2
0.33
0.33
0.4
0.4
AT/^
Ignoring thermal
residual stress
Considering
thermal stress
An12
(MPa)
a,,,,
(MPa)
T,,~,
(MPa)
(MPa)
amean
(MPa)
(MPa)
9.76
8.74
8.74
8.36
7.67
7.60
7.29
7.29
8.24
7.41
6.40
6.14
6.14
5.20
5.52
4.94
4.56
9.03
8.10
8.10
7.74
7.10
7.04
6.75
6.75
7.63
6.86
5.93
5.69
5.69
4.81
5.11
4.58
4.22
3.88
5.41
5.41
6.35
5.82
7.05
6.76
6.76
7.64
8.40
7.28
8.40
8.40
9.28
10.16
10.70
9.87
4.18
5.83
5.83
6.85
6.27
7.61
7.29
7.29
8.24
9.06
7.86
9.06
9.06
10.01
10.95
11.54
10.64
- 16.12
- 14.59
- 14.59
- 13.65
- 14.18
- 12.95
- 13.24
- 13.24
- 12.36
- 11.60
- 12.72
- 11.60
- 11.60
- 10.72
-9.84
-9.30
- 10.13
5.62
3.97
3.97
2.95
3.53
2.19
2.51
2.51
1.56
0.74
1.94
0.74
0.74
-0.21
-1.15
- 1.74
-0.84
T,,
17.5-.
.
.
.
r
.
.
8
h
a"
3
12.5 .
. .. .
. 7.
. .
9
.
.
.
.
m
'
8
.
2
.
m .
8
Maximum shear stress
v)
v)
0
A
5,
A
85 7.5 -
A
A
2
Amplitude of shear stress
2.5
-2
'
.
. . * . .
.
.
.
A
12.5 -
A
A
A
>
. ~.
.
A
A
A
A
A
A
A
E
A
A
Maximum stress in a cycle
v)
rn
2
-8
Amplitude of stress
8
-L
v)
7.5
~
.
L
-0.50
.
=
8
-0.25
a
0
Load ratio
LJ
.
0.25
0.50
(P- /Pm,,,)
(b)
Fig. 5.18. Influence of applied load ratio on (a) adhesive shear stresses and (b) peel stresses at initiation
for joint type 11, ignoring thermal residual stresses.
It can be seen in Table 5.5 that the amplitudes of both the shear stress and the
peel stress decrease rapidly with the increase in the applied load ratio, whereas the
maximum stresses increase slightly with the increase of load ratio. This is best
illustrated in Figure 5.18. Since the maximum residual peel stress is approximately
-20 MPa for these specimens, inclusion of the thermal residual stress would result
Chapter 5. Fatigue testing of generic bonded joints
123
Table 5.6
Initiation loads for the four joint types tested at a load ratio of zero.
Initiation load (kN)
Joint type (a)
Joint type (b)
Joint type (c)
Joint type (d)
22.5
24
26
23
Table 5.7
Initiation loads converted to stresses considering thermal stresses.
Initiation load (kN)
Range of shear stress (MPa)
Range of peel stress (MPa)
Maximum shear stress (MPa)
Maximum peel stress (MPa)
Joint I
tA=0.4mm
Joint 11
tA=0.4mm
Joint 111
zA=0.4mm
Joint IV
22.5
29.83
23.18
8.93
- 1.52
24
15.24
14.04
5.44
- 4.96
26
15.6
14.30
5.6
- 6.3
23
6.9
4.97
9.47
4.49
tA=3.0mm
in the maximum peel stress in a cycle being compressive. This suggests that crack
surface contact would occur throughout a loading cycle, rendering the peel stress
largely ineffective. In this case, the disbond would be driven mainly by the cyclic
shear stress. According to the crack-growth rate results shown in Figure 5.6(b) for
the 80 "C cure adhesive, the disbond growth rate corresponding to an applied shear
stress range of 15 MPa (R = 0) is expected to be approximately 7.2 x
m/cycle,
which is significantly lower than the detection limit (6 x 10-9m/cycle) of the
technique employed in this study.
The other three joint types, I, I11 and IV, were tested at a load ratio of zero only.
The average initiation loads for the four joints are shown in Table 5.6. The locus of
disbond initiation and subsequent propagation in joint I was within the ply of
boron/epoxy adjacent to the adhesive bondline, as with the DOFS. For joints 11,
111, and IV, the locus of the disbond tended to be mixed: some failure within the ply
of boron/epoxy adjacent to the adhesive bondline and some failure at the
aluminium to adhesive interface. The loads shown in Table 5.6 are converted to
stresses in Table 5.7 using the results given in Table 5.4.
It is rather surprising that the initiation loads of tapered joints (type I1 and 111)
are only slightly higher than for the untapered joint, contrary to the expectation of
stress-based fatigue criteria, e.g. the maximum adhesive stresses at fatigue initiation
would be a material constant. The large differences in the failure stresses indicate
that the adhesive stress is not a suitable correlating parameter.
5.3.3. Fracture mechanics approach
The experimental results shown in Table 5.7 clearly suggest that the maximum
stresses in the adhesive layer (either the peel stress or the shear stress) do not
provide an adequate fatigue failure criterion. In particular, joint IV, which has a
124
Advances in rhe bonded composite repair of metallic aircraft structure
Table 5.8
Initiation loads for the four joint types tested at a load ratio of zero.
Joint I
Joint I1
Joint I11
Joint IV
22.5
37.3
222
24
18.25
58
26
18.9
60.8
23
17.2
89.3
~~
Initiation load (kN)
Strain energy release rate AG, (J/m2)
Strain energy release rate AGll (J/m2)
much thicker adhesive layer, failed at even lower load than joints 11 and I11 with
thinner bond-lines. Such a large discrepancy in the stresses to initiate disbond
indicated that a fracture mechanics approach would offer a better criterion. As
discussed in Section 5.2.3, the range of the strain-energy release rate AG due to the
adhesive shear stress and peel stress are given by:
(5.15a)
(5.15b)
The results are summarised in Table 5.8, which indicates that the critical value of
the Mode I strain-energy release AGI seems to remain a constant for joints 11, 111,
and IV.
Further experimental and theoretical investigations are still needed to ascertain
whether the strain-energy release rate is an adequate fatigue failure criterion. In
addition, the effects of load ratios, thermal residual stresses, patch tapering, and
environment need to be quantified in order to develop a predictive tool for
assessing the durability of bonded repairs and joints.
5.4. Discussion
If it is accepted (a) that the genericjoints approach for generating basic materials
allowables on fatigue resistance of the patch system is reasonable and (b) that the
DOFS and SDS are appropriate specimens, then the most that can be said is that a
useful start on obtaining allowables data has been made.
The first requirement is to validate fatigue-damage criteria (FDC). Some of the
requirements for a suitable FDC are given in Table 5.4 where they are compared
with the use of AK effective as an FDC for fatigue crack growth in metals.
For the DOFS the strain-range criterion is suitable for use in patch-system
design, but needs much further validation. The issue of the relevance of this damage
parameter to the actual interface failure mode in composites needs to be resolved.
To add further to the complications, failure modes are quite likely to change to
cohesive in the adhesive at elevated temperature and particularly in hot/wet
conditions.
Chapter 5 . Fatigue testing of generic bonded joints
125
Table 5.9
Requirement of fatigue-damage criteria (FDC).
~
~~
~~
~
~
Requirements for FDC Bonded Joint/Generic Repair
~_____
0
0
0
-
0
0
0
~~
~
~
E.g. AK,, for Metal s
~
FDC functionally relatable to disbond damage initiation and growth
Invariant with geometrical parameters, such as adhesive thickness and joint
geometry
Relevant also for disbond locus changes in adhesive or resin matrix
may need dgferent FDC,for totally dqferent failure modes, e.g. peel or shear
[DOFS and SDS]
Readily calculated from external and internal (thermal) loading
Easily measured materials parameters for initiation or db/dN as f(FDC) for
each failure mode
Readily incorporated into design codes
J only for growth
J
J
J
/,
I
v
For the SDS insufficient work has been done to establish any suitable FDC.
There are some fundamental and contradictory issues to be resolved in relation to
residual stresses and negative peel stress before this can be done. Tests on all metal
specimens to separate out the issue of residual stress would seem to be required.
If FDC can be verified to be suitable for design purposes then the database on
materials allowables can be generated. There is a need to obtain the basic
allowables and then develop knockdown factors. Knockdown factors are factors
applied to the allowables to allow for the degrading influences of, for example:
0 Temperature and especially hot/wet conditions
0 Environmental fluids, other than water, e.g. fuel and hydraulic oil
0 Voids
0 Undercure
0 Spectrum loading
0 Differences between the generic repair situation and the actual stressing situation
References
I . Baker, A.A. (1997). On the certification of bonded composite repairs to primary aircraft structures.
Proceedings of Eleventh International Conference on Contposite Materials (ICCM-111,Gold Coast
Australia.
2. Chalkley, P.D. and Baker, A.A. (1999). Development of a generic repair joint for certification of
bonded repairs. Int. J. of Adhesion and Adhesives, 19, pp. 121-132.
3. Hart-Smith, L.J. (1973). Adhesive-bonded double-lap joints, NASA CR 112235. Langley Research
Centre, Hampton, Virginia, 23366, USA.
4. Hart-Smith, L.J. (1982). Induced peel stresses in adhesively-bonded joints, MDC J9422A, Douglas
Aircraft Company.
5. Wang, C.H. and Rose, L.R.F. (1997). Determination of triaxial stresses in bonded joints. Int. J.
Adhesion and Adhesives, 17, pp. 17-25.
6. Wang, C.H. and Chalkley, P. (2000). Plastic yielding of a film adhesive under multiaxial stresses. Int.
J. Adhesion and Adhesives, 20, pp. 155-164.
126
Advances in the bonded composite repair of metallic aircraft structure
7. Baker, A.A. (1996). Fatigue studies related to certification of composite crack patching for primary
metallic structure. FAA-NASA Symposium on Continued Airworthiness of Aircraft Structures,
Atlanta, August, pp. 28-30.
8. Brussat, T.R., Chiu, S.T.and Mostovoy, S. (1978). Fracture mechanics for structural adhesive
bonds, Phase 11, final technical report. AFML-TR-77-163, Wright-Patterson AFB, Ohio, 45433,
USA.
9. Lin, C. and Liechti, K.M. (1987). Similarity concepts in the fatigue fracture of adhesively bonded
joints. J. Adhesion, 21, pp. 1-24.
10. Russell, A.J. and Jonson, D. (1990). A damage tolerance assessment of bonded repairs to CF-18
composite components, Part 11: joint design, Technical Memorandum 90-3, Defence Research
Establishment Pacific Victoria, Canada.
11. Wassell, G.C., Clark, J.D., Crompton, J.S., et al. (1991). Fatigue within adhesive bonded. Int. J .
Adhesion and Adhesives, 11, pp. 117-120.
12. Wang, C.H. and Rose, L.R.F. (1997). Failure analysis of adhesively bonded joints. Advances in
Fracture Research, 6, Pergamon Press, pp. 3057-3064.
13. Mall, S. (1987). Stress ratio effect on cyclic debonding in adhesively bonded composite joints,
Composite Structures, 8, pp. 3145.
14. Russell, A.J. (1988). Fatigue crack growth in adhesively bonded graphite/epoxy joints under shear
loading. ASME Symposium on Advances in Adhesively Bonded Joints, Chicago, Nov. 2SDec. 2.
15. Chai, H. and Chiang, M.Y.M. (1988). Finite element analysis of interfacial crack propagation based
on local shear, part 1I-fracture. Znt. J. Solids Structures, 35, pp. 815-829.
16. Baker, A.A., et al. (1993). Reinforcement of the F-111 wing pivot fitting with a boron/epoxy doubler
system - material engineering aspects. Composites, 24(6), pp. 511-521.
17. Wang, C.H. and Rose, L.R.F. (2000). Compact solutions for the corner singularity in bonded lap
joints. Int. J. Adhesion and Adhesives, 20, pp. 145-1 54.
Chapter 6
EVALUATING ENVIRONMENTAL EFFECTS ON
BONDED REPAIR SYSTEMS USING FRACTURE
MECHANICS
Dr L.M. BUTKUS*
Department of Engineering Mechanics, HQ USAFAIDFEM US Air Force Academy,
CO, USA, 80840-6240
R.V. VALENTIN
Harris Corporation, Palm Bay, FL 32905
Dr W.S. JOHNSON
Schools of Materials Science & Engineering and Mechanical Engineering, Georgia
Institute of Technology, Atlanta, GA, USA 30332-0245
6.1. Introduction
As discussed in Chapter 5 effective design of repairs requires detailed analyses of
the mechanics of bonded joints that may be viewed as representative models of
those repairs. In addition, to ensure that designs using bonded assemblies have an
acceptable lifespan, the interaction of bonded joints with their service environments
is required.
Bonded joint mechanics were originally analyzed using stress-based approaches
[1,2]. However, fracture mechanics has also been shown to be a viable analytical
tool for bonded joint evaluation and is the method described in this chapter.
Adapted for use on bonded joints by Ripling, et al. [3], Shaw [4], and others,
fracture mechanics uses the strain energy release rate, G, to characterize fracture.
Research by Mall, et al. [5] also found that, when subjected to fatigue loading,
bonded joints exhibited crack growth rates that correlated well with applied strain
energy release rate levels. Johnson, et al. [6-81 subsequently: (1) developed a
fracture-mechanics-based design approach for bonded joints, (2) examined the
Mode I, Mode 11, and mixed mode monotonic toughness (GI,
G I I ,and GI;,,)of
* Previously graduate students, School of Mechanical
127
Engineering, Georgia Institute of Technology
Baker, A.A., Rose, L.R.F. and Jones, R. (eds.J,
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Published by Elsevier Science Ltd.
128
Advances in the bonded composite repair of metallic aircraft structure
select aerospace adhesives and composite matrix materials, and (3) proposed using
the total strain energy release rate (GT = GI GII GIII [if present]) as a design
criteria for bonded joints. Johnson and Butkus [9] in their investigations of bonded
metal joints exposed to aerospace service environments further examined these
design criteria.
The intent of this chapter is to describe additional work that employed fracture
mechanics in assessing the environmental durability of representative repair joints.
The system studied, boron-epoxy bonded to aluminum, represents bonded repairs
of cracked metallic aircraft structures, and has been used principally by the air
forces of Australia and the US [ 10,l I]. Prior to mechanical testing, specimens of
this bonded material system were exposed to temperature and humidity levels
encountered during service.
For the research presented in this chapter, monotonic and fatigue tests were
conducted on double cantilever beam specimens to examine Mode I fracture
toughness and fatigue behavior. Environmental effects were found to be
detrimental to the toughness and threshold crack growth of the representative
Al/b-ep repair system.
Although it should be understood that bonded joints are subject to significant
amounts of Mode I1 loading in service in addition to Mode I, their fatigue and
fracture behavior identified in this limited study should be carefully considered in
the design of adhesively bonded repairs and components.
+ +
6.2. Materials and specimens
The bonded boron-epoxy/aluminum aerospace repair system (A1-FMB73M-b/
ep) and its specific operating environments was examined. Fabrication was
performed by an airframe manufacturer using current surface preparation,
production methods, materials, etc.
6.2.I . Bonded material system and fabrication
The Al-FMB73M-b/ep system representing bonded airframe structural repairs,
consisted of a primarily unidirectional [O4/90/O3/9O/0],, pre-cured boron-epoxy
laminate bonded to a bare 7075-T651 aluminum adherend with a toughened
aerospace epoxy (Cytec’s [email protected] a non-woven polyester scrim cloth).
The surface of the 9.5mm (0.375in.) thick aluminum plate was prepared for
bonding using an FPL sodium dichromate etch and BR-127 primer. Individual
specimens were cut from the adhesively bonded panels.
6.2. I . I . Specimen geometry
Double cantiIever beam (DCB) specimens used for this research were nominally
25 mm (1 in.) wide and 305 mm (12 in.) long. [email protected] film prevented bonding
and created crack initiation sites at one end of each specimen. Loading was
accomplished using hinges bonded to the end of each adherend.
Chapter 6. Evaluating environmental effects on bonded repair systems
129
Due to the dissimilar adherends and a mismatch of thermal expansion
coefficients (CIA= = 22.1 x
"C [12.3 x 10-6/Oq, able+,= 4.5 x
"C [2.5 x
10-6/"F]), the specimens were distinctly curved.
6.3. Experimental procedures
Experiments were designed to compare the behavior of as-received specimens to
that of exposed specimens. Table 6.1 illustrates the combinations of pre-test
conditioning and testing environments that will be described in Sections 6.3.1 and
6.3.2.
6.3.1. Pre-test environmental conditioning
Prior to mechanical testing, selected specimens were subjected to either
isothermal exposure or thermal cycling. Isothermal exposure was performed using
an air-circulating oven and, if necessary, a humidity chamber inside the oven.
Thermal cycling was performed using a device with hot and cold chambers between
which specimens were automatically shuttled. No humidity control was possible
with the thermal cycling unit. No load was applied to the specimens during
exposure or cycling.
Exposure conditions were based upon service conditions for the material
systems. "Hot/wet" conditions simulated tropical runway operations. "Hot/dry"
conditions simulated high performance operations at mid- and low altitude. A low
temperature of -54 "C (-65 "F) used in this research represented subsonic flight at
high altitudes.
Selected specimens were exposed to one of the following three environments:
1. 100 thermal cycles between -54 "C (-65 "F)and 71 "C (160 "F) following 320 h
of pre-conditioning at 71 "C (160 "F), > 90% relative humidity (rh) (Figure 6.1)
2. 5000 h exposure to 71 "C (160 "F), > 90% rh (hot/wet conditions)
3. 5000 h exposure to 71 "C (160 O F ) , > 90% rh (hot/wet conditions) followed by
5000h exposure to a desiccating environment of 22°C (72"F), 1O%rh
(desiccation was performed to determine if hot/wet exposure effects could be
reversed)
6.3.2. Testing procedures
Monotonic tests were conducted under laboratory conditions (22 2 "C
[72 rt 4 "F], 50 & 5% rh) or at temperatures representing low (-54
2 "C
[-65 k 4 O F ] ) and high (71 & 2 "C [160 & 4 "F]) service temperature limits. These
tests were conducted under displacement control with a speed of lmm/min.
(0.04 in./min.). ASTM D3433-75 and ASTM D5228-94a were used as guidelines.
Table 6.1
Pre-test conditioning and test environments used for evaluating the Al-FMm73M-b/ep bonded system.
Test Conditions
Pre-test conditioning
As-received
"A
-No pre-test
conditioning
Monotonic Fracture Toughness
-displacement control
- 1mm/min. (0.04 in./min.)
Room Temperature 22 "C (72 "F)
Low Service Temperature -54°C (-65 OF)
High Service Temperature 71 "C (160°F)
Fatigue
-22°C (72°F)
-displacement control, 1 Hz
- b = amin/amax,
of 0.1
Thermal cycling
"C"
- 320 h exposure
to 71 "C (160"F),
> 90% rh followed by
- 100 thermal cycles
between -54°C (-65 "F)
and 71 "C (160°F)
b
Hot/wet
exposure
"E'
- 5000 h exposure
to7loC(160"FJ,
> 90% rh
Hot/wet exposure +
dessication
"E+D'
- 5000h exposure to
7loC(160"F), >90%rh
followed by
- 5000h exposure to 22 "C
(72"F), <lO%rh
9
2
2
9'
5
8-
t
5a3
$
,:
J
J
J
J
J
J
s3
z
$
E,
J
J
J
(J:tests conducted under indicated combination of pre-test conditioning and test environments).
=+
2
3
::
5
Chapter 6. Evaluating environmental effects on bonded repair systems
131
1 d"
250
100
150
50
Temp.
("C)
Temp.
50
0
(3)
-50
-50
-150
-100
0
10
20
30
Time (min.)
40
50
60
Fig. 6.1. Thermal cycling profile used for the Al-FM*j73M-b/ep bonded system.
Crack growth was not catastrophic, so the long bond line permitted single
specimens to be tested repeatedly and yield several toughness values.
Fatigue tests at laboratory conditions (22 & 2 "C,50 f 5% rh) and a frequency of
1 Hz were conducted under displacement control with a displacement ratio,
R6 = 6min/6,ax, of 0. I . This resulted in load shedding and facilitated identification
of G levels at threshold growth rates of da/dN= 10-6mm/cycle (4 x 10-8in./
cycle), a rate based on previous work [8,12].
6.4. Analysis
Due to the AI-FM R'73M-b/epspecimens' dissimilar adherends, residual thermal
stresses produced pronounced curvature and a residual Mode I1 strain energy
release rate (GI1) at the crack tip after curing. A closed-form solution could not
determine GI and GI, in this case, so finite element analysis was needed to
understand mode mixity [13].
The ABAQUS finite element code was used to analyze a 2D model of the DCB
specimen with 4927 nodes and 4658 elements. The adhesive was modeled with four
rows of four-noded quadrilateral elements; the A1 adherend was modeled with ten
rows; and the b/ep adherend was modeled with one row per ply.
Although ABAQUS is capable of analyzing material non-linearity, it requires
tensile stress-strain data. At the time this research was conducted, little was known
about the tensile stress-strain behavior of the adhesives. Therefore, all materials
were assumed to be linearly elastic. (More recent research [14] suggests that the
adhesive's nonlinear behavior of the adhesive is important above 3% tensile
strain. Thus, future finite element analyses should account for this characteristic
-
132
Advances in the bonded composite repair of metallic aircraft structure
behavior.) Plane-strain was assumed due to the large ratio of specimen width to
bond line thickness.
The analysis used experimental loads and crack lengths with a reduced
integration technique to provide crack tip nodal forces and displacements. The
Mode I, Mode 11, and total strain energy release rates were then computed using
the modified crack closure technique [ 151.
6.5. Results and discussion
Testing revealed effects of the environment on the fracture and fatigue properties
of the Al-FMB73M-b/ep system.
6.5.1. Fracture toughness
specimens exhibited an average as-received fracture toughness (GTc) of
-The
815 J/m2 (4.7 in. lb./in.2).
Fracture occurred in the boron-epoxy’s matrix near the composite-adhesive
*
interface (Figure 6.2). Little of the adhesive remained on the composite adherend
following fracture. A few boron fibers were embedded in the FMB73M remaining
on the aluminum adherend. The fracture paths of all specimens, regardless of pretest conditioning or test temperature, exhibited these characteristics.
Figure 6.3 shows the effect of pre-test environmental conditioning on the fracture
toughness of the system. Thermal cycling reduced the fracture toughness by 35%.
Some of this loss may be attributed to the 320 h during which the specimens were
exposed to hot/wet conditions prior to thermal cycling. However, the extent of this
effect is unknown.
Hot/wet exposure for 5000h resulted in a -50% loss in toughness. Such
exposure often decreases fracture toughness of bonded metals by attacking
insufficiently prepared adherend surfaces and causing failure at the metal-adhesive
interface.
However, the fracture surfaces of the hot/wet exposed specimens were similar to
those of the as-received specimens suggesting that the hot/wet environment
-
c
Boron fibers from b/ep adherend (black) embedded
in adhesive
L
[email protected] (golden color)
Fig. 6.2. Fracture surfaces of the Al-FMn73M-b/ep bonded system.
Chapter 6. Evaluating environmental effects on bonded repair systems
[email protected]
Double Cantilever Beam Specimens
(average GTvaluesshown numerically)
As-Received“A”
815 J/m2
(1 1 values)
-
A
t
El
400
200
Exposed &
Dessicated “E +D”
Exposed “E”
562 J/m2
415 J/m2
(5 values)
(7 values)
P
Cycled “C”
516 Jim’
(6 values)
{
’
r--3
600
133
- GI, values
8
x
I
m
+
I
3
i
+ GIvalues
- symbols GTvalues
Fig. 6.3. Effect of environmental exposure on the fracture toughness of the AI-FM“ 73M-b/ep system.
adversely affected the adhesive and/or composite matrix rather than the metaladhesive interface.
Following initial testing, one specimen used to determine the hot/wet exposure
values was placed in a desiccator at room temperature for 5000 h. After desiccation,
the toughness of this specimen recovered slightly but was still far below the asreceived toughness.
Figure 6.4 shows the effect of test temperature on fracture toughness. The
difference in adherend thermal expansion coefficients evidently magnified the
A1-FMe73M-b/ep
Double Cantilever Beam Specimens
(average GTvalues shown numerically)
As-Received “A”
tested 971 “C
841 Jlm’
1400-
1200-r
As-Received “A”
tested 9-22 “C
8 15 Jlm’
( I 1 values)
A
G C
(Jlrn’) .
t
600-
As-Received ‘bA”
tested @-54OC
.-.
,.345
345 Jim’
Jim’
.
(3 values)
.
*
4””
400-
1 I I E{-!,,
200 -
0-
- GI,values
values
+ GIvalues
I
symbols GTvalues
Fig. 6.4. Effect of test temperature on the fracture toughness of the Al-FMk73M-b/ep system.
134
Advances in the bonded composite repair of metallic aircrajl structure
thermally-induced strain energy release rate in the bond line at the lower test
temperatures. This magnification, combined with a probable lower ductility of the
adhesive at -54 "C (-65 OF), significantly reduced the fracture toughness.
6.5.2. Fatigue behavior
Fatigue test results are shown in Figure 6.5. Four characteristics of this data are
significant.
First, the system exhibited an extremely high degree of crack growth rate
sensitivity. If represented by a Paris Law relation of da/dN= C(AGT)" [I61 the slope
of the data (i.e. crack growth rate sensitivity) is equivalent to an exponent (n)on the
order of 10. This is far above the growth rate sensitivity of metals which falls in the
range of 2-3 [17].
Second, the threshold strain energy release rate range (AGT,th at da/
dN= 10-6mm/cycle [4x lo-' in./cycle]) is near 100J/m2 (0.6 in. lb./in?), far
below the fracture toughness, consistent with Johnson and Mall [6].
-
IE+OO
IE-OI
As Received "A"
A
Exposed "E" 8
IE-08
10
I 00
1000
AGT(J/m*)
IC
Fig. 6.5. Fatigue behavior of the Al-FMS73M-b/ep bonded system.
Chapter 6. Evaluating environmental effeets on bonded repair systems
135
Third, hot/wet exposure reduced AGT,th, but didn't affect the crack growth rate
sensitivity (n). Fourth. the fracture path in the fatigue specimens was identical to
that in the fracture toughness specimens.
6.6. Summary and conclusions
Although this research was limited to investigating primarily Mode I fracture
and fatigue behavior on a limited number of specimens, it highlighted potentially
important trends concerning the relationship between service environments and
bonded joint behavior.
As reported in this chapter, the primarily Mode I fracture and fatigue resistance
of AI-FM R'73M-b/ep can be detrimentally affected by environmental exposure.
The fracture paths in this bonded system indicated that the environment appeared
to have affected the adhesive and/or composite matrix materials to a greater extent
than the adhesive-adherend interfaces. Additionally, the crack growth rate
sensitivity of this bonded metal-composite system far exceeded that of metals.
Though unaffected by long-term environmental exposure, this high sensitivity
suggests that continued operation of bonded structures below the identified
threshold is necessary to avoid unanticipated rapid Mode I crack growth.
The behavior of the Al-FMR73M-b/ep bonded aerospace material system
identifies a need to carefully consider the service environment when specifying
bonding for primary structures or for structural repairs. Safe and economic
aerospace operations as well as modifications and protection of bonded material
systems depend on an understanding of the interaction between bonded joint
mechanics and operating conditions.
References
1. Goland, M. and Reissner, E.J. (1944). J. Appl. Mech., 11, pp. A17-A27.
2. Hart-Smith, L.J. and Thrall, E.W. (1985). In Adhesive Bonding of Aluminum Alloys (E.W. Thrall
and R.W. Shannon, eds.), Marcel Dekker, New York, pp. 241-322.
3. Ripling, E.J., Mostovoy, S. and Patrick, R.L. (1963). In Adhesion - STP 360. Philadelphia: ASTM,
pp. 5-19.
4. Shaw, S.J. (1993). In Adhesion 7 - Proc. 20th Conf. on Adhesion and Adhesives (K.W. Allen. ed.),
Elsevier, London, pp. 173-196.
5. Mall, S.. Johnson, W.S. and Everett, R.A., Jr. (1982). In Adhesive Joints: Formation Characteristics
and Testing (K.L. Mittal ed.), Plenum, New York, pp. 639-656.
6. Johnson, W.S. and Mall, S . (1984). Proceedings of the 5th Int% Congress on Experimental Mechanics
Montreal: Society for Experimental Stress Analysis, pp. 267-271.
7 . Johnson, W.S. and Mall, S. (1985). In Delamination and Debonding of Materials - STP 876 (W.S.
Johnson, ed.), ASTM, Philadelphia, pp. 189-199.
8. Johnson, W.S. and Mangalgiri, P.D. (1987). In Toughened Composites STP 937 (N.J. Johnson. ed.),
ASTM, Phifadelphia, pp. 295-3 15.
9. Johnson, W.S. and Butkus, L.M. (1998). Fat & Frac. qfEngrg. Matls. & Structs., 21, pp. 465478.
10. Belason, E.B. (1994). In Composite Repair of Military Aircraft Structures. AGARD, Seville,
pp. 2/1-2112.
136
Advances in the bonded composite repair of metallic aircraft structure
11. Baker, A.A. (1994). In Composite Repair of Military Aircraft Structures. AGARD, Seville,
pp. 1/1-1/14.
12. Marceau, J.A., McMillan, J.C. and Scardino, W.M. (1978). Adhesives Age, pp. 37-41.
13. Valentin, R.V., Butkus, L.M. and Johnson, W.S. (1998). J. Comp. Tech. andRes. 20, pp. 108-119.
14. Butkus, L.M., Mathern, P.D. and Johnson, W.S. (1998). J. Adhesion, 66, pp. 251-273.
15. Rybicki, E.F. and Kanninen, M.F. (1977). Engrg Frac. Mech. 9, pp. 931-938.
16. Roderick, G.L., Everett, R.A. and Crews, J.H. (1974). In Fatigue of Composites - STP 569. ASTM,
Philadelphia, pp. 295-306.
17. Skinn, D.A., Gallagher, J.P., Berens, A.P., ef ai. (1994). Damage Tolerant Design Handbook. West
Lafayette, Purdue Research Foundation.
Chapter 7
ANALYTICAL METHODS FOR DESIGNING
COMPOSITE REPAIRS
L.R.F. ROSE and C.H. WANG
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
7.1. Introduction
This chapter presents a comprehensive analysis of the mechanics of bonded
repairs, with emphasis on explicit formulas and principles pertaining to the design
and evaluation of repairs. Due to the multiple-layer structure of bonded repairs,
which involve bonding orthotropic composite patches to cracked plates using
polymeric adhesives, the stress states that exist in a bonded repair are very
complex, as will be evident later in this chapter. Consequently this chapter focuses
on presenting the results of recent research in such a convenient form as to be
suited to the requirement of engineers and designers. Numerous references to the
derivations of formulas and more detailed explanations are given, but for most part
these are limited to sources that are generally available in the achieved journals and
books.
The primary function of bonded repairs is to sufficiently reduce the stressintensity factor of the crack being repaired so that (1) the residual strength has been
restored to an acceptable level, and (2) the growth rate of the crack under fatigue
condition is sufficiently slow to ensure an acceptable residual life, or inspection
interval. Therefore the stress-intensity factor of a repaired crack will feature
prominently throughout this chapter. To focus on the fundamental theoretical
aspects of the mechanics of bonded repairs, we shall consider a relatively simple
repair configuration, namely a centre-cracked plate being repaired by an elliptical
patch, as illustrated in Figure 7.1. Since a bonded repair may fail in a number of
modes, such as failure of the adhesive layer, failure of the plate near the termination
of the patch, and failure of the patch, analytical formulas will be derived for the
following quantities which are the primary interest in assessing the efficiency and
the viability of the repair:
137
Baker, A.A., Rose, L.R.F. and Jones, R. (e&.).
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 0 2002 Published by Elsevier Science Ltd. All rights reserved.
Advances in the bonded composite repair of metallic aircraft structure
138
A+-
Fig. 7.1. Repair configurations and coordinates. (a) Plan view, (b) cross section along centre line ( x = 0)
with no bending deflection allowed, representing two-sided repair, (c) cross section of a one-sided repair
along the centre line, (d) cross section at x + co for one-sided repair, and (e) near crack region.
1.
2.
3.
4.
the
the
the
the
stress-intensity factor K, (defined below) in the repaired plate,
maximum stresses in the adhesive, ogax,
maximum tensile stress in the reinforcing patch, oEax
maximum tensile stress in the plate near the outer boundary of the patch,
4l,X.
7taX
5. thermal residual stresses resulting from curing, 00'.
The plan of this chapter is as follows. The basic problem which will be considered is
formulated in Section 7.2, while Section 7.3 summaries some results of the theory of
bonded joints which will be required in the sequel. An analysis of the symmetric
repair, which is supported against out-of-plane deflection, is presented in Section
7.4, while Section 7.6 presents the solutions pertaining to an unsupported, onesided repairs. The problem of residual thermal stress, which can be important in
practice (see Chapter ll), is dealt with in Section 7.7.
Chapter 7. Analytical methods for designing composite repairs
139
7.2. Formulation and notation
Referring to Figure 7.1, the problem to be considered is a cracked plate with a
patch adhesively bonded on one side. The plate, which has a thickness of t p ,
contains a through-thickness crack of length 2a. The thickness of the patch and the
adhesive layer are respectively t R and t A . The cross sections in the y z and xz planes
are depicted in Figure 7.l(b) and (c) . The Young’s modulus and the Poisson’s ratio
of each individual layer are denoted as E and v; here and in the following subscripts
P , R, and A will be used to distinguish properties pertaining respectively to the
plate, the reinforcement and the adhesive layer. In addition, the shear modulus of
the adhesive will be denoted as pA. The crack is along the line segment
la1 5 a , y = 0, and patch is over an elliptical region defined by,
which completely covers the crack ( A > a). After this repair, the plate is subjected
to a remote stress specified by,
By using the superposition principle it is easy to demonstrate that the above
problem can be decomposed into a tensile mode (P= 0 ) and a shear mode
(cF
= 0). In this chapter we will focus on the tensile mode, while the shear mode
[14] will be briefly discussed in Section 7.5.
From a geometrical consideration, bonded repairs as illustrated in Figure 7.2 fall
into two categories: two-sided (symmetric) and one-sided (asymmetric). In the
former case two identical reinforcements are bonded on the two surfaces of a
cracked plate. This symmetric arrangement ensures that there is no out-of-plane
deflection over the repaired region, see Figure 7.l(b), provided the cracked plate is
subjected to extensional loads given by Eq. (7.2). In actual repairs, however, onesided repair is often adopted in which composite patches are applied to only one
side of the panel [12]. This is because most often, only one face of a structure to
be repaired is accessible and sometimes only one side of a structure is allowed
to be patched, e.g. aircraft fuselage or wing sections. Provided the structure to be
repaired is well supported against out-of-plane deflection, for instance, by stiffeners
attached to one side, it is acceptable to ignore the out-of-plane bending, thus
permitting the problem to be treated as being symmetric. However, in the case of
un-supported, one-sided repairs, the out-of-plane bending caused by the shift of the
neutral plane away from that of the plate may considerably lower the repair
efficiency.
By using the superposition principle it is easy to demonstrate that the problem
depicted in Figure 7.1 is equivalent to solving the following perturbation problem:
a patched crack subjected to an internal pressure, -GO, acting on the crack faces, as
depicted in Figure 7.3. This allows the analysis to be divided into two stages [9].
First we consider the re-distribution of stress which would be caused by the
140
Advances in the bonded composite repair of metallic aircraft structure
ca
u
-
FA
U
t t ? t t t ? ?
Z
q - 4 4 4 4 4 4
4A'
-
U
(a)
(b)
Fig. 7.2. Inclusion analogy for stage I analysis. (a) Flow of load lines into reinforced portions; (b) Crosssection along centre line.
reinforcement if it were bonded to an un-crackedplate, see Figure 7.2. The quantity
of interest is the normal stress 00 along the prospective crack path in the uncracked
plate. For the case of symmetric repairs (no out-of-plane bending), this prospective
stress 00 is uniform through the plate thickness, whereas in the case of unsupported one-sided repairs, the prospective stress distributes linearly through the
plate thickness [12], as illustrated in Figure 7.3(b) and (c). At the second stage, we
determine the stress distribution around the crack subjected to an internal pressure
of -00. Due to the presence of the crack, a stress singularity exists at the two crack
tips at x = f a . Here the stress-intensity factor K, at the crack tip x = a is defined
as,
Z
(a)
(b)
(C)
Fig. 7.3. A patched crack subjected to internal pressure.
Chapter I . Analytical method for designing composire repairs
141
where the stress O;~(.Y, y = 0, z ) is yet to be determined in terms of the internal stress
and the repair dimensions and constituent properties. Depending whether the
repair is supported against out-of-plane bending, the stress-intensity factor may
vary through the plate thickness; details will be presented in Section 7.6.
In the absence of a reinforcing patch, the normal stress ocx parallel to the crack
would not affect the stress intensity factor, but this is no longer true for the repaired
plate. After the repair, K, will depend on the applied stress ratio 3. defined by Eq.
(7.2) and also on the aspect ratio B / A of the reinforcement. Provided the adhesive
layer remains elastic, the main unknowns K,, okax,7 i a x , o:ax, and o;,, will depend
linearly on the principal applied stress CFof Eq. (7.2). The analytical results which
will be derived in Sections 7.4, 7.5, and 7.6 will show clearly the parametric
dependence of these unknowns on the dimensions and material properties of a
repair configuration.
Since a bonded repair represents a multiple layered structure with a crack being
present in one layer only, an exact, analytical solution of this 3D problem is an
almost intractable task. Hence it is imperative to make appropriate simplifications
to enable the derivation of analytical solutions that can capture the essential
features of repairs. It should be noted that there is no fundamental difficulty in
employing a fully 3D finite element method to estimate the stresses and stressintensity factors in a patched structure. It is, however, often impractical nor
necessary to rely solely on time-consuming finite element computations for routine
engineering designs, especially if parametric analysis is required to optimise a
design and to study the sensitivities of repairs to varying geometry dimensions and
material properties. In this regard, analytical solutions would be preferred over
numerical solutions because the analytical solutions enable efficient optimisation of
designs.
00
7.3. Load transfer of bonded reinforcement
To facilitate the following analysis, let us now consider first the simple
reinforcement configuration shown in cross-section in Figure 7.4(a), in which a
reinforcing strip of length 2B and thickness t R bonded to an infinite strip of
thickness t p ; both strips are under plane strain conditions ( E =
~ 0). The choice of
axes is designed to correspond with that used for the repair configuration in
Figure 7.1.
The stresses and displacements in this reinforced strip can be calculated explicitly
using the conventional ID theory of bonded joints (see, e.g. [4,5]),which is based
on the following assumptions.
i. Each adherend is treated as an elastic continuum whose deformation under
plane strain conditions is specified by longitudinal displacement u and a
longitudinal tensile stress o, see Figure 7.4(b). The problem of bending
deformation will be considered later. The out-of-plane deformation, the stress-
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Advances in the bonded composite repair of metallic aircraft structure
I
(e)
-4u +
plate
..
:
.
:
i
!
..
j
-
U
4. b l. e
Fig. 7.4. Load transfer length for loaded reinforcement: (a) cross-section for bonded strips; (b) adhesive
shear stress distribution; (c) equivalent rigid bond configuration.
displacement relations for the plate and the reinforcement respectively are
ii. The adhesive layer acts as a shear spring with the adhesive shear stress T A given
by, referring to Figure 7.4(c)
Chapter 7. Analytical methods for designing composite repairs
...
111.
143
The shear tractions exerted by the adhesive on the plate and the reinforcement
can be replaced by an equivalent body force of Xp and XR, respectively, i.e.
x
p
TA
=-
tP
,
xR=--
TA
tR
In the present case, the equilibrium equations for the plate and the reinforcement
reduce to,
(7.7)
which lead to
which can be rewritten as
where
(7.10)
The general solution of the adhesive shear stress zA is given by
ZA
= C1 sinh By
+ C2 cosh by ,
(7.1 1 )
where C1 and C2 are two integration constants yet to be determined from the
boundary conditions. It should be pointed out that here the complexities of triaxial
stress, stress singularity, and stress concentration in the adherends are considered in
[13,15,20].
For the configuration of Figure 7.4(a) we require the adhesive shear stress z A to
be odd in y , therefore C2 = 0. The remaining constant C1 can be readily determined
from the following boundary conditions: op(y = fB) = o", OR(^ = B) = 0.
Therefore,
(7.12)
The important feature of this result is that for BB -g 1, the adhesive shear stress
decays exponentially from ends 0,= fB) of the overlap, as sketched in Figure
7.4(d); i.e. the load transfer effectively occurs over a length of order p-' at the ends of
the overlap. To better elucidate this point, let us integrate Eq. (7.7) twice to derive the
displacement up(y), one can readily verify that the overall stiffness between the end
points y = B of the reinforced strip in Figure 7.4(a) is the same as that of a strip
Advances in the bonded composite repair of metallic aircrafi structure
144
+
with a step change in stiffness from ~ p t p / 1( - v’,) to Eptp/( 1 - v’,)
E R t R / ( 1 - vi)
over a central potion ly( 5 B - b, as indicated in Figure 7.4(e), with b given by
1
1
b = - tanh j?B-
B
“P
’
(BB< 1)
(7.13)
This equivalence will be exploited in Section 7.4 to assess the redistribution of stress
due to a bonded reinforcement.
The prospective stress in the plate directly underneath the reinforcing strip,
00 = o p ( x = 0), can be readily determined by integrating Eq. (7.4),
(7.14)
with S denoting the stiffness ratio given below,
(7.15)
which is an important non-dimensional parameter characterising a repair. As will
be shown in the following section the actual prospective stress 00 is somewhat
higher than that given by Eq. (7.14). This under-estimation is primarily due to the
ignorance of the “load attraction” effect in a 2D plate associated with reinforcing.
7.4. Symmetric repairs
We return to the solution of the problem formulated in Section 7.2, assuming
that the repaired structure is supported against out-of-plane bending or the cracked
plate is repaired with two patched bonded on the two sides. The analysis will be
divided into two stages as indicated in Section 7.2.
7.4.1. Stage I: Inclusion analogy
Consider first the re-distribution of stress in an uncracked plate due to the local
stiffening produced by the bonded reinforcement. As illustrated in Figure 7.2(a),
the reinforced region will attract more load due to the increased stiffness, leading to
a higher prospective stress than that given by Eq. (7.14). The 1D theory of bonded
joints (Section 7.3) provides an estimate of the load-transfer length j?-’ for load
transfer from the plate to the reinforcement. If that transfer length is much less
than the in-plane dimensions A, B of the reinforcement, we may view the reinforced
region as an inclusion of higher stiffness than the surrounding plate, and proceed in
the following three steps.
1. Determine the elastic constants of the equivalent inclusion in terms of those of
the plate and the reinforcing patch.
2. Determine the stress in the equivalent inclusion.
Chapter 7. Analytical methodsfor designing composite repairs
I45
3. Determine how the load which is transmitted through the inclusion is shared
between the plate and the reinforcement, from which the prospective stress 00
can be calculated.
Step (2) is greatly facilitated by the known results of ellipsoidal inclusions [3]: the
stress and strain within an ellipsoidal inclusion is uniform. as indicated
schematically in Figure 7.2(a). The uniform stress state can be determined
analytically with the help of imaginary cutting, straining and welding operations.
The results are derived in [SI for the case where both the plate and the reinforcing
patch are taken to be orthotropic, with their principal axes parallel to the s - y
axes. We shall not repeat here the intermediate details of the analysis but simply
recall the results for the particular case where both the plate and the reinforcement
are isotropic and have the same Poisson's ratio, v p = V R = v. The prospective stress
in the plate along y = 0 within the reinforced region (1x1 I A ) is
6 0 = &T=
(7.16)
~
where
'[
B
A
A
B
4 ~ 4-+ 2 - + 2 - + S
Z
(7.17)
with
2 = 3( 1
+ S ) 2 + 2( 1 + S ) ( B / A + A / B + v S ) + 1 - v2S2
(7.18)
It is clear that the stress-reduction factor 4 depends on three non-dimensional
parameters: (i) the stiffness ratio S, (ii) the aspect ratio B / A , (iii) the applied stress
biaxiality i.. The parameters characterising the adhesive layer do not affect 00, but
we recall that the idealisation used to derive Eq. (7.17) relies on B-' < A , B, and p-'
is of course dependent on adhesive parameters.
To illustrate the important features of Eq. (7.17), we show in Figure 7 3 a ) the
variation of the stress-reduction factor 4 with aspect ratio for two loading
configurations: (i) uniaxial tension (
=
i0), and (ii) equal biaxial tension
corresponding to pure shear (A = -l), setting S = 1 and v = 1/3 for both cases.
It can be seen that there is little variation for aspects ratio ranging from B / A = 0
(horizontal strip) to B / A = 1 (circular patch), so that for preliminary design
calculations, one can conveniently assume the patch to be circular, to reduce the
number of independent parameters. It is also noted from Eq. (7.17) that for v = 1/3
and a circular patch ( A / B = I), the stress-reduction factor cp becomes independent
of the biaxiality ratio A. As illustrated in Figure 7.5(a) the curves for 1 = 0 and
;L = -1 cross over for B / A = 1, indicating that, for a circular patch, the transverse
stress gFXdoes not contribute to the prospective stress, so that this parameter can
also be ignored in preliminary design estimates. In this particular case, the stressreduction factor 4 depends on the stiffness ratio S only, as depicted in Figure
7.5(b), together with the first-order approximation given by Eq. (7.14). It can be
seen that the first-order solution ignoring the load attraction effect of composite
146
Advances in the bonded composite repair of metallic aircraft structure
Uniaxial tension(X=0)
0.9
Pure shear(X=-1)
". .
0
0.2
0.4
0.6
0.8
Aspect ratio of patch B/(A+B)
1 .o
(a)
1.o
0.9
0.8
a 0.7
-8
0.6
2
0.5
2
0.4
2
0.3
0.2
o Exactsolution
-+ = (1+0.277S-O.O712S2)/(l+S)
0.1 - - - & = 1/(1+S)
0
0
0.5
1.o
1.5
2.0
Stiffness ratio S
(b)
Fig. 7.5. Variation of reduced stress with (a) aspect ratio for an elliptical patch of serni-axes A and B
under uniaxial tension and biaxial tension equivalent to pure shear; (b) stiffness ratio S for a circular
patch.
patch overestimates the reduction in plate stress. An improved solution can be
obtained by constructing an interpolating function based on the exact solution,
$=
1
+ 0.277s - 0.0712S2
l+s
,
(7.19)
which is shown by solid curve in Figure 7.5(b), indicating a very good fit to the
exact solution.
The inclusion analogy also gives, as a natural by-product, the stress in the plate
outside the reinforced region. The stress at the point x = 0, y = B+ is of particular
interest, because this stress represents the increased stress due to the so-called load
Chapter 7. Analytical methods for designing composite repairs
147
attraction effect; a load attraction factor Q L can be defined as the ratio of the plate
stress just outside the patch to the remote applied stress
(7.20)
It is clear from Figure 7.5(a) that for the case of a balanced patch ( S = 1) under
uniaxial tension, this load attraction factor ranges between 1 for patch of infinite
width to 2 for patch of zero width. For the typical case of circular patch, the load
attraction factor is approximately 1.2.
7.4.2. Stage 11: Stress intensity factor
Once the stress at the prospective crack location is known, one can proceed to the
second stage of the analysis in which the plate is cut along the line segment
(1x1 5 a, y = 0), and a pressure equal to g o is applied internally to the faces of this
cut to make these faces stress-free. Provided that the load transfer to the
reinforcement during this second stage takes place in the immediate neighbourhood
of the crack, the reinforcement may be assumed to be of infinite extent. Thus the
problem at this stage is to determine the stress intensity factor K, for the
configuration shown in Figure 7.3(a).
Without the reinforcement, the stress-intensity factor would have the value KO
given by the well-known formula,
(7.21)
KO = ~ o f i
This provides an upper bound for K,, since the restraining action of the patch
would reduce the stress-intensity factor. However, KO increases indefinitely as the
crack length increases, whereas the crucial property of the reinforced plate of
Figure 7.3(a) is that K , does not increase beyond a limiting value, denoted by K,,
as will be confirmed later. That limiting value is the value of the stress intensity
factor for a semi-infinite crack. It can be determined by deriving first the
corresponding strain-energy release rate as follows. Before we proceed, let us first
determine the deformation of the reinforced strips shown in Figure 7.3(b). The
adhesive shear stress ZA is governed by the differential Eq. (7.9), which has the
following solution for the particular case of semi-infinite strip,
~ A ( Y )= ZA,rnaxe-’.’
,
(7.22)
where rmax can be determined from the simple equilibrium condition,
QOtf =
ZA ( Y P Y ,
so“
ZA,max =
P~P~o
(7.23)
Recalling Eq. (7.4), the opening displacement of the plate at y = 0 can be readily
Advances in the bonded composite repair of metallic aircraft structure
148
determined,
(7.24)
Let us denote the total opening as 6 = 224,. The above equation can be rewritten as,
(7.25)
with
(7.26)
Consider the configuration shown in Figure 7.6. If the semi-infinite crack extends by
a distance da, the stress and displacement fields are simply shifted to the right by da.
The change in the strain energy UE is that involved in converting a strip of width da
from the state shown as section AA' in Figure 7.6 to that shown in section BB', as
depicted in Figure 7.7. Consequently the change in the potential energy
for a
crack advancement ha, which is defined as the difference between the strain energy
change UE (= 1/2ootp6) and the work performed by the external load W (= G o t p J ) ,
1
n=uE-w=--rJ
OtPd
(7.27)
The crack extension force, Le. the strain-energy release rate G, is given by
(7.28)
which can be re-written as, recalling Eq. (7.25),
(7.29)
B4
B
A
A
* A'
A'
+Z
B'
B'+
Fig 7 6 A patched crack subjected to internal pressure
Chapter 7. Analytical methods for designing composite repairs
149
s
6
(a)
(b)
Fig. 7.7. Illustration of the interpretation of G , as a complementary energy. (a) Elastic adhesive and (b)
elastic-plastic adhesive.
From the above equation, assuming that the usual relation holds between the strainenergy release rate G and the stress-intensity factor K [22], we obtain,
K
00
(7.30)
--
"-&
It is clear from this derivation that K , is an upper-bound for K,. The validity of this
formula will be substantiated by an independent finite element analysis to be
discussed later.
7.4.3. Plastic adhesive
The stress-intensity factor solution derived in the previous section is valid only if
the adhesive remains elastic. If the maximum adhesive shear stress does exceed the
shear yield-stress, the relationship between 00 and the crack-opening displacement
6 will become non-linear, as illustrated in Figure 7.7(b), which also shows the
correct area corresponding to G,. For an adhesive that is elastic-perfectly plastic
with a shear yield-stress z y , the adhesive begins to yield at the following stress,
boy
ZY
(7.31)
=BtP
It can be shown that for
ZYtA
=- P A
[
1+
00
~
(;y)2]
2 boy the crack opening-displacement 6 is given by,
I*)$(
=E
[I +
(7.32)
(00 2 b o y )
>
Following the method outlined in the previous section, the strain-energy release
rate G , can be determined,
s
G , = o06 - /bods =
0
/
0
/
60
00Y
6doo
+
0 0Y
cri
6doo = kEp
[
P3+3P-1
3p2
]'
(7.33)
Advances in the bonded contposite repair of metallic aircraft structure
150
where
p = -c0
(7.34)
0 0Y
Then, the stress-intensity factor for P 2 1 can be expressed as
(7.35)
where K,,el denotes the value which would be obtained from Eq. (7.30) for the
stress a0 ignoring the plastic yielding in the adhesive. As can be seen from
Eq. (7.35), the increase in Km due to adhesive yielding depends only on the
plasticity ratio P defined by Eq. (7.34), as shown in Figure 7.8.
7.4.4. Finite crack size
1.4
4
\
hi
8
d
1.3
b
'I*
1.2
."A
2
D
LI
1.1
.0
CI
1.0
Adhesive plasticity ratio P
Fig. 7.8. Increase in stress-intensity factor due to adhesive yielding.
Chapter 7. Analytical methods for designing composite repairs
151
h
g
1.00
5
3
>.I
..3
)
2 0.75
sC
.3
r(I)
n
E
Y
.e
0.50
C
0
.e
Y
0
-m
S
2
0.25
0.01
0.1
1
Nomalised crack length ku
Fig. 7.9. Reduction in stress-intensity factor for various patch configurations. Symbols denote the exact
solutions by the Keer method, solid curves denote the interpolating function, and dashed curve denotes
the solution of crack bridging model.
reduction factor Fdepends strongly on the parameter k given by Eq. (7.26) and to a
lesser extent on the stiffness ratio S, as shown by the symbols in Figure 7.9. Based
on the solutions of the integral equation [141, the following interpolating function
can be constructed,
112
F(ku) = [nLu
-tanh (1 : z k u ) ]
’
(7.37)
where constant B has been determined by curve fitting the numerical solution of the
integral equation, which gives B = 0.3 for balanced repairs ( S = 1.O) and B = 0.1
for infinitely-rigid patch ( S + a).
A simple yet more versatile method of determining the reduction in stressintensity factor after repair is the crack bridging model [lo], which has been
recently extended to analyse the coupled in-plane stretching and out-of-plane
bending of one-sided repairs [17]. From the previous analysis it is clear that the
essential reinforcing action at the second stage is the restraint on the crack opening
by the bonded reinforcements. The basic idea underlying the crack bridging model
is that this restraining action can be represented by a continuous distribution of
springs acting between the crack faces, as illustrated in Figure 7.10. This
idealisation reduces the problem at stage TI to two parts: (i) determine the
appropriate constitutive relation (i.e. stress-displacement relation) for the springs,
and (ii) solve a one-dimensional integral equation for the crack opening,
6(x) = ulr(x,y
+ Of)
- .,’(x,y
+ 0-)
= 2u;(x,y + O + ) , 1x1 5 a
(7.38)
It is assumed that distributed linear springs act between the crack faces over the
152
Advances in the bonded composite repair of metallic aircraft structure
go
t t t t t t t t t t l
X
Fig. 7.10. Schematic representation of a centre-crack reinforced by distributec jprings.
crack region so that the boundary conditions on y = 0 are
u,,(x) = 0,
1x1 2 a
,
(7.39b)
where k denotes a normalised spring constant which has dimension length-’. It is
worth noting that this normalised spring constant k has already been determined in
Section 7.4.2 and is given by Eq. (7.26). With these boundary conditions, the
problem of determining the crack opening displacement u,(x) can be reduced to
that of solving the following integral equation [lo, 171,
(7.40)
The integral in the above equation is interpreted as a Hadamard finite part [24],
which can be viewed as the derivative a Cauchy principal value integral. The above
equation can be efficiently solved using either Galerkin’s method or collocation
methods. Once the crack-opening displacement u J x ) is determined, the stressintensity factor K, can be calculated by
(7.41)
Detailed numerical results for K, are available in reference [lo], which also
provided the following interpolating function constructed based on the numerical
153
Chapter I . Analytical methods for designing composite repairs
,patch
- adhesive
,plate
(b)
Fig. 7.11. Finite element mesh (a) quarter model and (b) mesh near crack tip.
results,
F(ka) =
1
1 + 2.23ka
+ 4.776ka + 7 ( k ~ ) ~
(7.42)
154
Advances in the bonded composite repair of metallic aircraft structure
0.06 I
D
1
- -E) FE ITSUI~S
s-
1.0
k = 0.096 mm-'
0'
-0.45-0.30-0.15
0
0.15 0.30 0.45
Normalii coordinatez l t p
(a)
0
.-
0.03
*
w
s
-
1.0
k = O.096mm'
0.02
o
FEmults
- Equation (36)
Equation (40)
30
60
90
120
Crack length a (mm)
(b)
Fig. 7.12. Comparison between finite element solution and analytical predictions.
which is shown in Figure 7.12(a). As compared to the exact solutions by the Keer
formulation (Eq. 7.37), the crack-bridging model (Eq. 7.42) slightly over-estimates
the reduction in stress-intensity factor for balanced repair (S= 1) in the short crack
limit. Both the two interpolating formulas, Eqs. (7.37) and (7.42) recover the
asymptotic solution of Eq. (30) in the long crack limit as a + co.
7.4.5. Finite element validation
To substantiate the theoretical solutions obtained so far, an extensive finite
element analysis has been performed for various crack lengths [12]. Due to
symmetry only a quadrant of the repair shown in Figure 7.l(a) was modelled. No
Chapter 7. Analytical methods for designing composite repairs
I55
Table 7. I
Dimensions and material properties of a typical repair.
Layer
Young’s modulus
(GW
Poisson’s ratio
Thickness
(mm)
Plate
Reinforcement
Adhesive
71
207
1.89
0.3
0.3
0.3
3.0
1 .O
0.2
debond between the plate and reinforcement or adhesive plasticity was considered.
The finite element mesh near the crack tip region is shown in Figure 7.1 1. All three
constituents, the patch, the adhesive, and the plate are assumed to deform
elastically only, and are each modelled by 20-noded isoparametric brick elements.
The dimensions and material properties of the repair configuration being
considered are summarised in Table 7.1. For this repair, we have the shear stress
transfer length b-’ = 5.634 mm, and the normalised spring constant
k = 0.096 mm-’ . From the finite element results, the stress-intensity factor is
calculated using Eq. (7.41), with Ep being replaced by the plane-strain value
E p / ( 1 - v2).
Figure 7.12(a) shows a comparison between the theoretical estimate and the finite
element results for a long crack ( k a z lo), indicating an excellent agreement within
the mean stress-intensity factor through the plate thickness. It is also clear that the
stress-intensity factor at the outer surface away from the adhesive layer is
somewhat higher than near the adhesive layer. The asymptotic behaviour of the
stress-intensity factor is shown in Figure 7.12(b) together with the two analytical
estimates (37) and (42). The crack-bridging solution seems to slightly over-estimate
the repair efficiency.
7.5. Shear mode
Although cracks that are likely to be encountered in practice are generally
aligned in a direction perpendicular to the principal tensile stress (or strain), giving
rise to mode I cracking, there are at least two circumstances where mixed mode
cracking is a major concern in the context of bonded repairs. Firstly, application of
bonded reinforcements, which are frequently anisotropic, may alter the local stressstate near the crack region so that the maximum principal stress may no longer
remain perpendicular to the crack plane. Secondly, structures are frequently
subjected to non-proportional loading in which the principal stress-strain axes
rotate with time, thus cracks may experience a time-dependent mixed mode
loading. If the bonded repair technique is used to repair mode I1 cracks. one
important question that needs consideration is the effectiveness of repairs.
For simplicity let us consider the particular case of an isotropic circular patch
( A / B = I ) with a Poisson’s ratio v = 1/3. In this case, the prospective stress in the
plate after repair can be determined using the general solution for biaxial tension
Advances in the bonded romposite repair of metallic aircraft struriure
156
presented in Section 7.4.1, namely Eq. (7.19),
70
=
1 + 0.2773 - 0.0712S2
r"
l+S
1
(7.43)
Detailed solution of the stress-intensity factor K, for shear loading can be found in
[14]. We shall not repeat here the intermediate details of the analysis but simply
recall the results for the upper-bound and the interpolating function. The upperbound solution of Kr is given by an equation similar to that for tensile mode,
(7.44)
where the normalised shear spring constant kI1 is given by
kII =
AS
2(1 +S)(1 + v ) '
(7.45)
with
(7.46)
It is evident that kII is lower than the spring constant pertinent to mode I. For
instance, in the case of isotropic patch kI1 is related to the spring constant kI for
mode I crack,
(7.47)
For finite crack size, the stress-intensity factor Kr can also be expressed as [14]
with F ( x ) being given by Eq. (7.37) or Eq. (7.42).
An important implication arising from the difference in the spring constants is
that when strongly anisotropic reinforcements with low in-plane shear modulus,
such as unidirectional plastic reinforced composites, are used to repair a crack
under shear loading (with the fibres being perpendicular to the crack), the repair
efficiency will be much lower than that could be expected on the basis of mode I
analysis. It should of course be mentioned that under remote shear loading, the
crack would be aligned perpendicular to the maximum tensile stress, hence aligning
the fibres perpendicular to the crack is still the optimal configuration.
Chapter 7. Analytical methods for designing composite repairs
157
7.6. One-sided repairs
So far we have ignored the tendency for out-of-plane bending that would result
from bonding a reinforcing patch to only one face of an un-supported plate, so
that, strictly speaking, the preceding analysis is more appropriate for the case of
two-sided reinforcement, with patches bonded to both faces, or one-sided repairs to
fully supported structures. For the case of un-supported one-sided repairs, it is
again convenient to divide the analysis into two stages. In Section 6.1 the stress
reduction due to stage I will be anaiysed within the framework of geometrically
linear elasticity [121, whereas a geometrically non-linear analysis [171 will be
presented in Section 7.6.2. These two solutions will provide an upper and lower
bound to the actual stress distribution. In both cases the geometrically linear
analysis is all that needed for stage 11. For stage I we shall consider the particular
case where the reinforcement covers the entire cracked plate, ignoring the load
attraction effect.
7.6.I . Geometrically linear analysis
Consider first the effect of one-sided reinforcement on an un-cracked plate which
is subjected to a uniaxial tension. Assuming that the reinforcement is far greater
than the shear stress transfer length, we treat the reinforced region as a composite
plate with a rigid bondline. The stress distribution in the plate and the
reinforcement can be determined using the conventional theory of cylindrical
bending of plates, i.e. we shall assume that the bending deformation of the
reinforced portion satisfies the usual kinetic condition that plane sections remain
plane. The position of the neutral plane of the composite plate consisting of the
base plate and rigidly-bonded reinforcement is denoted by F, referring to Figure
7.13,
(7.49)
The moment of inertia of the reinforced region Zl is
zI
=
zp + z ~ E ; / E ; ,
(7.50)
where E’ refers to the plane-strain Young’s modulus (E’ = E/( 1 - v2)), and
zp =
4/12
+ tpP ,
(7.51)
The stress distribution in the patched plate is assumed to be linear in the thickness
direction, so that it can be specified in terms of the membrane force NO and a
bending moment Mo per unit length in the x-direction, as depicted in Figure 7.13
Advances in the bonded composite repair of merallic aircraft structure
158
c
neutral axis of
composite section
(b)
Fig. 7.13. Stress distribution in an un-cracked plate reinforced with a patch (a) composite plate
subjected to uniaxial tension; (b) stress distribution in the plate.
(see [12,17] for more details),
No
P t p
oyY(y= 0,z)dzE -
=
rJmt;9
1+s+I, ’
(7.53)
4P/2
1
IP
Mo = -
I2
rJ* t;2
ay,,(y = 0,z)zdzE -
121,
(7.54)
Comparison between Eqs. (7.14) and (7.53) clearly shows that the plate in a onesided repair is transferring more membrane stress than in an equivalent two-sided
repairs. Therefore, due to out-of-plane bending induced by load eccentricity, the
stress distribution along the prospective crack path before the crack appears is
higher than for a corresponding two-sided reinforcement. In addition, there is a
bending moment acting on the prospective crack faces. Consequently, due to the
shift of neutral plane, one-sided repairs would experience not only an increase in
the net force that the plate is transmitting, but also a secondary bending moment;
both contributing to a considerable increase in stress-intensity factor.
In stage 11, analysis of the crack-tip deformation requires the use of the shear
deformation theory, which yields that the stress intensity factor varies linearly
through the plate thickness,
Chapter I . Analytical methods for designing composite repairs
159
No
(b)
Fig. 7.14. (a) Single strap joint representing one-sided repairs subjected to membrane tension and
bending moment, and (b) notations and boundary conditions.
where K,,,, and Kb denote respectively the membrane and bending stress intensity
factors. The strain-energy release rate can be determined following the method
outlined in Section 7.4.2, except that the change in the potential energy now
consists of two terms: work done by the membrane force and the bending moment
[12], referring to Figure 7.14,
tpG: = Nouo
+ MoOo ,
(7.56)
where the superscript "* " refers to the strain-energy release rate for one-sided
repair, and uo and 190 denote the opening displacement and the angle of rotation of
the crack faces, which are related to the membrane force NO and MO via the
following relation [ 171,
(7.57)
Advances in the bonded composite repair of metallic aircraft structure
160
with
(7.61)
Egt;
Dp =-
(7.62)
12 '
(7.63)
(7.64)
Therefore the total strain-energy release rate can be expressed as
*
1
+ (Ci2 + ~21)NoMo+ C22M;]
G, = - [CIIN;
tP
(7.65)
which can be simplified to become
*
(o"o)2 0
G , =(1+q2
2
'
(7.66)
where k is given by Eq. (7.26), and the term o is well approximated by the following
expression [12],
Chapter 7. Anal.vtica1 method7 for designing composite repairs
0.3,
. ~~.
~~.
.~~
...
...
161
--.
-.-
0.2
0.1
R
--
~
c1
FE results (PAFEC)
Two-sided repair
"0
50
150
Half crack length a (mm)
100
I
200
Fig. 7.15. Comparison between analytical solution and finite element results for one-sided repairs.
Symbols denote the results of three-dimensional finite element analysis and the curves indicate the
theoretical formulas.
Consequently the root-mean-square stress-intensity factor K3c,rmsfor one-sided
repair can be expressed as,
(7.68)
It is now possible to define a spring constant for one-sided repairs,
(7.69)
With this spring constant, the stress intensity factor for a one-sided repair can be
expressed in a similar form as for two-sided repairs,
6"
Kms(u)= -&Fi(k*a)
1+s
,
(7.70)
where F, is given by Eq. (7.37). Figure 7.15 shows a comparison between Eq. (7.70)
and the results of 3D finite element analyses. The repair configuration being
considered is the same as that analysed in Section 7.4.4. The same problem has been
analysed using two different finite element codes, namely ABAUQS [26] and
PAFEC [25];both yielded approximately the same result. It can be seen that the
above formula is in good correlation with the finite element results. It is also worth
noting that the results confirm that the stress-intensity factor Krmsfor a one-sided
repair is much higher than that for an equivalent two-sided repair, indicating the
importance of out-of-plane bending.
Advances in the bonded composite repair of metallic aircraft structure
162
+
Fig. 7.16. A plate with a through crack reinforced with tension and bending springs.
The root-mean-square stress-intensity factor Kms is related to the membrane and
bending stress intensity factors [12],
(7.71)
Although the root-mean-square of the stress intensity factor has been derived, the
maximum and minimum stress intensity factors still remain unresolved. It is
apparent that the energy method alone is insufficient determine the membrane and
bending stress intensity factors, as an additional equation is required to partition
K,
into membrane and bending components. To this end, let us now briefly
discuss a crack-bridging model which is capable of analysing the combined tensile
stretching and bending of one-sided repairs.
7.6.2. Crack bridging model
The perturbation problem of stage I1 for a one-sided repair can be reduced by
representing the patch by distributed springs bridging the crack faces [ 171, as
illustrated in Figure 7.16. The springs have both tension and bending resistances;
their stiffness constants are determined from a ID analysis for a single strap joint,
representative of the load transfer from the cracked plate to the bonded patch. The
spring constants are given by Eq. (7.57). For the purpose of parametric
investigation, we introduce the following non-dimensional variables,
hl(X)
=- ,
U
1
6
h 2 ( x ) = -etp/a
(7.72)
Chapter I . Analytical methods for designing composite repairs
163
By using Reissner’s plate theory, the normalised crack face displacement hl and
normalised crack face rotation h2 are solutions of the following coupled integral
equations [ 171,
1
1 -2x-
Jm
dq
-I
NO
+ (ktta)hl( r )+ (ktba)h2(r)= ,
EP tP
(7.73a)
where
(7.76)
with KOand K2 are the modified Bessel functions of the second kind. The integral
equations can be readily solved by expanding the unknowns using Chebyshev
polynomials of the second kind. The membrane and bending stress intensity factors
K, and Kb are directly related to the values of hl and h2 at q + 1.
With the prospective membrane force NO and bending moment MOare given by
Eqs. (7.53) and (7.54), respectively, the membrane and bending stress intensity
factors can be solved. For the repair configuration specified by Table 7.1, the results
are shown in Figure 7.17 together with the finite element results. Considering the
approximate nature of the crack bridging model and the finite element method, the
reasonably good correlation between the predictions and the finite element results
confirms the validity of the above theoretical model.
7.6.3. Geometrically non-linear analysis
The geometrically linear analysis presented in the preceding section is strictly
speaking applicable only when the out-of-plane deflection is negligible relative to
plate thickness, i.e. when the applied stress om is very low. Otherwise the
geometrically non-linear deformation, as indicated in Figure 7.18, has to be taken
Advances in the bonded composite repair of metallic aircraft structure
164
Fig. 7.17. Theoretical predictions and finite element results for a typical one-sided repair assuming
geometrically linear deformation.
t"
.-.-.-.-.-.-.-.-.-.___.__.-.-.-.-.-.-.--.-.-.-.-.-.^.-.-.
zf
y ;
s
U
-
U
.r/
: + B 4 4 - - - - l . ~ ;
Fig. 7.18. Geometrically non-linear deformation of a single strap joint representing one-sided repairs.
into account. We shall use the rigid-bond approximation and denote the deflection
of the plate as w. The governing equation for the deflection of the beam inside and
outside the repaired region is,
d2w
EpIt -= ~ " O t p ( w 2)
dY2
+
d2w
EpZp-
dY2
=P t p w
,
a
, IyI 5 B ,
(7.77a)
5 JyI 5 B + L ,
(7.77b)
where It and I p are given by Eqs. (7.50) and (7.51) respectively. The boundary
condition is
w(y = B + L) = 0
(7.78)
The general solution of the deflection w is
w = { C1coshp+C2sinhp-z
C3 cash xPy + C4 sinh xPy
(Iyl < B )
,
(a 5 Iyl I
B
+ L) ,
(7.79)
Chapter 7. Analytical methods for designing composite repairs
165
where
(7.80)
and constants C1, CZ,C3, and C, can be determined from the boundary condition
(78) and the following continuity and symmetry conditions,
.C(y = 0) = 0
,
(7.81)
W(Y = B-) = ~ ( =yB+)
(7.82)
d ( y = B - ) = W’(Y = B+)
(7.83)
After some derivation the following constants are determined,
z
CI =
- r: tanhz B-tanhxp(B+L)] tanhXB
1
’
(7.84a)
~,[I-qanh~~Btanh~,(B+L)]
c2=0
(7.84b)
1
c
3 =
-C1
c
4 =
-
xsinh~Btanhx,(B+ L )
xp cosh xpB[l - tanh xpB tanh xp(B
c
3
+L)] ’
+
tanh x p ( B L )
(7.84~)
(7.84d)
The deflection at the centre of the reinforcement is given by
M’(Y = 0) = CI - z
(7.85)
The above solution has been verified for a particular strap-joint representing the
one-sided repair specified in Table 7.1. In the finite element analysis, the lengths B
and L are taken to be 80 and 200 mm. The results for the deflection at the centre of
the joint y = 0 are shown in Figure 7.19(a) together with the analytical prediction
(85), indicating the accuracy of the beam theory solution. Similarly the finite
element results for the deflection along the joint and Jhe analytical solution are
shown in Figure 7.19(b), together with the analytical solution (79), indicating a
good agreement. From the above analytical solution it is clear that the
displacement w at the centre of the strap joint w depends on three non-dimensional
parameters, xB, x p / x , and LIB. It is easy to show that w approaches -2 as
xpB + x,provided LIBZO. This limiting case corresponds to when the neutral
axis of the patched region is aligned perfectly with the path of the applied load.
Advances in the bonded composite repair of metallic aircrafi structure
166
Normalised overlap length ZB
0
-
3
9
nO
s
-
i
.
e- -
.7
l
i
200
100
0
FE results (non-linear)
Analytical solution
400
300
Applied stress om (MPa)
(a)
t- -
-
~
-1.2'
0
"
'
"
FE solution (non-linear) .
Analytical solution
loo
'
'
'
" '
200
'
"
'
300
Coordinatey (mm)
(b)
Fig. 7.19. Deflection of a one-sided strap joint accounting for geometrically non-linear: deformation: (a)
centre of overlap, and (b) along the joint.
Since the bending moment at the centre of the overlap is
M(y =0) = C,Ptp
,
(7.86)
the prospective membrane force and bending moment can now be determined,
No =
A40 =
omtp
1+s+
c,a-t$z
It
7
(7.87a)
(7.87b)
Chapter I . Analytical methods for designing composite repairs
167
With the prospective force and bending moment given by Eqs. (7.87), the coupled
Eqs. (7.73) can then be solved numerically. The superposition principle used in the
previous section to reduce the problem of a one-sided repair subjected to remote
tension to a simple perturbation problem where the crack is internally pressurised
is, strictly speaking, not valid should the structure undergo geometrically nonlinear
deformation. However, an upper bound solution can be obtained by a hybrid
method, in which the prospective stress distribution is solved using geometrically
nonlinear elasticity theory, the stage I1 analysis is carried out using the
geometrically linear theory, i.e. the crack bridging method developed in Section
7.5.2. A proof that this hybrid method will provide a conservative prediction of the
stress intensity factors can be found in [17]; a validation using the geometrically
non-linear finite element method will be presented later.
For a given repair configuration, the prospective membrane force (Eq. (87a))
increases with the load P while the bending moment (Eq. (87b)) decreases,
resulting in a net increase in the stress intensity factors, although the rate of
increase is slower than that expected from geometrical linear considerations. This is
illustrated in Figure 7.20(a) for the case of half crack length a of 20mm. It is seen
that the minimum stress-intensity factor &in
determined by the hybrid method
correlates very well with the finite element results. However the hybrid method
over-predicts the maximum stress-intensity factor, Kmax,confirming that the hybrid
method is an upper-bound solution [17]. A similar trend can be observed in
Figure 7.20(b) which shows the asymptotic behaviour of the stress-intensity factors
as the crack length increases. The remote applied stress oJ:is kept to be 400 MPa.
Again the minimum stress-intensity factor Kmindetermined by the hybrid method
correlates very well with the finite element results, whereas the maximum stressintensity factor Kmaxdetermined by the hybrid method is greater than that obtained
from finite element analysis.
7.7. Residual thermal stress due to adhesive curing
The process of adhesive bonding using high-strength structural adhesives
(thermal-plastics) generally requires curing the adhesive above the ambient
temperature. For instance, in a typical repair applied to aircraft structures the
reinforced region is initially heated to a temperature of 120 "C,under pressure, for
approximately one hour (the precise curing cycle depends on the adhesive being
used). Upon cooling the fully cured, patched structure to the ambient temperature,
thermal stress will inevitably develop in both the plate and the reinforcement, due
to cooling a locally stiffened structure, especially when the reinforcing patch has a
lower coefficient of thermal expansion than the plate being repaired. Thermal
stresses may also arise when the patch structure experiences thermal cycling in
service. Therefore thermal residual stresses represent a major concern to the repair
efficiency of a repair. This is because the resulting thermal residual stresses post
cure in the metal plate are inevitably tensile, owing to the increase in the stiffness of
the patched region and the lower coefficient of thermal expansion of the composite
168
Advances in the bonded composite repair of metaIlic uircraft structure
Geometrically ,I
linear solution ,'
\,
.,,/
u
ili
2l
rn
n
i,
0
100
200
300
Applied stress nm(MPa)
(a)
<
e4
400
4
High crack length a (mm)
(b)
Fig. 7.20. Geometrically non-linear deformation of a single strap joint representing one-sided repairs.
patches. This tensile residual stress will increase the maximum stress-intensity
factor of the crack after repair, hence may enhance fatigue crack growth rate (see
Chapters 11 and 12).
7.7.1. Temperature distribution
Solutions of the thermal residual stresses in symmetric repairs and one-sided
repairs have been developed in [181 and [191, respectively. In the following, only the
results pertaining to symmetric repairs will be presented; details of solution for onesided repairs can be found in reference [19]. Consider the configuration shown in
Figure 7.21(a), in which an isotropic plate is reinforced by a circular patch of radius
Ri.The coordinate system xy is chosen so that the principal axes of the orthotropic
Chapter I . Analytical methods for designing composite repairs
169
plate
Fig. 7.21. An infinite plate reinforced with a circular composite patch. (a) Configuration and (b)
temperature distribution during heating and cooling.
patch are aligned and parallel to the x, y axes, with the major direction along the yaxis. The objective here is to determine the thermal stresses in the patch, in the plate
both inside the bonded region and just outside the patch.
During the first step of bonding, suppose that the inner portion ( r 5 Ri)is heated
to a temperature Ti during the curing process, with the usual convention that the
Advances in the bonded composite repair of meiaIlic aircraft structure
170
ambient temperature is taken as the zero of temperature. The temperature field
satisfies the Laplacian Eq. (7.88) [21],
V2T=0,
(7.88)
which has the following solution,
(7.89)
where the superscript H denotes the temperature change corresponding to the first
step: heating. A schematic of the temperature distribution is shown in Figure
7.2 1(c).
7.7.2. Residual stress due localised heating
Due to this non-uniform temperature distribution given by Eq. (7.89), thermal
stresses (equal biaxial) develop in the plate, which can be readily derived [21],
#c
1
2
= - -apEpAT
,
(7.90)
where AT = - To, u p and Ep denote the thermal expansion coefficient and
Young's modulus of the plate. Since Ti - To > 0 during heating, the above thermal
initial stress is compressive. It should be noted that this thermal stress arises only in
the case of localised heating of a large structure; for the case of a finite size
specimen being uniformly heated to Ti,no thermal stress will develop. This stress
distribution serves as the initial stress that will be added to the thermal stress
induced by cooling the patched region down to the ambient temperature.
Now consider the case of a circular plate of radius Ro whose outer edge r = R, is
constrained by a continuous distribution of springs of stiffness 0 according to the
following relation,
(7.91)
arr(r= R,) = - O E p u r ( r = R,)
The cases of free edge and a clamped edge r = R, can be recovered by setting 0 = 0
and 0 -+ co,respectively. In this case, the thermal stress can be determined from
Eq. (7.96), to be discussed in the next section, by setting S = 0,
00" = -apEpAT
1 - e/ap
l+I+hJp-vVp
'
(7.92)
Chapter 7. Analytical methods for designing composite repairs
171
where
(7.93)
(7.94)
(7.95)
It can be shown that with the following spring stiffness 0,
@in[
=
1
(7.96)
(1 +VP)&
the solution for an infinite plate, Eq. (7.90), can be recovered as a special case by
setting3!, = 0, i= I , and e = 0.
7.7.3. Residual stresses after cooling from cure
For the second step of adhesive bonding we assume that there is no shear stress
in the adhesive layer during curing, so that the reinforcing patch expands freely
without developing any stresses. After the adhesive is fully cured, the patched plate
is then cooled down to the ambient temperature. In other words, the temperature
change over the entire patched plate is subjected to the following temperature field,
referring to Figure 7.21(c),
ATc(r) = - A T H ( r )
,
(7.97)
where the superscript C denotes the temperature change corresponding to the
second step: cooling. Now the problem is to determine the thermal stress 00' on
cooling to ambient temperature after curing. The final stress in the plate
(7.98)
During this cooling process, it is assumed that the adhesive bond between the
composite patch and the metal plate is absolutely rigid, so that the same strain-state
prevails in both the patch and the plate directly beneath the patch. Details of a
general solution for orthotropic patch are given in [18]. It is interesting to note that
even for an orthotropic patch, the thermal residual stress 00" in the plate is well
approximated by the solution for an isotropic patch, which takes the major
properties of the orthotropic patch [IS]. Therefore in the following we will present
172
Advances in the bonded composite repair of metallic aircraft structure
Fig. 7.22. Spring representation for simulating finite size effect.
only the solution for an isotropic patch with a coefficient of thermal expansion a ~ ,
(7.99)
The above solution applies strictly for an infinite plate. In practice, however,
structures to be reinforced may be finite in size or constrained by the surrounding
structure. To quantify the effect of this constraint, consider the configuration
shown in Figure 7.22, in which an un-cracked circular plate of radius Ri is
reinforced by a concentric patch of radius R,. The outer edge r = Ro is constrained
by a continuous distribution of springs according to the following relation (91). In
this case the thermal residual stress due to the cooling is given by [18],
where the parameters e, 1,and B are given by Eqs. (7.93-7.95).
For the special case of an infinite patch (Rj/Ro + 0, Ojnf = 1/(1 vp)R,),
one can further show that the residual thermal stress in the plate, point A in
Figure 7.21(b), reduces to, noting A = 1 and e = 0,
+
(7.101)
It is evident that in the special case of isotropic patch, the final solution is
dramatically simplified, providing a simple estimate of the residual stress in the
plate. The thermal stress in the plate just outside the patched region, point C in
Figure (7.21b), is
(7.102)
Chapter 7. Analytical methods for designing composite repairs
173
Similarly, the stresses in the patch, point B in Figure 7.21b, can be derived,
(7.103)
7.7.4. Thermal stress due to uniform temperature change
Often it is necessary to determine the thermal stresses in a patched structure
undergoing uniform temperature change, such as changes in operating temperature. In this case, the temperature is essentially uniform. However, since the patch
region has a higher stiffness than the surround area, thermal stress would occur.
Omitting the details of derivation, expressions of the thermal stresses in the plate
and the patch are
(7.104)
(7.105)
Verification of the above presented formulae will be discussed in the next section.
7.7.5. Validation
To validate the present theory and to examine the accuracy of the solution for
finite size plate, a detailed finite element analysis is carried out for both an isotropic
patch and an orthotropic patch, simulating a cross-ply laminate composite patch.
The properties and dimensions of the isotropic patch and the orthotropic patch are
summarised in Tables 7.2 and 7.3. The ratios of the outer radius to inner radius,
R,/Ri, will be varied to investigate the size effect. A comparison of the stresses in
the plate as obtained using the finite element method and the analytical solutions is
shown in Figure 7.23. It is seen that the closed-form solution [18] is in very good
agreement with the finite element results. More importantly the solution based on
an equivalent isotropic reinforcement, which takes the major properties of the
orthotropic reinforcement, provides a reasonably good correlation with the finite
element results.
Table 7.2
Properties and dimensions of isotropic reinforcement.
Material
Young's modulus
GPa)
Poisson's ratio
Thickness
(mm)
Thermal coefficient
Plate
Reinforcement
71
156
0.3
0.3
I .o
0.5
23 x
6.24 x
Advances in the bonded composite repair of metallic aircraft structure
174
Table 7.3
Properties and dimensions of orthotropic reinforcement.
Material
Plate
Reinforcement
Young's modulus
(GW
71
El = 156
E2 = 29.7
V."
Poisson's ratio
0.3
~ 2 =
1 0.1097
~ 1 =
2 0.5762
Thickness
(mm)
Thermal coefficient
3.0
1.5
C(I
23 x
= 6.24 x
t(2 = 16.96 x
1
3
5
7
9
11
13
Ratio of outer radius to inner radius RJRi
Fig. 7.23. Thermal residual stress resulting from cooling a circular patch over a concentric plate with
outer edge being clamped.
References
1. Baker, A.A. and Jones, R. (ed.) (1988). Bonded Repair of Aircraft Structures, Martinus Nijhoff
Publishers.
2. Baker, A.A. (1993). Repair efficiency in fatigue-cracked aluminium components reinforced with
boron/epoxy patches. Fatigue Fract. Engng. Mater. Struct., 16(7), pp. 753-765.
3. Eshelby, J.D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related
problems. Proceedings of Royal Society of London, A241, pp. 376-396.
4. Goland, M. and Reissner, E. (1944). The stresses in cemented joints. J. Appl. Mech, 11, pp. A17A27.
5. Hart-Smith, L.J. (1982). Induced peel stresses in adhesively bonded joints, Douglas Aircraft
Company, MDC J9422A.
6. Jones, R. (1988). Crack patching: design aspects, in Bonded Repair of Aircrufi Structures (A.A.
Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 40-76.
7. Ratwani, M.M. (1979). Cracked, adhesively bonded laminated structures. AIAA Journal, 17(9),
pp. 988-994.
8. Rose, L.R.F. (1981). An application of the inclusion analogy for bonded reinforcements. I n / . J.
Solids and Structures, 17, pp. 827-838.
9. Rose, L.R.F. (1982). A cracked plate repaired by bonded reinforcements. Int. J. Fracrure, 18(2),
pp. 135-144.
10. Rose, L.R.F. (1987). Crack reinforcement by distributed springs. J. Me&. Phys. Solids, 35(4),
pp. 383405.
Chapter 7. Analytical methods for designing composite repairs
175
11. Rose, L.R.F. (1988). Theoretical analysis of crack patching, in Bonded Repair of Aircraft Structures
(A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 77-105.
12. Wang, C.H., Rose, L.F.R. and Callinan, R. (1998). Analysis of out-of-plane bending in one-sided
repair. Int. J. of Solids and Structures, 35, pp. 1653-1675.
13. Wang, C.H. and Rose, L.R.F. (1997). Determination of triaxial stresses in bonded joints. Inr. J. of’
Adhesion and Adhesive, 17, pp. 17-25.
14. Wang, C.H. and Rose. L.F.R. (1998). Bonded repair of cracks under mixed mode loading. Int. J. qf
Solids and Structures, 35, pp. 2749-2773.
15. Wang. C.H., Heller, M. and Rose, L.R.F. (1998). Substrate stress concentrations in bonded lap
joints. J. of Strain Analysis, 33, pp. 331-346.
16. Wang, C.H., Heller, M. and Rose, L.R.F. (1998). Substrate stress concentrations in bonded lap
joints. J. of Strain Analysis, 33, pp. 331-346.
17. Wang, C.H. and Rose, L.R.F. (1999). A crack bridging model for bonded plates subjected to tension
and bending. Int. J. of Solids and Structures, 36, pp. 1985-2014.
18. Wang, C.H., Rose, L.R.F., Callinan, R., et al. (1999). Thermal stresses in a plate with a circular
reinforcement. Int. J. of Solids and Structures, 37, pp. 45774599.
19. Wang, C.H. and Erjavec, D. (1999). Geometrically linear analysis of the thermal stresses in onesided composite repairs. J. of Thermal Stresses, 23, pp. 833-851.
20. Wang, C.H. and Rose, L.R.F. (2000). Compact solutions for the comer singularity in bonded lap
joints. Int. J . of Adhesion and Adhesives, 20, pp. 145154.
21. Timoshenko, S.P. and Goodier, J.N. (1970). Theory of Elasticity, McGraw-Hill Book Company.
22. Lawn, B.R. and Wilshaw, T.R. (1975). Fracture of Brittle Solids, Cambridge University Press,
Cambridge, UK.
23. Keer, L.M., Lin, C.T. and Mura, T. (1976). Fracture analysis of adhesively bonded sheets. J. of
A p p k d Mechanics, 98(4), pp. 652-656.
24. Hadamard, J. (1952). Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover
Publications Inc., New York.
25. PAFEC Users’ Manual (1995). PAFEC Limited, Strelley Hall, Nottingham, United Kingdom.
26. ABAQUS (1997). User’s manual, Version 5.6, Hibbitt, Karlsson and Sorensen, Inc., Rhode Island.
Chapter 8
RECENT EXPANSIONS IN THE CAPABILITIES OF
ROSE’S CLOSED-FORM ANALYSES FOR BONDED
CRACK PATCHING’
Dr. L.J. HART-SMITH
Phantom Works, The Boeing Company, Mail Stop H013-A316, 5301 Bolsa Ave,
Huntington Beach, California 92647-2099, U.S.A.
8.1. Introduction
In the beginning, there was the “Blue Book” [l]. This now classic work,
commonly referred to as the “Bible” on the subject, contains the outline [2] by Dr.
Francis Rose of the analytical methods he developed for bonded crack-patching
repairs a long time ago, at what was then known as the Aeronautical Research
Laboratory in Fishermans Bend, Melbourne, Australia. These tools provided the
understanding that led to the fleet-wide application of composite patches on the C130 and C-141 metallic wings, making it possible to keep the aircraft flying when
riveted repairs would have been ineffective, or possibly even harmful. The
techniques were also applied to many other aircraft, some such repairs being
described in reference [3] by Dr. Alan Baker, leader of the team at what is now
known as AMRL. The present paper shows how these pioneering analyses have
been expanded, as part of the Composite Repairs of Aircraft Structures (CRAS)
program 1 being conducted at Boeing, in Long Beach, California, under contract to
the USAF Research Laboratories at WPAFB, Ohio.
Rose’s original analyses were for linearly elastic adhesives. They have been
extended to non-linear adhesive behavior in the form of an elastic-plastic adhesive
model [4] developed by this author at an even earlier date. Rose’s original analyses
were for isotropic patches. They have been extended to orthotropic elliptical patches
’
Several engineers are involved in this program, addressing many issues beyond the coverage of this
paper. What is addressed here is the portion of the CRAS program focussed on deriving closed-form
analyses of the type employed by Dr. Francis Rose, but with a far greater range of applicability than
originally envisaged. Also, there are some additional variables not covered in the original work, on which
everything presented here is based.
111
Baker. A.A., Rose, L.R.F. and Jones, R. (e&.).
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
(Q 2002 The Boeing Company. Published by Elsevier Science Ltd. All rights reserved.
178
Advances in the bonded composite repair of metallic aircraft structure
by new analyses that account for both patch material anisotropy and thermal
mismatch. Rose’s original solution was limited to isotropic patches. (It is surprising
how similar the predictions are throughout most of the design domain.) Rose’s
analyses had erroneously been believed to be limited in applicability to simple flatplate configurations. It is shown here that they are equally applicable to integrally
stiffened structures like wing skins. The introduction of the concept of a “negativethickness” patch has enabled Rose’s solutions to be applied directly to the assessment
of the load redistribution associated with local corrosion cavities. Patches over
corrosion damage can now be designed using the same tools developed earlier for
patching through cracks. These methods, once devised for patching structures that
had cracked in service, can also be used to design local reinforcement to be applied at
the time of initial manufacture, with the goal ofpreventing the initiation of cracks in
service. The methods can even quantify the severe stress concentrations associated
with poorly designed stiffener run-outs, which are often terminated short of the ends
of integrally stiffened panels in order to simplify the splice plates. In short, Rose’s
original analyses have opened a veritable Pandora’s box of additional capability with
which to maintain existing aircraft structures and to design better ones in the future.
(This is not to imply that there are no remaining problems to solve in this
discipline. On the contrary, work on new analyses continues in America, England,
and Australia, to expand the application of bonded crack patching. But it is
unlikely that the impact of Rose’s novel use of the inclusion model to generate
closed-form solutions for the stresses in and under bonded patches will ever be
surpassed by later work.)
8.1.1. Rose’s use of the inclusion model to establish stressjields
The issue of interest here, in the simple form analyzed by Rose, in reference [5],is
a local perturbation in an otherwise uniformly loaded infinite plate, as shown in
Figure 8.1, when the perturbation is in the form of an elliptical inclusion with axes
parallel to the principal remote stresses. Rose was able to establish an analogy
between this problem, for which an exact solution existed, and the situation of a
bonded patch over a local crack in a very large skin.
In the special case of a homogeneous elliptical inclusion of constant thickness in a
constant-thickness skin, the stresses in the inclusion are uniform and parallel to the
remote stresses. Perhaps the most comprehensive set of solutions for stresses in and
around the inclusions, for isotropic inclusions, at least, is to be found in reference [6],
where expressions are given for the stresses in and under the patch, and for the radial
and tangential stresses just outside the extremities of the patch. Rose’s specific
solution, for the stress in the skin just outside the ends of the patch, is
=
{ 1 + ;[ + 2(
1
B
1 + S ) - (1 - VC)
A
+ (1 + s
-
VS)(C -
1
41 ’
Chapter 8. Recent expansions in the capabilities of Rose’s closed-form analysis
%
.
179
€I
SKIN
c
PATCH
U O
.X
ADHESIVE
\
-0
REMOTE STRESS
CROSS
SECTION
u-
CRACK(HAS
NO EFFECT
ONLOADATTRACTION
ANALYSIS)
Fig. 8.1. Inclusion model as the basis of analyzing patches and stress concentrations.
in which
D
= 3( 1
[::S
+ S)2+ 2( 1 + S) + + vS] + 1 -
-
The stress in the patch, under the skin, is related to the remote stress perpendicular to
the crack by
Yes, this powerful solution is no more complicated than these simple explicit
expressions. Here cr defines a variety of stress components, v is the Poisson’s ratio
that is taken to be common for both skin and patch, C = crxm /gym is the ratio of the
remote stress parallel to the crack, in the x direction, to the dominant stress
component perpendicular to the crack, in the direction. The width and length of the
elliptical patch are 2A and 2B, in the x and y directions, respectively, and S is the
patch stiffening ratio (Et)patch/(Et)skin.
The location of the crack and locations
remote from the crack are identified by the subscripts 0 and 00, respectively, along
they axis. The crack extends for a total distance of 2a in the x direction, as shown in
Figure 8.1, symmetrically about the y axis.
The brilliance of Rose’s analysis is that, even though the load transfer through
the bonded joint around the periphery of the patch is not instantaneous in the
manner of the inclusion model, it is so close to it that the differences have no effect
in the vicinity of the crack. Similarly, a crack, no matter how long it is, has no
Advances in the bonded composite repair of metallic aircraft structure
180
significant width, as long as the skin on each side of it remains bonded to the patch.
Rose was able to separate the two steps of his analysis without any significant loss
of accuracy. The first stage, referred to as the load-attraction analysis, establishes
the stress in and under the patch, and in the skin just outside each end of the patch,
by neglecting the presence of the crack (or other local damage). This leads to the
establishment of one uniform set of stresses in the skin, parallel to the axes of the
elliptical patch, and a parallel second set of uniform stresses in the patch. The
analysis of the immediate vicinity of the crack, which constitutes the second stage,
then proceeds as if the patch extended uniformly to infinity.
8.1.2. Rose’s solution for stress-intensity factor K at the crack tips
The second stage in Rose’s analysis establishes the crack-tip stress-intensity
factor K, as affected by the bonded patch, from which it is possible to establish the
reduced (or zero) rate of subsequent crack growth. This is customarily referred to
as the constant-K solution, which is discussed below. As long as the crack does not
progress to the sides of the patch, any subsequent crack growth will be at a constant
rate - provided, in addition, that there are no disbonds adjacent to the crack.’ This
has been confirmed by tests, but it had already been explained by Rose’s analysis.
When a long crack in the skin is covered by an adhesively bonded patch, it is
effectively reduced to two very short half-cracks, each of length A, separated by a
bonded joint throughout which the crack opening is constant. Rose’s result for this
characteristic length is
.=‘(I+$),
xa
in which 1 (Rose uses the symbol B for this purpose) is the exponent of the adhesive
shear stress distribution given by
in which the additional terms are G for the adhesive shear modulus, t, for the
thickness of the adhesive layer, t&in for the thickness of the skin, and Eskinfor the
Young’s modulus of the skin.
Rose’s expression for the crack-tip stress-intensity factor, which determines crack
growth rates once the crack has grown long enough for the bonded-joint load path
to limit any further crack opening, is
K, =c
T
)
m
l
,
*There is a further exception, for very “short“ cracks. If a crack is so short, in relation to governing
parameters, that its crack growth rate has not yet built up to its stable value, an initially increasing crack
rate would be followed by a long period of constancy.
Chapter 8. Recent expansions in the capabilities of Rose‘s closed;form analysi.7
181
Were it not for the bonded patch, the crack would grow at an ever increasing rate
governed by the solution for an unpatched crack:
Rose’s characteristic length is typically very short, so the reduction in stress
intensity is very important. Indeed, it is now apparent that the residual thermal
stresses induced by hot bonding of composite patches are so severe that bonded
crack patches would be reIatively ineffective were it not for this particular
mechanism.
The total length 2a of the crack does not then control any subsequent crack
growth rate, unless the patch or bond is broken. The physics of these phenomena
are depicted in Figure 8.2.
Rose’s mathematical explanation of these phenomena is shown in Figure 8.3, in
which his two asymptotic equations are portrayed. The first, for very short cracks,
assumes that the adhesive is so flexible that the patch cannot restrain the crack
opening. The second is in the form of a plateau, established by Rose’s bonded-joint
analogy. The point at which these two independent solutions cross defines the
effective crack length 2A. This characteristic length, which Rose defined in terms of
adhesive, skin, and patch properties, reliably represents the crack growth rate once
the crack has grown beyond that length, which is usually extremely short and far
less than critical lengths for unrepaired cracks. If the skin is thin enough, and the
adhesive strong enough, the value of K can be reduced below the threshold for any
subsequent crack growth, completely “killing” the crack. If not, the rate of growth
will be retarded, in accordance with the difference between the patched K, shown in
non-dimensionalized form as unity, and the projection of the curve shown for
unrepaired cracks.
ACTIVE HALFCRACK,
CHARACTERISTIC
LENGTH A
IDENTICALSTRESS
INTENSITY FACTORS, K, FOR
ALL TOTAL CRACK LENGTHS
PRINCIPAL STRESS, u
BONDED JOINT REGION
,EFFECTIVE CRACK
LENGTH2A
P--\!’
I
TOTAL CRACK LENGTH
- / ,A-+
;<I
4
WIDTH OF BONDED PATCH
-$-+
86lJ88€lJlQ6.088QQ84L8
PRINCIPAL STRESS, u
Fig 8.2 Patched crack model as bonded joint separatlng two short fixed-length half-cracks
182
Advances in the bonded composite repair of metuIlic aircruft structure
A
2 -
UNREPAIREDCRACK
/
0
0
/
0
/
0
/
NORMALIZED
STRESS
INTENSITY
FACTOR, K/K-
/
0
SEMI-INFINITE
BONDED JOINT
0
00
0
0
/
0
1/
v
1
/
/
I
/
I
ROSE’S CHARACTERISTIC LENGTH
I
I
t
0
I
I
I
I
I
1
2
3
4
5
*
6
NORMALIZED HALF-CRACK LENGTH, a /A
Fig. 8.3. Rose’s solution for crack-tip stress-intensity factor under bonded patch.
Whereas the overall understanding of these phenomena has been cleverly
explained by Rose, there is an inherent problem in his transitional formula. This is
of no numerical consequence if the adhesive remains linearly elastic regardless of
the crack length. However, it is simply not possible, according to his Eq. (5.23a) in
reference [2] for the crack to ever grow long enough to exceed the elastic capability
of the adhesive. In reference [7], the present author added a compatibility-ofdeformations analysis to those by Rose and established a slightly different
transitional formula in which K reached its limiting value (for elastic behavior) at a
crack length exactly four times as long as that defined by Rose’s characteristic
length 2A. This modification, which does not change the significance of A in
relation to the plateau level of K, is shown in Figure 8.4.
While the values of the two solutions are not all that different, because they are
both governed by the same two limiting equations, this modification is necessary as
a prelude to being able to analyze for the effects of adhesive non-linearity
(plasticity) that are discussed later.
Although not discussed here, Rose’s analyses do address the stresses in the
adhesive as the load is transferred through very narrow zones adjacent to the crack
and the periphery of the patch. In addition, there is an explanation of the thermal
stresses induced by bonding composite patches that are thermally dissimilar to the
underlying metallic skins, resulting in the crack often being preloaded in the
opening mode before any mechanical load is applied. Rose and his colleagues have
improved upon this aspect, in reference [8]. The effects of the constraint provided
by surrounding structure that is not heated during the cure process are discussed
later, now that the CRAS team has developed a model that can be compared to
Chapter 8. Recent expansions in the capabilities of Rose’s dosed-form analysis
2
-
UNREPAIREDCRACK
0
0
0
0
183
0
0
0.
0
0
those of Rose and his colleagues. The original analysis in reference [2] also includes
an accounting of the geometrically non-linear out-of-plane bending associated with
one-sided patches, an issue also addressed in reference [9]. In short, while they left
room for others to improve upon their work, Rose and his colleagues made the
major contribution to this field by developing explicit comprehensible models
governing the dominant variables in the design of bonded patches for cracked
metallic structures.
8.2. Universal efficiency charts for isotropic patches
Rose’s original analyses are in closed form, making it easy to perform parametric
studies of the effects of the governing variables. This is an attribute inevitably lost
whenever total reliance is placed on finite-element analysis, no matter what other
benefits may be added in the form of being able to analyze non-standard geometries
for which no closed-form solution exists. The CRAS team took visualization of the
results one stage further when it was recognized that Rose’s Stage I equations could
be plotted in the form of an almost universal preliminary design chart.
This chart, presented in Figure 8.5, makes it easy to understand the effects of
patch stiffening ratio and of the aspect ratio of elliptical patches. There is no
universal “best” point design, but it is clear that excessive stiffening ratios are to
avoided because they dump so much load into the skin at the ends of the patch. In
the terminology of Figure 8.5, k, is then too high. Long, skinny, patches (high B / A
ratios) are also to be avoided, for the same reason. Long patches are also seen to be
Advances in the bonded composite repair of metallic aircraft structure
184
(ISOTROPIC PATCH; NO THERMAL MISMATCH BETWEEN SKIN AND PATCH)
0
1.o
0.9
0.8
0.7
STRESS
REDUCTION
FACTOR UNDER
PATCH
0.3
0.2
0.1
0
0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
PATCH ASPECT RATIO, BLA, (LENGTHIWIDTH)
Fig. 8.5. Patch design chart for isotropic patches, showing stress reduction under patch and load
attraction at ends of patch as functions of patch stiffening ratio and shape.
less effective than wide patches in reducing the stress level beneath the bonded
patch, in the skin around the crack, as defined by the ratio o0/om,where the stress
in the denominator is the remote stress at infinity, perpendicular to the crack.
This same informative depiction of the analyses is used here, later, to show the
effects of corrosion cavities and of orthotropic composite patch materials. The
specific solutions in Figure 8.5 are effectively restricted to isotropic patches made
from the same material as in the basic structure, because they omit consideration of
residual thermal stresses induced by bonding or co-curing thermally dissimilar
skins and patches together. Nevertheless, it will be seen that these are still a useful
approximations for practical composite patch fiber patterns, which are not all -0"
plies, despite the fact that these are the only plies to contribute appreciably to
holding the crack tip shut. The Warner Robins team in Georgia, led by Bill
Schweinberg, has found that composite patches are prone to longitudinal splitting
if too few transverse plies are included in the design. The latest CRAS analyses for
orthotropic patches include provision for assessing this phenomenon.
8.3. Equivalence between octagonal and elliptical patch shapes
The closed-form analyses of the type pioneered by Francis Rose are restricted to
elliptical patches only because this is the only shape for which explicit closed-form
Chapter 8. Recent expansions in the capabilities of Rosek closed-form analysis
185
solutions are possible. Most of the patches actually applied are octagonal in shape
because it is difficult to trim boron-epoxy patches to an elliptical shape. The CRAS
team has approached this issue from two directions. A power-series solution was
developed by Duong, in reference [lo], for octagonal patches. This overcame the
restriction, albeit at the expense of considerable added complexity and the
introduction of mathematical singularities at each corner of the patch. These are
not physically significant, however, because the flexibility of the adhesive there
would eliminate them from more detailed analyses. More significantly in the
present context, another CRAS member, J.J. Wang, used this analysis to establish
that, while the stress surrounding the crack under typical octagonal patches is not
absolutely uniform, as it would be for truly elliptical patches, it is very close to
uniform until the crack length 2a approaches the width 2A of the patch. It was also
shown to be within a few percent of the Rose’s solution for an elliptical shape that
circumscribed the octagon. This author approached the same problem from a
different perspective, reasoning that the stress field outside the patch would be
determined by the volume of the patch, which is uniformly stressed in Rose’s
solution. Therefore, there should be an equivalent elliptical patch for each
octagonal patch - one that would create both the same nominally uniform stress
around the crack and the same intensity of load attraction at the end of the patch.
The ideal equivalent elliptical and octagonal shapes for uniformly thick patches are
identified in Figure 8.6, which also presents Wang’s solution. The designs are seen
to be very similar, confirming that analyses for elliptical patches can be applied as
reasonable approximations to some octagonal patches. The restriction to elliptical
patch shapes may not be a serious limitation on the applicability of Rose’s analyses,
after all.
-
OPTIMAL
OCTAGONAL
PATCH
EQUIVALENT
ELLIPTICAL
PATCH OF
SAMEAREAJ
PARALLEL
SLOPES
x\
[\
I
I
1I
// 1
’b+
b
I
-
0.345a F a - I
Fig. 8.6. Equivalence between elliptical and octagonal bonded patches of uniform thickness.
186
Advances in the bonded composite repair of metallic aircrafi structure
If the trimming of the corners of the octagonal patch does not match that shown
in Figure 8.6, one could use the (as yet unverified) techniques suggested in reference
[l 11 to deduce an equivalent elliptical patch shape on which to base the present level
of analyses. It should be noted, however, that the use of an octagonal shape with
far more or far less trimmed off the corners than is suggested in Figure 8.6 will
result in less effective stress reduction under the patch or in more severe load
attraction at the ends of the patch.3
8.4. Effects of patch tapering on the adhesive stresses
The nature of load transfer through adhesive bonds whereby virtually all of the
transfer is confined to the immediate vicinity of any discontinuity in load patch,
such as at a crack and at the ends of the patch, means that the exact distribution of
the adhesive stresses and strains has little effect on the skin and patch stresses
outside those immediate areas. Therefore, Rose’s sequential approach to
independent analyses can be employed in this context, too.
In the area immediately adjacent to the crack, the governing conditions will be
the stress oo in the skin, reduced with respect to the remote stress os, that is
interrupted by the crack and diverted through the adhesive into the patch and back
to the skin again on the other side of the crack. Even though it is customary not to
taper the skin on the back side of the crack to reduce the severity of the adhesive
bond stresses, there is significant relief with respect to what a unit-strip analysis
along the middle of the patch would predict. In the absence of any tapering of the
patch at its ends, the adhesive there would be subject to a combination of intense
peel stresses, whether for a one-sided patch with out-of-plane bending or for a twosided symmetric patch with no apparent bending deformations, and shear stresses
aggravated by the locally higher than nominal skin stresses. It is essential, at least,
to apply local tapering of the ends of the patch, to reduce the induced peel stresses
to a tolerable level. It is customary to reduce the severity of all of these adhesive
stresses by far more widespread tapering of the kind shown in Figure 8.7. A slope
on 1411-50 is typical for boron-epoxy p a t c h e ~There
. ~ has been no indication of any
problems associated with such tapered patches other than for compressive remote
loads or very thick patches - and the problem then is caused by residual thermal
stresses, not the tapering.
It is intended to publish an assessment of the constant-volume analogy for off-optimum octagonal
patches with confirmation of the underlying skin stresses by finite-element analyses at some future date.
It is also common practice to use rectangular patches in which the thickness at the ends of the patch have
been tapered very gently, to dramatically reduce both the shear and peel stresses in the adhesive at those
locations. Whether or not the sharp corners still presented a load-attraction problem after tapering
would be established by these same systematic numerical analyses.
The magnitude of adhesive stresses associated with extensively tapered patches is another issue to be
covered by CRAS analyses. The issue of adhesive stresses is not in doubt; the tapering really does work.
What has yet to be confirmed is the magnitude of any relief with respect to load attraction, particularly
for patches with sharp corners.
Chapter 8. Recent expansions in the capabilities of Rose’s closed+orni ana1ysi.s
a
PATCH
1
SKIN
187
[email protected]
I
SQUARE-CUT EDGES
HIGH ADHESIVE PEEL STRESS
AND HIGH SKIN BENDING MOMENT
TAPERED EDGES
LOW ADHESIVE PEEL STRESS
AND LOW SKIN BENDING MOMENT
0
’
NOTE THE SAME TECHNIQUE ALLEVIATES THE PEAK ADHESIVE SHEAR STRESSES, TOO
Fig. 8.7. Tapering of bonded patches to prevent premature failures at the ends of the overlap.
Even though the process of transferring load through the adhesive is confined
to very narrow bands adjacent to the crack or to untapered edges of the patch,
there is a minimum overlap needed for the bond to ensure that the adhesive will
not fail by creep rupture under sustained loads. There must be a long elastic
trough in the adhesive shear-stress distribution to ensure that the minimum
adhesive shear stress is sufficiently low to prevent creep in at least some of the
bonded overlap. An estimate for this length was prepared during the PABST
program [ 121 for bonded double-lap joints that were free from bending effects.
This simple formula is
Here, P is the load transferred per unit width, per bond layer, T,, is the peak
adhesive shear stress, G, is the adhesive shear modulus, t, is the thickness of each
adhesive layer, and E and t are the Young’s modulus and thickness of the skin and
patch, as appropriate. The exponent I defines the distribution of the adhesive shear
stresses. (Rose uses the symbol for that purpose, but p is already customarily used
for other purposes in the context of stress-intensity factors at cracks.) The load P in
this equation has traditionally been taken as the remote load 0 , &kin in establishing
minimum patch lengths. This formula is still good for bonded splices, even though
the factor six could be reduced to five as explained below. However, for bonded
patches, it is now apparent that this value for P i s unnecessarily conservative for the
adhesive adjacent to the crack and too low to account for the load attraction at the
ends of the patch, where the skin stress is boosted to (1 +S) @xtt,kin, where
188
Advances in the bonded composite repair of metallic aircraft structure
EQUAL AREAS
i
“THIN” PATCH
r
EQUIVALENT UNIFORM PATCH
TAPERED PATCH
“THICK’ PATCH
Fig. 8.8. Calculation of equivalent tapered patch length, with respect to nominal length for uniformly
thick patch.
S= [(Et),,,,h/(Et),kin)]
is referred to as the stiffening ratio for the patch. In addition,
the process of deducing the bonded overlap 1 in Eq. (8.8) as the sum of the lengths
of the load-transfer zone(s) and that of the elastic trough has been refined by taking
account of the small increment of load transferred through the elastic trough. It is
now recommended by the CRAS team to use the formula
(8.9)
based on conditions in the adhesive adjacent to the crack. If only what is referred to
as anti-peel tapering were employed at the ends of the patch, the g a t s k i n , in
Eq. (8.9) would be increased by the factor k, to account for the load attraction.
A taper angle as low as even 1-in-30 is assumed to be sufficient to ensure that the
adhesive is more critical adjacent to the crack than at the ends of the patch. The
manner in which the tapering extends the length of the patch, for a constantvolume model, is explained in Figure 8.8. The patch width 2A is related to the
equivalent uniformly thick patch length 2B in Figure 8.5, not with the actual larger
tapered patch length.
The manner in which the adhesive shear stresses are influenced by tapering the
patch thickness is illustrated schematically in Figure 8.7. With sufficient tapering,
the adhesive will always be more critical adjacent to the crack than around the
periphery of the patch. The criticality of the adhesive adjacent to the crack can be
alleviated by employing a patch on both sides of the cracked skin, or by tapering
Chapter 8. Recent expansions in the capabilities of Rose’s closed:form analysis
189
the skin on the side opposite the patch as suggested in reference [7]. Obviously,
either of these approaches relies on there being access to both sides of the skin. A
slight tapering on the patch side, to thicken the adhesive layer locally in the manner
commonly used to relieve induced peel stresses, would also add to the flexibility of
the patch across the crack, resulting in a higher value of the stress intensity factor
K. Consequently, tapering the skin on the patch side would be counterproductive.
In the absence of access to both sides of the patch, the only way to enhance the
effectiveness of the bonded patch in restraining the opening of the crack is to use a
stepped patch like that shown in reference [7], after the manner employed by the
RAAF for damage to skins too thick to be repaired by standard one-sided patches.
8.5. Universal charts for the effects of corrosion
If Rose’s calculations for the load attraction caused by an inclusion that was
stiffer than the basic skin were extended to one that was less stiff, it would be
possible to characterize the effects of local loss of material due to corrosion. This
can be done simply by replacing the customary positive patch thickness and
stiffening ratio by negative values. No changes are needed in Rose’s equations
because, in this case, the “patch” material really is isotropic, and the same as the
material in the skin. Figure 8.9 shows the results of such calculations, for varying
depths of corrosion, which is modeled as a uniformly deep elliptical corrosion
cavity with axes aligned with the principal remote stresses. As before, the volume of
the corrosion damage is the same as for the actual loss of material. Thus, the plan
10
8
6
5
STRESS
4
CONCENTRATION
FACTOR
UNDER
3
CORROSION
2
1 .s
..-0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
IO
CORROSION CAVITY RATIO, B/A, (LENGTHWIDTH)
Fig. 8.9. Universal design charts with which to characterize the effects of local corrosion.
190
Advances in the bonded composite repair of metallic aircra& strueture
VOLUME OF
CIRCULAR
PARABOLOID
VOLUME OF
ELLIPTICAL
PARABOLOID=%mbh
VOLUMEOF
CIRCULAR
CYLINDER
= Rr ' ( hI 4
'i
Fig. 8.10. Geometric details of the actual and as-modeled corrosion cavity.
form of the idealized corrosion cavity is an ellipse, with axes oriented parallel to the
remote principal stresses, with an area roughly equal to that of the actual corrosion.
In contrast with the bonded patches, there is no increase in skin stress at the ends
of the cavities. Indeed, there is a reduction in average longitudinal stress there,
although, in reality, the peak value remains constant at the ends of the patch. This
stress diffuses into the uniform lower value a slight distance outside the cavity.
With the cavity, including the extreme case of a through-thickness hole, the stress
concentration of concern is the tangential skin stress just beyond the sides of the
patch, in the area for which the classical stress concentration factor of three applies
for circular holes interrupting a uniform uniaxial load. Of course, if the corrosion
damage is not blended out smoothly, there can also be concern about stresses at the
sharp corners around the base of the corrosion cavity, as indicated in Figure 8.10.
In any event, while analysis is for a uniformly deep approximation to the actual
variable damage, finite-element analyses have confirmed the expected still higher
value at the thinnest section below the cavity. The present method of analysis can
be applied a second time, as explained in reference [4], to refine the estimate from
the present analysis.
Figure 8.9 appears to confirm the classic stress-concentration factor of three for a
full-thickness circular hole. Actually, this is not so. The formula for the tangential
stress outside the cavity is slightly different from that for the stress under the cavity,
as is shown in reference [4].
Experience has often shown that the best thing to do about local corrosion
damage is to blend it out smoothly, removing the corroded material, and not to
repair it, since repairs will raise the stress level by attracting more load. The analysis
embodied in Figure 8.9 confirms these findings. Whereas a short wide patch is
better than a long skinny patch over a crack in a skin, as indicated in Figure 8.5, the
converse is true for minimizing the interruption of a uniform uniaxial stress by a
corrosion cavity, as shown in Figure 8.9. (In both cases, of course, a closer to
circular shape would be best for equal biaxial remote stresses.)
Chapter 8. Recent expansions in the capabilities of Rose’s closed-fonn analysis
191
8.6. Design of patches to compensate for corrosion damage
In the event that corrosion has been sufficiently extensive that repairs are needed,
an adhesively bonded patch can be the best option, since it requires no holes
through the original structure. Nevertheless, for widespread surface corrosion
rather than isolated deep cavities, it can be necessary to take a small surfacing cut
to level out sufficient of the area to be bonded that the adhesive can effectively
transfer loads between the skin and the patch. If the adhesive layer is too variable in
thickness, virtually all of the load will be transferred through the thinnest bond
areas. Worse, the load that should have been transmitted through the thicker bond
areas will be diverted and overload the thin bonds even more. If the underlying
structure is metallic, which is likely since composites do not corrode, and there are
no sharp cracks in the damage, the best patch material is more of the same metal, to
avoid generating residual thermal stresses that would be tensile if a composite patch
were bonded to a metallic skin. (Likewise, if a patch were being bonded over impact
damage to a composite skin, the patch material should be the same composite
material and fiber pattern for precisely the same r e a ~ o n . ~ )
The process for designing a patch over a small finite area of damage is much the
same as for a patch over a skin crack, except that the use of Rose’s two-stage
analysis now ought to require that the patch dimensions be about three times larger
than the damaged area. If this is not possible, because the corrosion is too
widespread, there will be a small error caused by following this procedure, but not
as great an error as would ensue from totally neglecting the load-attraction aspects
of the patch. The one refinement that has been incorporated in reference [13] is to
allow for a decrease in load attraction because of the added flexibility created by
the corrosion in the skin, as explained in Figure 8.11. The effect on the total
inclusion, skin and patch, would be proportionally less, and would require
IDEALIZED
UNIFORMLY
THICK PATCH
-
EFFECTIVETHICKNESS OF “INCLUSION” * tekIn(I
AB h k h
Fig. 8.1 I . Refinement included in the process of designing patches over corrosion cavities.
For cosmetic (non-structural) repairs to fibrous composite structures, it is common practice to use
low-modulus glass fibres throughout the patch to limit the load it will attract.
Advances in the bonded composite repair of metallic aircraft structure
192
accounting for any different elastic properties between the two. Otherwise, the new
analysis and that by Rose are identical, except for the absence of critical adhesive
conditions at the crack that is not there. With gently tapered patches, it is unlikely
that the adhesive will ever become critical in such a case. With no crack from which
to establish a crack-tip stress-intensity factor K or an effective crack tip half-length
A, life predictions for the patched structure are based on the reduced stress level 60
created under the patch.
Again we see a previously unrecognized field of application of Rose's analysis
that can assist in keeping even more aircraft airworthy while adding to existing
damage far less than conventional riveted repairs would.
8.7. Analysis of patches over cracks in stiffened panels
It is a commonly held, but totally erroneous, belief that Rose's methods of
analysis are restricted to simple unstiffened skins, probably because the application
of the method was first reported in that context. However, as shown in reference
[14], the original formulation is directly applicable to many of the most common
stiffened-panel problems, too. Whenever there is a primary unidirectional load
parallel to the stiffeners, as with wing skins under bending loads, for instance, the
area in the stiffener can simply be flattened out and added to the skin, as if by
unfolding the original structure, as shown in Figure 8.12, or by refolding it as
shown in Figure 8.13.
A
+
t---+
hr
WEEP HOLE
RISER PITCH r, ,-\-t
V
1
T
t EQUIVAL~NTRISER
SKIN
t
0:
<
W,
W,=h
'.
' f*
Chapter 8. Recent expansions in the capabilities of Rose’s closed-form analysis
193
FATIGUE CRACK(S)
RISER PITCH rP-----+---+
ACTUAL CROSS SECTION
t,
W,=h,x
1;
.-..-..-..-..-..-...-..-..-..-..FREE EDGE
“SKIN” CRACK
EQUIVALENT FLAT-PLATE MODEL
Fig. 8.13. Conversion of stiffened skin construction into equivalent semi-infinite uniform flat plate.
The choice between these two approaches depends on the location of the initial
damage, and whether or not a crack has developed in the skin or in a stiffener. With
a cracked stiffener and an intact skin, the approach is Figure 8.12 would be
preferable because the transformed damage is a simple single crack in the middle of
an infinite sheet. A crack in the skin, with the stiffeners intact, is better represented
by the model in Figure 8.13, with a crack near the edge of a semi-infinite plate,
because of the complexity of the process for computing crack-tip stress-intensity
factors for two disconnected cracks in proximity. Either model would work equally
well for Step I of Rose’s analysis to establish the stress fields near the damage. It is
only in Stage I1 that the right choice needs to be made.
Figure 8.14 shows the design of a sample patch to limit further growth of cracks
initiating at weep holes in stiffened wing skins. Such cracks have been found in
service on both the C-141 and F-111 aircraft. The derivation of this design is
reported in reference [14], using only Rose’s equations to assess the load attraction
and the skin stress under the patch. When flattened out, the aspect ratio B / A for the
equivalent single total patch is far smaller than for each individual patch segment.
The same approach is equally applicable for repair of damage from local
corrosion, too. This technique is most obviously applicable for spanwise stresses
caused by a dominant wing-bending load case. If the primary load were one of
torsion, the stiffeners would be far less effective. Indeed, in a case of pure in-plane
shear loading, there would be no significant stress in the stringers at all. Their
influence would therefore be minimal and it would then be appropriate to omit
them from such an analysis.
194
Advances in the bonded composite repair of metallic aircraft structure
0.21 INCH -7
Fig. 8.14. Typical design of bonded repairs for cracks in stiffened structures
8.8. Designing to avoid crack initiation
The very same analyses could also be used to establish how much local
reinforcement would be needed to prevent the occurrence of cracks at such local
stress concentrations. Exactly the same analysis would be used, since no allowance
was made in Stage I of the analysis for any adhesive flexibility. Consequently, the
same result would be predicted if there were not any adhesive and the “patch” was
now part of the original structure. Such local reinforcement obviously attracts
more load than would be present in the absence of any local reinforcement, and
Rose’s adaptation of the inclusion model is the perfect tool for assessing the
situation. Figure 8.15 shows the result of the analysis/design process corresponding
to that in Figure 8.14. The integral reinforcement can be more compact because
there is no need to consider any load-transfer lengths through an adhesive layer
that is far weaker than the metal in an integral patch.
Yet again, it should be noted that this design was prepared with no analysis/
design tools other than those developed by Rose in reference [2].
As noted earlier, stress concentrations caused by holes in integrally stiffened
structures are usually far less of a problem than inappropriately designed stiffener
run-outs - because the latter are only rarely recognized as such, no matter how
many times such problems had been encountered in the past. Now, at last, it will be
possibly to reliably and simply estimate such stress concentrations. In the limit, for
very long stiffeners terminated too abruptly inside the edges of any panel subjected
to in-plane loads around its boundary, the associated stress concentration factor is
Chapter 8 . Recent expansions in the capabilities of Rose's closed-form analysis
195
Fig. 8.15. Typical design of integral local reinforcement to prevent cracks in stiffened structures
given by
k r = l + t . &ringer
stnnger
kt=l+-
x &kin
hstringer
in general
,
(8.10)
for blade stiffeners .
&kin
Here, h is the depth of the blade stringer, assumed to be of locally constant
thickness. The effective height would be greater if the stringer included an
interrupted inner flange as well. Stress concentrations in excess of 10 from this
source are not at all uncommon. Rivet holes usually generate stress concentration
factors of only about three - lower if the holes have been cold-worked and
somewhat higher if designed to excessive bearing stresses. However, the cure for the
stringer run-out problem is not local reinforcement; it is continuing the stiffeners
uninterrupted from one end of the panel to the other, as shown in Figure 8.16, even
if doing so does complicate skin splices and frame/stringer intersections.
An exactly analogous situation arises with the traditionally segmented shear ties
between frames and fuselage skins. The end rivets of each segment act as hard
points, attracting considerable load and sometimes initiating fatigue cracks. Again,
the load on these end rivets can be estimated reliably without the need for complex
finite-element models by simply assuming a common circumferential strain and
sharing the interrupted load in the shear ties between the skin and the frame.
Experience has shown that the frame can suffer from the same problem; it need not
be confined to the skin.
196
Advances in the bonded composite repair ojmetallic aircruft structure
STIFFENER TERMINATED
PREMATURELY WHERE
SKIN STRESSES ARE
STILL HIGH
EDGE OF
AVOIDED
//
/
I
FATIGUE-CRACK
0
Fig. 8.16. Preferred and undesirable stringer run-outs.
8.9. Universal efficiency charts for orthotropic patches
So far, attention has focussed on mainly further applications of Rose’s original
analysis methods. This section, and the next, addresses extensions of Rose’s
pioneering work, using the same kind of analyses. Rose’s solution in Eqs. (8.1)
through (8.3) has been simplified by the assumption of an isotropic patch as well as
an isotropic skin, for a common Poisson’s ratio throughout. In a new derivation
reported in reference [15], these limitations have been lifted, even though the new
solutions are still formulated in terms of elliptical patches. These analyses include
biaxial remote loads aligned with the axes of the patch and crack, orthotropic patch
properties, thermal dissimilarity between skin and patch, and the effects of
constraints from surrounding structure as the area to be patched is hated to cure
the adhesive. For the special case of a unidirectional composite patch, it is
reasonable to set the transverse patch stiffness to zero. In this case, for a uniaxial
remote load perpendicular to the crack and parallel to the fibers in the patch,
Rose’s solution is replaced by
-_
(8.11)
while the stress concentration in the skin, just outside the ends of the patch, would
, , ~ ) would be
likewise nor be the simplistic approximation (1 S , ) ( ~ J ~ O / but
+
Chapter 8. Recent expansions in the capabilities of RoseS closed-form analysis
197
(ORTHOTROPIC PATCH; THERMAL MISMATCH EFFFECTS OMITTED)
0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
PATCH ASPECT RATIO, B/A, (LENGTHIWIDTH)
Fig. 8.17. Patch design chart for unidirectional composite patches, showing stress reduction under patch
and load attraction at ends of patch, as functions of patch stiffening ratio and shape.
determined by adding the forces, in the y direction, in the skin and patch, in
accordance with the new solution. This result is plotted in Figure 8.17, which shows
both striking similarities with respect to Figure 8.5 for isotropic patches (both
diagrams omitting thermal effects) as far as the stress reduction under the patch is
concerned and some unexplained differences with respect to the constant loadattraction contours for thin (soft) patches.
The predictions of these two analyses are so similar that either could be used with
confidence, as appropriate. The differences arise in the relative capabilities with
respect to thermal mismatch and induced stress effects. Both researchers have
accounted for this effect, subject to specified limitations, and both have used quite
different approaches to the problem, which is so severe that it must not be
overlooked.
8.10. Effects of residual thermal stresses on bonded repairs
Residual thermal stresses develop whenever the patching material has a much
lower coefficient of thermal expansion than does the skin, as is always the case with
fibrous composite patches for conventional aluminum structures. The problem is
not removed even by the use of room-temperature-curing adhesives, because the
absence of thermal stresses is lost whenever the operating temperature is lowered,
198
Advances in the bonded composite repair of merallic aircraft structure
SHRINKAGE OF
ALUMINIUM SKIN OVER
COMPOSITE PATCH
DURING COOL-DOWN
AFTER CURE
OVERALLLENGTH
BY PATCHTHAN WITHOUT If
.-.
8
8
0
,,
0
CONSTRAINEDBY
STRONG, STIFF,
BORON-EPOXYPArcn
--Y--K
d
ZERO REMOTE STRESS
Fig. 8.18. Effect of residual thermal stresses associated with composite patches bonded to metallic
structures.
as for high-altitude flight of aircraft. In any event, most room-temperature-curing
adhesives are either softer or weaker than heat-cured adhesives, so that approach
could entail a reduction in effectiveness of the bonded patch to hold the crack shut.
The origin of these stresses is as follows. At high temperature, while the adhesive is
uncured and still liquid, the adhesive does not transfer loads so the patch and the
structure can expand independently of each other. The skin will normally have
expanded appreciably, but the length of a composite patch will be virtually
unchanged in any direction for which there are fibres. Consequently, after the
adhesive has set and the heat source is removed, the skin under the patch wants to
contract - away from the edges of the patch and away from the crack, thereby prestressing the rack in the open position, as shown in Figure 8.18. This is aggravated
by further reductions in operating temperature. Nevertheless, as long as the bond
remains intact, a long crack will still behave like two separated half-cracks in the
manner of Eq. (8.4), only the half-crack lengths A will be larger than they would in
the absence of thermal effects. Consequently, the crack-tip stress-intensity factor
K , would also increase, in accordance with Eq. (8.6), and so would the crack
growth rates.
If the structure being repaired is stiff enough, andflat enough too, some of the
thermally induced stresses in the skin under the patch will be reduced by
compressive stresses that develop during the cure if the surrounding structure,
which is not heated, constrains the patch area. The AMRL team has quantified
these phenomena in reference [8] for circular composite patches. The CRAS team
has recently done the same for elliptical composite patches. (Rose’s original
Chapter 8. Recent expansions in the capabilities of’ Rose’s closed-form analysis
199
analysis in reference [2] had omitted any effects of orthotropy.) It is now apparent
that, even under the best of circumstances, the relief provided by restraint during
sure will typically amount to only some 25% of the total thermal stresses at the
minimum operating temperatures. Nevertheless, such a reduction in operating
stress levels has a pronounced effect on fatigue lives. What is more concerning is
that it is now evident that these thermal stresses, for boron- or carbon-epoxy
patches will have roughly the same effect on the stresses in the skin under the patch
as the remote mechanical loads do. This provides considerable support for the
advocates of the use of GlarecE1
patches which, despite their lower stiffness than for
composite patches, have virtually no thermal mismatch with respect to aluminum
alloy structures.
Another significant effect of the thermal mismatch is that it seriously affects the
adhesive stresses developed between the skin and the patch. At the ends of the
patch, the adhesive is pre-loaded in the opposite direction to what a tensile remote
load would cause. Consequently, this is a benign effect for the adhesive, and the
ends of the patch, for tensile mechanical loads, but is an adverse effect for
compressive mechanical loads. Cracks grow only when opened up by tensile loads,
so this is not always a problem. However, some structures dominated by tensile
loads, like lower wing skins, are also subjected to lesser compressive loads, from
gusts and from inertia on the ground. This effect of the thermal stresses has an
insidious effect on the fatigue life of adhesive bond. When loaded monotonically, at
the adhesive level, the adhesive can tolerate a certain level of cracking that occurs
when it is strained beyond its elastic limit, as shown in Figure 8.19. Apart from a
reduction in macro-level stiffness, most adhesives are remarkably tolerant of such
damage, tolerating much higher loads until failure finally occurs.
However, a very different set of circumstances applies if the adhesive bond is
subjected to reversed loads. The hackles would try to develop in both directions
LOAD
LOADS BELOW ELASTIC
CAPABILITY OF ADHESIVE;
NO HACKLES
LOADS BEYOND ELASTIC
CAPABILITY OF ADHESIVE;
HACKLES BEGINTO FORM
LOADSWELL BEYOND ELASTIC
CAPABILITY OF ADHESIVE
HACKLESSPREADAND
EVENTUALLY LINK UP
Fig. 8.19. Hackles that develop in adhesive bonds loaded beyond their proportional limit.
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Advances in the bonded composite repair of metallic aircraft structure
r ADHEREND OR FIBRE
PRIMARY LOAD
SECONDARY LOAD
FAILURE
Fig. 8.20. Saw-tooth fractures developed in adhesive bonds subject to severe reversed loading.
then, resulting in a complete saw-tooth surface separating the two adherends, as
shown in Figure 8.20.
Although the remote loads may appear to be monotonic, the adhesive is usually
subjected to reversed loads when the residual thermal stresses are accounted for,
with an associated reduced fatigue life. This potential problem is a total non-issue
for thin structures, for which the adhesive cannot be loaded beyond the
proportional limit, but may explain some of the troubles experienced with some
bonded repairs to thick bonded structure - defined as such, regardless of actual
dimensions, by the ability to overload the adhesive. As if to confirm the analyses in
this regard. no such problems have ever been encountered in service or test for what
really are patches over obviously thin structure.
8.11. Effects of adhesive non-linearity and disbonds on crack-tip stress-intensity
factors
Rose’s original Stage I1 analysis is restricted in applicability to linearly elastic
behavior of the adhesive. As part of the CRAS program, this limit has been
removed by modifying his solution to account for an elastic-plastic adhesive model.
This simple model is defined in Figure 8.21.
Since the load that can be transferred through an adhesive bond between two
nominally uniformly thick adherends is limited by the square root of the adhesive
strain-energy, it is clear that the added area under the extended stress-strain curve
in Figure 8.21 is very significant, in spite of the concerns expressed in the previous
section. The further along the stress-strain curve that the adhesive is loaded, the
more micro-damage will be done in the form of micro-cracks that may eventually
link up. (Figure 8.21 is a very useful macro-level model for analysis, but it does not
Chapter 8. Recent expansions in the capabilities of Rose’s closed-form una1ysi.s
20 1
A
?
!
l
ADHESIVE
SHEAR
STRESS
(?e + ?P)
0
*7
?e
ADHESIVE SHEAR STRAIN y
Fig. 8.21. Elastic-plastic representation of adhesive non-linear behavior in shear
mean that the adhesive actually behaves like a ductile metal. If it did, it would
unload with a permanent offset; actually, it unloads with hysteresis but almost to
the origin.)
The results of the new elastic-plastic analysis, documented in reference [7], are
depicted in Figure 8.22, in the same non-dimensionalized form as for Rose’s elastic
solution in Figure 8.3. The value 1 on the ordinate of Figure 8.22 represents the
elastic solution.
It is clear that the added strain energy of ductile adhesives, with respect to brittle
ones with no non-linear capacity, is to reduce the stiffness of the load over the
ADHESIVE
TRANSITIONAL CRACK
LENGTHWHEN COD
REACHES LIMIT SET BY
THE ADHESIVE BOND,
ELASTIC
4
3
/ / -
-/--
RATIO OF
ELASTICPLASTICTO
ELASTIC
STRESS
INTENSITY
FACTORS
16.
CHARCTERISTlCSOF
UNPATCHED SKIN CRACK AT
INCREASING LOAD LEVELS
1
ELASTIC ADHESIVE
OI’
0
I
1
I
I
I
I
I
I
I
2
3
4
5
6
7
8
NONDIMENSIONALIZEDHALF-CRACK LENGTH, &A
I
I
9
10
*
Fig. 8.22. Effect of elastic-plastic adhesive behavior on crack-tip stress intensity factors underneath
bonded patches.
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Advances in the bonded composite repair of metallic aircrafi structure
crack, for sufficiently high loads. This, of course, is undesirable, since it increases
the stress intensity K. On the other hand, the same added flexibility goes hand-inhand with increased joint strength, enabling bonded patches to be applied to
thicker cracked structure than can be repaired with elastic adhesives - unless one is
willing to employ stepped patches to decrease the load transferred per step and, at
the same time, decrease the eccentricity in load patch for one-sided patches.
The new, longer, effective half-crack tips and higher stress-intensity factors have
been derived in [7] as
(8.12)
where the elastic values are defined in Eqs. (8.4)and (8.6).
Reference [7] also contains an assessment of the effects of disbonds adjacent to
the crack. It is predicted there that these disbonds cannot initiate until the crack has
grown sufficiently and that, thereafter, any shear-dominated disbonds will grow in
a stable manner, in concert with further crack extension. In other words, the width
of any disbond is limited by, and eventually proportional to, the length of the crack.
(The behavior of peel-induced disbonds has yet to be examined by closed-form
analysis.) Disbonds render bonded patches far less effective; avoiding them justifies
the use of more complex stepped patches let into stepped recesses cut into the skin
around the crack. The choice between nominally uniform (or linearly tapered)
patches on a uniform substrate or stepped patches bonded into a stepped recess cut
from the structure seems to be difficult to establish, because so many factors have
been omitted from older analyses that the patches have often out-performed the
predictions. Nevertheless, the distinction is exceedingly simple to grasp; patches
with complex geometries are needed whenever the structure is so thick and so highly
loaded that the simple patches cannot do the job.
8.12. Out-of-plane bending effects with one-sided patches
Rose’s original analysis includes the necessary geometrically non-linear bending
analyses for the effects of the eccentricity in load patch inherent in one-sided
bonded patches. He correctly established that the so-called Stage I correction factor
is very small. Analyses under the CRAS program, reported in reference [I6], have
confirmed this need. Indeed, the tendency for the centroid of the skin/patch
combination to align itself with the plane of action of the remote load is so great
that, in the worked example in reference [16], a linear bending analysis would have
Chapter 8. Recent expansions in the capabilities of RoseS closed-form analysis
203
over-estimated the deflection in the patch, over the crack, by a factor of 18-to-1.
Linear analyses are totally inappropriate for this class of problem.
The author’s analyses in reference [16] include an improvement with respect to
the model used by Goland and Reissner in their classical analysis of bonded singlelap joints. This model assumes that plane sections remain plane, even though the
overlap area is treated as a single layer twice as thick as the individual adherends.
Such an approximation is obviously unrealistic immediately adjacent to the ends of
the overlap or, in the present context, immediately adjacent to the skin crack. The
author removed this constraint by adding a flexible adhesive layer only in narrow
zones adjacent to the ends of the patch and on each side of the crack. The analyses
were made more accurate because of this refinement, but it was shown that,
numerically, the Goland and Reissner level of model is sufficiently accurate. Rose
relied upon these same phenomena when he modeled the load transfer between skin
and patch as being instantaneous. It really isn’t - but a more precise derivation
often does not change the answer significantly.
Such simplifications are not always valid, however. No matter how precise the
Stage I bending analysis, it is going to predict almost zero bending moment in the
patch over the crack, provided that the lengths are long enough to allow the
transverse deflections to occur. Nevertheless, both Rose’s original analysis, and the
more recent one in reference [17], have included Stage 11 bending analyses in the
immediate vicinity of the crack. The reason for this is that there is a local abrupt
eccentricity in load path too short to effect the global bending. The same
phenomenon is described in reference [161. It would be fair to say that this aspect of
the problem is not yet adequately characterized. It is clearly not a classical planesections-remain plane linear bending analysis, because finite-element analyses
performed as part of the CRAS program have confirmed the absence of curvature
in that region, even with five elements through the thickness. So most of the
eccentricity must be accommodated by shear-lag, as Wang, Rose, and Callinan
recognized in preparing their reference [171 based on Reissner’s plate-bending
analysis. However, it seems to the present author that the whole issue might be
moot. The only interest in this particular bending moment is possible unequal crack
opening across the thickness of the skin. But, surely this is more dominated, at the
crack tips, by the uncracked and unbent very stiff laminate of skin and patch just
ahead of the crack tips. It is obvious that the crack opening will vary from the patch
side to the unrepaired side of the skin in the “bonded joint” zone of Figure 8.2, and
that this might impart a slightly greater displacement than developed in the
adhesive alone, but this seems to be far from the dominant effect at the crack tip. It
must be remembered that only those portions of the crack within the very short
length A are important here.
Curiously, shear lag is known to be important in the patch, directly over the
crack in the skin. Composite patches have very little transverse shear stiffness, in
comparison with that of aluminum alloy skins, because a11 such load must be
transmitted through the resin matrix. Consequently, those layers of fibers closest to
the skin are locally loaded far more highly than those located far away on the
outside of a thick patch. (The same phenomenon was observed at Douglas Aircraft
204
Advances in the bonded composite repair of metallic aircraft structure
during the PABST program, where the splice plates in double-strap metal-to-metal
joints were far more prone to fatigue failures, where the skins butted together, than
the nominally equally stressed portions of the skins.)
8.13. Remaining challenges involving closed-form analyses
Despite the abundance of Rose’s work, and that of the whole team led by Alan
Baker, as well as the more recent contributions by the CRAS team, there are still
challenges waiting to be addressed. Some may never be solved in this manner
because it will be found that finite-element analyses are absolutely necessary.
Nevertheless, some of the remaining tasks that will be attempted by the CRAS
team include the following.
1. Adhesive stresses associated with patches with very long tapers.
2. Load transfer between the skin and the patch for thick structures (and patches
to match).
3. Further studies of disbonds, particularly those associated with adhesive peel
stresses.
Other investigations will continue with ways to improve or facilitate finite-element
analyses, and these are no less important than the closed-form solutions discussed
here. However, they lie beyond the scope of this article.
8.14. Concluding remarks
It is hoped that, more than a decade after the publication of Rose’s classical
treatise on this subject, and the thousands of bonded patches that have been
successfully applied by the RAAF and USAF, in particular, that it is now clear
what a vital analysis it was. Also, as this paper shows, the techniques used have
spawned a large number of refinements and expansions that retain the original
simplicity while enabling the effects of far more parameters to be assessed
parametrically.
One must wonder whether or not Rose knew, at the time, that the precise
transverse stiffness of composite patches was not to have a dominant influence on
his Stage I analysis for the load attraction at the ends of the patch and the stress in
the skin under the patch, where the crack existed. Certainly, it is now apparent that
orthotropic composite patches designed with his analysis for isotropic patches
would not be all that different if the composite patch analysis had been derived
earlier.
Rose’s foresight in recognizing the importance of a uniform stress surrounding
the crack under the patch means that the restriction he accepted to elliptical patches
to achieve that goal was sensible. Although octagonal patches are easier to make, it
is important that the trimming of their corners lead to a patch that is equivalent to
some elliptical patch. Otherwise, there will be regions of higher-than-average stress
Chapter 8. Recent e.upansions in the capabilities of Rose’s closed-form analysis
205
for the crack to grow into. Again, what others have mistaken for a restriction on
applicability is now revealed as good design advice.
It is known that Rose had not anticipated the direct application his analysis to
corrosion damage, simply by using a negative patch thickness. Nevertheless, once
the idea had been suggested he was able to help the present author complete that
task, so that Rose’s original analysis can be applied to a whole further class of
problems. It should also be noted that the original analysis, intended for the
analysis of repairs to structures damaged in service, can also be applied to yet
another task - that of designing optimally sized local integral reinforcement to be
left n place when the parts are first machined, so that they will not develop fatigue
cracks in service. These very same tools can also be applied to prevent further
instances of poorly designed stringer run-outs, which have been a chronic source of
fatigue cracks in the past. Now there are simple closed-form analyses available to
quantify potential hot pots before the designs are frozen.
It is also now known that the idea of being able to directly apply Rose’s model to
integrally stiffened structures is sound, and that, henceforth, they need not always
be limited to the simple flat-plate geometries that formed the basis of the idealized
model Rose first analyzed.
It would take remarkable insight to predict where all of the extensions of Rose’s
work will end. The author will make no such attempt. However, he will state the
obvious, that much of the CRAS closed-form analysis work would not have been
possible had Rose not taken that first giant step so many years ago.
References
1. Baker, A.A. and Jones, R. (1988). Bonded Repairs of Aircraft Structures (A.A. Baker and R. Jones,
eds.). Martinus Nijhoff Publishers.
2. Rose, L.R.F. (1988). Theoretical analysis of crack patching. In Bonded Repairs of Aircrgfi Structures
(A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 77-106.
3. Baker, A.A. (1988). Crack patching: experimental studies, practical applications. In Bonded Repairs
of Aircrafr Strucfures. (A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 107---173.
4. Hart-Smith, L.J. and Rose, L.R.F. Characterizing the Effects of Corrosion Damage Using
Analytical Tools Developed for Bonded Composite Crack Patching. Boeing Paper MDC 00K00100,
in preparation.
5. Hart-Smith, L.J. (1 973) Adhesive-Bonded Double-Lap Joints. NASA Langley Contract Report
NASA CR-112235, January.
6. Rose, L.R.F. (1981). An application of the inclusion analogy for bonded reinforcements. Int’l. J.
Solids and Structures, 17, pp. 827-838.
7. Hart-Smith, L.J. (1999). On the relative effectiveness of bonded composite and riveted patches over
cracks in metallic structures. Boeing Paper MDC 99K0097, Proc. 1999 USAF Aircraft Structural
Integrity Program Corzf., San Antonio, Texas, 30 November-2 December.
8. Wang. C.H., Rose, L.R.F., Callinan, R., et ul. Thermal stresses in a plate with a circular
reinforcement. Int. J. Soli& and Structures, 37, pp. 4577-4599.
9. Hart-Smith, L.J. (2000). Analyses of bending deformations in adhesively bonded one-sided doublers
and patches over skin cracks, Boeing Paper MDC 00K0024, Proc. of’the 4th Joint DoDIFAAINASA
Conf. on Aging Aircrufi, St. Louis. Missouri, 15-18 May.
206
Advances in the bonded composite repair of metallic aircraft structure
10. Duong, C.N., Wang, J.J. and Yu, J. An approximate algorithmic solution for the elastic fields in
bonded patched sheets. Int. J. of Solids and Structures, Vol. 38, 2001, pp. 46854699.
11. Hart-Smith, L.J. (1999). Nonlinear closed-form analyses of stresses and deflections in bonded onsided splices and patches. Boeing Paper MDC 99K0069, Proc. of the 3rd Joint FAAIDoDINASA
Conf. on Aging Aircraft, Albuquerque, New Mexico, 20-23 September.
12. Hart-Smith, L.J. (1983). Adhesive bonding of aircraft primary structures, Douglas Paper 6979,
presented to SAE Aerospace Congress and Exhibition, Los Angeles, California, 13-16 October,
1980; SAE Trans. 801209; reprinted in High Performance Adhesive Bonding, (L. De Frayne, ed.).
Society of Manufacturing Engineers, Dearborn, Michigan, pp. 99-1 13.
13. Hart-Smith, L.J. and Duong, C.N. Use of bonded crack-patchinganalysis tools to design repairs for
non-crack-like (Corrosion) damage, Boeing Paper MDC OOKOOlOl, in preparation.
14. Hart-Smith, L.J. (2001). A demonstration of the versatility of Rose’s closed-form analyses for
bonded crack-patching, Boeing Paper MDC 00K0104, presented to 46th International SAMPE
Symposium and Exhibition, Long Beach, California, 6-10 May.
15. Hart-Smith, L.J. (2001). Extension of the Rose bonded crack-patching analysis to orthotropic
composite patches, also accounting for residual thermal stresses, Boeing Paper MDC 00K0102, to be
presented to 5th Aging Aircrufi Conference, Kissimmee, Florida, 10-13 September, 2001.
16. Hart-Smith, L.J. and Wilkins, K.E. (2000). Analyses of bending deformations in adhesively bonded
one-sided doublers and patches over skin cracks, Boeing Paper MDC 00K0024, presented to the
Fourth Joint DoDIFAAINASA Con$ on Aging Aircraft, St. Louis, Missouri, 15-18 May.
17. Wang, C.H., Rose, L.R.F. and Callinan, R. (1998). Analysis of out-of-plane bending in one-sided
bonded repair, Int. J. of Solids and Structures, 35, pp. 1653-1675.
Chapter 9
NUMERICAL ANALYSIS AND DESIGN
R. JONES
Department of Mechanical Engineering, Monash University, Wellington Rd,
Clayton, Victoria 3168, Australia
9.1. Analysis and design
This chapter describes a number of complementary approaches to the analysis
and design of bonded repairs. First, an approach based on the two dimensional
finite element method is presented and illustrated by an application to an actual
repair. An analytical approach for the design parameters for repairs to rib stiffened
panels is then presented. Section 4 subsequently compares the predictions with both
experimental and numerical results. Design studies for repairs to thick sections are
described in Sections 9.5-9.8. Section 9.9 presents a methodology for allowing for
adhesive non-linearities and visco-plasticity. Section 9.10 discusses how to extend
existing design methodologies to allow for variable adhesive thickness. Section 11
presents the solution for composite repairs t'o cracked fastener holes or corrosion
damage under bi-axial loading. Section 9.12 summarises the findings for repairs to
primary structures, and also discusses the applicability of a range of commercially
available finite element programs.
There are several methods available for designing composite repairs to cracks in
thin metallic skins, i.e. typical thickness less than 3 mm. The finite element method
was the first to be developed [l], and has been used to design several complex
repair schemes, such as the repair of fatigue cracks in the lower skin of Mirage
aircraft [2], and cracks on the upper surface of the wing pivot fitting of F l l l C
aircraft in service with the Royal Australian AirForce (RAAF), see [3]. Following
the development of this approach the work presented in [4] revealed that the stress
intensity factor for a patched crack approached a constant value as the crack
length increased, thus simplifying the initial design process. This approach was
based on the premise that, for a sufficiently long crack in a structure which is
subjected to a remote uniform stress field, the central region of the patch, over the
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Baker, A.A.. Rose, L.R.F. and Jones, R. (ed.s.),
Advances in ihe Bonded Composiie Repaim of Metallic Aircraft Structure
2002 Elsevier Science Ltd. All rights reserved.
208
Advances in itre bonded composiie repair of metallic uircrafi structure
crack, behaves like an overlap joint. From this premise it follows that the stress
distribution in this central region should be independent of crack length, see
Chapter 7 for more details.
As a result of this analogy the problem of a bonded symmetric lap joint can be
used in the initial design process. The analytical formulae are particular easy to use
and provide a first estimate for the patch design. In some cases, this first estimate is
sufficient. However, there are situations in which the repair is critical and a long life
is required. In these cases, a full finite element analysis is necessary. As a result, the
finite element approach will be discussed first and illustrated by considering the
design of a repair to the lower wing skin of a Mirage I11 aircraft. At this stage it
should be noted that whilst much of the initial impetus for composite repairs arose
from the need to maintain the structural integrity of military aircraft [1-41 the
concepts, analysis and design tools are also applicable to repairs to civilian aircraft
[5-lo].
9.2. The 2D finite element formulation
A variety of numerical techniques are now available for analysing composite
repairs. These include 2D finite element techniques [I], boundary element
formulations [ 113, finite element techniques using of Mindlin plate bending
elements [12], 2D and 3D finite element alternating techniques [13] and fully 3D
finite element analysis [3]. Of the various techniques the 2D finite element and 2D
alternating finite element techniques are the simplest to apply. When a more
detailed analysis is required or it is necessary to determine the interlaminar stresses
in the repair then it is best to use 3D finite element analysis since Mindlin plate
bending elements cannot capture the true ‘three dimensional stress states at the
patch adhesive interface. The current 3D finite element alternating technique has a
similar shortcoming. However, recent, as yet unpublished, work has shown that it
is possible to use the 3D alternating technique to obtain a sub-structure like model
of the cracked region and combine this with a standard finite element model for the
remaining region and the repair. A detailed discussion of the relative applicability
of a range of commercial finite element analysis programs is given in Section 9.12.
In general the best results are obtained using 21 nodded hex elements or cubic isoparametric elements. Variants of these elements are available in a range of
commercial finite element programs, viz: PATRAN, NE-NASTRAN and PAFEC.
Standard quadratic iso-parametric elements can also be used but care must be
taken to avoid ill conditioning.
When analysing bonded repairs to cracked metallic sheets it is first necessary to
develop a realistic mathematical model for the behaviour of the adhesive layer
bonding the patch to the sheet. Under in plane or transverse loading, shear stresses
are developed in the adhesive. If we define the x and y axes to lie in the plane of the
sheet with the z axis in the thickness direction, then these shear-stresses can be
Chapter 9. Numerical analysis and design
209
expressed in terms of the displacements in the sheet and the patch, viz:
Here z,~, and t,Ty
are the values of the shear stresses in the adhesive K I ,K2, K3, &,K5
and K6 are spring constants whose values depend on the material properties and
thickness of the adhesive, skin and composite patch. The terms U R , UR and up>up are
the displacements at the mid-surface of the patch and the skin respectively while IV
is the vertical deflection. It is often a reasonable assumption that for the composite
patch, which from here on will be considered to be unidirectional with the fibres
perpendicular to the crack, G13 = G23 = GIZ(GR),i.e. the interlaminar shear moduli
are equal. This assumption is unnecessary and the full form for the Kl’s is
contained in [l]. However, it dramatically simplifies the analysis and has little effect
on any quantities of interest. With these assumptions we obtain, in the case of a
patch on one side of the skin:
where t A , t R and tp are the thicknesses of the adhesive, patch (composite overlay)
and skin respectively and G A ,GR and Gp are the shear modulii of the adhesive,
patch and skin.
These formulae were presented in [l] and make full allowance for the shear
deformation which occurs throughout the composite patch and skin. With this
approach, the u and v displacements through the patch, adhesive and skin are given
by:
210
Advances in the bonded composite repair of metallic aircraft structure
and a similar expression for v.
If the patch is placed on both sides of the skin, then the term 3tp/8Gpappearing
in the above equations is replaced by t p / 4 G p .These assumptions result in a shear
stress profile which is piece wise linear.
9.2.1. Element stiffness matrix
Having obtained the nature of the stress field in the adhesive we can now derive
the stiffness matrix for the adhesive layer. When there is no bending, the sheet is
assumed to be in a state of plane stress and it is usually modelled by isoparametric
membrane elements while the patch is modelled by isoparametric membrane
elements with an orthotropic stress strain law. The adhesive is also assumed to only
carry the shear stresses zxz and zyz. As a result, the total strain energy of an element
of the repaired structure is:
(9.4)
where Kp and KR are the stiffness matrices of the skin and patch respectively. The
last term in this expression is the contribution due to shear deformation. To be
completely accurate, the z integration should be over the total thickness of the skin,
adhesive and patch, whilst the x , y , integration is over the surface area of the
element.
We first define a vector f such that:
where the components of N are generalised functions of position and
aT = (6,T ,6'T ... sf)
Here the element is considered to be an arbitrary shape with m nodes and
The strain vector may be expressed as:
Chapter 9. Numerical analysis and design
21 1
where the matrix D is a function of z and where:
(9.9)
It thus follows that z can be written as:
z = AN6
,
(9.10)
where
(9.11)
As previously mentioned, the assumed deformation profile results in a quasi-linear
shear stress. The shear stresses zxz and .,z, vanish at the top of the patch, increase
linearly to the values of ,z and zsy respectively in the adhesive and then decay
linearly to zero at the free surface of the skin (or plane of symmetry in the case of a
patch on both sides of the skin). This results in the matrix D having the form:
D
=fO
[
Gp 0
'1
in the skin, i.e. 0 5 z 5 tp
1
1 0
in the adhesive tp 5 z 1. tp
GA 0 1
[ ]
+ tA
(9.12)
with the term tp being replaced by t p / 2 in the case of a patch on both sides of the
skin.
Here:
(9.13)
Making use of the expression for ,,z,
=2
/1
/(ANb)'(/f(z)Dd,)
yxz, etc. we now find that:
(9.14)
AN6dxdy
As a result, we find that the stiffness matrix Ik" for the adhesive layer, plus the shear
212
Advances in the bonded composite repair of metallic aircraft structure
coupling in the skin and patch, is given by:
(9.15)
For a patch on both sides of the skin, the stiffness matrix for both layers of
adhesive and the shear coupling in the skin and patch is:
(9.16)
A more general expression for R including bending effects is given in [l].
Having thus obtained the stiffness matrix for adhesive layer, it is now possible to
analyse complex repair schemes.
To illustrate the versatility of this approach, we will consider the boron fibre
repair to fatigue cracks in the lower wing skin of Mirage I11 aircraft in service with
the RAAF. This problem highlights the recommended approach to designing
bonded repairs to cracked metallic wing skins.
9.2.2. Repair of cracks in aircraft wing skin
In the late 1970s a boron fibre patch was developed for cracks in the lower wing
skin of a number of Mirage I11 aircraft. These cracks were pre-dominantly found at
an angle of 45" to the main spar. To investigate the feasibility to a b/ep repair, a
design study was undertaken into the repair of a crack whose tips were 111 mm
apart and which lay at 45" to the spar (see Figure 9.1). This crack represented the
longest crack which had been found in service.
As a first step in the design of the repair, a study of the cracked, but unpatched,
region was undertaken. A detailed finite element model of the area surrounding the
drain hole region was developed. The loads applied to this model were obtained
directly from the stress distribution which resulted from a previous finite element
model of this region and which correspond to a 7.5 g load case. The study gave the
values of the stress intensity factors to be K I = 72 MPa m'/* and K2 = 3.3 MPam'/*
at the tip closest the spar and K1= 68 MPa m1I2,K2 = 0.5 MPa m1l2at the tip closest
to the root rib. These values were consistent with a fractographic examination of
the crack which showed that the crack was essentially growing as a mode 1 fracture
and that of the two crack tips the tip closest to the spar was growing the faster.
Indeed, the tip closest to the spar was found to be very close to final failure.
Having thus obtained a reasonable model for the unpatched crack, we add to this a
finite element representation of the repair. Six boron epoxy patch configurations
were considered, each with the same plan form, see Figure 9.1. Each patch was
modelled using approximately 380 of the "bonded" elements described in Section
9.2.
213
Chapter 9. Numerical analysis and [email protected]
Main Spar
Inboard
Forward
T = 10 MPa
0
Fig. 9. I . Geometry of cracked drain hole region and patch.
All of the six patches considered were unidirectional laminates and were
internally stepped, i.e. with the longest ply on the outside. The fibre direction was at
ninety degrees to the crack.
Initially, it was uncertain if carrying the fibres over the drain hole was necessary,
or how frequently the drain hole was used in service. As a result, in three of the
patches considered a hole was left so as not to interfere with the draining of the
wing. In the other three patches, varying amounts of the hole were covered. In one
case, one third of the total area of the hole was covered, while in the other cases
virtually all of the hole was covered.
For each of the patches, the maximum shear stresses in the adhesive bonding the
patch to the wing skin occurred at points A, B, C and D (see Figure 9.1). The
maximum stresses in the fibres occurred at point D for the patches with a hole in
the patch, and in the fibres over the hole in the patches with the hole partially
covered. The values for these stresses, along with the percentage reduction of the
stress intensity factory K1 at each tip, achieved by each patch are shown in
214
Advances in the bonded composite repair of meiallic aircrafi struciure
Table 9.1
Effect of drain hole patch: 7.5g load case.
~
Patch number
Maximum patch2
Thickness (mm)
Adhesive thickness
(mm)
Thickness of first layer
(mm)
Covering of drain
1
~
~~
2
4
3
5
0.762
0.762
0.776
0.889
0.889
0.889
0.102
0.102
0.102
0.203
0.203
0.203
0.127
0.254
0.127
0.254
0.254
0.127
substantially
covered
substantially
covered
Open
open
113
open
covered
Adhesive shear stress
(MPa) at points:
A
B
C
D
Maximum fibre stress
(MPa)
Reduction in stress
intensity factor K I , Le.
l-Kip/Kiu,at:
1. Spar tip
2. Root rib tip
6
181
153
953
43
79
179
153
930
55
164
131
760
31
58
120
98
911
26
42
63
50
450
18
30
64
51
455
91%
99%
91%
99%
91%
99%
91%
99%
92%
99%
91%
99%
29
55
29
Table 9.1. Here Klu and K b are the values of the stress intensity factors before and
after patching respectively.
We see that all of the six patches achieve a reduction in the stress intensity factor
Kl of at least 91%. Consequently, they would all significantly retard growth.
Similarly for all of the patches, the fibre strains are below the maximum working
levels of 0.005 which corresponds to a stress of 1 GPa, although of the six patch
numbers, 5 and 6 have by far the greatest factors of safety. As a result, the patch
design was finally chosen primarily on the basis of the magnitude of the shear
stresses developed in the adhesive. On the basis, patch numbers 1, 2, 3 and 4 were
rejected. The two remaining patches are patch numbers 5 and 6. Of the two, Table
9.1 shows that the adhesive shear stresses along the edges of the patch, are
substantially higher for patch number 5 than for patch number 6, although both
are below the threshold value for fatigue damage. As a result, patch 6 is much less
likely to suffer fatigue damage to the adhesive bond. Hence, patch number 6 was
adopted as the final repair.
Consulting Table 9.1, we see that at locations C and D in patch 6 the shear stress
in the adhesive is sufficiently high so as to cause concern over the possibility of
fatigue damage occurring in the adhesive. However, these high values occur in the
interior of the patch at the intersection of the crack with the drain hole, and are
very localised. As a result, any damage which does occur should not spread and
should have virtually no effect on the stress intensity factors at the crack tips or on
the fibre stresses.
Chapter 9. Numerical analysis and design
215
Let us now summarise the criteria which were used to finalise the patch design.
1. The peak fibre stresses must be less than the maximum permissible tensile
strength. For boron epoxy this is approximately 1 GPa.
2. The peak adhesive stress must be less than its fatigue threshold value. For the
AF126 epoxy nitrile adhesive used, this is approximately 40 MPa.
3. A significant reduction in the stress intensity factor K, must be achieved.
Wherever possible, it is desirable to reduce K, to below the fatigue threshold
limit of the wing skin.
Let us now consider the effect that the difference between the coefficients of
thermal expansion of the boron patch and the aluminium alloy wing skin has on
the residual stresses left in the skin after the patch has been applied. Patching the
skin involved heating the area to be repaired to approximately 120°C. The patch
which also been heated to 120°C, is then attached and the patched structure is
allowed to cool to ambient temperature. It is during this cooling phase that the
difference in the coefficients of expansion between the patch u1 = 4.5 x [email protected] per "C
per "C, causes a
and a2=20 x
per "C, and the wing skin, u = 2 3 x
residual thermal stress to be left in the structure. (Note that CII is the coefficient of
expansion in the fibre direction and a2 is that perpendicular to the fibre direction.)
In order to analyse this phenomenon the shear modulus of the adhesive was
taken as zero at 120°C and was assumed to increase linearly, as the temperature
decreased, to a value of 0.965 MPa at ambient temperature, i.e. 40 "C. At each step
decrease in temperature the adhesive layer was modelled using the finite element
method described above. As a result of this analysis, it was found that when the
skin was assumed to be restrained from in plane movement by the spar and root rib
attachments, the mean residual stress left in the skin under the patch was a tensile
stress of 8.7 MPa. This stress should not significantly alter fatigue behaviour of the
patched panels.
A more detailed discussion of the effects of thermal mismatch is given in [2].
Following patch design a series of fatigue tests were then performed both under
constant amplitude loading and using a detailed flight spectra. The results of this
test program are shown in Figure 9.2 where it can be seen that the patch essentially
stopped crack growth.
9.3. Initial design guidelines
As mentioned in Section 9.1 externally bonded composite patches have proved to
be an effective method of repairing cracked, or damaged, structural components,
[I-IO]. A variety of approaches are now available for the design of composite
repairs to cracks in thin metallic skins, i.e. typical thickness less than 3 mm. One
such technique is based on the fact that the stress intensity factor for a patched
crack approaches a constant (limiting) value, defined as K,, as the crack length
increases. This approach was based on the premise that, for a sufficiently long crack
in a structure which is subjected to a remote uniform stress field, the central region
of the patch, over the crack, behaves like an overlap joint [4]. From this premise it
-
216
Advances in the bonded composite repair of metallic aircraft structure
Crack length mm
120
ao
LC
Fig. 9.2. Effect of patch on crack growth rate.
follows that the stress distribution in this central region and the stress intensity
factor should become independent of crack length.
As a result of this analogy it has been found that the problem of a bonded
symmetric lap joint can be used in the initial design process. Indeed, the resultant
analytical formulae are particularly easy to use and provide a first estimate for the
patch design.
It is possible to increase the accuracy of the current approximate 2D formulae,
initially developed by Rose in [4], for the limiting stress intensity factor K , for a
crack repaired with an externally bonded composite repair, by (partially)
accounting for through-the-thickness effects. To this end the value of Km can be
approximated, see Chapters 7, 8 and 12, by the formulae:
(9.17)
where
(9.18)
Y is a geometry factor, m ich accounts for repairs to center or ekge cracks;
Y is a geometry factor = 1 for a repair to a center crack
= 0.9 for a repair to an edge crack ’
and OL is the load attraction factor. For long uni-directional fibre patches it has
Chapter 9. Numerical analysis and design
217
been found that the term !& can be approximated as follows
= 318
1./( 1 + XErtr/(BEptp)) - (Eptp/(Ertr + E p t p ) ) ,
(9.19)
(9.20)
(9.21)
(9.22)
Here Xis the width of the patch, B is the width of the plate/skin, t,, tp and tr are the
thickness’ of the adhesive, plate, and patch respectively, G and E denote the shear
and Young’s modulus and the subscripts a, p and I denote their values for the
adhesive, plate, and patch respectively.
Until now we have ignored bending effects. However, even if the wing skin is in a
state of plane stress, the location of the neutral axis of the patch-adhesive-skin
section will differ from the neutral axis of the wing skin itself. Hence, forces applied
to the skin will result in an out of plane bending which will reduce the efficiency of
the repair.
There are several methods that can be used. One approach, developed at
Northrop see [I41 for more details, can be used to account for this out of plane
bending. Other more precise methods are discussed in Chapters 7 and 12. In the
*
Northrop method, the apparent stress intensity factor K,, at the mid surface of the
sheet is given by:
K:
=
( 1 +BC)Kp
(9.23)
where BC is a bending correction factor. Here,
where Ks is the value of the stress intensity factor before patching, tp and t R are the
thicknesses of the sheet and patch respectively, y,,, is the distance of the lower
unpatched surface of the plate from the neutral axis of the section (i.e. sheet plus
patch). I is the moment of inertia of the section and a is the crack half length. This
formulation has several analytical shortcomings and more recent, and exact,
developments are presented in Chapters 7 and 12.
Advances in the bonded composite repair of metallic aircraft structure
218
The value of Kp* can be related to J, the energy release rate for self similar crack
growth, in the usual way, viz:
K,*2
E
(9.25)
J = - -
If growth is non self-similar with the maxiyum growth occurring at the lower free
surface, then it may be best not to use K,, or J but to design on the basis of the
which is given by:
maximum stress intensity factor
Kp""
= (1
+ 2BC)Kp
(9.26)
These formulae have been validated by comparison with in excess of 2400 different
numerical examples solved using 3D finite element analysis.
If the adhesive is behaving plastically then the asymptotic solution Kooe-,,,where
the subscript e-p indicates that it is the elastic plastic solution, can be related to
Kme, where the subscript e indicates that it is the elastic solution, as follows, see
~91.
Kme-,, = K a e j 1
+f
[
(1
+ 2;)'-1]
(9.27)
Here y,, and ye are the elastic and the plastic components of the peak shear strain
acting over the crack, see Chapter 8 and [29], and K,,, is as given in Eq. (9.17). In
this case it is essential to have an accurate representation of the elastic plastic
behaviour of the adhesive. The formulation given in [29] and in Chapter 8 treats the
adhesive as being rate independent. Unfortunately this simplification is invalid.
Most commonly used structural adhesives are highly visco-plastic and exhibit
extensive strain rate dependency, see Section 9.8. As a result when calculating y,,
and y e , for use in Eq. (9.27), a more realistic visco-plastic formulation is required.
One such formulation is given in Section 9.8. Sections 9.8 and 9.9 also show how to
use Glinka's hypothesis [191 plus valid visco-plastic formulation for the adhesive to
obtain accurate values for y p and ye without the need for a fully non-linear finite
element analysis. An extension of these formulae to account for cracks at holes and
load biaxiality is given in Section 9.10.
To illustrate the accuracy of these formulae let us first consider an externally
bonded composite repair (patch) to a center crack in a 3 mm thick aluminium panel
with E = 72000 MPa and v = 0.33. Two patch thicknesses were analysed viz: 1.O and
1.85mm, and the patch was assumed have the following mechanical properties:
El = 208000 MPa,
E22 = 25432 MPa,
v12 = 0.183,
and
GI2= GI3=
Gz3= 7241 MPa. The plate was assumed to have dimension of 200 (length) x 290
(width) x 3mm and the patch was assumed to have a plan form of 100
(length) mm x 82 (width) mm. The adhesive was taken to be 0.25 mm thick with
a shear modulus of 375MPa and v=O.33. The analysis used 20 noded
isoparametric 3D brick elements with two layers of elements through each of the
Chapter 9. Numerical analysis and design
219
plate, patch and adhesive. The plate was subjected to a remote uniform stress of
229.8 MPa and global bending, after patching, was prohibited.
In this analysis symmetry was used and only a quarter of the structure was
modelled. The resultant mesh consisted of 4889 nodes and 1132 elements and, to
simulate the crack tip singularity, the near tip elements had the mid side nodes
moved to the 1/4 points. The resultant solution was well conditioned and the
accuracy of the solution was evaluated by performing two separate analyses. The
first used optimum integration, Le. 2 x 2 x 2 Gaussian quadrature points, to form
the stiffness matrices of the elements whilst the second used full integration, i.e.
3 x 3 x 3 Gaussian quadrature points, to form the stiffness matrix. These analyses
gave results which agreed to within 1%.
Following this analysis the composite repair to edge notch cracks in a 200
(length) x 145 (width) x 3mm plate was then considered. In this study the patch
was assumed to be 1.85mm thick and have a plan form of 100 (length) mm x 41
(width) mm. The results both these repair configurations are presented in Tables
9.2-9.5.
The third study involved similar repair configurations where skin thicknesses of
2 mm, 3.15 and an adhesive shear modulii of 700 MPa were also considered. For the
first two repair configurations the differences between the present approximation
Table 9.2
K values for a repaired edge notch panel, patch thickness 1.85mm.
Crack length
5mm
6mm
7mm
lOmm
20mm
Patched surface
Middle
Bottom
10.6
11.6
11.7
10.8
11.7
11.9
10.9
11.9
12.0
10.9
12.1
12.2
10.4
12.9
12.7
Table 9.3
K values for repaired center notch panel, patch thickness I .85 mm.
Crack half length
5mm
6mm
7mm
lOmm
20mm
Patched surface
Middle
Bottom
11.2
11.9
12.0
11.5
12.4
13.16
11.8
12.7
12.9
12.0
13.3
13.4
11.6
14.3
14.1
Table 9.4
K values for a repaired center notch panel, patch thickness 1 mm.
Crack half length
5mm
6mm
7mm
lOmm
20mm
Patched surface
Middle
Bottom
14.6
15.5
15.6
15.2
16.3
16.4
15.6
16.8
17.0
16.1
17.8
17.9
15.7
19.4
19.1
Advances in the bonded composite repair of metallic aircraft structure
220
Table 9.5
Comparison of solutions for K , for a patch thickness 1.85mm.
Crack configuration
Crack length
Predictied
K finite element
Center crack
Edge crack
20 mm
20 mm
14.I
12.7
14.1 to 14.3
-12.7 to 12.9
-
and the finite element results are summarised in Table 9.5. The differences for the
third study are summarised in Table 9.6. In each case the agreement is shown to be
quite good. The analytical formulae are also quite accurate for the case when
bending is allowed, see Tables 9.7-9.9. However, in this case the accuracy of the
simple analytical formulae decreases when the crack length approaches a half of the
patch width (8.
For repairs to rib stiffened panels the bending correction factor BC must be
modified. This modification involves a parameter, which we will call the stiffener
correction factor, SCF.
( P x ln(10'21,) - Q)
SCF =
(9.28)
9
102
where, to a first approximation, P and Q are only functions of the ratio E,t,/E,t,.
Table 9.6
Comparison of prediction for K, for various patch configurations.
_ _ _ _ _ _ _ _ _ _ ~
~
Crack configuration
Crack
length
Edge crack
= 344.8 MPa
20mm
Center crack
B = 344.8 MPa
20mm
Center crack
B = 229.8 MPa
20mm
Configuration
Predicted
~
(F
Center crack (~=229.8MPa 20mm
A
K finite
element
____________
SkinA 2 mm, patch = 0.75 mm
G, = 375 MPa
t , = 0.25 mm
SkinA 2 mm, patch =0.75 mm
G, = 375 MPa
tu = 0.25 mm
SkinA 3 mm, patch = 1 .OO mm,
G, = 375 MPa
to = 0.25 mm
SkinB 3mm, patch=0.889mm,
G, = 750 MPa
t, = 0.165 mm
21.6
17.8-22.4
23.6
19.8-24.0
19.2
15.7-19.1
16.2
15.7-15.8
The planform of the skin and patch were as previously described.
Planform of plate was 320 mm x 150mm (wide) with a semi-circular patch, radius = 80 mm.
Chapter 9. Numerical andysis and design
22 1
Table 9.7
Comparison of prediction for bending problems, Case 1.
~
K,,,
MPam"
Edge
center
predicted
f.e.
Center 40
48.3
41.4
amm
rpmm EpMPa
72000
3.16
____________
r,mm
G,MPa
r,mm
G,, MPd
uMPa Xmm
Bmm
1
208030
0.2
375
158
200
200
Table 9.8
Comparison of prediction for bending problems, Case 2.
KIT%,,
MPa m':?
Edge
center a m m
predicted
f.e.
Edge
85.2
83.4
20
tpmm Ep MPa
t,mm
G,MPa
t,mm
G,MPa
a M P a Xmm
Bmm
2
0.75
208030
0.25
375
34s
200
200
72000
Table 9.9
Comparison of prediction for bending problems, Case 3.
~
MPa m','2
Edge
center
predicted
f.e.
Center 20
62.1
59.2
K,*X
amm
tpmm E,, MPa
71000
3
t,mm
G,MPa
t,mm C,, MPa
ri MPd
Xmm
B mm
0.89
208000
0.17
230
41
I45
Stiffness ratio Ert,/Epip
0.73
0.91
I
1.15
1.28
1.3
I .62
I .65
2.1
750
"P"
"Q"
2.8
10
2.4
12
18
13
2.7
1.9
2.2
2.5
1.6
1.9
1.4
18
23
17
22
21
The new stress intensity factor, which included stiffener effects, for rib stiffened
panels thus becomes:
Kp = (1 - SCF)Kp
(9.29)
This approximation has been validated by comparison with more than 2000
different 3D numerical examples, see Figure 9.4.
222
Advances in the bonded composite repair of metallic aircruft structure
Fig. 9.3. Schematic of three dimensional 1/4 finite element model of stiffened panel.
To illustrate the accuracy of this formulae a 3D finite element study for the
composite repair of cracked rib stiffened panels was undertaken. In this study the
stiffeners were assumed to be riveted to the skin. Symmetry considerations enabled
only a 1/4 of the structure to be modelled. The typical geometries investigated is
shown in Figure 9.3. In this study the crack length, patch thickness, skin thickness,
Stiffener Second moment of Area (4)mm4
0
25
20000
40000
60000
80000
1
Stiffness Ratio
?/Skin
-
0.73
-
0.91
* I
1.15
1.28
-20
x
1.3
x
1.62
'
1.65
+
2.1
Fig. 9.4. Plot of percentage difference in the value of KI,,,, defined as y, of numerical analysis from
closed form solution v's x , the second moment of areas (Is)for a range of stiffness ratios.
Chapter 9. Numerical analysis and design
223
stiffener width, stiffener spacing, and stiffener depth were varied to determine their
effects on the stress intensity factors.
The difference between the predicted, using Eqs. (9.17), (9.23) and (9.24), and the
computed values of K,,, are summarised in Figure 9.4. From this we see that even
without allowing for effect of the stiffener and the predicted values lie within 18%
of the numerical values. When allowing for the stiffeners using the stiffener
correction factor (SCF), i.e. Eq. (9.29) the approximate formulae was accurate, for
all (200+) test cases, to within 5%.
To confirm the accuracy of these formulae an experimental study into the
composite repair of cracked rib stiffened panels was also undertaken. The test
geometry, for which bending was not restrained, was as shown in Figure 9.5.
Test matrix
Case and number of specimens
Skin thickness
Stiffner broken or unbroken
Crack length
Case 1: 3
Case 2: 3
1.25
1.25
Unbroken
Broken
40 mm
40 mm
-
In each test case the loads were adjusted to give a peak stress in the skin of
120 MPa. In the first test case we had a skin thickness of 1.25 mm and a width of
133 mm. The area of the skin A, was thus:
A,= [ 1 3 3 ~ 1 0 - ~ m ] x [ 1 . 2 5 ~ 1 0 - ~ m ]
= 1.665 x
m2
For this test configuration the cross sectional area of the stiffener A, was
A , = [50x IO-’ m] x [2.2 x lo-’ m] + [23 x IO-’ m] x [2.2 x IO-’ m]
= 1.606 x 10-4m2
This gave a total cross sectional Area ( A , ) of 3.271 x lOP4m2.In this case the
maximum Fm,, force needed to be applied was
F,,,
= CJ x
At = 39.5 kN
The fatigue test program was performed with an R ratio of 0.5. Consequently,
the loads applied in the fatigue test were Fmin= 1.96 kN and F,,, = 39.5 kN. The
exception to this was the first test specimen where the minimum and maximum
loads applied were Fmin
= 2.0803 kN and F,, = 41.6 kN respectively. In this case
the stress amplitude, rather than the maximum stress, was 120 MPa.
From the results of the first test sample (Sample 2/40.1), see Figure 9.7, which
had an intact stiffener we found that the crack growth rate was constant and that
-
da
dN
-= 5.578 x
mm/cycle
= 21.96 x
in/cycle
224
Advances in the bonded composite repair of metallic aircruft structure
Fig. 9.5. Schematic representation of the panel test geometry.
Fig. 9.6. View of patched surface and underside of the test configuration with cracked stiffener.
Note adhesive seepage through the rivets.
Chapter 9. Numericai analysis and design
225
70
65
60
h
E
E 55
W
5
M
s
W
50
I
1
+ 1.2 mm intact stiffener
-Linear (1.2 mm intact
stiffener)
30 1
0
I
5000
10000
15000
20000
30000
25000
35000
Number of Cycles
Fig. 9.7. Crack growth for a 1.25 mm thick specimen (intact stiffener) Au = 120 MPa
In this case from the results' given in [31], page 8.9-84, for an R ratio of 0.02 and a
plate thickness of between 0.02" to 0.2", we found that the experimental crack
growth rate corresponds to an (experimental) value of AK of 1 1 MPam'". This
compares quite favourably with the values of AK of 12.2MPa m''2, obtained using
the semi-analytical formulae, and 12.5 MPa m"2 obtained via a detailed 3D finite
element analysis2. For the subsequent tests the stress amplitude was 11.4 MPa.
The growth rate again was constant and da/dN of -3.72 x 10-4mm/cycle, see
Figure 9.8. The experimental crack growth rate corresponded to an (experimental)
value of AK of 10.0MPam''2 compared with a predicted value of 11.5MPam''2
and 1 1.8 MPa m'!2 obtained using 3D finite element analysis.
When the stiffener was broken the stress in the skin under the stiffener increased
to 238 MPa. In this case we obtained a predicted value of AK of 23.9 MPa mli2,
obtained using the semi-analytical formulae, and a value of 21 .23MPa m''2
obtained via a 3D finite element analysis. From the experimental test results. see
Figure 9.9, we again obtained a constant growth rate with a da/dN of -2.39 x
-
-
-
-
-
I In this case the growth law can be approximated as d a / d N g 1.64 x 10-9(AK)2.3s.
'This value was obtained for a 40mm (tip to tip) crack. For a 14mm crack the value obtained was
11.5MPam"'.
'This value was obtained for a 40mm (tip to tip) crack. For a 14mm crack the value obtained was
-22.6MPam':'.
-
226
-z
G
Advances in the bonded composite repair of metallic aircraft structure
53
55
51
1
49
47
8 45
39
37
35
1
0
2000
4000
6000
8000
10000 12000 14000 16000 18000
Number of Cycles
Fig. 9.8. Crack growth for a 1.25mm thick skin specimen with an intact stiffener, max stress of
120 MPa.
lop3mm/cycle. In this case using the results given in [31] this growth rate gave a AK
of -22.3MPam'/2, which is in reasonable agreement with the numerical
predictions. The tests results were extremely repeatable, as can be seen from
Figure 9.9.
90
80
1
7
+ Test1
m
Test 2
- Linear (Test 2)
40
30 I
0
I
2000
4000
6000
8000
10000
Number of cycles
Fig. 9.9. Crack growth for a 1.25mm thick skin specimen with a broken stiffener.
Chapter 9. Numerical analysis and design
227
During the fatigue tests it was found that failure generally initiated at rivet holes
outside of the patched area. The location of the initiation site was essentially
random and appeared to associated with the initial fabrication of the specimen.
9.4. Comparison with experimental results for non rib stiffened panels
To further illustrate the accuracy of these simple formulae let us consider
a centrally located crack, 38mm long, in a rectangular sheet of aluminium alloy
with dimensions 300mm x 320mm x 2.29mm. The crack is patched, on
one side only, with a uni-directional boron epoxy laminate with dimensions
160mm x 160mm x 0.889mm and bending is prohibited, see Figure 9.10. The
adhesive is 0.1651 mm thick and has a shear modulus of 700 MPa. The aluminium
alloy has a Youngs modulus E of 7.2.86 GPa and a Possoin’s ratio of 0.3, whilst the
Fig. 9.10. Geometry of edge cracked edge notch test specimen.
Advances in the bonded composite repair of metallic aircrajl structure
228
.95
(.93)
.51(0.47)
Fig. 9.11. View of the repaired region showing the ratio of measured strains to the far field strain, finite
element values in brackets.
moduli of the boron epoxy laminate are taken as
Ell
= 208.3 GPa, E22 = 24.5 GPa, v12 = 0.1667,
= 7.24GPa
We first analyse this problem, making use of symmetry using a fully 3D finite
element model. The aluminium sheet is modelled by forty-one twenty-noded
isoparametric bricks and thirteen of the fifteen-noded isoparametric elements whilst
the composite patch is represented by twenty-one of the twenty-noded isoparametric bricks and thirteen of the fifteen-noded isoparametric elements.
The elements at the crack tip are triangular in plan form and have the midpoint
nodes moved to the quarter points in order to simulate the r-''2 singularity at the
crack tip. The elements at the crack tip are triangular in plan form and have the
midpoint nodes moved to the quarter points in order to simulate the r-1'2
singularity at the crack tip. To avoid problems with numerical ill conditioning and
the use of elements with large aspect ratios, reduced integration, or preferably
directionally reduced integration, must be used whenever a full 3D analysis is
undertaken. In addition, on 32 bit machines the formulation of the stiffness
matrices and the solution must be done using double prevision.
Let us now compare these results with those obtained experimentally for this
repair configuration. Figure 9.1 1 shows a comparison of the numerically predicted
surface strains with those measured strains on the surface of the patch at four
locations. The clip gauge openings measured near the mouth of the crack are given
in Table 9.10 as are those predicted numerically and those using the analytical
approach.
Chapter 9. Numerical analysb and design
229
Table 9.10
Clip gauge opening.
Clip gauge
opening (mm)
Predicted using F.E.M.
Predicted analytically (overlap joint analogy)
Measured
0.037 mm
0.032 mm
0.041 mm
This clearly shows that the finite element approach is capable of accurately
representing realistic repairs and that the analytical formulae provide a good first
estimate of the clip gauge opening and hence the adhesive stresses/energy.
9.5. Repair of thick sections
In recent years, a number of boron epoxy patches have been used to repair
surface flaws in thick sections, e.g. the repairs to the Macchi and Mirage main
landing wheels and the repair to the console truss in F111 aircraft (see [IO]). In each
case, the crack section was 12mm thick.
In the case of the Mirage and Macchi landing wheels, the repairs are installed
when the crack reaches a total length of 24 mm. In each case, the cracks were found
to be nearly semi-elliptical in shape with a surface length of 24mm and a maximum
depth of 6mm. In order to study the effect on such a crack, an investigation was
undertaken on the repair of a similar semi-elliptical crack centrally located in a
rectangular block of aluminium with dimensions as shown in Figure 9.12, (in this
figure, only one quarter of the structure is shown). The block was subjected to a
uniform uniaxial stress, and the effect that various boron fibre patches had on the
crack were calculated using a detailed 3D finite element analysis. Table 9.I 1 shows
the calculated values of the stress intensity factors at point d, the point of deepest
penetration, and s, the point at which the crack intersects the free surface. The fibre
stresses af are a maximum over the crack and vary through the thickness of the
-
Boron epoxy patch
50 m m
Fig. 9.12. Repair of surface flaw (1/4 structure modelled).
Advances in the bonded composite repair of metallic aircrafi structure
230
Table 9.11
Semi-elliptical flaw A = 12mm; C = 6 mm;
K,= 12.45 MPam'l2, at s, K1= 12.5MPam'/2.
unpatched
values at
Number
layers
boron
Stress intensity
factor Kl at:
d
S
Fibre stress over
crack o f / o at points
1
2
3
Adhesive shear
stress over
crack T / U
5
8.33
7.222
662
365
21 1
3.481
1.918
1.271
0.874
0.587
0.451
0.353
0.304
0.277
0.262
10
15
20
25
4.396
3.3463
2.979
2.709
2.588
4.256
2.572
1.810
1.364
1.073
5.293
3.670
2.907
2.488
2.244
d,
Table 9.12
Semi-circular flaw A = C = 6 mm
Number
layers
boron
Stress intensity
factor at K I at:
d
S
Fibre stress over
crack an o at points:
1
2
3
Adhesive shear
over crack T / U
stress
5
10
15
20
25
882
232
5.842
5.605
5.465
3.333
2.113
1.541
1.153
0.852
0.402
0.337
0.300
0.276
0.261
5.412
4.552
4.035
3.712
3.509
3.966
2.672
2.005
1.576
1.276
4.811
3.615
2.972
2.582
2.337
patch. These values are also shown in Table 9.12 along with the peak adhesive
stresses over the crack. In this study, the adhesive was taken to be AF126, an epoxy
nitrile, 0.1016mm thick with a shear modulus of 0.7GPa. Table 9.12 also shows the
corresponding values of stress intensity factors, fibre stresses and adhesive stresses
for the case when the surface flaw is semi-circular, rather than semi-elliptical, with a
surface length of 12mm.
As a second example let us consider the problem of a 40.12mm (surface crack
length) by 5.71 mm (crack depth) surface flaws in rectangular aluminium alloy
section with dimensions 300mm x 128mm x 11.2mm, see Figure 9.13. This
section is subjected to a remote uniform stress o of 68.9 MPa acting at right angles
to the crack plane. The structure is assumed to be repaired using a ten ply boron
epoxy laminate, i.e. 1.27 mm thick, bonded over the crack with using the, 0.106 mm
thick, structural film adhesive FM73.
To illustrate the effect of surface crack length three different surface lengths were
considered; viz: 10.066, 20.066 and 30.66mm and the values of K,, at the surface,
and K, at the point of maximum depth computed, see Table 9.13. To illustrate the
effect of crack depth a case when the surface length was 10.066 and the crack depth
was 3.0mm was also considered.
From Table 9.13 it is apparent that the stress intensity factors are dependent on
the surface crack length and the depth of the crack. However, the value of
maximum stress intensity factor K, increases only slightly as the surface crack
Chapter 9. Numerical analysis and design
23 1
510 mm
3 mm aluminium honeycombe
Bonded boron patch
Bonded boron patch
Fig. 9.13. Geometry of the surface flaw specimen.
Table 9.13
Stress intensity factors for a semi-elliptical surface flaw after repair.
Surface crack half length
mm
K,
MPa m’!*
K,
MPa m’!’
10.066
20.066
30.066
10.066 surface length by 3.0mm deep crack
1.4
0.73
0.48
0.68
4.5
5.3
5.46
3.56
length increases from 20.66 mm to 30.66 mm. This “asymptotic” phenomenon was
discussed previously. However, for 3D surface flaws it should be stressed that the
value of the maximum stress intensity factor, in this case K,, will depend on the
depth of the crack.
9.5.1. Experimental results
To illustrate the significant reductions in the stress intensity factors and hence in
the rate of crack growth, a series of fatigue tests were performed. The specimens
were 2024 T4 aluminium alloy, 11.1 mm thick, 108.3 mm wide and 304mm long,
and contained a centrally located surface crack. The surface length of the crack was
37mm and it was 6mm deep, see Figure 9.13. A 3D finite element analysis was
performed and the ratio of the patched stress intensity factor to the unpatched
232
Advances in the bonded composite repair of metallic aircraft structure
value was found to be 0.22, at the upper surface, and 0.44 at the deepest point in the
aluminium. Five specimens were tested under a constant amplitude stress of
65 MPa and R = 0.01. A further six specimens were repaired with a ten ply thick
boron fibre patch. In confirmation of our previous results, the unpatched specimens
lasted an average of 22.450 cycles whilst the patched specimens lasted an average of
527000 cycles.
From Tables 9.11 and 9.12 we see that the peak fibre and adhesive stresses are
relatively insensitive to the surface lengths of the crack. Consequently, we can
estimate the peak values of these stresses in the specimens, viz:
of = 3.67 x 65 MPa = 238 MPa and
zmaX= 0.353 x 65 MPa = 22.94
These values are considerably lower than their critical design values. Several
specimens were also loaded at 130 MPa with no evidence of fibre breakage or patch
debonding.
Tests were also performed using FALSTAFF loading with a peak stress of
138.9MPa. The fatigue lives of these test specimens are given in Table 9.14.
This illustrates that under FALSTAFF loading the repair has increased the
fatigue life of the component by a factor of approximately 5.8. This is significantly
lower than the value of -22 obtained using constant amplitude loading. This was
due to a variety of effects:
0 Fatigue damage in the adhesive due to the higher loads.
0 Growth of disbond/delamination directly over the crack.
0 Plastic strain of the adhesive which results in a higher K, see Eq. (9.27).
0 Load history effects due to the visco-plastic nature of the adhesive.
Although there was adhesive disbonding during the tests, final failure was in the
boron epoxy composite and was due to delamination of the upper nine plies from
the (1st ) ply next to the adhesive boron interface, see Figure 9.14. Indeed, this
failure mechanism has been observed in a range of composite repairs and
Table 9.14
Fatigue of repair to thick section under FALSTAFF loading.
Patched/unpatched
Specimen
Cycles to failure
Unpatched
9/22U
5/6U
3/4u
7/8U
mean
344039
326560
411595
334778
3541 17
Patched
14/15P
18/19P
16/17P
12/13P
mean
1954783
2699357
I923680
1632406
2052557
Chapter 9. Numerical analysis and design
233
Fig. 9.14. Close up of failure surface showing 1st layer of repair still attached to the specimen.
composite joints [3,15]. Consequently when designing repairs to primary structural
components this highlights the need to:
1. Allow for interlaminar failure in the composite repair.
2. Allow for the visco-plastic behaviour of the epoxy.
At the moment this level of analysis can only be done using advanced finite
element tools. Hence for primary structures repairs need to be designed using 3D
finite element analysis. A methodology for allowing for material non-linearities
without the need to perform a fully non-linear finite element analysis will be given
in the following sections.
9.6. Repair of cracked holes in primary structures
Let us now consider the repair of corner flaws, with a surface length of c and a
depth of a, at a through the thickness holes of radius r, see Figure 9.15. The
material is a 2024-T4 aluminium alloy with E=72.4GPa and v-0.33. The
thickness of the structure was taken to be t = 11.2 mm, its width w = 72 mm and the
total length to be 2h = 200 mm. Two repair cases are considered. In the first we use
a 1.27mm, i.e. a 10 ply, patch with an adhesive thickness of 0.1016mm and where
the fibres are orientated perpendicular to the crack. In the second we augment the
patch with a 1 mm thick steel sleeve which is assumed to be bonded into the hole.
The structure is subjected to a uniform remote stress of 68.9MPa. The resultant
values for the stress intensity factors at point s on the crack front nearest the patch
and at point d down the bore of the hole are given in Table 9.15.
Advances in the bonded composite repair of metallic aircrafi structure
234
Surface length c
Fig. 9.15. Geometry of cracked hole.
Table 9.15
Stress intensity factors MPa mi’* for patched specimens.
Location
Unrepaired
value
a = c = 3 mm,
r=3mm
S
D
74
10.61
3.17
7.97
2.43
3.66
a = c = 3 mm,
r=Smm
S
d
7.89
12.63
3.8
9.7
2.96
4.7
a = 3 c=6mm,
r=3mm
d
3.62
10.8
1.77
7.89
1.02
3.48
4.0
3.06
68 on the
unpatched
surface
Through crack r = 3 mm,
c=3mm
S
s
9.42
11.5 at the
mid- surface
Case 1:
Patch only
Case 2: Patch
and steel sleeve
Case
11.1 on the
unpatched
surface
The point to note here is that, as we saw in the previous cases, the patch alone
has only a relatively small reduction in K a t the point d deepest into the structure.
To reduce K a t this point requires further action. In this case the use of a steel sleeve
bonded into the hole.
Chapter 9. Numerical analysis and design
235
To obtain a first estimate of the worst (highest) value for K it is possible to use
the solution for a through crack. Table 9.15 allows us to predict the effect of the
patch on fatigue life. For the case of a patch only with a = c = 3 mm we see that the
ratio of the unpatched stress intensity factor to unpatched value is 10.6/7.97. As a
first approximation the rate of crack growth can be related to AK the stress
intensity range during cycling by the Paris growth law,
da
dN
-= C(AK)"
,
-
where for aluminium alloys PI 3. Thus as a first approximation the increase in life
due to patching can be estimated as:
L, =
repaired fatigue life - (AKunpatched)n
repaired fatigue
(AKpatcheJ '
which for the case when a = c = 3 mm and r = 3 mm this gives a value of 2.35. For
the case when a = c = 3 mm and r = 5 mm we obtain a value of 2.21.
To illustrate the effectiveness of this approach a series of constant amplitude
fatigue tests were performed for each of the two repair cases listed in Table 9.15.
The results of this investigation are shown in Table 9.16. Table 9.17 compares the
Table 9.16
Fatigue test results for repair of cracked holes.
Specimen configuration
u=c=3mm, r=3mm
Un-repaired
Repaired Case 1
Repaired Case 2
u=c=3mm, r = 5 m m
Unrepaired
Repaired with patch only
*Specimens failed in grips.
Number
Fatigue life cycles
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
AI I
A12
94240
104150
137830
1 17930
1 19800
179160
277310
285351
623630f
2,347300'
2,253500'
5,078200'
B1
B2
B3
B5
B6
B7
B8
97600
86600
1OO700
162500
147000
258000
248 100
Average cycles
113537
215405
N/A
94967
203900
236
Advances in the bonded composite repair of metallic aircrafi structure
Table 9.17
Comparison of fatigue life increase due to patch only.
Case
Predicted
Measured
a = c = 3 m m , r=3mm
a = c = 3 m m , r=Smm
2.35
2.21
1.9
2.1
Section A A'
i
20 mm
diameter
hole
145 mm
50 mm
Fig. 9.16. Schematic diagram of lug with 20mm diameter hole.
predicted increase in life with that obtained experimentally and as can be seen the
agreement is quite good.
9.7. Repair of cracked lugs
Let us now consider the repair of an aluminium (7075-T651) lug, see Figure 9.16,
which was designed to be representative of a cracked, load-bearing, fastener hole.
The specimen was 8mm thick, 145mm long and 50mm wide and contained a
Chapter 9. Numerical analysis and design
237
50
Fig. 9.17. Schematic diagram of lug repair, all dimensions in mm.
20 mm diameter hole, see Figure 9.17. In this investigation the specimen also had a
1mm notch machined on one side of the loading hole. A fatigue crack was initiated
from this notch and grown an average length of 1 mm to give a total crack length of
2 mm.
The traditional approach to the design of a bonded composite repair is to restore
the local stiffness. For the present problem this would require a 2.8 mm thick (or 22
ply) boron/epoxy doubler. However, the available specimen load transfer and taper
lengths restricted the repair thickness to 0.8mm (or 6 ply) per side, see Figure 9.17.
A doubler was applied to each side of the specimen giving a total repair material
thickness of 1.6mm. Thus only a 55% stiffness restoration was possible. The
doublers were made from boron/epoxy prepreg tape and bonded to specimens
using an epoxy-based structural-film adhesive in an autoclave.
In an effort to further reduce the stress intensity at the crack front, two
specimens were also repaired with a combination of composite doublers and a
1mm thick steel-sleeve insert was then bonded into the fastener holes using a twopart acrylic structural paste adhesive. A test matrix outlining the specimen
configurations is given in Table 9.18.
To ensure accurate bonding of the sleeves in the holes a bonding jig was used to
locate both the sleeve and specimen. This ensured that the bondline thickness was
constant around the circumference of the sleeve. The adhesive was allowed to cure
at room temperature and atmospheric pressure prior to removal of the repaired
specimens from the bonding jig.
238
Advances in the bonded composite repair of metallic aircraft structure
Table 9.18
Test matrix for lug repair specimens.
Specimen Number
Description
Spare
Repaired with doublers
Repaired with doublers and a sleeve
Repaired with doublers
Repaired with doublers and a sleeve
Unrepaired, as reference
Unrepaired, as reference
9.7.1. Numerical analysis
A 3D numerical analysis of the pin-loaded specimen was performed using
symmetry in the z direction. The structure was loaded to 36MPa, which was
equivalent to applying a load of 14.4kN to the end of the specimen (Figure 9.16).
The load transfer at the hole is a complex problem which was modelled using a
non-linear gaps analysis.
Two repair configurations, as described above, were analysed. The first
configuration was modelled with 3D iso-parametric brick elements representing
both the adhesive layer and the boron/epoxy laminate. The second configuration
was analysed in the same way, except that the pin size was reduced and the adhesive
layer and steel sleeve were also modelled.
In each case the finite-element analysis needed to be 3D and used both 20-noded
iso-parametric brick elements and 15-noded iso-parametric prism elements. To
avoid problems associated with the use of large aspect ratios, reduced integration
was used. At the crack tip, triangular elements were used with their mid-side nodes
relocated to the quarter point location closest to the crack tip. For increased
accuracy the size of the crack-tip elements should be set at 1/15 the length of the
crack.
For each specimen configuration five crack lengths were analysed and an analysis
of the un-cracked specimen was also performed. The crack lengths examined were
2 mm, 4 mm, 6 mm, 8 mm and 10mm. In each case the crack was assumed to grow
directly towards the outer edge of the specimen. The finite element meshes used for
this analysis are shown in Figure 9.18. In all cases the boronlepoxy laminate was
uni-directional, 0.8 mm thick (6 plies).
For each crack length the stress intensity factors ( K ) were calculated at the
surface and at the mid-point of the specimen. The results for all three
configurations can be seen in Figure 9.19. The results for the repaired configuration
show that the stress intensity factor reduces to an asymptotic value. This
phenomena has been discussed earlier. The effect of the idealised sleeve in the
hole is to further reduce the stress intensity factor.
-
239
Chapter 9. Numerical analysis and design
.-----.-
Repaired Surface
Repaired Sleeve Middle
_.--. Repaired Sleeve Surface
8 -
----
.
--.e
---_ - ---_ _ _ _ -_- -- --*.. -..
---~..~------.-.-.-.---*-.-.--.+.--- ..._
..
.......-....-.._.-_.______
*.
4
_"
--*.I-.
*
-----=.*----
2------------,----_.-.-.---.-.-.0
I
I
I
I
t
"I
240
Advances in the bonded composite repair of metallic aircraft structure
9.7.2. Experimental test
To assess the effectiveness of the repair a total of six specimens were fatigue
tested at constant-amplitude load. The three specimen configurations, as described
in Table 9.18. The specimens were loaded from 1 .O kN to 14.4 kN using a sinusoidal
wave-form at a frequency of 5 Hz.
In the case of Specimens 6 and 7 (the unrepaired group) the length of the crack
was measured on both sides of the specimen using a travelling vernier microscope.
The crack length of the remaining repaired specimens was measured nondestructively through the boron/epoxy repair using an eddy-current instrument.
For the repaired specimens it was not possible to monitor the crack for more than
approximately 10-1 1 mm of growth due to interference from the outer edge of the
specimen as crack growth progressed.
The loading mechanism consisted of a 100 kN static (50 kN dynamic) load cell
attached to the upper crosshead of a servo-hydraulic testing machine. Each
specimen was loaded using a simple pin and clevis grip with the unreinforced lower
end of the specimen clamped in flat hydraulic grips. To avoid premature fatigue
failure of the specimen within the test-machine grips, end tabs, as shown in
Figure 9.11, were bonded to the unreinforced end of the specimen.
The results of this test program are shown in Table 9.19 and in Figure 9.20. For
the unrepaired specimens the failure was due to complete failure of the ligament
containing the crack and subsequent inability to sustain load. For the repaired
specimens, failure was defined as the appearance of the crack on the outer edge of
the ligament running from one face to the other. At this stage the mean load
(7.7 kN) was still sustainable. To evaluate the residual strength a subsequent static
test was carried out on Specimen 2. This specimen failed at a load of 25.29 kN and a
far field strain of 9 3 0 p .
The average crack growth rate versus crack length relationship for the three
specimen types is shown in Figure 9.20. From this figure it can be seen that a
composite repair is capable of significantly increasing the fatigue lives of cracks in
an 8 mm thick aluminium alloy.
Table 9.19
Fatigue test results for repaired lug.
~
Specimen
Unrepaired
6
7
2
4
3
5
11900
+
Boron patch only
~~
Patch plus steel sleeve
12500+
168034
130000*
2 13000
176000
Test was stopped immediately prior to failure.
* Test was stopped and doubler removed to confirm crack length.
Chapter 9. Numerical analysis and design
.003
24 1
growth rate
m d c ycle
.002 --
Spec 6 4 7
3
e
m
B
II
.OO 1
-
J"""
.A
,000#?
y
. t &.%AI$-
Spec 31.5
&@
k
e
L
,
9.7.3. Discussion
The numerical analysis predicted that the boron/epoxy repair was capable of
reducing K by approximately 60%, see Figure 9.19. A further 15% reduction of K
was predicted if the specimen was repaired with a combination of a composite
doubler and a steel-sleeve insert. For the repaired cases, the analysis again shows
that K reduces asymptotically to a constant value implying that during constant
amplitude loading, as the crack length increases, the crack growth rate should
rapidly become constant.
In the region of constant crack growth rate, at a crack length of more than 6 mm,
using the predicted value of K from Figure 9.20 and interpolating the K versus da/
d N curve for the specimen material, for the crack growth rate for the repaired
specimens was predicted to be between 1.7 x
to 2.2 x 10p4mm per cycle.
(This range of crack growth is a result of the scatter band in the experimental crack
growth data for the material). This compares favourably with the experimentally
obtained value, this crack length, of 2.5 x 10p4mm per cycle.
An average fatigue life of 12200 cycles was achieved by the unrepaired specimens.
The repaired specimens on average, discounting specimen 4 where cycling was
stopped prior to specimen failure, achieved a fatigue life of 185000 cycles (a 15
times increase in life expectancy).
The numerical and experimental results again illustrate that the stress-intensity
factors, and hence the crack growth rate, for a bonded composite repair to a
cracked lug rapidly approach an asymptotic value as the crack length increases.
Additionally a substantial reduction in crack growth rate was obtained. This
implies that the crack growth may be arrested by an optimum choice of the
thickness of the repair. In this case the thickness of the repair should be such that
242
Advances in the bonded composite repair of metallic aircraft structure
the resultant asymptotic value of stress intensity factor is below the threshold value
for crack growth.
Given that the maximum life to failure of the two un-repaired specimens was in
the vicinity of 12200 cycles, under the loading conditions applied, the bondedboron/epoxy repaired specimens revealed at least a 10 fold increase in the fatigue
life. Furthermore a static test to failure of a repaired specimen containing fatigue
failure of the ligament demonstrated that the specimen was capable of sustaining a
load of approximately 25 kN, which is nearly twice the applied fatigue load, before
total structural failure.
9.8. Repairs to interacting surface flaws
The phenomenon of aging structures has focused attention on the problem of
multiple-site damage (MSD) and wide spread fatigue damage (WFD). In isolation
each flaw or crack may be safe. However, the cumulative effect of multiple,
interacting cracks may significantly degrade the damage tolerance of the structure.
In the civilian arena the importance of understanding and managing ageing
structures was highlighted by the failure of the Aloha 737 on April 28, 1988. This
failure was essentially due to the linking, into one large crack, of numerous small
cracks at a number of fastener holes, see [7]. Although the phenomenon of MSD
was first observed in civilian aircraft, MSD and WFD also play a major role in
determining the fatigue life military aircraft.
To illustrate the mechanism by which composite repairs reduce crack interaction
and improve the damage tolerance of structures containing MSD let consider the
problem shown in Figure 9.8. In this case there are two 40.12mm (surface crack
length) by 5.71 mm (crack depth) surface flaws in the rectangular aluminium alloy
section, which has dimensions 300mm x 128mm x 11.2mm. As previously this
section is subjected to a remote uniform stress 0 of 68.9 MPa acting at right angles
to the crack plane. The structure is again assumed to be repaired using a ten ply
boron epoxy laminate, i.e. 1.27mm thick, bonded over the crack with using the,
0.106mm thick, structural film adhesive FM73. In this case the associated
solutions, for different surface distances between the adjacent surface crack tips,
are given in Table 9.20.
From these results we see that, when using a composite repair, even when the
crack tips are 5 mm apart the interaction between the cracks was less than 10% at
the surface. At the point deepest into the body, which in this case is the point with
Table 9.20
Stress intensity factors for two interacting semi-elliptical surface flaws.
K, MPa m’”
K, MPa m”*
One
crack only
Two cracks:
Distance between tips = 5 mm
Two cracks:
Distance between tips = 10 mm
0.73
5.3
0.79
0.79
5.3
5.3
Chapter 9. Numerical analysis and design
243
the maximum stress intensity factor, the interaction was negligible. It should be
noted that slightly different meshes had to be used in each case and that the slight
difference in the solution for the one crack and the crack case may well be due to
the difference in the meshes. Consequently, when performing a damage tolerance
assessment of this repair each crack could be considered separately. A more
detailed study of repairs to MSD is given in [6-8,12].
9.9. Material nonlinearities
When designing bonded repairs, or adhesively bonded joints, the stress/strain
response of the adhesive plays a central role in determining both the load carrying
capacity and the fatigue performance of the repair or joint, see [16-18]. We have
also seen in Section 9.2 and Chapter 8 that the formulae for Kp depends on the level
of plastic strain in the adhesive. To this end we need a test methodology capable of
accurately and consistently reproducing this behaviour. In this context Chiu, et al.
[161 have developed a variant of the ASTM thick-adherend short over-lap adherend
test specimen for characterising the stress/shear behaviour of thin film adhesives,
see Figure 9.21. The results revealed that the properties of the film adhesive FM73
exhibited significant visco-plasticity, even at room temperature, see Figures 9.2 1
and 9.22. Chiu, et al. [16] also developed a unified constitutive model to describe
this visco-plastic behaviour.
This section assesses the structural significance of this visco-plastic behaviour, in
a realistic symmetric double lap joint/repair, via a detailed finite element analysis.
Here we show that the stress/strain behaviour of the adhesive in a bonded joint is
dependent on both the loading rate and the load history. We also see that when the
joint is subjected to monotonic loading, with a constant loading rate, the energy
density, which is the primary adhesive design variable in a bonded repair, at the
worst point in the joint is essentially time independent. This is very important as it
allows the existing design tools to be used even though the adhesive exhibits
significant visco-plastic behaviour, and as a result is strongly rate dependent.
However, in order to estimate the stress intensity factor after patching KooePp,
see
Eq. (9.27), it is necessary to correctly account for these visco-plastic effects.
Unfortunately, the peak adhesive shear stresses and strains are strongly effected
by the loading history, and hence this can significantly effect the stress intensity
factor Km,_,. Since the shear stresses are continuous across the interface an accurate
knowledge of the interlaminar stresses in the composite repair requires these viscoplastic effects to be incorporated in the analysis. To this end a simple methodology
1~
4
19mm
,
II
eAdhesive -0.2
I
mm thick
1 9 0 m m d
Fig. 9.21. Schematic diagram of the ASTM D 1002 thick adherend test specimen.
Advances in the bonded composite repair of metallic aircraft structure
244
I
L
1
1
I
Shear Stress
Strain rate
50
Experiment
Predicted
--.--
*+
10-2
0
10-3
10-4
40
30
20
10
b
0
Shear Strain
*
I
t
I
I
1
,
I
Fig. 9.22. Stress strain curves for FM73 at room temperature, from [16].
Chapter 9. Numerical analysis and design
245
will now be presented which uses the Glinka hypothesis [16] and which negates the
need for a complex non-linear finite element analysis. Details of the analytical
methodology enabling this time-dependent inelastic deformation of the adhesive to
be included in the design process are given below.
9.9.I . Governing differential equations for bonded jointstrepairs
In the previous section we have seen that thin film adhesives exhibits significant
visco-plastic effects. The question thus arises:
How do we account for this in both the analysis and design of a composite
repair/joint?
To this end let us consider a symmetric double lap joint, see Figure 9.24,
subjected to a remote load P where the lower and the upper adherend thicknesses
and Moduli are TI, El and T2, E2 respectively and where the adhesive has a
thickness t and an elastic shear modulus of G,. The governing differential equations
relating the stresses in the adherends al,02, where the subscript differentiates
between the lower and the upper adherend, to the adhesive shear stress 7, in the
joint are:
(9.30)
(9.31)
If the adherends are elastic then Hooke’s law applies and the displacements in the
lower and the upper adherents, defined as u1 and u2 respectively, are related to the
stresses through the Young’s moduli; viz:
(9.32)
(9.33)
whilst the shear strain y in the adhesive is related to the relative displacements in the
L
T
i
t
Fig. 9.24. A schematic diagram of a symmetric double lap joint.
Advances in the bonded composite repair of metallic aircrafi structure
246
adherends; viz:
Y=
(u1 - u2)
t
(9.34)
This system of equations results in the following relationship between the adhesive
shear stresses and shear strains; viz:
(9.35)
where from equilibrium considerations the load P applied to the upper adherend
must equal the integral of the adhesive shear stresses; viz:
I
(9.36)
P = Jrdx,
0
where I is the overlap length of the joint. To complete this system of equations it is
necessary to prescribe the relationship between the adhesive shear strain y and the
adhesive shear stress T. Since this relationship is usually in-elastic it best to consider
a general functional form; viz:
Y‘
=f(d)
9
(9.37)
where the inelastic shear strain rate y‘ is considered to be an arbitrary function,
f(z,i)’) of the shear stress T and the shear strain rate $ I .
This formulation extends the approach, used by Hart-Smith [181, to allow for the
visco-plastic response of the adhesive. At this stage it should be stressed that it is
well known that the computed values of peak stresses and strains in a simple joint
are strongly dependent on the mesh density, and in particular the number of
elements used through the adhesive, and the element type used in the analysis (201.
On the other the peak value of the strain energy density ( W = Jogd&q)is relatively
insensitive to these variables, see [17] for a more detailed summary of this
phenomena. This means that, as recommended by Hart-Smith [15], it is best to use
the strain energy density as the primary design variable.
The solution to this set of nonlinear time dependent equations can be quite
messy and time consuming. To over come this we use Glinka’s [19] technique for
estimating the peak stresses and strains in the adhesive.
Structural components, albeit composite repairs, bonded joints or stiffener
runnouts, are frequently subjected to complex loading spectra. These alternating
loads tend to initiate fatigue cracks at notches and at other regions of high stresses.
Historically the field of fatigue has been classified into a number of specific areas; viz:
high-cycle and low-cycle fatigue; fatigue of notched members; the initiation and
propagation of cracks and fatigue life extension techniques. Fatigue initiation and
crack growth programs require an accurate knowledge of the local notch tip stresses
Chapter 9. Numerical analysis and design
241
and strains. These quantities can be determined in several ways, viz: via direct strain
gauge measurements, using finite element analysis or by using approximate methods,
such as the Glinka’s approach [19], that relate local stresses and strains to their remote
values. To this end we will first briefly outline the Glinka approach for calculating the
peak shear stresses and shear strains. Attention is then focused on developinga simple
method which combines modern constitutive theory with the Glinka approach to
calculate the peak (visco-plastic) adhesive stresses and strains.
Let us first define the peak adhesive shear stresses and strains obtained via an
elastic solution as z and y(= z/G) respectively. Let us next define the peak adhesive
shear stresses and strains obtained via an in-elastic solution as z and y respectively.
In this case, Hooke’s law cannot be used to relate the peak shear stress, z, to the
peak strain, y . Instead Glinka’s rule [19] can be used to compute the peak stresses
and strains. According to this hypothesis the peak in the strain energy density field
obtained via in an elastic plastic analysis is the same as the peak strain energy
obtained via a purely elastic analysis; viz:
(9.38)
It should be noted that this relationship also follows from the Hart-Smith
solution [18]. As such the Hart-Smith solution is contained as a special case of
Glinka’s hypothesis. However, in [ 151 visco-plastic effects were not considered.
The solution process required to determine the true visco-plastic response thus
involves first solving for the peak elastic stresses and strains in the repair. Once a
valid stress strain relationship for the epoxy is known we then use Eq. (9.35)
together with the elastic solution to determine the peak (in-elastic) adhesive stresses
and strains.
In the past few years there has been an increasing interest in the use of unified
constitutive models for predicting the inelastic response of structural materials, i.e.
visco-plasticity, creep, stress relaxation etc. These models overcome many of the
deficiencies of the classical approaches to the inelastic behaviour of materials. The
present work uses the formulation presented in [16] to represent the visco-plastic
response of thin film adhesives.
This formulation uses two internal state variables, back stress Q, (deviatoric)
tensor and drag stress 2 to define the state of the material. Here the inelastic
deformation is driven by the over stress which is defined as ( S , - nu).Similar types
of theories have been widely used to describe the behaviour of thermoplastics.
In this approach, the flow equation is defined as:
E)
where
)”I
[-A (2’
2 3Kz
= Dexp -
(Sjj - Q,)
a ’
(9.39)
is the inelastic strain rate tensor, Sv is the deviatoric stress and
Here D, A and n are material constants. The term
( S , - Qz,)/fi
in Eq. (9.39) is the normalised overstress and defines the straining
K2 =
8;
4( S , - Qu)(Sg - Q,).
Advances in the bonded composire repair of metallic aircraft structure
248
direction. The drag stress is history dependent and evolves with the effective
inelastic strain ci. The initial drag stress is Z,, final Z1,and mo controls the rate of
evolution. The "growth" of the drag stress is defined by Eq. (9.40).
z = 2 1 + (zO + ~ 1 ) e - " ~ "
(9.40)
The back stress is initially zero and its evolution is controlled by an evolution
equation, viz:
2
' 3
n..
= f& + f,&!. - - f l
9
2
d$e$k
(9.41)
sz,,
where ci =
is the effective inelastic strain rate. Here, f,, f2 and Qm,, are
material constants. The effective inelastic strain rate is defined in the normal fashion.
Illustration
Consider the symmetric double lap joint shown in Figure 9.25. This joint has an
overlap length of 90mm, and consists of two identical aluminium adherends with
an elastic modulus E = 70000 MPa, and 1 = 1.5mm. The aluminium adherends and
doublers were assumed to be bonded together using FM73. The adhesive, FM73
film, was 0.2 mm thick and had a shear modulus G of 750 MPa. Its visco-plastic
behaviour is described using the state variable formulation described above. The
material parameters for the constitutive law for FM73 at room temperature are
given in Table 9.21.
This joint was analysed using both the Glinka approach, described above, and
the ABAQUS finite element analysis program together with the associated UMAT
material subroutine. In each case a remote stress of 401 MPa was assumed to be
monotonically applied to the ends of the inner adherend with the load increasing
from 0 to its maximum load in either 0.1 s, 1 s, 10s or 100 s. A comparison of the
calculated peak shear strains y in the joint is shown in Table 9.22.
Application to the analysis of double lap joints
Having thus validated the Glinka approximation a further series of finite element
analysis of various double lap joints (Figure 9.25) were then performed. The joints
The worst point in the
mmI thick
Fig. 9.25. A quarter of a symmetric double lap joint.
Chapter 9. Numerical analysis and design
249
Table 9.21
Typical material parameters for FM73 film at room temperature.
Room temp.
A
D
f, (MPa)
f2
n
mo
R
,
Zo (MPa)
Z , (MPa)
1
10000
800
0.2
0.85
10
12.5
120
350
Table 9.22
Comparison of peak shear strain y with 1D Glinka
formulation, L/2t = 15.
Dimension
Loading time (sec)
ID algorithm
Finite element 2D/3D
% Diff
0.1
0.143
0.152
5.9
1
0.152
0.165
7.9
10
0.163
0.179
8.9
100
0.177
0.189
6.3
analysed in this paper had (L/2t) ratios of 7.5 and 15 and a range of load histories
were evaluated. These joints had overlap lengths of 90mm (for L/2t = 15), and
45 mm (for L/2t = 7.5) respectively. The elastic modulus of the adherends was
E = 70000 MPa. The thicknesses were 3 mm (for the inner adherend) and 1.5mm
(for the doubler). The aluminium adherends and doublers were assumed to be
bonded together using FM73. The FM73 adhesive was 0.2mm thick and had a
shear modulus of 750 MPa. These joints were loaded to a maximum remote stress
of 401 MPa. with the load going from 0 load to its maximum value in either 0.1 s,
1 s, 10s or 100s. The stress-strain relationship at the worst (critical) point in the
adhesive layer during these load up sequences is shown in Figure 9.26 (L/2t = 15)
and 9.27 (L/2t = 7.5).
- .5
-f
-0.4
+0.1
-0.2
-0.3
sec
+I
-0.1
sec
z
-
u)
e
L
m
c
v)
Far field strain (mmlmm)
Fig. 9.26. Adhesive shear stress-strain curves at a critical point in the joint, L/2t = 15.
250
Advances in the bonded composite repair of metallic aircrafi structure
-0
+0.1
B
+10sec
v
sec
-%-
1 sec
+- 100sec
-e
u)
u)
2
c
u)
I
I
-35
Shear strain ( m d m m )
Fig. 9.27. Adhesive shear stress-strain curves at a critical point in the joint, L/2t = 7.5.
These figures illustrate that the stress/strain behaviour of the adhesive exhibits
significant visco-plasticity and, as a results, is dependent on the loading rate (the
higher the loading rate, the higher is the apparent yield stress). The maximum stress
level (apparent yield stress) in the adhesive is higher when the joint is loaded more
rapidly. These figures also show that the strain level in the adhesive is dependent on the
loading history. Here the higher loading rate resulted in lower adhesive strain levels.
In contrast to the stress or strain based approaches Hart-Smith’s [I81 analysis of
a double lap joint revealed that the load carrying capacity of the bond can be
estimated from the energy density at the worst point in the adhesive. This design
methodology was based on the assumption that the adhesive behaviour can be
approximated using a single bi-linear stress/strain curve. This simplification is not
necessarv. With the extended analysis given in this report the adhesive can be
allowed to undergo both creep and visco-plastic behaviour. As shown in Figs 9.26
and 9.27 the stress/strain relationship at any location along the adhesive layer will
be governed by the local adhesive strain rate (Le. the higher the local adhesive strain
rate, the larger will be the apparent yield stress of the adhesive).
To determine how the visco-plastic behaviour of the adhesive affects the load
carrying capacity of the joint the energy density at the worst point in the adhesive
layer was also calculated. The results are shown in Table 9.23. The first observation,
apparent from this table, is that the energy density at the worst point is slightly
higher when the L / 2 t ratio is 7.5. Hence one would expect the joint with a lower (L/
2t) ratio to have a slightly lower load carrying capacity. More importantly we find
that, whilst the local stress/strain behaviour of the adhesive are largely dependent on
Chapter 9. Numerical analysis and design
25 1
Table 9.23
Effect of loading rate on energy density both L/2r = 7.5 and 15 at room temp.
Energy Density (MPa)
L/2t
Loading Time (sec)
7.5
Adhesive layer
Adhesive layer
I5
0.1
42.6
41.6
1
10
100
% Diff
44.4
43.7
46.1
44.9
47.1
45.1
9.5
7.8
the loading rate, the energy density at the worst point in the adhesive is relatively
independent of the loading rate. There is only approximately 8% variation, refer to
Table 9.23, in the energy density from the slowest to the fastest loading rate.
This work thus confirms that the design hypothesis first presented by the HartSmith [18] for estimating the load carrying capacity of a double lap joint can be
used for thin film adhesives, such as FM73 and FM300, which exhibit significant
visco-plastic effects provided that failure occurs in the adhesive.
Traditional design approaches [ 181 do not cover interlaminar failure in the
composite patch. In this case, since the shear stresses are continuous across the
patch adhesive interface it is necessary to determine the stress state in the adhesive
which, as we have seen, requires an allowance for the visco-plastic response of the
adhesive.
Remarks
This analysis reveals that, even at room temperature, when the loading history is
simply monotonic the visco-plastic nature of the adhesive in the double lap joint
has limited effects on the strain energy density, and thus on the load carrying
capacity of the adhesive bond (repair). In contrast the peak adhesive shear stresses
and strains are strongly effected. Consequently, since the shear stresses are
continuous across the composite patch-adhesive interface, for an accurate
knowledge of the interlaminar stresses in the composite repair it is important
that these visco-plastic effects to be incorporated in the design. Similarly when
estimating the effect of yield in the adhesive on K i t is important that these viscoplastic effects to be allowed for. This can easily be achieved by using Glinka’s
approach.
9.10. Effect of variable adhesive thickness
Let us now address the problem of variable adhesive thickness. In this section we
will show that the Glinka extension to the Hart Smith design formulae can be used
for those cases when the adhesive thickness is not constant. However, before
examining the inelastic behaviour of joints with variable adhesive thickness let us
first consider the elastic response.
Advances in the bonded composite repair of metallic aircraft shucture
252
Ax
I )&
UI
I
Displacement
Equilibrium Equations
u l + ~ u lT~
U2+&
X
-+-/Tk
TI+ATI
TAx-
T
Ax
z
~
-
~
T2+AT2
Ax
Fig. 9.28. Schematic of the adhesive joint.
Consider the joint as shown in Figure 9.28, the governing equations for this joint
are:
TI ,x = -z
T2,r = --z
(9.42)
(9.43)
>
9
and
U]
(9.44)
- u2 = t y
From Hooke's law for the adherends we find that:
(9.45)
(9.46)
and for adhesive
(9.47)
z = Gy
where E1;2 and h1;2 are Young's modulus and thicknesses of adherends, G and t are
the shear modulus and thickness of the adhesive. Other parameters are as shown in
Figure 9.28.
Let us consider the case when the adhesive thickness is variable i.e. t = t ( x ) . In
this case Eqs. (9.42) to (9.47) produce the resultant differential equation, viz:
(v>,= P2(X)Yt
9
where D2(x)= $$ ((Elhl)-I+(&h2)-').
(9.48)
Chapter 9. Numerical ana1ysi.y and design
253
In the case of a constant adhesive thickness Eq. (9.48) reduces to the well-known
equation for the shear stress in adhesive, viz
T,, =B'T
.
(9.49)
where /?' = $ ((E1hi)-'+(E2h2)-*).
For a constant thickness adhesive joint the concept of a characteristic length E is
commonly used. This distance ,iis given by the formulae:
"
3
(9.50)
"7
and represents the length of the adhesive playing the major role in the load transfer
process transferring the loading.
Equation (9.48) has no general analytical solution. However by using the
transformation z = (yt).y/yl it can be reduced to the special Riccati Eq. (9.27):
2,
+ a 2 = P2(.)
(9.5 1)
~
with a = 1. This Eq. (9.14) can be solved for a wide class of function /!(x),
particularly when this function has the form B2(x) = bx".
Consider the following example. Let the adhesive thickness in the vicinity of the
edge is distributed as t ( x ) = fox4.In this case f12 = P2(x) has the form
B'(x)
= h2-f4,
(9.52)
where b - to (Elh1)-'+(E2/22)-').
2 - G (
We thus require a solution to the following equation:
(Yt).,=
h . ~ - ~ y tat
Xo
5x5
,%
(9.53)
The solution of this equation results in the following expression for the adhesive
shear stresses
~ ( x ="(c.
) t,,X3
cash(:)
+asinh(:))
(9.54)
The constants a and c in this solution can be found from the boundary conditions,
which can be taken in the following form
(9.55)
which represents the balance of forces acting on the adherends and
(9.56)
Advances in the bonded composite repair of metallic aircraft structure
254
From the boundary conditions we find that
PElhl
P
b2 to
C=
G
E l h i +E2h2
E2h2
(9.57)
’
and
+ 5 sinh(b/xo) - c
_ _E&
a=
cosh(b/xo)
(9.58)
sinh(b/xo) - b/xo cosh(b/xo)
In the special case when Elhl = E2h2 = Eh we have c = 0 and
’
(9.59)
and the expression for the shear stresses becomes
T(X)
P G
sinh(b/x)
Eh lox3b/xo cosh(b/xo) - sinh(b/xo)
= --
(9.60)
The criterion proposed by Hart-Smith for failure of adhesive joints, see Chapter
9, can be written in the form
Wmax
2
wcr
(9.61)
3
where W,,, is the maximum value of the strain energy density in the adhesive, and
Wc,is the critical value for the energy determined from standard materials tests.
In this problem the maximum strain energy density occurs at the edge of the
joint, i.e. x = XO,where the shear stress
T(X0)
=
, , ,z
P G
1
Eh lox3 b/xocoth(b/xo)
= --
-
1
’
(9.62)
where coth(b/xo) is the hyperbolic cotangent.
Consider the case when the value of b/xo 1, this corresponds to small changes
of the thickness of the adhesive on the characteristic length of the stress
distribution, then
+
1
b/xo coth(b/xo) - 1
xo
b
(9.63)
In this limiting case the solution for W,,, reduces to
P2
1 P2
w,,, = -41 Ehtox;f 4 Eht
(9.64)
This formula, which is independent of the stress-strain relationship for the
adhesive, coincides with the maximum strain energy density for an adhesive with a
constant equal to the thickness at the edge x = XO. This means that the present
Chapter 9. Numerical ana/ysis and design
255
w,, 1.5
wo
1.4
1.3
1.2
1.1
SO0
1000
1500
2000
2500
G, MPa
Fig. 9.29. Dependence of the maximum strain energy density on the adhesive shear modulus.
solution asymptotes to the solution for the constant thickness of the adhesive as .YO
reduces to zero.
Let us now we consider the case when the adherends are an equal thickness
aluminium alloy with h, = h2 = 3 mm, and E1 = E2 = 73GPa. The thickness of
the adhesive is distributed in accordance with a power law in the following form
r(x) = rosy4where the thickness at the edge is 0.1 mm and increases to 0.2 mm after
a distance of (a) 5 mm, (b) 10 mm, and (c) 20mm from the edge. In this study the
shear modulus of the adhesive was allowed to vary from 500 MPa to 2500 MPa.
This range covers most practical situations.
The ratio of maximum strain energy density, for the non-uniform adhesive
thickness, to the maximum strain energy for the case when the joint has a constant
adhesive thickness of 0.1 mm is shown in Figure 9.29. From this figure we see that
the maximum strain energy is now dependent on the shear modulus of the adhesive.
However, for cases (b) and (c), where the rate of change of the adhesive thickness
with respect to distance is relatively small, this dependence is rather weak. Even for
case (a) where the adhesive thickness doubles over a distance of 5 mm the variation
in extreme values of the energy density is approximately 25%. Since the load
carrying capacity of the joint is proportional to the square root of the maximum
energy density this corresponds to a variance in the failure load of approximately
10%.
This figure also reveals that the energy density is a function of the local geometry
of the joint. As such the Hart-Smith formulation cannot be used to predict the
strength of the joint. In this case we must use the Glinka extension to the HartSmith formulation. Indeed, a feature of the solution, for a constant adhesive
thickness is that the maximum strain energy W,,,, obtained using the elasticperfectly-plastic solution, is exactly equal to that obtained via a purely elastic
solution W,,,,. In the present case the elastic plastic solution reveals that, as a first
estimate, Glinka’s hypothesis is valid, i.e. W,,, / WmaxE 1, see Figure 9.30.
256
Advances in the bonded composite repair of metallic aircraft structure
1.1
1
0.9
0.8
0
20
40
60
80
100
-/J%
Fig. 9.30. Ratio of the maximum strain energy for the elastic-perfectly-plasticsolution to value obtained
via an elastic analysis for a non-uniform adhesive thickness.
9.10.1. The effect of variable adhesive thickness and material non-linearity
Having established the Glinka hypothesis to be applicable to bonded joints with
global bending prohibited let us now consider the effect of both variable adhesive
thickness adhesive plasticity. We have seen that the energy density is a weak
function of the adhesive shear modulus. It should thus follow that the hypothesis
will also hold if the adhesive thickness is variable.
To evaluate this effect let us consider a symmetric double lap joint with a lower
adherend (halothickness TI of 3 mm, an upper adherend thickness T2 of 2 mm, and
El = E2 = 73000 MPa. The adhesive, which was assumed to be FM73, was allowed
to be either one or two layers thick, i.e. 0.1 mm or 0.2 mm thick, and had a Young’s
modulus of 1890MPa and a Poisson’s ratio of 0.35. Whilst the adhesive was
assumed to have a post yield slope E’ of 250MPa and the yield stress of the
adhesive was allowed to vary, see Table 9.24. Furthermore, at the critical end of the
Table 9.24
Percentage difference in W and values of W, c = 360 MPa.
~~
A (mm), the local increase in the adhesive thickness.
Yield stress and adhesive thickness
uy = 40 MPa
I, = 0.2 mm
uy= 68 MPa
tCt= 0.2 mm
u? = 40 MPa
t,=O.lmm
cry = 68 MPa
t,=O.lmm
0.025
18.1
W = 13.27
13.9
W = 14.65
25.0
W = 16.95
21.6
W = 18.76
0.05
17.0
W = 11.54
11.5
W = 13.12
22.7
W = 14.80
17.7
W = 16.75
0.075
15.5
w = 10.22
9.5
W = 11.78
20.5
W = 12.87
15.33
W = 14.59
Chapter 9. Numerical analysis and design
257
joint the thickness tf, was assumed to vary according to the following equation
(9.65)
where ,,c A , JC,and XI are the nominal adhesive thickness, the amplitude of the
perturbation of the thickness, the distance from the end of the joint and a
characteristic length. In this initial study we chose, on the basis of past experience,
.VI to be 3 mm, and varied the values of A . At this stage only monotonic loading was
considered and to increase the amount of yielding the remote stress, in the lower
adherend, was taken to be 360 MPa. The results of this analysis are summarised in
Table 9.24.
To further illustrate the validity of Glinka’s hypothesis for variable adhesive
thickness let us consider the case when the adhesive is two layers thick, i.e.
t , = 0.2 mm, and A = 0.05 mm. This corresponds to a perturbation in the adhesive
thickness equal to 25% of the base line thickness. In this case the distance over
which the perturbation occurred, Le. xlrwas varied from 1.5 to 5 mm and the results
are shown in Table 9.25.
In the previous section we saw that for a variable thickness adhesive the
analytical solution for the peak in the energy density field W,,, was a weak
function of the adhesive shear modulus. This contrasts with the analytical solution
for a constant thickness joint where W,,, is independent of the shear modulus.
From this we would expect that, for repairs with a variable thickness adhesive,
Glinka’s hypothesis may be less accurate as the plasticity becomes more extensive.
The present finite element results appear to support this conjecture. Nevertheless,
for monotonic loading, Glinka’s hypothesis still appears to be a reasonable first
approximation with error levels consistent with those for notched isotropic bodies.
Indeed. Tables 9.24 and 9.25 also show that, even for joints with a variable adhesive
Table 9.25
Percentage difference in J W and values of W (MPa), A =0.05mm.
Remote stress o (MPa)
Yield stress and post yield slope
o,,
= 68 MPa
t,=O.Zmm. XI = 1.5mm
o) = 40 MPa
r,, = 0.2 mm. xI = I .5 mm
= 68 MPa
I,, = 0.2 mm, x, = 3 mm
6,.
= 40 MPa
r,, = 0.2 mm, xI = 3 mm
ct.= 68 MPa
t,, = 0.2 mm, sI= 5 mm
= 40 MPa
t , = 0.2 mm, x I= 5 mm
144
200
240
288
360
0.0
W=2.58
8.7
W=3.05
0.0
W=2.68
7.3
W=3.09
0.0
W=2.80
6.6
W=3.I8
0.4
W=4.90
5.5
W=5.49
0.5
W=5.08
4.3
W=5.59
0.8
W = 5.28
3.7
W=5.75
2.5
W=6.81
2.2
W=6.85
2.8
W=7.03
3.5
W=7.08
3.2
W = 7.28
3.0
W=7.32
6.0
W=9.11
9.0
W=8.53
6.4
W=9.39
9.4
W=8.80
6.9
W = 9.70
9.9
W=9.09
11.1
W=12.7
16.7
W=11.1
11.5
W=13.12
17.0
W=11.54
12.1
W = 13.53
17.5
W=11.91
258
Advances in the bonded composite repair of metallic aircraft structure
thickness, W,,, is also a (relatively) weak function of the yield stress of the
adhesive.
This finding infers that, for bonded composite repairs, even if there is variability
in the thickness of the adhesive bond the energy field and hence the strength of the
joint, provided failure is due to failure of the adhesive, can be estimated from a
purely linear elastic analysis of the joint. This has the potential to significantly
simplify the design/assessment process particularly in the case where fabrication
problems, or the inability to control the local localised flow or cure temperatures,
can give rise to a variable adhesive thickness repair.
We thus see that, for monotonic loading, although variable adhesive thickness
changes the stress and the energy fields Glinka’s hypothesis is still valid. This means
that, for the present class of problems, even if there is variability in the thickness of
the adhesive bond the energy field W,, can be computed using only the elastic
solution. The strength of the joint, provided failure is due to failure of the adhesive,
can be then estimated from a purely linear elastic analysis of the joint. This will
occur at the load level when
Wmax = Wcrit
(9.66)
This finding has the potential to significantly simplify the design process for
repairs with a variable thickness adhesive.
9.11. Repairs to cracked holes under bi-axial loading
The problem of composite repairs to cracks at a hole or notch was first studied
by Baker, et al. [2], which deals with repairs to cracks a fuel decant hole in Mirage
I11 aircraft, and later by Atluri, et al. [12]. For this problem as the crack length (I )
gets larger, i.e. I + co, the solution should approach that of a patched crack
without a hole. Hence when I/p is large, the stress intensity factor should tend to an
asymptotic value K,, which is independent of the size of hole.
Let us begin by considering the problem of a crack emanating from a notch, see
Figure 9.31. Schijve [30] presented an excellent review of the existing literature and
proposed that the stress intensity factor could be expressed in the form, viz:
K = F C T ~ ,, , ~
(9.67)
where omaxis the peak stress at the notch. In this work he also proposed that the
geometry factor F was only a function of the ratio I/p.
Using this technique we can present an approximate solution, for the problem of
a composite repair to a cracked hole subjected in the form, viz:
K = F ( l / p )W ( 1 / 2 d ) K
(9.68)
Here K is the solution to the problem of a center notch crack 21 long, i.e. an
embedded crack, in an infinite plate acted upon by the same stress field (cy,z) as
Chapter 9. Numerical analysis and design
y L
at the notchc= (Oj,
259
7)
/
Fig. 9.31. Schematic diagram showing notch, crack and the stress field at the notch.
!
i
vi<
Fictitious crack with
same (mirrored) stress
field as for the original
notch
........... .............
The curved notch boundary is
ignored and replaced by a line
of symmetry
:
!
.
j1
I
I
I
!
i
Fig. 9.32. Schematic picture of the problem used to determine K .
found at the notch, see Figure 9.32. In this formulation we create a fictitious crack
of equal length and the stress field is mirrored across the boundary of the notch, see
Figure 9.32. Since Kis the starting solution in the finite element alternating solution
this formulation can be thought of as a marriage of the alternating solution and the
method, see [32]. The values for F a r e given in Table 9.26. It is often convenient to
express F as an analytical function of l / p . The function F can be approximated as:
1
I
E: = -- (1.12 - -)
d3
d3
exp(-d/p)
,
(9.69)
which satisfies the requirements that F -.+ 1.12 as l / p -.+ 0, and F 4 1/J2 as
l / p -.+ co, so that the expression for K has the correct asymptotic limits at both
I/p
0, i.e. for short cracks, and l / p -+ co, i.e. for long cracks. The functional
form used in this work, which agrees with the values presented in Tables 9.26 to
within -5%, was:
-.+
CI
= 0.8(1.0 - O.31/p
+0.13(1/~)~)
(9.70)
260
Advances in the bonded composite repair of metallic aircraft structure
Table 9.26
Recommended values for F.
1.12
1.10
1.063
1 .OS3
1.033
1.015
0.977
0.948
0.924
0.882
0.854
0.820
0.800
0.778
0.765
0.757
1lJ2
0.0
0.04
0.1
0.12
0.16
0.2
0.3
0.4
0.5
0.75
1
1.5
2
3
4
5
33
Here the function W describes the transition from the small crack solution I 4 0 to
the long crack solution 1 -+ co. Here I is the half length of the crack. At this stage
we will use the functional form given by Wang and Rose [32].
(1
(1 + 2.231/d)
+ 4.771/d + 7(1/7d)*)
1
(9.71)
This solution has the correct bounds for the stress intensity factor for both short
and long cracks at a cracked hole repaired with an externally bonded composite
patch.
The accuracy of this approach can be illustrated by considering the problem of a
crack at a centrally located hole in an infinite sheet subjected to a either remote
uniform stress ( 0 ) or a remote (equal) bi-axial stress o1= 0 2 = B . The predicted Rs
for this case are shown in Figure 9.33, along with the analytical solutions due to
Tweed and Rooke [33]. Here KO = c,/(d), where 0 is the remote stress acting
perpendicular to the crack.
To illustrate the ease of application of this solution let us consider the case of a
crack of length I emanating from a hole with a radius R of 3mm, this size was
chosen to represent a typical fastener hole, in an infinite Aluminium alloy plate
(skin) subjected to a uniform remote stress of 100 MPa. The plate is repaired using
a uni-directional boron epoxy patch that covers its entire width. The patch also
contains a 3 mm radius hole and the fibres are orientated perpendicular to the
crack, i.e. in the direction of the load. The moduli of the aluminium skin (plate) are
E=72000MPa and v=O.33. The patch was assumed to have the following
Chapter 9. Numerical analysis and design
26 1
3.5
3
2.5
'Tweed et al, uniaxial
g
2
- -Predicted
Bi-axial
1.5
1
0.5 -/
0
I
0.5
1
1.5
2
2.5
3
3.5
4
I/P
Fig. 9.33. Comparison of the predicted and analytical solutions for a crack at a circular hole.
mechanical properties: El 1 = 208000 MPa, E22 = E33 = 25432 MPa, v12 = 0.183, and
G I 2= G I 3= G23= 7241 MPa. The adhesive was taken to be FM73 and was 0.2 mm,
Le. two layers, thick with a shear modulus of 750 MPa and v = 0.35.
Two different plate and patch thicknesses were considered:
Case (i) A plate thickness of 1.2mm and a patch thickness of 0.52mm, i.e.
approximately four plies thick.
Case (ii) A plate thickness of 3mm and a patch thickness of 0.889mm, i.e.
approximately seven plies thick.
The first case was chosen to approximate a crack at a fastener hole in the fuselage
skin of a wide-bodied transport aircraft. The second case was chosen to
approximate a crack at a fastener hole in the wing skin of a military fighter
aircraft. In each case the patch thickness was chosen to approximate the stiffness,
i.e. the product of the modulus and the thickness, of the plate (skin). The resultant
stress intensity factors are presented in Figure 9.34.
This section has used the formulae, for the function W, developed by Wang and
Rose [32]. However, recent work by Hart-Smith [29] has produced a slightly
different formulae. The difference between these two approaches is shown in
Figure 9.35, which shows how the stress intensity factor approaches the asymptotic
value.
When performing fatigue life calculations for unrepaired structures it is often
sufficient to only consider the stress field acting perpendicular to crack. For small
cracks at holes this simplification can lead to erroneous results. This is because the
load bia-xiality ratio can have a significant effect on K , see Figure 9.33.
Consequently, when designing repairs to cracked holes, or to cut outs resulting
from the removal of corroded material, load bi-axiality needs to be considered.
This effect is discussed in more detail in [31].
Advances in the bonded composiie repair of metallic aircraft structure
262
~~~~
~
+1.2 mm skin, 0.52 mm patch
-
K
8
3mm skin, 0.889 m m patch
I
‘I
”’
2
1
0
3
l/R
Fig. 9.34. Composite repairs to cracked holes.
9.12. Findings relevant to thick section repair
As a result of this chapter we find that the major design considerations are, viz:
The maximum stress intensity factor, allowing for the visco-plastic nature of the
adhesive, should be as low as possible and preferably below the critical value
Kth for fatigue crack growth in the material. For cracks at holes or notches, or
repairs to corrosion damage load bi-axiality should be accounted for in the
design process.
L. The maximum adhesive stresses/energy should be below the value at which
fatigue damage accumulates in the adhesive, see [8,16,21]. For FM73 this
2
UNREPAIREDCRACK
/
0
0
0
0
#
0
#
NORMALIZED
STRESS
INTENSITY
FACTOR, WK.
/
SEMI-INRNITE
HART-SMITH’S SOLUTION
TRANSITIONFROM
SHORTTOLONGCRACK
1
.-..-..-..
-..-.*--
ROSES SOLUTION
ROSES CHARACTERISTIC LENGTH
I
I
I
I
I
1
2
3
4
5
6
NORMALIZED HALF-CRACK LENGTH, a/ll
Fig. 9.35. Crack-tip stress-intensityfactors for “short” and “long” cracks, from [29],
*
Chapter 9. Numerical analysi.7 and design
263
value is -25 MPa. However, to minimise errors in measuring and computing
the adhesive stresses and allowables, see [20], it is best to compute and
measure the energy in the adhesive W = 1/20gsg = 1ogdsg. These measurements are best performed using the ASTM thick adherend test, ASTM D
1002, see [16].
3. The composite patch must not experience failure by interply delamination. This
can be checked by ensuring that the polynomial failure criteria is not greater
than one. The commonly used failure criteria are: Tsai-Hill, Hoffman and TsaiWu. These failure criteria are generally written in the form:
Tsai-Hill criterion: Failure is assumed to occur when
(9.72)
Here the material is assumed to have equal strengths in tension and
compression, i.e. X , = X , = X and Y , = Y, = Y
Hoffman criterion: Failure is assumed to occur when
Tsai-Wu criterion: Failure is assumed to occur when
The coefficient Fl2 is experimentally determined from test specimens under
biaxial loading and F12 must satisfy a stability criterion of the form
(9.75)
creates some complication in the use of this theory. It has been suggested that
F12be set to zero.
The symbols used in Eqs. (9.76) to (9.79) are defined as:
X , Allowable tensile stress in the principal x (or 1)-direction of the material
X , Allowable compressive stress in the principal x (or 1)-direction of the
material
Y, Allowable tensile stress in the principal y (or 2)-direction of the material
Y, Allowable compressive stress in the principal y (or 2)-direction of the
material
S Allowable shear stress in the principal material system
At the moment one shortcoming in the certification process for composite joints/
repairs and rib stiffened panels is the lack of understanding of the matrix
dominated failures. The vast majority of the analysis tools assume that the
composite is behaving in the linear elastic regime. However, there are instances, see
[22-241 when material nonlinearities, in the composite adherends, play a significant
264
Advances in the bonded composite repair of metallic aircraft structure
role in these failures. Unfortunately, it is currently uncertain as to when these
effects need to be considered, for more details see [22-241.
4. The average stress, over any one ply through the thickness of the boron patch,
should not exceed 1000 MPa.
It must be stressed that for repairs to primary structures a full 3D finite
element analysis must be performed. (Even for repairs to thin skins the stresses
and strain fields are dependent on the mesh density and element type used in the
analysis, see Section 9.9.1 and [20] for a more detailed summary of this
phenomena.) This analysis should include a damage tolerant assessment of both
the structure and the composite repair performed in accordance with the current
FAA procedures for damage tolerant assessment, as given in [25]. As discussed in
[26] this analysis should be supported by test evidence in the appropriate
environment, unless (as stated in [25]) “it has been determined that the normal
operating stresses are of such a low order that serious damage growth is
extremely improbable”, that:
(a) The repaired structure, with the extent of damage established for residual
strength evaluation, can withstand the specified design limit loads (considered
as ultimate loads); and
(b) The damage growth rate both in the structure, the adhesive and the composite
repair, allowing for impact damage, interply delamination and adhesive
debonding under the repeated loads expected in service (between the time the
damage becomes initially detectable and the time the extent of damage reaches
the value for residual strength evaluation) provides a practical basis for
development of the inspection program.
The analysis/testing program should allow for impact damage, interply
delamination and adhesive debonding under the repeated loads expected in service
(between the time the damage becomes initially detectable and the time the extent
of damage reaches the value for residual strength evaluation) provides a practical
basis for development of the inspection program.
9.12.1. Comparison of commercial finite element programs for the 3 0 analysis of
repairs
A variety of commercial finite element programs can now be used to design
composite repairs. The most widely used programs are: MSC-Nastran, NENastran, ABAQUS, PAFEC, and ANSYS. To obtain the necessary accuracy, and
to assess all possible failure modes, the finite element analysis of most composite
repairs needs to be 3D. Since the adhesive bond line is typically 0.2mm thick this
means that it is often necessary to work with elements with large aspect ratios. As a
result any analysis should use elements with at least one mid-side node. With this in
mind the relative advantages and disadvantages of these programs are presented
below.
Chapter 9. Numerical analysis and design
265
Program
Name
Advantages
Disadvantages
ANSYS
Widely used for mechanical design.
ABAQUS
ABAQUS is recognised as being an
excellent non-linear program.
PAFEC
Can automatically link 2D and 3D
models.
Can use cubic as well as parabolic elements.
The Nastran data structure is very widely
used and many structural
models are MSC-Nastran based.
Cannot cope with very large aspect
ratio elements.
Cannot cope with very large aspect
ratio elements.
If the aspect ratio is large it can
yield poor results when the adhesive
yields.
Requires the use of the PAFEC
graphics pre and post processor.
MSC-Nastran
NE-Nastran
The data structure is compatable with
MSC-Nastran.
Has the ability to use enriched 3D
elements. i.e. 21 noded bricks e f c .
As such it can tolerate very large aspect
ratio elements.
Can model both material and geometric
non-linearities using both 20 and 21
noded elements.
Cannot cope with very large aspect
ratio elements.
When using 3D parabolic elements.
i.e. 20 noded bricks erc. the analysis
options are quite severely reduced.
Limited number of pre and post
processors available. On PC’s it
uses the same pre and post processor,
i t . FEMAP (SDRC). as MSCNastran.
Essentially limited to mechanical
and aeronautical structural analysis.
In 3D elasticity the displacements u, v and w must satisfy the differential
Eq. (9.34)
V4tl=0
~
V4v=O
,
and V 4 w = 0
(9.76)
The use of P-element based finite element analysis can violate this fundamental
requirement, if the order is greater than three, and as such the use of P-element
based analysis is not recommended for 3D problems. As pointed out by Liebowitz,
et al. [35] this means that “the basic equilibrium conditions of the basic f.e.
equations is violated”. Furthermore, the use of high order P elements can result in
localised oscillations in the solution, see Zenkiewicz, et al. [36] for more details. As
such the use P-element formulations for fracture and composite repair analysis
should be avoided.
When performing a 2D analysis of a joint the best results are obtained using nine
noded elements, which have a node at the centroid, or the CQUADR element, or
the equivalent element with drilling degrees of freedom. The advantage of these
elements is that they can accommodate large aspect ratio’s and extensive mesh
distortion.
266
Advances in the bonded composite repair of metallic aircraft structure
References
1. Jones, R. and Callinan, R.J. (1979). A design study in crack patching. J. of Structural Mechanics,
1(7), pp. 107-130.
2. Baker, A.A., Callinan, R.J., Davis, M.J., et al. (1984). Repair of mirage iii aircraft using BFRPcrack
patching technology. Theoretical and Applied Fracture Mechanics, 2( I), pp. 1-16.
3. Molent, L., Callinan, R.J. and Jones, R. (1989). Structural aspects of the design of an all boron/
epoxy reinforcement for the F - I l I C wing pivot fitting - Final report. Aeronautical Research
Laboratory, Research Report 1, ARL-RR-I, November 1992. See also Composite Structures, 11( I),
pp. 57-83.
4. Rose, R.F. (1942). A cracked plate repaired with bonded reinforcements. Jnt. J. of Fracture, 18,
pp. 13S144.
5. Bartholomeus, R.A., Paul, J.J. and Roberts, J.D. (1991). Application of bonded composite repair
technology to Civilian aircraft - 747 demonstrator program. Proc. Jnt. Conf. on Aircraft Damage
Assessment and Repair (R. Jones and N.J. Miller, eds.). Published by The Institution of Engineers
Australia, ISBN (BOOK) 85825 537 5, July.
6. Jones, R., Bartholomeusz, R., Kaye R., et al. (1994). Bonded-composite repair of representative
multi-site damage in a full-scale fatigue-test article. J. Theoretical and Applied Fracture Mechanics,
21, pp. 4149.
7. Jones, R., Molent, L. and Pitt, S. (1999). A study of multi-site damage in fuselage lap joints.
Theoretical and Applied Fracture Mechanic.y, 32, pp. 81-100.
8. Molent, L., Bridgford, N., Rees D., et al. (1992). Environmental evaluation of repairs to fuselage lap
joints. Composite Structures, 21(2), pp. 121-130.
9. Jones, R. (1991). Recent developments in advanced repair technology. Proc. Int. Con$ on Aircraft
Damage Assessment and Repair, Melbourne, August 1991, Published by Institution of Engineers
Australia, ISBN (BOOK) 85825 5375, July.
10. Baker and Jones, R. (1988). Bonded repair of aircraft structures, Martinus Nijhoff, The
Netherlands.
11. Dowrick, G., Cartwright, D.J. and Rooke, D.P. (1980). The effects of repairs patches on the stress
distribution in a cracked sheet, Royal Aircraft Establishment Technical Report 80098, August.
12. Atluri, S.N., Park, J.H., Punch, E.F., et al. (1993). Composite repairs of cracked metallic aircraft,
Federal Aviation Administration, Contract Report, May, DOT/FAA/CT-92/32.
13. Sun, C.T., Klug, J. and Arendt, C. (1996). Analysis of cracked aluminium plates repaired with
bonded composite patches. AIAA Journal, pp. 369-374.
14. Ratwani, (1981). Development of bonded composite repairs for cracked metal structure. Proc. Int.
Workshop on defence applications of repair technology, NRL, Washington D.C., 22-24th July, 198 1,
pp. 3 0 7 4 3 .
15. Jones, R., Chiu, W.K. and Hanna, S. (1994). Potential failure mechanisms of bonded composite
repairs for metal and concrete. Theoretical and Applied Fracture Mechanics, 21, pp. 107-1 19.
16. Chiu, W.K., Chalkley, P.D. and Jones, R. (1994). Effects of temperature on the stress/strain
behaviour of film adhesives FM73, Computers and Structures, pp. 1-7.
17. Thrall, E.W. (1979). Primary adhesively bonded structure technology (PABST): Design handbook
for adhesive bonding, USAF Technical Report, AFFDL-TR-79-3119.
18. Hart-Smith, L.J. (1973). Adhesively bonded double lap joints, NASA Langley Research Center
Report NASA CR-112235, January.
19. Glinka, G. (1985). Calculation of inelastic notch-tip strain-stress histories under cyclic loading.
Engineering Fracture Mechanics, 22(5), pp. 839-854.
20. Chiu, W.K. and Jones, R. (1992). A numerical study of adhesively bonded joints. Int. J. of Adhesion
and Adhesives, 12(4), pp. 219-225.
21. Chiu, W.K., Rees, D., Chalkley P., et al. (1994). Designing for damage tolerant repairs. J. of
Composite Structures, =(I), pp. 19-38.
22. Mignery, L.A. and Schapery, R.A. (1991). Viscoelastic and nonlinear adherend effects in bonded
composite joints. J. of Adhesion, 343, pp. 1740.
Chapter 9. Numerical analysis and design
267
23. Wang, S., Srinivasan, S . , Hu, H.T., et al. (1995). Effect of material nonlinearity on buckling and
postbuckling of fiber composite laminated plates and cylindrical shells. Composite Structures. 33,
pp. 7-15.
24. Jones, R., Alesi, H. and Mileshkin, N. (1998). Australian developments in the analysis of composite
structures with material and geometric nonlinearities. J. Composite Structures, 41, pp. 197-214.
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Circular, 25.571-IA, (1986).
26. Composite Aircraft Structure, Federal Aviation Administration Advisory Circular, 20-1 07A,
(1984).
27. Korn, G. and Korn, T. (1961). Mathematical handbook for scientists and engineers, Second,
enlarged and revised edition, McGraw-Hill Book Company, New York.
28. Damage Tolerance Design Handbook, Volume 4, December.
29. Hart-Smith. L.J. (1999). On the Relative Effectiveness of Bonded Composite and Riveted Patches
over Cracks in Metallic Structures, Boeing Paper MDC 99K0097, Proc. of The 1999 USAF Aircraft
Structural Integrity Program Conference, San Antonio, Texas, 30 November-2 December.
30. Schijve, J. (1982). The stress intensity factor of small cracks at notches. Fatigue of Engineering
Materials and Structures, 5(1), pp. 77-90.
3 1. Jones, R. (2001). Effect of load bi-axiality on composite repairs. Proc. 12th Inf. ConJ on Composite
Structures, Melbourne 2001, to be reprinted in Journal of Composite Structures.
32. Wang, C.H. and Rose, L.R.F. (1999). A crack bridging model for bonded plates subjected to tension
and bending. Int. J. of Solids unnd Structures, 36, pp. 1985-2014.
33. Tweed, J. and Rooke, D.P. (1973). The distribution of stress near the tip of a radial crack at the edge
o f a circular hole. Int. J . of’Engineering Science, 11, pp. 1183-1195.
34. Filenko-Borodich, M. (1 959). Theory of Elasticity, Foreign Languages Publishing House, Moscow.
35. Liebowitz, H., Sandhu, J.S., Menandro S.C.M., et ai. (1995). Smart computational fracture of
materials and structures. Engineering Fracture Mechanics, 50(5-6), pp. 639-65 1.
36. Zenkiewcz, O.C., De. J.P., Gago, S.R., et ai. (1983). The hierarchical concept in finite element
analysis. Compurers and Structure, 16( I+, pp. 53-65.
Chapter 10
SHAPE OPTIMISATION FOR BONDED REPAIRS
M. HELLERand R. KAYE
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
10.1. Introduction
Bonded repairs function by transferring some portion of the load from the
reinforced component through the adhesive bond layer, thereby reducing the range
and mean of the cyclic stresses in the repaired component. The relative stiffness of
the reinforcement, as compared to the repaired component, determines not only the
portion of load attracted, but also the level of peak stresses in the adhesive layer,
and the intensity of associated stress concentrations in the repaired component.
Hence a key technical objective addressed in this chapter is the use of automated
numerical procedures to determine optimised repair designs, which reduce the
magnitude of these critical stresses. There are essentially two load paths for a plate
with a bonded repair/reinforcement, where each can be approximated by a distinct
2D idealisation. The first is through-thickness load transfer, where the repair
configuration can be represented as a single or double lap joint [l]. Secondly we can
refer to in-plane load transfer, where a finite width patch can be approximated as
an inclusion, which locally attracts load in excess of the load based on nominal
remote stress. The finite element stress analysis approach [2-51 is ideally suited to
investigate such load transfer and the estimation of the induced internal stresses for
these types of problems. It is important to note that due to airworthiness
considerations, when applied to primary structural components, bonded repairs are
typically used as a measure to prevent crack initiation and retard crack growth. It is
generally required that the component has adequate static strength with or without
the bonded repair. Hence, in some cases it is necessary to restore residual static
strength before application of a bonded repair. This can be achieved by precise
rework shape optimisation [6-111, which has recently been shown to be a highly
effective procedure for concurrently removing any pre-existing cracks and reducing
269
Baker, A.A., Rose, L.R.F. and Jones, R. leds.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 8 2002 Published by Elsevier Science Ltd. All rights reserved.
270
Advances in the bonded composite repair of metallic aircraft structure
local stress concentrations (thereby increasing residual strength) in metallic
components, prior to application of a bonded repair. Such optimal reworking
also helps to further increase the fatigue life extension benefits provided by bonded
repairs.
10.1.1. Context for finite element based shape optimisation
Early applications of bonded reinforcements were to thin section components
such as skin panels, These skin panels were usually stiffened by internal structure
such that there was no out-of-plane bending present. Here the theoretical stress
analysis has usually been based on an analogy with a one-dimensional lap-joint
analysis, where 100% of the load is carried by the reinforcements, [1,12]. A key
quantity of interest being the adhesive stress concentrations at the extremities of
load transfer regions, [13,14]. Often yielding of the adhesive can occur at these
locations, and this can possibly lead to premature adhesive failure depending on the
severity of the in-service loading history. Some more recent practical problems have
been concerned with reinforcement to thick section airframe components. These
cases are usually complicated by the presence of curvature of the surface to be
bonded and the need to transfer more load into the reinforcement because of the
thick sections (Le. 3D solid type components) [15,16]. Here unacceptably high
adhesive stresses can occur (shear and peel) in the adhesive layer, which can
compromise the integrity of the adhesive layer. This also leads to an unfortunate
associated trade off, where the stiffness of the patch needs to be lowered to enable a
reduction in peak adhesive stresses, thereby limiting the amount of stress reduction
in the repaired component that can be achieved. It is important to note that for
both thin and thick section reinforcements to practical applications theoretical
solutions are not available, and hence trial and error finite element analyses have
typically been used to arrive at a suitable practical design. However, for thin section
cases (with no bending), the analytical formulations given in [ 11, provide useful
initial design estimates. It should also be noted that all practical applications to
date have essentially used a constant adhesive thickness, as well as a constant
reinforcement thickness (except for tapering at the ends of the reinforcement).
Published work on the optimal design of bonded repairs/lap joints to reduce
adhesive stress is very limited. However, some investigations of specific scope have
been undertaken, such as the consideration of optimal tapering at the ends of a
continuous reinforcement/repair. For example, an analytical treatment of the
optimal tapering at the ends an isotropic reinforcement for a uniaxial loaded lap
joint is provided is given by Ojalvo [17]. In other work given by Heller, et al. [6,7],
the same problem is considered by using a 2D gradientless FE method. Groth and
Nordland [18] have used FE based design sensitivity methods to also optimise
essentially the same configuration. In all three references above, the analyses are
confined to the consideration of reinforcement tapering and do not consider
variation in adhesive thickness. More recently at Air Vehicles Division (AVD)
sensitivity based methods have been used for 2D optimal through thickness shaping
of both the reinforcement and adhesive layer, [8,19].
Chapter 10. Shape optimisation for bonded repairs
27 1
10.1.2. Finite element modelling considerations
The finite element method [2-51 is ideally suited for meeting two essential
requirements for design optimisation of bonded reinforcements. Firstly, accurate
stresses can be obtained for realistic practical geometries, and loading conditions,
(which analytical methods cannot provide), and secondly the method is amenable
to automation as an iterative process, which can improve an initial non-optimal
design. For all FE work presented in this chapter, the analyses were conducted
using a Hewlett-Packard K series 9000 computer at AVD. One of two codes were
used, MSC.NASTRAN Version 70 for sensitivity based shape optimisation, (with
MSCPATRAN level 7.5 code used for pre and post processing of the models) or
PAFEC level 8, which has been extended with AVD code to undertake gradientless
shape optimisation. For all analyses presented, linear elastic material properties
were used, with elements being eight noded isoparametric rectangles or six noded
triangles unless noted otherwise. For the through-thickness analyses plane strain
conditions were assumed, while for the in-plane analyses plane stress was assumed.
10.1.3. Outline of chapter
It appears that there is very little work on optimisation relating to bonded
reinforcements, hence by necessity most of the work presented is focused on work
undertaken in the last few years in AVD. Here the focus is on through-thickness
optimisation for minimising adhesive stress, since it is considered that this a key
technical issue, which offers significant scope for improvement. Also, some
preliminary work on in-plane shaping effects is given. In Section 10.2 a 1D
analytical formulation is provided for a simple configuration of a double lap joint.
This leads to strategies for minimisation of adhesive shear stresses in the tapered/
stepped region of a typical patch, where each step is allowed to be of arbitrary
height, modulus and length. Finite element analyses, which demonstrate reductions
in peak adhesive stresses and plate stress concentrations, for the improved
configurations discussed in Section 10.2, are given in Section 10.3. Automated
through thickness optimisation using a free-form gradientless finite element method
is then considered in Section 10.4, for typical taper region. In Section 10.5 the
automated sensitivity based free-form shape optimisation is discussed, €or single
and double sided joint configurations, where both typical taper and crack regions
are considered. Specific aspects of the finite element optimisation procedure are
given in some detail as the key features are also used in the subsequent Sections
10.6 and 10.7. Section 10.6 gives the application of the sensitivity-based approach
for determining optimal reinforcementladhesive configurations for minimising
adhesive stresses. Section 10.7 then presents the application of precise rework shape
optimisation (to remove cracking) in combination with subsequent bonded
reinforcement for the life extension of F/A-18 inboard aileron hinges. The
reworking is essential from an airworthiness perspective, to restore initial surface
stress as discussed above in the first paragraph. The subsequent reinforcement
stepping is then designed using an iterative approach to minimise peak adhesive
272
Advances in the bonded composite repair of metallic aircraft structure
stresses. Finally in Section 10.8 the issue of improved in-plane shaping of patches,
for reducing plate stress concentrations is investigated using finite element analysis.
10.2. Analytical formulation for improved stepping in patch taper region
The large peak in adhesive shear strain, which occurs near the end of a typical
stepped patch can potentially cause failure of the adhesive system. To reduce the
severity of this peak, uniform stepping of multi-layer patches is currently used for
bonded repairs on RAAF aircraft, with the typical step length being 3 or 4mm per
lamina ply. However, having uniform step lengths is not optimal (in terms of
minimising peak adhesive shear strain). One possible approach for reducing the
peak adhesive strains is to increase the length of the uniform steps of the composite
patch, where each step consists of one unidirectional lamina [13]. However to
achieve a significant benefit as compared to a standard patch configuration, the
length of the stepped region needs to be much increased, hence resulting in an
undesirable increase in the overall length of the patch. It is interesting to note that
for the non-linear continuous (i.e. not stepped) tapering of the patches, it has been
shown that it is possible to maintain the shear strain at a minimised and constant
level. [6,17]. Hence this is what is desirable for stepped taper regions. Rees, et al.
[20] have undertaken a finite element analysis of a practical repair application for a
multi-layer composite patch, where the step length was allowed to be non-uniform,
and this was shown to be beneficial. However no analytical formulation or attempt
to optimise the stepping scheme was presented. Hence it is desirable to further
investigate the stress behaviour analytically, for minimising the peak adhesive shear
strain where each step is allowed to be of different height and modulus, and of nonuniform step length.
10.2.1. General configurationfor symmetric stepped patches
The general configuration of the problem under study is shown in Figure lO.l(a).
A thin plate of uniform thickness ti is subjected to a uniaxial remote load P (per
unit width in the z direction). Each side of this plate is reinforced with an identical
adhesively bonded patch, thereby symmetry is retained with respect to the plate
mid-plane y = 0, where the origin of the axis system is at the left hand end of the
patch The adhesive thickness is uniform and is denoted q. Each patch has a
maximum length of L, and is stepped at each of its ends identically, with symmetry
being retained with respect to the line x = L/2. Its maximum thickness is denoted
to. The geometry and notation for the stepping arrangement is shown in
Figure lO.l(b). There are n steps at the end of each patch which are allowed to
be of different thickness, modulus and of non-uniform length. For an arbitrary step
k, the thickness is denoted t:, the modulus is E t , and the position of the beginning
of the step is denoted x(k-1). It should be noted here that the step height is defined
as the difference in total step thickness from one step to another, i.e. t t - tt-' is the
height for step k.
Chapter 10. Shupe optimisution for bonded repairs
P
+
1
--
u2
1
t
N.,
__
__
.: ...: .:k.:l_.
W
273
Patch
.. .: .: .: .;_. _.:' .: _:
_._... .. .: .: .: .: ._. .: ....: _..:~.
X
dhesive
P
4
Plate
..................................................
4
Patch
t'
I
I
I
I
I
I
I
I
I
I
I
I
io
x,
i*
xk-1
XI
I
X)
Q+l
.;. ' ------I
(b)
Fig. 10.1. Plate with bonded symmetric stepped patches: (a) general arrangement, and (b) notation and
geometric definitions for stepped regions.
10.2.2. Analvsis for single step case
The standard elastic adhesive shear lag formulation [12,21,22], for this case is
given here, as it provides relevant expressions required subsequently for the multistep analysis and bounding case. A 1D idealisation is taken, for a thin vertical slice
of width A x through the patch and plate, so that displacements in the inner and
outer adherends are assumed to be constant across their thicknesses respectively.
For the adhesive a uniform shear deformation is assumed across its thickness. For
any position x,the tensile forces per unit width of the inner adherend (plate) and
outer adherend (patch) are denoted Ti and To respectively, and T is the shear stress
in the adhesive layer per unit depth. Also di and 6, are the displacements in the x
direction of the inner and outer adherends respectively. For the thin vertical slice,
Advances in the bonded composite repair of metallic aircraft structure
214
the equilibrium of forces in the x-direction for the outer and inner material
respectively, gives the following two equations
dT O
--
and
z=O
dx
d Ti
-++T=O
dx
(10.1)
Assuming 1D linear elastic stress-strain relations, we can write the strains E,, and ~i
for the outer and inner adherends respectively as
(10.2)
where E, and Ei are the elastic moduli of the outer and inner adherends
respectively. Since the shear strain y in the adhesive is assumed to be constant
across its thickness is given by
y=-
6,
- 6i
(10.3)
v
Differentiating Eq. (3) with respect to x and substituting from Eq. (2) gives
(10.4)
Differentiating again, substituting from Eq. (l), and writing in terms of strain gives
-d2Y
-A2y=0,
dx2
where A =
[g(L+&)]',
v
(10.5)
Eoto
and G is the shear modulus. The general solution to Eq. (10.5) is
+
y = ClePAX ~ 2 e + *, ~
(10.6)
where C1 and C2 can be determined from the boundary conditions. At the end of
the patch, we have from equilibrium the conditions Ti(0) = P, T,(O) = 0, while at
the centre of the patch, we have the condition y(L/2) = 0. From these conditions,
and Eqs. (10.4) and (10.6) we have the adhesive shear strain as
-Psinh (Ax - A L / 2 )
y(x) = vEitiA cosh ( A L / 2 )
(10.7)
10.2.3. Analysis for patch with multiple steps
For the case where the patch has multiple steps, Eqs. (10.4) to (10.7) given above
are appropriate when interpreted as representing the shear strains in each step
separately. However the boundary conditions at the ends of each step are now
different to those presented previously. Referring to the geometry and notation
Chapter 10. Shape optimisation for bonded repairs
215
given in Figure lO.l(b), we can consider an arbitrary step, k for which we have from
Eq. (10.6)
yk = cfe-Akx + c t e + A k x
(10.8)
+
From force equilibrium, we have the condition, 2T,k Ti = P, at any section x
through the patched plate. Hence differentiating Eq. (10.8), and using this
condition with Eq. (10.4), gives the load in the step, T f , as
T,k =
(m+ &) (
1
-1
+
-AkyCfe-AkX AkyCteAkx
(10.9)
Due to equilibrium we require that the force T," is continuous where one step ends
and another begins. Also, the shear strain y has to be continuous at this location
from kinetic considerations. Hence at the beginning of step k, (i.e. at x = xk-'), we
have yk-' = y k and Tf-I = Tk
o , wh'de at the at the end of step k, (i.e. at x = x k ) ,we
have y k = yk+' and Tf = Tf+l. Two further boundary conditions are also known,
namely To(0)= 0 and y(L/2)= 0. Using these continuity and boundary conditions,
in conjunction with Eqs. (10.8) and (10.9), yields a set of linear simultaneous
equations which can be solved for the coefficients Cf and C; for k = 1, . . . ,n. The
adhesive shear strain distribution can be readily evaluated once the coefficients are
determined from Eq. (10.8). A useful iterative numerical procedure to solve for
adhesive shear strains has been given in [14]. In this approach we start in the first
step, and use the condition To(0)= 0, and take an arbitrary assumed value of y(0).
From these two initial values, C1 and C2 are estimated for the first step using Eqs.
(10.8) and (10.9) and consequently the values of To and y(x) at the other end of the
first step are determined from these two equations. Then using the above conditions
for To and y, Eps. (10.8) and (10.9) give C1 and C2 in the next step. The whole
process is repeated for every subsequent step until an estimated value for y(L/2)is
found at the centre of the patch. If the required condition y(L/2)= 0 at the centre of
the patch is not satisfied, then another value of y(0) is assumed and the process
repeated to determine a new estimate of y(L/2). By using an interval halving
technique to determine improved estimates for y(0) the method is repeated until the
correct value of y(L/2)= 0 is obtained. A suitable upper bound first estimate for
y(0) can be obtained assuming the patch has uniform thickness, and typically a
converged solution is obtained after approximately 60 iterations with a typical
accuracy in shear strain of
10.2.4. Estimate for optimal first step length
It is helpful here to obtain an estimate of a suitable first step length, X I , which can
be used in the numerical solution method. We wish to determine approximately the
distance from the beginning of the first step such that the peak shear strain has
decayed to almost zero (assuming there are no other steps). Hence if the next step
was started here, its presence would have minimal effect on the magnitude of the
Advances in the bonded composite repair of metallic aircraft structure
276
peak at the end of the patch. To determine the required length we make use of the
single step formulation as given in Section 10.2.1. At the beginning of the first step,
and at the position, x = XI, we have the respective shear strains from Eq. (10.7) as
Psinh (AkL/2)
and
' ( O ) = rEjtjAkcosh ( A k L / 2 )
( 10.10)
-Psinh (&XI - A k L / 2 )
= qEitiAkcosh ( A k L / 2 )
y(xl)
Choosing the case where the strain value y(x1) has reduced to 1% of the peak value,
y(O), we have from Eq. (10.10)
-(e(Ak~~-AkL/2)
- e-(Akxl-AkL/2))
0.01 =
(10.11)
eAkL/2- e-AkL/2
Rearranging Eq. (10.1 1) and setting
required length of the first step is
= 0, we have since x1 G L/2, that the
5
Ak
(10.12)
XI = -
10.2.5. Minimum bound for peak shear strain due to patch length
It is convenient here to consider one theoretical lower bound on adhesive shear
strain. This bound equates to the case where the shear strain is uniform along the
patch (except for a region close to x = L/2, where the strain must vanish to zero).
Equilibrium of forces gives the relation
P = 2To f Ti
(10.13)
In this case for a patch of sufficient length, the load transferred to the patch at the
centre of its length is given by combining Eq. (10.13) with (10.2)
To=(
)
Eo to
Eiti f 2E0t0
(10.14)
This is also the load that the adhesive must transmit by shear deformation over the
half length of the patch. Hence for a constant adhesive shear stress over this length
we have
(10.15)
Hence from Eqs. (10.14) and (1 0.15) we have one lower bound for a uniform shear
Chapter 10. Shape optimisation for bonded repairs
277
strain distribution as
(10.16)
10.2.6. Minimum bound for peak shear strain due to stiffness o f j r s t step
Another key bound equates to the peak value of shear strain corresponding to
the case where there is a long first step, which can be estimated by putting x = 0 in
Eq. (10.7) and letting L tend to infinity. This gives the estimated lower bound as
(10.17)
10.2.7. Numerical examples
In this section the proceeding formulation presented in Section 10.2.3 is applied
to a number of illustrative problems. It is important to make clear here that each
step can consist of one or multiple laminae. Hence the value of the effective
stiffness, E$& as used in the formulation of Section 10.2.3 will be different for each
step, and will depend on the properties of the individual lamina within the step. For
a particular step, the effective stiffness is given by
(10.18)
where the subscript 1 refers to an individual lamina, and m denotes the number of
laminae in the step. To provide a meaningful comparison for the various patch
configurations presented, a number of parameters and boundary conditions were
kept the same for all cases, namely: (i) remote loading (ii) plate properties, (iii) the
adhesive shear stress has reduced to zero at the centre of the patch, x = L/2, and
(iv) the maximum effective stiffness E,t, for the patch is equivalent to that for ten
unidirectional boron/epoxy laminae. Hence the same amount of load was
transferred to the patch for each analysis case, where the plate remote loading
was P = 2000 kN/m. The material and geometric properties were as follows: (i) for
the aluminium plate Young’s modulus was 71000 MPa and the thickness was 6 mm,
(ii) for the boron/epoxy lamina used to compose multi-layer patch Young’s
modulus in the unidirectional orientation was E, = 208000 MPa, Young’s modulus
in the cross-ply orientation was E, = 20800 MPa, thickness t = 0.13 mm, and the
maximum length was L = 80 mm, and (iii) for the typical structural adhesive, the
shear modulus was G = 590 MPa, and thickness q = 0.1 mm.
In Figure 10.2(a) the adhesive shear strain distribution is shown for the case
where each patch consists of one step only. The solution for this case provides an
upper bound to the value of the peak adhesive shear strain for multiple stepped
!
E
l
fcIl
Advances in the bonded composite repair of metallic aircrafl structure
278
Y
I
01
om 0
5
1
0
1
5
2
0
2
5
y
1
3
5
4
006
OM
C
0 02
0
0
5
1
0
1
5
X
1
2
5
1
)
3
5
U
1
Distance from patch end (mm)
(b)
Y
Y
Distance from patch end (rnm)
Distance from patch end (mm)
(4
(4
/\
Y
0.015
0 01
om5
'
0 0
Distance from patch end (mm)
(e)
5
1
0
1
5
2
3
X
3
3
3
5
4
0
Distance from patch end (mm)
(f)
Fig. 10.2. Comparison of adhesive shear strain results for bonded symmetric stepped patches: (a) patch
with one unidirectional step, (b) patch consists of two unidirectional steps, each of same height, (c)
unidirectional patch consists of ten steps of equal height with uniform step length of 3mm, (d) patch
consists of two unidirectional steps, the first of one lamina thick, (e) unidirectional patch consists of ten
steps of equal height with non-uniform step lengths, (f) patch consists of 11 unequal step heights, and a
combination of cross-ply and Unidirectional laminae.
patches. The peak and exponential decay, in the adhesive shear strain distribution
at the end of the patch can be readily seen. The adhesive shear strain distribution
for the case where there are two steps of equal length and height is shown in Figure
10.2(b). It can be seen that this configuration provides a significant improvement as
compared to the single step case. The adhesive shear strain distribution for the case
of 10 equal step heights, and a uniform step length of 3mm is given in Figure
10.2(c). Results for this patch case are also given in [13], and the present results are
in very close agreement with those finite element and analytical results. This
stepping scheme is typical of that recommended by the RAAF Engineering
Chapter 10. Shape optimi.sution for bonded repuirs
279
Standard on Bonded Repairs [23]. It is important to note that while the peak shear
strain is significantly reduced as compared to the single step case, the highly
localised peak in adhesive shear strain at the end of the patch is still evident and
there is significant interaction between the first and second stress peaks. Also, the
maximum shear strain in the adhesive is significantly greater than the lower bound
of y = 0.0237 determined from Eq. (10.16) for the given length of the patch. Hence
it is evident that there is scope for minimising the magnitude of the peak strain.
One obvious approach for minimising the interaction of the first and second
peak, for a patch comprising unidirectional laminae is to use a longer first step.
Figure 10.2(d) shows the adhesive shear strain distribution when the patch has two
steps, where the first step is very thin, of thickness 0.13 mm (typical of one lamina),
and 15 mm long. It can be seen that there is now minimal interaction between the
two peaks at each step, hence the first peak has been reduced to its limiting value
for the given load and relative material properties. Clearly, splitting the second step
into multiple steps would further reduce the value of the second peak. We now
consider the case where we again have a long first step but the second step is further
split into nine steps. The adhesive shear strain distribution for such a case is given
in Figure 10.2(e). Here the patch has a thin long first step of length I9mm
consisting of one lamina. Subsequent steps each consist of one lamina and have
equal lengths of 0.5 mm, (except for the last step which has a length of 17 mm to
take up the remaining half length of the patch). It is evident that this method of
having maximal length for the first thin step gives a reduction of about 20% in the
peak shear strain at the edge of the patch, as compared to the standard method
given, represented in Figure 10.2(c).
To reduce the magnitude of the peak further the value of the effective stiffness
E&, of the first step must be lowered. One possible method of achieving this is to
replace the unidirectional lamina in the first step with a cross-ply, so that the new
Eoto value is equivalent to about one tenth of that for a typical unidirectional
lamina. Hence one possible general stepping arrangement can be proposed where
the first step consists of one cross-ply lamina, and a combination of cross-ply and
unidirectional lamina are used for the remaining steps, with non-uniform step
lengths. To allow a direct comparison with the previous cases, the maximum value
of Eoto for the patch is kept the same as previously. One way of meeting this
requirement easily is to replace the first unidirectional step, used in the previous
cases, with ten cross-ply laminae further split into three steps, while keeping the
step heights of the remaining 9 steps unchanged (each consisting of one lamina).
Hence this patch consists of 11 steps, with a combination of 19 unidirectional and
cross-ply lamina with the geometric details as given in Table 10.1. Here the step
lengths were chosen such that the highest shear strain was minimised. The resulting
shear strain distribution is shown in Figure 10.2(f), and it can be seen that the peak
strain value has been reduced by about 60% from that given by Figure 10.2(~).Due
to the dominant effect of the stiffness of the first step, it is believed that a similar
reduction can be achieved by adding just one extra layer of cross ply lamina,
underneath a typical DSTO unidirectional patch, which would only require 11
lamina in total.
280
Advances in the bonded composite repair of metallic aircraft structure
Table 10.1
Geometric details for patch on one side of plate for nonuniform stepping case.
Step
number
Step length
(mm)
Lay-up order of laminae within step
(C refers to cross-ply laminae)
(U refers to unidirectional laminae)
1
1.O
2.0
5.0
4.5
3.5
2.5
1.5
1.5
1.5
0.5
16.5
IC
3c
6C
lOC,lU
10c,2u
10C,3U
10C,4U
10C,5U
10C,6U
10C,7U
10C,9U
2
3
4
5
6
7
8
9
10
11
For the case shown in Figure 10.2(f) the value of maximum shear strain has been
lowered to be approximately twice the theoretically lowest bound as given by
Eq. (10.15), (where the total patch length has been constrained to 80mm). If this
lower bound for the maximum shear strain is to be approached, E,t, of the first ply
step must be further reduced, and more gradual changes in E,r, across step
interfaces would be desirable. A patch composed of different materials, using
appropriate step lengths, offers this possibility.
10.2.8. Discussion
Without recourse to increasing the overall patch length, the formulation given in
this section has shown that an improved stepping arrangement can significantly
reduce the peak adhesive shear strain, as compared to standard patch with 3 mm
length uniform stepping. For the case where the patch material is of one type and
all lamina thicknesses are the same, the best stepping procedure is to have a
relatively long first step (Eq. (10.17)) while successive steps can be quite close
together. Significant further reductions can be achieved for such a patch, by making
use of cross-ply laminae in the first two steps. Clearly, the use of a patch composed
of different laminae materials offers the potential of further improvement, via a
reduction and more gradual change in E,t,, This would theoretically enable a stress
distribution approaching the lower bound as given by Eq. (10.17) to be achieved.
Here the minimum attainable value of peak shear strains will depend primarily on
E,t, of the first step and secondly on the total permissible length of the patch. It
should also be noted that there may be practical difficulties in the manufacture/
application of a patch with cross-ply laminae of the different materials, and this
needs to be investigated.
Chapter IO. Shape optimi.sation.for bonded repairs
28 1
10.3. FE analysis for adhesive stress and plate stress concentration
It is clear from the results presented in Section 10.2, that minimising the adhesive
strain is essentially equivalent to smoothing the load transfer from the plate to the
patch. It is reasonable to expect that minimising the adhesive shear strains will
naturally lead to a reduction in the detrimental stress concentration outside the
patch [24], as has been postulated in [14]. Inspection of the results given in [20] gives
evidence supporting this conjecture, as does recent analytical work [25] and two
dimensional finite element stress analysis [26]. In [25], an analytical formulation is
given to describe the stress concentration in the plate and to determine what type of
shear stress distribution in the adhesive gives the best reduction in the plate stress
concentration. It has also been determined in [27] that the combination of adherend
tapering, and the inclusion of an adhesive fillet at the edge of the overlap produced
a significant increase in joint strength, due to a reduction in adhesive stresses. In
this section, results from finite element (FE) analyses are given to highlight the
influence on the plate stress concentration for a bonded repair specimen of the
following: (i) modification of the shear stress distribution in the adhesive by
changing the distribution of the patch stiffness and stepping arrangement, and (ii)
introduction of an adhesive fillet at the end of the patch.
10.3.1. Conjiguration andJinite element analysis method
Analyses were undertaken for the three key patching cases indicated in Section
10.2, (i) patch with one step, Le. a uniform thickness patch comprising 10
unidirectional laminae, (ii) patch with 10 steps, each consisting of one unidirectional lamina, where the first nine steps are each 3mm long (i.e. standard AVD
approach), (iii) patch with multiple non-uniform step lengths, unequal step heights
and different lamina moduli via unidirectional and cross-ply orientations. This layup is the same as indicated in Table 10.1 of Section 10.2. In view of the symmetry,
only one quarter of the actual specimen was modelled. An existing finite element
model of a cracked plate repaired with a one step patch was used as a starting point
for the current investigation [26].It was assumed here that the end of the patch was
sufficient distance from the crack, so that interaction between these two regions was
not a dominant effect. Typical patch geometries with and without fillets are shown
schematically in Figure 10.3. Typical finite element meshes for each of the three
cases without fillets are shown in Figure 10.4, while Figure 10.5 shows the highly
refined mesh around the region near the end of the patch with a full height
rectangular adhesive fillet. Unless otherwise noted, the following material and
geometric properties and loading conditions were used in all the analyses
undertaken: (a) For the aluminium plate: (i) Young’s modulus, E= 71 GPa, (ii)
Poisson’s ratio, v = 0.33, (iii) assumed length, I = 104mm, (iv) thickness, ti = 6 mm
and (v) remote stress, 0,=71 MPa. (b) For the adhesive: (i) shear modulus,
G = 590 MPa, (ii) Poisson’s ratio, v = 0.35 and (iii) thickness, q = 0.1 mm. (c) For a
given unidirectional boron lamina: (i) Young’s modulus, El = 208 GPa and
E2 = E3 = 20.8 GPa, (ii) Poisson’s ratio, v = 0.3, (iii) maximum length, L = 80 mm
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Advances in the bonded composite repair of metallic aircraft structure
(4
Adheslve fillet
-I4
(b)
Fig. 10.3. Typical patch geometnes with and without rectangular adhesive fillets: (a) single step patch
case, (b) typical multiple stepping arrangement.
(4
(b)
(c)
Fig. 10.4. Typical finite element meshes for three patch stepping cases: (a) single step case, (b) uniform
stepping case, (c) non-uniform stepping case.
Patch
Adhesive
layer
Plate
Fig. 10.5. Typical finite element mesh around region at the end of patch for full height rectangular
adhesive fillet.
Chapter 10. Shape optimisation for bonded repairs
283
and (iv) thickness t = 0.13 mm. It should be noted that for all analyses, the adhesive
shear stress results are presented along the mid-surface of the adhesive layer. For
the presentation of direct stresses in the plate, the results are given at the interface
with the adhesive layer.
10.3.2. Results for no-fillet case
Results for the shear stress distribution for all three stepping cases, without an
adhesive fillet, are shown in Figure 10.6(a). The dominant peak stress at the start of
the patch is clear for the single step case, and this then decreases to a minimum at
the centre of the half patch length and, as expected, increases to another peak as it
approaches the crack and dips down to zero at the crack location. For the patch
with multiple uniform steps there is a significant reduction in the adhesive stress at
the start of the patch, as compared to the single step case. The large reduction in
adhesive stress for the non-uniform stepping case is clearly seen. A comparison of
results for the plate direct stresses on the patched surface, near the start of the patch
@.e.at x=40mm), is given in Figure 10.6(b). The highly localised peak for the
single step case is apparent, along with the significant advantage of the nonuniform stepping case over the uniform stepping case. The results given in Figures
10.6(a) and 10.6(b) are consistent with the expectation that the non-uniform patch
stepping arrangement serves to make the transfer of load from the plate to the
patch less abrupt as compared to the previous no-fillet cases. A summary of stress
results is given in Table 10.2.
10.3.3. Results for fillet case
Initially the influence of different sizes of a rectangular adhesive fillet, on the
stress distribution in the region of concern, was investigated for a patch of one step.
For convenience, the length of the fillet (b)from the end of the patch was varied, as
shown in Figure 10.3(a) for the following cases; (i) 0.4 mm, (ii) 1mm, (iii) 2 mm and
r
30 F
lM)
V
Patch cases
Patch cases
-
Single step
E
U n i f o m steps
Uniform steps
Non-unif. Steps
39
Distance along plate (mm)
(a)
40
42
Distancealong plate (mm)
(b)
Fig. 10.6. Stress distributions for no fillet cases: (a) shear stresses in adhesive layer, (b) plate direct
stresses on patched surface.
Advances in the bonded composite repair of metallic aircraft structure
284
Table 10.2
Adhesive shear stress and plate stress concentrations.
Cases considered
Adhesive shear stress (MPa)
Plate stress concentration
26.9
2.22
20.9
20.3
20.0
19.6
1.76
1.45
1.42
1.42
14.7
1.65
11.8
11.2
11.1
11.0
1.34
1.26
1.24
1.21
No jiiiet
5.6
1.28
Rectangular 2 mm fillet length
Every step fillet height
4.9
1.17
Patch with single step
No fillet
Rectangular $[let cases
0.4mm length
1mm length
2 mm length
12mm length
Patch with uniform stepping
No jillet
Rectangular 2 mm fillet length
Adhesive level fillet height
First step fillet height
Second step fillet height
Every step fillet height
Patch with non-uniform stepping
(iv) 12mm. The values obtained are given in Table 10.2, where it is seen that for
both the adhesive shear and plate direct stress peaks, there exists a similar trend
whereby with the increase in fillet length, a subsequent reduction in the peak value
occurs. However it can be seen that the values of the peaks near the end of the
patch, for both distributions, do not change significantly for fillet lengths greater
than about 2mm. It is also interesting to note, as expected, there are stress peaks
(relatively low in magnitude) in the adhesive and the plate near the end of the
adhesive fillet. (these have not been tabulated). The adhesive shear stress
distributions determined from the detailed 2D finite element analyses are in good
agreement with the analytical predictions from the 1D stress analysis for the
various no-fillet cases given in Section 10.2.
Next the effect of fillet heights (hf), as shown in Figure 10.3(b). was investigated
for multiple step patches, all with 2 mm length rectangular fillets. For the uniform
step patch, adhesive fillet heights were varied, ranging from (i) adhesive level fillet
height -here the layer of adhesive between the patch and the plate was extended to
2 mm outside the bonded patch, to (ii) every step fillet height - in this instance the
height of the adhesive fillet was extended from the adhesive level right up to the
very top of the stepped patch. The adhesive stress distributions for the first step and
every step fillet height cases are plotted in Figure 10.7(a), where it can be seen that
there is no significant reduction in the peak adhesive shear stress values for different
fillet heights. With the plate direct stress distributions, see Figure 10.7(b), there are
also two peaks in the vicinity of the end of the patch, one under and just past the
end of the patch, and the second (smaller) at the end of the fillet. For the patch with
non-uniform stepping an adhesive fillet was used that covered the entire height of
285
Chapter 10. Shape optimisation for bonded repairs
Uniform steps, every step FH
Non-unif. steps. every step FH
10
20
30
Distancealong plate (mm)
(a)
40
Distancealong plate
(mm)
(b)
Fig. 10.7. Stress distributions for multiple step cases with rectangular fillets: (a) shear stresses in adhesive
layer, (b) plate direct stresses on patched surface.
the patch. Figures 10.7(a) and 10.7(b) display the adhesive and plate stress results
obtained. Here the adhesive shear stress distribution remains virtually the same as
for the no-fillet case, except for a small reduction in the peak value at the end of the
patch, and the occurrence of a second smaller peak at the end of the fillet. As for
the other patch configurations, there are two peak locations for the plate direct
stresses, one just beyond the end of the patch, and the other at the end of the fillet.
However, this is the first case where the peak at the end of the fillet is greater than
that at the end of the patch. Clearly tapering the fillet profile, and also extending
the fillet length if needed could reduce the peak at the end of the fillet.
10.3.4. Discussion of results
A summary of all results for all cases is given in Table 10.2. The finite element
results provide confirmation that the plate stress concentration is integrally related
to the magnitude of the shear stress peak within the adhesive layer. Minimising the
adhesive stress peak reduces the plate stress concentration. The type of stepping
arrangement significantly influences the plate stress concentration. A non-uniform
stepping combined with cross-plies yields a significantly greater reduction than a
uniform stepping (with no cross-plies) configuration, as compared to the single step
case. The addition of an adhesive fillet to the end of a patch, with or without
stepping, can significantly reduce peak adhesive shear stresses, and plate stress
concentrations.
10.4. Gradientless FE method for optimal through-thickness shaping
In the case of bonded repairs, the initial design has typically been based on
simplified analytical formulations, and then finalised by undertaking standard finite
element analyses. Often the design of the bonded repairs has been confined to
rectangular patches of constant thickness with linear tapering around the patch
286
Advances in the bonded composite repair of metallic aircraft structure
boundary. FIE based optimisation methods offer the potential to determine
improved designs, in an automated manner. In this section, results obtained using a
simple yet efficient computational gradientless optimisation method are given. The
aim of the method is to achieve constant (or near constant) stresses at region of
stress concentration, by correctly moving boundary nodes. The method was
initially developed for minimising stresses at stress concentrators in metallic
components, however it is also well suited to minimising adhesive stresses in
bonded reinforcements. First we consider the continuous shaping of a patch end,
and then the continuous shaping of the adhesive layer for a bonded reinforcement
[6,71.
10.4.1. Optimal adherend taper projile at the end of a bonded joint
Figure 10.8 shows the configuration under study, which is representative of a 2D
idealisation of a bonded repair to a cracked plate. The inner adherend is a plate of
4 mm thickness, which is loaded by a remote stress of 100 MPa. An outer adherend
(i.e. patch) is bonded to each side of this plate by an adhesive layer having a
uniform thickness of 0.15 mm. Thereby, symmetry is retained with respect to the
plate mid-plane O,=O), and hence plate bending is eliminated. The thickness of
each patch is denoted to and is 2mm. As is commonly advocated, an initial linear
taper with a 1:lO slope was used at the ends of each patch to reduce the magnitude
of the adhesive stress concentration at the end of the patch. The material properties
for both the plate and the patch were taken as Young’s modulus E = 70 GPa, and
Poisson’s ratio v = 0.32. For the adhesive, a Young’s Modulus of 840 MPa and a
Poisson’s Ratio of 0.3 was used. In this optimisation the aim is to alter the shape of
the tapered region of the patch, so as to achieve as closely as possible a constant
adhesive stress distribution. The procedure used was to reduce the patch thickness
(at a given x co-ordinate) where the adhesive stresses were high, while increasing
patch thickness where adhesive stresses were low. Here an iterative procedure is
used, where for each iteration, each node on the free boundary of the patch was
moved by an amount dependent on its stress value in relation to a reference (i.e.
20mm
20mm
L
Applied Stress
100MPa
+
A
20mm
L A
20mm
L A
r-
t0=2mm
.,
,
X
20mm
-.A
r-
q=0.15mm
T1
7,
20mm
r-
*
Applied Stress
100 MPa
--w
Chapter IO. Shape optimisation for bonded repairs
287
threshold) stress. The amount to move each node is then given by
(10.19)
where positive d; indicates material addition to the patch outer boundary, zi is the
shear stress at the adhesive mid-plane node i, Tth is a threshold shear stress at the
adhesive mid-plane, r is an arbitrary characteristic dimension and s is an arbitrary
step size scaling factor. It is clearly evident that movements are less for locations
having stresses closest in value to the threshold stress.
The finite element mesh of the initial geometry, making use of quarter symmetry,
is shown in Figure 10.9(a). A very dense mesh was used near the end of the patch to
accurately model the high stress gradients in this region. The optimisation
procedure was applied with the parameters r = 2 m m and s = 0.1. One further
practical constraint was introduced such that the patch thickness could not be less
than 0.01 mm, corresponding to a minimum thickness that can be reliably
machined, and not greater than 2 mm (Le. original thickness). The solution
geometry obtained after 89 iterations is shown in Figure 10.9(b). As a comparison,
a 1D theoretical analysis given in [17] was found to give the profile shown in
Figure 10.9(c), where the thickness in the tapered region as a function of position is
given by
(10.20)
where x is the distance from the start of the tapered region, to is the maximum
thickness of the patch, and 1 is the length of the tapered region. In Figure 10.10 the
Fig. 10.9. Comparison of various taper profiles for bonded double lap joint, (a) linear taper, (b)
numerically optimised taper, and (c) analytically optimised taper.
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Advances in the bonded composite repair of metallic aircraji structure
0
1
2
3
4
5
6
7
8
9
10 I 1
12 13 14 15 16 17 18 19 20
Distance in x direction from start of patch (mm)
Fig. 10.10. Adhesive shear stress distributions for bonded double lap-joint with a unidirectional applied
stress for various taper profiles (for taper region only).
adhesive shear stresses are plotted for the following three taper profiles: (i) linear
taper, (ii) numerically optimised taper, and (iii) analytically optimised taper [17]. It
can be seen that the process provided a good result in reducing the initial peak
shear stress of 8.2MPa by about 30%, and rendering the shear stress distribution
relatively uniform. The 1D analysis gives almost as large a reduction in the peak
adhesive stress. It must be noted that the advantage of the finite element method is
that key parameters such as loading type and material properties are easily
changed.
10.5. Sensitivity FE method for optimal joint through-thickness shaping
In this section an automated sensitivity-based shape optimisation procedure is
presented for the optimal design of free-form bonded reinforcements, with the aim
of achieving reduced adhesive stresses [191. The approach is demonstrated through
application to a number of single and double sided configurations. Particular
features of the present approach include: (i) free form shapes, where the outer
adherend and/or the adhesive thicknesses are allowed to be non-uniform, and are
optimised, (ii) a “least squares” objective function is used to obtain a true optimal
for the specified constraints, and (iii) multiple shape-basis vectors from the analysis
of an auxiliary model are used to specify allowable shape changes. In this
investigation, the finite element meshes consisted of mostly four noded elements in
preference to eight noded elements. This was done since the four noded elements
are more convenient to use with the NASTRAN two noded beam elements, which
were an important part of the modelling for optimisation.
Chapter IO. Shape optirnisasationfor bonded repairs
289
10.5.1 Initial geometry, materials and loading arrangement
For all analyses the initial configuration under study was a typical bonded
double lap joint as defined in Figure 10.8. The geometry is also representative of the
2D idealisation of a bonded repair to a cracked plate [1,12], as discussed in the
previous sections. For all cases, the inner adherends have a thickness of 4 mm and
are subjected to a remote uniaxial stress of l00MPa. The outer adherends are
bonded to the inner adherends by an adhesive layer having a nominal thickness of
q = 0.15 mm. The outer adherends are both 120 mm in length and have a thickness
of 2 mm if aluminium, or 0.67 mm if boron/epoxy. As is commonly advocated, an
initial linear taper with a 1:lO slope was used at the ends of the outer adherends to
reduce the magnitude of the adhesive stress concentration at the end of the patches.
As indicated on Figure 10.8, the joint has been divided into three load transfer
regions on each side of the symmetry line x = 60 mm, having an arbitrary length of
20mm each. In the taper and joint regions most of the load transfer takes place
between the patches and the plate, and this is where the shape changes were
undertaken. It is common practice to have a region in between where there is no
Ioad transfer, termed here as the separation region. This region is essentially a
safety buffer zone (i.e. potential load carrying region), should there be adhesive debonding in the nominal load transfer regions.
For all analyses the following material properties were used as appropriate: (i)
for aluminium, isotropic material behaviour was assumed with Young’s Modulus,
E = 70000 MPa, and Poisson’s Ratio, v = 0.35,(ii) the isotropic epoxy adhesive had
Young’s Modulus E=840MPa, and Poisson’s Ratio, v=O.3, and (iii) the
unidirectional boron/epoxy adherend was taken as 2D orthotropic with
El I = 210000 MPa, E22= 25400 MPa, v12 = 0.18, and G I 2= 7200 MPa where the
subscript 1 refers to the direction of the fibres and 2 is the through thickness
direction. Here the 1 and 2 directions are aligned with the x and y axes respectively.
10.5.2. Oprimisation method
Shape optimisation was achieved using the general sensitivity-based optimisation
technique available in the MSC/NASTRAN code [28]. In broad terms, the
approach involves changing the position of nodes defining a boundary shape, based
on the computation of rates of change of nodal stresses with respect to shape
changes. Hence the general problem definition for shape optimisation can be stated
as
minimise/maximise : objective function
subject to :
constraint functions
where :
design variables
The software allows for very wide scope as to how to define the quantities above,
which is left to the analyst to determine. The objective function used in this work
has been termed the least squares objective function in prior AVD work. It seeks to
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Advances in the bonded composite repair of metallic aircraft structure
minimise the deviations from the average von Mises adhesive stress value in both
the joint region and the taper region, and is given in equation as
i= 1
minimise :
f&j
j= 1
(oavt- oil2+
=
i=n
2
(oavj- oj>
,
(10.21)
j=k
where i and j are the number of an individual adhesive element in the taper and
joint regions respectively, y1 and k are the total number of adhesive elements in the
taper and joint regions respectively, and oavtand oav,are the average adhesive
element stresses in the taper and joint region respectively. The adhesive was
modelled using three rows of elements and the stress values are taken at the
centroids of centre row elements. This objective function takes advantage of the
constant stress characteristic of optimal geometries, and uses responses in both
load transfer regions simultaneously, as indicated by the first and second
summations in the equation above. This function appears to achieve better
convergence than using the peak stress as the quantity to be minimised, avoiding
local minima. It is interesting to note that for typical sectional stress values across
the adhesive thickness and away from corner singularities, the variation is less than
10% with the centre row having the highest values. This applies for the thick
adhesive regions of the solution shapes as well as for the initial configurations. A
key feature of the optimisation process is the way that shape changes are defined as
design variables. Here, a set of displacement fields was generated by using an
auxiliary model with a set of dummy loads applied normal to the movable
boundary. This auxiliary model must have the same geometry and node numbers as
the primary model however, the material and element properties can be varied so as
to give suitable shapes. These fields are called basis shape vectors in NASTRAN
and can be considered as a set of vectors Tj as follows:
Tj =
................
................
(10.22)
AGKx, AGKy
where j is the basis shape vector number, AGx and AGy are the nodal displacement
in the x and y direction respectively, and K is the total number of nodes (same in
both models). Typically, for the analysis cases, 25 load-cases were used to generate
25 displacement fields and consequently 25 design variables were defined in the
optimisation data file. These load application points, along the movable part of the
boundary or interface, are shown in Figure 10.11. While the auxiliary model
provides absolute displacements which are dependent on the size of the applied
dummy load, the whole displacement field is scaled up or down as required by the
optimisation process. At each iteration i+ 1, the new shape comes from taking the
nodal positions at iteration i, and adding the displacements from all of the basis
Chapter 10. Shape optimisation for bonded repairs
liiiit
29 1
loads
(b)
(21)
Fig. 10.11. Finite element mesh and loading arrangement for generating basis shape vectors in auxiliary
model: (a) taper region, and (b) crack/joint region.
shape vectors multiplied by their scaling factors, as given by Eq. (10.23) below:
GI, Gf,
...........
[.fl 1 ] j
=g(
.........
/sx;
S...........
f
j=1
+Cx;ITj
,
where
;=.l
(10.23)
...........
Sf
/sx;
Here G, and G, are the x and y coordinates respectively of nodes k = 1 to K (all
nodes in model), i is the iteration number, j is the design variable number in the
rangej= 1 to J , X is a design variable (i.e. multiplier applied to T), S f l S X is the
sensitivity of the objective function with respect to a design variable, and g is a
function to represent the search algorithm described in [28].
The scaling factors Xi,(one per basis shape) are the unknown design variables to
be found by the optimisation process. As it is only the nodal displacements that are
used from the auxiliary model, the elements and their properties can be selected so
as to give a smooth deformation over a suitable region. In the cases presented
circular beam elements have been added along the boundaries (using the existing
nodes only). The stiffness of the beam elements in relation to the neighbouring 2D
elements was chosen to give a suitable shape and region of deflection. Hence
circular beam elements of 25mm radius were used in conjunction with plate
elements of 0.5 mm thickness, noting that both had the same elastic modulus. The
beam elements were typically 0.25 mm in length and the dummy load points were
typically 3 mm apart. It should be noted that, three and four noded 2D elements in
the structural and auxiliary model were not up-graded to six and eight noded
elements, as three noded beam elements were not available. Clearly, an important
requirement of the numerical approach is the appropriate choice of the basis shapes
and particular care must be taken. However, if a poor choice has been made, it
would be evident in the final boundary stress distribution (i.e. non-uniformity) and
remedial action could be taken. Certain constraints are dependent on the particular
configuration case and are discussed in the following sections. A constraint on
minimum adhesive thickness of 0.15 mm was consistent across all analyses.
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Advances in the bonded composite repair of metallic aircraft structure
10.5.3. Analysis f o r symmetric crack repair with aluminium patch
Here the aim is to optimise the repair shape to minimise peak von Mises adhesive
stresses, such that the repair effectiveness was unchanged as compared to a nominal
geometry. For the initial configuration, the maximum thickness of the patch has
been selected to be equivalent to that of the plate. The finite element mesh used in
the quarter symmetric analysis is shown in Figure 10.12(a). A very dense mesh
refinement was used to obtain accurate stress results, as well as represent small
geometric changes in the subsequent optimisation analyses. The stresses obtained
from this analysis are presented in Figure 10.13, and are as expected. For the taper
region they agree with those presented in [6,7] where the finite element code
PAFEC was used. For the joint region they also agree well with other published FE
results. For example the predicted adhesive stress peak is 25.8 MPa as compared to
24.0MPa given in reference [26]. More importantly, for the present context, the
opening displacement of the centreline node, half way through the plate thickness
in the x direction was 0.0086 mm (equivalent to the total opening of 0.0172 mm in
the full configuration). For the idealisation of 2D crack patching, the stress
(4
Fig. 10.12. Optimal shape for symmetric crack repair with aluminium patches: (a) initial arrangement
(b) optimised arrangement, (c) detail in taper region, and (d) detail in joint/crack region.
Chapter 10. Shape optimisation for bonded repairs
293
30
Taper Region
Separation Region
I I-
CracWjoint region
Initial
Optimised
0
0
10
20
30
40
50
60
Distance from end of patch (mm)
Fig. 10.13. Von Mises stress distribution in adhesive for symmetric crack repair with aluminium patches.
intensity factor in the inner adherend is directly related to the opening displacement
by the following equation from [l]
(10.24)
where KT is an upper bound stress intensity factor for a long crack under a patch,
Ep is the elastic modulus of patch, 4 is the stress reduction in the uncracked plate
due to the patch (factor less than 1) at the prospective crack location, 0 is the
remote applied stress, and A is the crack opening due to the remote applied stress.
For the optimisation analyses all 25 design variables were active (but restrained
from going negative). For the taper region the patch was allowed to vary in
thickness while the adhesive thickness was kept constant at 0.15 mm. This choice
was made to allow direct comparison with some existing published solutions. In the
crack region, both the patch and the adhesive thickness were allowed to vary. A
constraint on crack opening was applied at the centreline node, half way through
the plate thickness, to maintain the same repair effectiveness as the nominal repair.
Hence the constraint applied was lA/2( < 0.0086 mm, where: lA/21 is the
displacement in the x direction at the node described above. The overall solution
shape obtained after seven iterations for the total geometry is shown in
Figure 10.12(b). Figures 10.12(c) and 10.12(d) show more detail for the taper
and crack/joint regions respectively. The resultant von Mises adhesive stress results
are given in Figure 10.13. For the taper region the shape obtained is very similar to
the 2D FE solutions given in other investigations [6,18]. Here there is a rapid
reduction in patch thickness at the start of the taper leading to a very fine tip at the
end of the patch. In the taper region the process has arrived at a good result, in
reducing the initial peak stress of 14.4MPa by about 50%, and achieving a
relatively uniform stress distribution. The slight deviations from complete
uniformity of these adhesive stresses are mainly due to the fact that there are
low sensitivity values between the patch shape and the adhesive stresses as the
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Advances in the bonded composite repair of metallic aircraft structure
Table 10.3
Adhesive shear peel and Von Mises stress components for symmetric loading case with aluminium alloy
patches.
~~~~
~~
Shape and location
~~~~
Peel stress (MPa)
Shear stress (MPa)
Von Mises stress (MPa)
~
Initial shape, taper region
2.5
7.2
12.7
- 3.6
- 14.4
25.1
1 .o
3.7
6.5
- 3.6
4.1
7.8
(x = 0.1 mm)
Initial shape, crack region
(x = 59.5 mm)
Optimised shape. taper region
(x= 0.1 mm)
Optimised shape, crack region
(x = 59.5 mm)
optimal solution is approached. Obviously, if the taper region was increased in
length the adhesive stresses would have been further reduced as the same load
transfer would take place over a longer region.
The solution stress plot given in Figure 10.13 also shows a good result in the
crack/joint region with a near constant von Mises stress in the adhesive. A very
large stress reduction of about 70% is evident in this linear elastic analysis (in
practice, for this load level, the stress peak for the initial shape would be smaller
due to local yielding of the adhesive). In Table 10.3 results for von Mises, shear and
peel stresses are given near the ends of the two load transfer regions respectively.
These indicate that the reduction in von Mises stress come about mainly by
reduction in the shear component. Both the adhesive thickness and the patch
thickness have increased to meet the optimisation objective and constraint
requirements. Here the load transfer through the adhesive has been be diverted
away from the joint symmetry line at x = 60 mm, to be distributed more evenly over
the 20mm length comprising the crack/joint region. An optimisation analysis for
this case with boronlepoxy patches has also been undertaken [19], with very similar
results, except the patch thickness is about one-third as expected.
10.5.4. Analysis for non-symmetric crack repair with boronlepoxy patch
In this case the patch is bonded to one side of the plate only. Application of the
remote stress will cause secondary bending, and hence a more severe adhesive stress
distribution will result (particularly for peel) Again the aim is to optimise the repair
shape to minimise peak adhesive stress such that the repair effectiveness is
unchanged as compared to the nominal geometry.
For the analysis of the initial geometry the finite element mesh is virtually the
same as that given for the preceding case except that the through-thickness
symmetry restraint, along the line y = O has been removed. Hence there is no
support to eliminate the out-of-plane bending induced by the presence of the single
patch. Also, at the stress application region, out-of-plane rotation has been
restrained to represent a plate which is globally flat but able to deflect near the
crack/joint region. In this analysis, the patch is now of thickness 0.67 mm. The von
Chapter 10. Shape optimisation for bonded repairs
295
(c)
Fig. 10.14. Optimal shape for non-symmetric crack repair with a boron/epoxy patch: (a) general
arrangement, (b) detail in taper region, and (c) detail in joint/crack region.
Mises stresses obtained from this analysis are presented in Figure 10.15. It can be
seen that in the taper region the stresses are significantly higher as compared to the
previous case. For example the peak here is 30.0MPa as compared to 14.4MPa
previously. Also in the joint region the adhesive stresses are higher, with a peak of
8
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I
Taper region
Separationregion
CracWjoint region
OptimiSed
04
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-..-
-
....................
.:
296
Advances in the bonded composite repair of metallic aircraft structure
64.0 MPa as compared to 26.2 MPa previously. The opening displacement of the
centreline node half way through the plate thickness in the x direction was
0.096 mm, as compared to 0.0086 mm previously.
For the optimisation analysis the same solution procedure was used as before
except that basis shapes were modified to allow non-zero movable boundary slopes
at the centreline. This was necessary because of the very large initial stress
concentration, however it produces a discontinuous slope over the crack. The
solution shape for the total geometry obtained after seven iterations is shown in
Figure 10.14(a),while the von Mises stresses are given in Figure 10.15. In the taper
region the optimal patch profile is similar to that of the previous section (scaled by
1/3), although the adhesive stress range is 2.6 to 11.9MPa, which is marginally
higher than that of the previous section due to the effects of bending. In the joint
region the optimisation has produced a radical change of shape due to the very high
initial adhesive stresses. The adhesive and patch thicknesses have increased by a
factor of three. For the joint region the optimisation process has provided stress
reductions, which are larger than for the previous example. Here the stress
reduction is approximately 78%. The results given in Table 10.4 highlight the extent
to which the presence of bending has changed the adhesive stresses in both load
transfer regions. All values are higher and while the shear stress component is still
dominant for the initial shape in the taper region, the peel component is larger in
the crack region. The optimisation process has reduced both components in both
regions. In this case, the large variation in adhesive stress in the taper region is due
to this solution having an excessively long fine taper with thickness less than
0.01 mm for much of its length. It is clear that if desired, with an increased number
of basis shapes, a more uniform stress solution could be determined. In practice it is
expected that the effective stiffness of the long fine taper region will need to be
achieved by using a lower modulus first ply, possibly a cross ply of boron/epoxy.
Table 10.4
Adhesive shear, peel and Von Mises stress components for non-symmetric loading
case with orthotropic boron patches.
Shape and location
Initial shape, taper region
(x= 0.1 mm)
Initial shape, crack region
(x= 59.5 mm)
Optimised shape, taper region
(x=O.lmm)
Optimised shape, crack region
(x = 59.5 mm)
Peel stress
(MPa)
Shear stress
(MPa)
Von Mises stress
(MPa)
3.9
15.3
26.8
61.1
42.6
90.1
0.9
7.5
14.5
17.7
5.0
20.0
Chapter 10. Shape opiimisaiion for bonded repairs
297
10.6. Optimal through-thickness shaping for F/A-18 bulkhead reinforcement
In this section the automated sensitivity-based shape optimisation for the bonded
reinforcements for a realistic practical problem is presented. The practical problem
under consideration is a major structural component of an F/A-18 aircraft, namely
the F/A-18 470 Bulkhead [8]. Particular features of the present approach include: (i)
free form shapes, (ii) a “least squares” objective function is used to obtain a true
optimal for the specified constraints (i.e. constant stresses at critical region), (iii)
multiple shape-basis vectors from the analysis of an auxiliary model are used to
specify allowable shape changes, and (iv) both the adhesive thickness and the
reinforcement thickness are allowed to be non-uniform and are optimised. Results
for two distinct configurations for an optimal reinforcement for an optimal
reinforcement are given, depending on the selected adhesive stress to be minimised
(Le. shear or peel). Both reinforcement configurations are constrained to be
equivalent in effectiveness (stress reduction in the metal) to a nominal constant
thickness reinforcement.
10.6.1. Initial geometry, materials and loading arrangement
The 2D finite element mesh shown in Figure 10.16 indicates the in-plane
geometry of the F/A-18 470 Bulkhead. The bulkhead is an aluminium alloy frame
made up of flanges and webs of thicknesses ranging from 6-81 mm. It is a highly
loaded component since it supports the attachment of the wings. The initial MSC/
NASTRAN model is semi-symmetric about the y-axis (Le. vertical centreline) and
consists of three noded and four noded plane stress elements. The bulkhead is
aluminium alloy and isotropic material behaviour was assumed with Young’s
modulus E = 72000 MPa, and Poisson’s ratio v = 0.35. Also, the isotropic epoxy
adhesive had Young’s Modulus E = 840 MPa and Poisson’s ratio v = 0.3, while the
unidirectional boron/epoxy reinforcement was taken as 2D orthotropic with
El = 207000 MPa, E22= 25400 MPa, v12 = 0.18 and GI2= 7200 MPa where the
-
1439KN
1391KN
\
Critical region
2213mm
I_
b
Fig. 10.16. F/A-18 470 bulkhead finite element mesh and dominant loading.
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Advances in the bonded composite repair of metallic uircruft structure
Adhesive bondline
Reinforcement
Aluminium alloy bulkhead
Fig 10 17 FE mesh for analysis of standard rework with nominal 18 layer reinforcement
subscript 1 refers to the direction of the fibres and 2 and 3 are the transverse fibre
directions. All solutions are for the design ultimate load case. For this example
problem, the local curved region has been re-profiled locally to a shape termed ECP
[29]. This shape provides a reduction in the local bulkhead stresses of about 15%,
before reinforcement. Before considering an optimised reinforcement, a standard
finite element analysis was undertaken with a nominal constant thickness 18-layer
reinforcement. This has a uniform thickness of 2.34mm (except at its ends remote
from the region of interest) and a uniform thin adhesive layer of 0.13 mm thickness
is used. The geometry is shown in Figure 10.17 for the standard reinforcement case,
which provides a reduction in the peak bulkhead boundary stress of 25% against
the un-reinforced case.
10.6.2. Parameters for reinforcement optimisation analyses
For the optimisation analyses, the aim is to achieve the same reinforcement
effectiveness as before (via a constraint), with a reduction in the peak adhesive
stresses. For these runs there are consequently three boundaries under consideration with the following features (i) the interface between the bulkhead and the
adhesive is fixed in location and is where the effectiveness of the reinforcement is
determined by the bulkhead nodal stress values, (ii) the interface between the
adhesive and the reinforcement is a boundary that has been made variable in
position and has ultimately been located by the optimisation process, and (iii) the
outer free boundary of the reinforcement has also been made variable and has been
located by the optimisation process. The boundary mesh density (as compared to
that described in Section 10.6.1) has again been increased in the region of interest,
to better model the adhesive using lower aspect ratio elements. Three rows of
elements are used across the initial adhesive thickness of 0.13mm. A similar
optimisation strategy as was used in Section 10.5 is implemented and hence the
Chapter 10. Shape optirnisation for bonded repairs
299
objective function used is
(10.25)
where: ~i is the stress at element i (i.e. structural response), cavis the arithmetic
average of element stress values over a selected bond line segment (i.e. reference
stress), and IZ is the number of elements included in objective function evaluation.
Here the stresses used in the above equation are the mid-layer element centroid
stresses, and these are also the ones presented in the subsequent figures. Reducing
the number of stress points in the objective function by including only every fifth
element enhanced numerical performance. The regions of bond line that were
included in the analyses for the two distinct cases are given in Figure 10.18. Outside
this region the bulkhead boundary stresses and adhesive load transfer were
negligible. The peak stress on the bulkhead boundary has been constrained to the
value of 380 MPa, which was given by standard reinforcement. Constraint bounds
were applied to design variables to prevent the adhesive reducing in thickness. Also,
for the minimum shear stress solution the peel stress was constrained from rising
above its peak value for the nominal reinforcement. Similarly for the minimum peel
stress solution the adhesive shear stress was constrained from rising above its peak
value for the nominal reinforcement. Figure 10.18 also shows the loading
arrangement in the auxiliary model for generating the 23 basis shapes. It should
be noted that the auxiliary model loads are applied to the interface between the
adhesive and the reinforcement and the free edge of the reinforcement. In the
Bulkhead
Bond
-=
-
//I/ -h /
-
I
Unit loads
Reinforcement
Region of bond line used for minimal
peel stress objective hnction
Region of bond line used for
shear stress objective function
Y
Fig. 10.18. Finite element mesh and loading arrangement for generating basis shapes, also showing
bond line regions for objective function calculation.
300
Advances in the bonded composite repair of metallic aircraft structure
auxiliary model, beam elements of 25 mm diameter were applied along both edges
of the reinforcement to smooth the deflections caused by the point loads. All
materials in the auxiliary model were changed to aluminium alloy and all 2D
elements were reduced in thickness to 0.5 mm.
10.6.3. Stress results for optimal reinforcement designs
The resulting shape and the adhesive stresses for the minimum shear stress
solution are shown in Figure 10.19. The solution was obtained after seven
iterations. It can be seen that the shear stress has been made more uniform by the
increase in adhesive thickness at the high stress region near the curved part of the
boundary. The initial stresses plotted in Figure 10.19 are those of the nominal 18layer reinforcement and show that the 20% reduction in shear stress has been
achieved without an increase in adhesive peel stress. It can be seen that the adhesive
has been made thicker in the regions of high initial shear stress near the curved
parts of the boundary. The resulting shape and adhesive stresses for the minimum
peel stress solution are shown in shown in Figure 10.20. The main difference from
the previous result is that the increase in thickness occurs near the centreline region
where the initial peel stresses were highest. The size of the reduction in peel stress is
brought about by the reinforcement bridging the concave region and comes
without increase in shear stress. A feature of this solution is that the peaks in shear
and peel are now at different locations, where the high shear stresses have been
moved outboard (in the x direction). This is advantageous since experience with
bonded joints indicates they are more prone to failure when both peel and shear are
high at the same location.
10.6.4. Discussion
It is important to note that with both these solutions the constraint on
reinforcement effectiveness has been met, that is, the adhesive stress reductions
have not come at the expense of an increase in hoop stress in the parent material of
the bulkhead. The capability of the optimisation process to move both the adhesive
and patch boundaries simultaneously to arrive at the desired solution is also
significant.
10.7. Optimisation for F/A-18 aileron hinge reinforcement
This section presents the numerical stress analysis undertaken to design an
appropriate reinforcement for the aft strut of the aileron hinge which has
experienced in-service cracking, (further background information is given in [ 1 I]).
The fundamental approach followed is to first remove existing cracks with a
suitable precise rework shape before reinforcement. This precise rework shape is
determined using structural optimisation procedures, to minimise the peak stresses
for an un-reinforced hinge. The optimisation of the reworking is essential from an
Chapter 10. Shape optimisation.for bonded repairs
a"
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(b)
Fig. 10.19. Results for optimal 470 bulkhead reinforcement with minimal adhesive shear stress: (a) shape
solution, (b) stress solution.
airworthiness perspective, to restore the boundary stresses to about the same peak
values as for the uncracked, un-worked hinge. The subsequent reinforcement
stepping is then designed using an iterative approach to minimise peak adhesive
Advances in the bonded composite repair of metallic aircraft structure
302
h
2
2
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(b)
Fig. 10.20. Results for optimal 470 bulkhead reinforcement with minimal adhesive peel stress: (a) shape
solution, (b) stress solution.
stresses. Since in practice various crack depths will exist before possible
enhancement, it is proposed here to explain in detail the limiting case where the
rework depth is 2mm at the crack location.
Chapter 10. Shape optimisation for bonded repairs
303
2634
Fig. 10.21. Finite element mesh and loading (KN) for the nominal un-worked hinge analysis, where the
dotted line represents the prospective patch location.
10.7.1. Initial geometry, materials and loading arrangement
The initial plane stress finite element mesh, in the MSC.NASTRAN, code is
shown in Figure 10.21 with dominant loads corresponding to the WO 39 case. For
all analyses isotropic material behaviour under ambient conditions was assumed
for the aluminium hinge, the steel bearing, and the FM73 adhesive layer.
Conversely for the elements comprising the boron/epoxy reinforcement the
material was taken as orthotropic. The material properties were as follows; (i)
for the aluminium hinge the Young’s modulus, E, was taken as 70.38GPa,
Poisson’s ratio, v, was taken as 0.33; (ii) for the steel bearing and pin in the lower
lug, Young’s moduli were taken as E=213.90GPa, and Poisson’s ratio was
v=0.30; (iii) for FM73 adhesive, E= 1.43GPa, v-0.35; (iv) for the boron,
Ell = 208.95 GPa, E22 = E33= 19.18GPa, v12 = 0.21, ~ 2 =
3 0.3 and ~ 3 1 =0.02 where
1 refers to the direction of the fibres and 2 and 3 are the transverse fibre directions.
10.7.2. Shape optimisation before reinforcement
Rework shape optimisation (with or without subsequent reinforcement) to
minimise notch stresses in metallic airframe components has been a focus of recent
work in AED [Gl13. In the present example the design sensitivity approach using
MSC.NASTRAN code, as discussed in Sections 10.5 and 10.6, is used. In the
304
Advances in the bonded composite repair of metallic aircraft structure
ioo.0
Fig. 10.22. Typical auxiliary model used in the shape optimisation procedure for F/A-18 aileron hinge,
showing point loads (KN) for generating shape basis vectors with fully restrained nodes indicated by
dark line.
present case the aim is to remove material from the prospective crack location while
still achieving a minimised notch stress. Hence the objective function used is
(10.26)
where oiare the nodal hoop stress along the along boundary to be moved, oavis the
average nodal hoop stress around boundary, and k is number of boundary nodes to
be moved. As discussed in the preceding sections, meeting this objective effectively
means that a more constant hoop stress is achieved along a boundary region being
optimised, which corresponds to minimising the peak stress in that region. In this
work the objective function convergence was defined when two consecutive
optimisation iterations produced the same objective function result within a 1%
tolerance. For all analyses the constraints employed are nodal movement
constraints which effectively limit allowable boundary shape changes per iteration
(i.e. to a maximum rework of about 2mm). A typical auxiliary model used in the
shape optimisation procedure, for generating the shape basis vectors, is shown in
Figure 10.22.
The resultant finite element mesh shape obtained after seven iterations of the
rework optimisation is shown in Figure 10.23(a) for the 2mm rework. The shape
obtained (termed the “0” profile) is compared to the initial boundary in
Figure 10.23(b) while the corresponding stresses are given in Figure 10.23(c). It
can be seen that the stresses for the rework have been rendered constant in the
critical region, and are essentially the same magnitude as those for the nominal
geometry, even though 2 mm of material depth has been removed. If a typical nonoptimal rework shape had been used instead, the peak strut stresses could be
Chapter 10. Shape optimisation ,for bonded repairs
305
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expected to be about 20% higher. If a reinforcement is applied directly to the
optimised rework, there is a local peak stress in the adhesive, at the location near
x = 40 mm (the peak is due to the local change in curvature of the optimal profile
shape at x = 40 mm) which would be greater than the adhesive yield stress, at DLL.
Hence this rework profile can be further developed to meet the needs of minimal
peel and shear stress in the adhesive, in addition to minimising the peak stress in the
strut. To achieve this, the slight curvature discontinuity in the 0 rework profile
(near x = 38 mm) is manually smoothed, which then resolves this problem
regarding this adhesive stress peak. Of course as expected, the trade off due to
this profile change is a 9% increase in the strut stresses if the patch were to be
removed. This effect is clearly shown in Figure 10.23(c) by comparing strut stresses
for the “0”and “OSR” profiles.
10.7.3. Iterative reinforcement design
As discussed in Section 10.1, for the design of a typical bonded reinforcement to a
component, there are two particular regions of concern for the adhesive layer. These
306
Advances in the bonded composite repair of metallic aircraft structure
are respectively; (i) near the end of the reinforcement where shear stresses can be
very high, and (ii) locations under the reinforcement where it is desired to reduce the
stress concentration in the repaired component; typically shear and/or peel stresses
are high here. Clearly, due to load transfer, the reinforcement effectiveness increases
with increasing numbers of plies, while simultaneously the adhesive stresses at the
two key locations also increase. Hence a suitable final reinforcement design will be a
compromise between these two requirements, i.e. adequate reinforcement effectiveness for reasonable adhesive stress magnitudes. In view of the above, it was decided
to undertake a ply-by-ply interactive design procedure for the multi-ply reinforcement. This enabled firstly the relationship between the number of plies and the peak
adhesive stresses and the associated reductions in plate stresses to be determined.
Secondly, it enabled the best non-uniform stepping of reinforcement plies near the
end of the reinforcement to be designed to minimise peak adhesive shear strains. It
should be noted that the position of the ends of the reinforcement were selected to be
adequately remote from the critical strut region, such that they would not
compromise the ability of the reinforcement to reduce the stress in the critical region.
The patch location is shown by the dotted line in Figure 10.21. Also, due to the
higher stresses at the strut end of the reinforcement, the non-uniform stepping was
only applied to this end of the reinforcement. The region at the lug end of the
reinforcement has low stresses, and hence the step lengths at this end were simply
made constant at 2mm, except for the step length from the first to the second ply,
which was 4mm. These step lengths are summarised in Table 10.5.
The initial FE model used an adhesive layer thickness of 0.4 mm, consisting of two
layers of elements through the thickness of the adhesive. The strut end of the
adhesive layer began 153 mm from the centre of the lower lug and continued to the
end of the “horizontal” section around the lug, as indicated in Figure 10.24. The first
ply of the boron/epoxy reinforcement was then applied where one layer of elements
was used to represent each layer of boron/epoxy. The shear stress in the adhesive (in
the local element axes) and the principal stress reduction in the strut were noted. An
estimate of an appropriate first step length (17.8 mm) was made using the Eq. (10.12)
given in Section 10.2 and the second ply of boron/epoxy was added to the model and
the stress results recorded. The step length was then slightly altered (and the analysis
Table 10.5
Step lengths at strut end of patch as determined from interactive FE design
method.
Layer
Step length at strut end (mm)
1st ply (from the start of the adhesive layer)
2nd ply
3rd ply
4th ply
5th ply
6th ply
7th ply
8th ply
1.7
18.6
15.8
11.8
7.9
3.9
3.9
3.9
307
Chapter 10. Shape optimisation for bonded repairs
Fig. 10.24. Mesh refinement in the region at the beginning of the strut end of the F/A-18 aileron hinge
patch.
re-run) such that the addition of the second ply did not increase the previous peak
value of the adhesive shear stress at the start of the first ply. This process was then
repeated, with step lengths being obtained such that the adhesive shear stress peaks
at the beginning of each new step were well below the peak at the start of the first
step. The addition of boron/epoxy plies was then stopped when adequate stress
reductions in the critical region of the radius were achieved while also keeping the
shear stress in the adhesive (at DUL) below the “knee” value. This corresponded to
an eight-ply reinforcement. Figure 10.25(a) summarises results for each successive
addition of non-uniform boron/epoxy plies, while Figure 10.25(b) gives a
comparison between non-uniform optimised and uniform 4 mm stepping arrangements. The step lengths determined from this procedure are listed in Table 10.5. The
advantages of the non-uniform stepping are clearly evident. It is noted that the
addition of the full patch provides approximately a 20% stress reduction along the
strut edge for the optimal reworks. Similar reductions are provided by the patch for
the 1 mm depth rework and 0.2 mm depth reworks [ 111.
15
20
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111
2n
in
dn
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70
8n
Distance from strut end of the patch (mm)
(b)
Fig. 10.25. Shear stresses in the adhesive for the optimised stepping near the strut end of the F/A-18
aileron hinge patch: (a) results for each successive additions of non-uniform boron/epoxy plies, and (b)
comparison between non-uniform optimised and uniform 4 mm stepping arrangements.
308
Advances in the bonded composite repair of metallic aircraft structure
10.7.4. Discussion
The benefits of rework shape optimisation before reinforcement are clearly
demonstrated by this practical application. Also, when used in conjunction with
FE, the iterative ply addition approach for determining an appropriate reinforcement stepping arrangement, is highly convenient and effective for obtaining
minimised adhesive stresses.
10.8. In-plane shaping effects
Previous sections in this chapter all relate to advances in through-thickness
shaping or tapering of patches. These improved shapes are shown by mathematical
or numerical analysis to alleviate stress concentrations in the adhesive and/or
parent material. For all these cases there was no stress variation across the width of
the patch, the assumption being that the patch covered the full width of the
component. While this can be the case when a patch is applied to the edge of a thick
component or to a slender component such as a spar cap, when a patch is applied
to a large flat surface such as a wing or fuselage skin load is drawn in from the
width direction as well as up through the repaired component. This creates a region
of higher stress immediately outside the ends of the patch. Historically, rectangular
patches have been the most common for practical applications. In this section, the
aim is to investigate the extent to which alternate shapes may give reduced stress
concentrations, and to provide candidate configurations to be used as initial
estimates for possible subsequent shape optimisation. Hence these issues are
addressed by conducting exploratory numerical analyses, where the in-plane load
attraction effect of a patch is approximated as a 2D inclusion in a relatively large
plate. For comparative purposes a full 3D model of a one layer patch, including an
adhesive layer, on a large rectangular plate is also presented.
10.8.1. Geometry, loading and modelling considerations
The 2D geometry under consideration is shown in Figure 10.26 and consists of a
flat square plate of 3mm thickness with 400mm sides. The plate was modelled
taking advantage of quarter symmetry and using only 2D plane stress elements.
Here the patch was confined to a design space of 80 mm by 80 mm at the centre of
the plate and was represented as an inclusion by a region of elements with an
increased thickness of 3.381 mm. This thickness gives an increase in stiffness
approximately equivalent to one layer of boron. A remote unidirectional stress of
100MPa was applied in the y direction along the edges y = & 200 mm. Isotropic
aluminium alloy properties of E = 71000 MPa and v = 0.3 were used throughout the
model. Initial analyses for rectangular patches indicated that patches of the same
shape give better results as they get wider. Hence to compare shape effects alone it
was necessary to consider only patches with the same overall aspect ratio, which is
Chapter 10. Shape optirnisation for bonded repairs
309
100 MPa
t t t t t.....................................
tttt
patch
400
dimensions in mm
~~
+---400____*
111111111
MPa
100
Fig. 10.26. Geometry and loading arrangement for in-plane analysis of patch on plate using inclusion
analogy.
defined as the maximum length of the patch in the y direction divided by its
maximum width in the x direction.
The 3D model of a one layer patch represents a ’/* portion of a plate with length
400mm, width 120mm and thickness 6mm. A centrally located patch of length
80 mm and width 40 mm had a thickness of 0.13 mm and was joined to the plate by
a 0.13 mm thick layer of adhesive. The plate is subjected to a unidirectional stress in
its length direction of 100MPa. Material properties used areas follows: For the
plate Young’s modulus, E = 71000 MPa and Poisson’s ratio v = 0.32, for the
adhesive, Young’s modulus, E = 2190 MPa and Poisson’s ratio v = 0.3, and for the
unidirectional boron/epoxy, El = 203836 MPa, E22 = 18468 MPa, E33= 18468,
v I 2= 0.18, ~ 2 =
3 0.3,
~ 3=
1 0.0208,
G12= 5,582 MPa, G23 = 7098 MPa and
G31= 5582 MPa, where the subscripts 1, 2 and 3 refer to longitudinal, transverse
and through-thickness directions respectively. In order to achieve 1% convergence
in peak stress it was necessary to use 3D elements of P (polynomial) formulation.
These elements allow for a complex stress variation to be accurately represented
within the element and reduce the need for mesh transitioning near a stress
concentration. The bulk of the model consisted of 3D P elements of order 2. The
region near the end of the patch was modelled with P elements of order 4.
10.8.2. Determination of K, from FEA output
Numerical values of element centroid major principle stresses were extracted for
all elements in the high stress region, and the stress concentration K , is expressed in
percentage terms of the largest value as compared to the applied remote stress of
100MPa. The major principle stress term was used as this is the quantity that
would determine fatigue life if a defect was located in this region. Typically, the
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Advances in the bonded composite repair of metallic aireraft structure
orientation of the major principal stress is very slightly different to the applied
remote load direction due to the patch drawing in load sideways. Element size in
the high stress region was kept to about 1/12000 of patch size. To give an indicative
result, accuracy of the peak stress value was checked for convergence and finite
width effect for the 3:4 aspect ratio patches and total error in stress was found to be
less than 0.3%. For this work the K, (stress concentration) values are provided only
for comparing shapes. While the absolute values may have some small error the
authors believe that for comparison purposes only, the Kfvalues can be quoted to
the nearest 0.1 %. This is because the same process and mesh was used in each case,
the only variation being the shape of the patch.
10.8.3. Uniaxial loading and patches with aspect ratios of 2:1
Results obtained for this aspect ratio are summarised in Figure 10.27. The first
observation is that the raised stress region is distributed evenly across the end of the
rectangular patch as seen in Figure 10.27(a). This is an indication of optimality. A
small perturbation in the slope of the end of the patch was then made, which gave
worse Kt values and made the stresses less uniform as shown in Figures 10.27(b) &
(c). Results for elliptical and diamond shape patches are then given in Figure
10.27(d) & (e). From these results it is clear that the rectangular shape is very close
to being fully optimal for this aspect ratio, although it is possible that further study
may show slight improvement. As a useful comparison, Figure 10.27(f) shows the
stress distribution for a 3D analysis of the rectangular patch. Accurate modelling of
such a localised high stress region in 3D (for a bonded repair configuration) has
only recently become possible through the availability of more computer power
and the use of variable order P elements. In this 3D analysis both the throughthickness and in-plane load attraction effects are captured. For this single layer
case, the through-thickness effect dominates with a small rise attributable to the inplane effect. It can be seen that the high stress region modelled in 3D is also spread
evenly along the end of the patch, as in the 2D in-plane analysis case. Further
details regarding the full 3D stress distributions are given in [30].
10.8.4. Uniaxial loading and other patch aspect ratios
For the aspect ratio of 1:1, all Kfvalues are lower than the 2:1 aspect ratio case,
with the rectangular patch being better than the ellipse, as shown in Figure 10.28.
For the recent case it can be seen that the raised stress region is not as evenly spread
in the rectangular case suggesting that some improvement could be made through
an optimisation process, such as the gradientless method presented above in
Section 10.3. For the wider patch of 1:2 aspect ratio, the results are also given in
Figure 10.28, where it can be seen that the ellipse performs better than the
rectangle, and has an evenly spread raised stress region along the part of its
boundary nearest the centreline. Wider ellipses (not shown in the figures) give
further reductions in K, and longer boundaries with even stress distribution.
Chapter 10. Shape optimisation for bonded repairs
(e)
(4
311
(f)
Fig. 10.27. Kt values and major principal stress plots for doublers with aspect ratio 2:1 (a) rectangle, (b)
sloped end, (c) reverse sloped end, (d) ellipse, (e) diamond, (f) rectangle in 3D model.
I
(4
o?)
(c)
(4
Fig. 10.28. KI values and major principal stress plots for doublers with aspect ratios: (a) 1:l rectangle,
(b) ellipse, (c) 1:2 rectangle and (d) 1:2 ellipse.
10.8.5. Analogy with hole-in-a-plate problem
It is well known that for a uniaxially loaded plate with an elliptical hole, Kt
reduces with increasing aspect ratio (Le. ratio of length to width) of the hole. The
results above suggest that wide elliptical patches (i.e. low aspect ratio) are better in
the same remote uniaxial stress field. Since a hole is a represents region of reduced
stiffness and a patch is a region of increased stiffness, it appears that the problems
are complementary in some way, and the solution of one gives an indication as to
the solution of the other.
Advances in the bonded composite repair of metallic aircraft structure
312
10.8.6. Stress reduction at the centre of the patch for uniaxially loaded plate
The purpose of applying a patch is to bypass some of the load away from a
defect, usually located near the patch centre. For patches that draw in load from
the sides this plate stress reduction varies with patch shape as well as with patch
thickness. The present results indicate that this stress reduction in the direction of
remote loading (at the prospective defect location) is less than that predicted by a
ID analysis based on comparing the stiffness’s of the plate and patch with that for
the plate alone. For example the ID analysis predicts a plate stress reduction of
50%, while the present 2D FE for a 2: 1 aspect ratio rectangular patch gives a 32.5%
reduction at the patch centre, and the 2:1 aspect ratio elliptical patch gives a 33.1%
stress reduction throughout the patched region.
10.8.7. Summary of results and discussion
The Kbvalues are plotted for rectangles and ellipses at different aspect ratios in
Figure 10.29. It shows that rectangular patches perform better than ellipses at
aspect ratios larger than 3:4. Because of the need for long load transfer lengths and
space limitations most real patch applications have to be at least twice as long as
their width. Hence this work suggests that the commonly used rectangular shapes
are good if not optimal (for aspect ratios of 2:1 and higher) in terms of in-plane
shape. However if for a practical application the opportunity arose to implement a
wide patch some benefit could be gained by using an elliptical shape. The results
stated here are for one layer only and the actual benefit would be larger for a typical
multi-layer patch.
7
I
.
-..
6
5
4 -
5
3
*.
g
2
I
0
2
1.8
(Narrow patch)
1.6
1.4
1.2
1
0.8
Patch aspect ratio
0.6
0.4
0.2
0
(Wide patch)
Fig. 10.29. In-plane plate KI values of rectangular and elliptical shaped I layer patches with various
aspect ratios.
Chapter 10. Shape optimisationfor bonded repairs
313
10.9. Conclusions
Optimal stepping and tapering of the ends of bonded repairs has been
investigated in detail by analytical and numerical means in Sections 10.2 to 10.5.
All methods give as one conclusion that by transitioning the effective stiffness of
the repair in the taper region large stress reductions can be achieved using realistic
configurations. However to fully realise the potential maximum improvements at
the very ends of the patch, it is desirable to reduce the effective stiffness of the first
ply to below that of a typical unidirectional single layer of boron/epoxy layer.
Hence the use of cross-ply boron layers or of other more compliant materials has
been suggested and it is envisaged that such options will soon be investigated by
further modelling and laboratory testing at DSTO. Throughout these sections
effort has been focused on the adhesive stresses under the patch. The authors are
aware that adhesive cracking often starts in the adhesive fillet region outside the
end of the patch and that the modelling has shown significant adhesive stress
concentrations in this region regardless of fillet shape. The use of a more compliant
first layer would relieve these stresses as well.
Sections 10.5 and 10.6 show the benefits of using numerical shape optimisation
techniques to define variation of adhesive thickness (as well as reinforcement
thickness) such that the load transfer through the adhesive can be more evenly
spread along the bond line. This results in significant reductions in peak stress.
These improvements are demonstrated near a crack or joint for the case of a lap
joint, or over a curved region in the case of the F/A-18 470 bulkhead. Hence the
optimal variation of adhesive thickness has been shown numerically to be an
effective method in reducing adhesive stress concentrations. The benefits of
combining optimal rework shaping with a boron/epoxy reinforcement have been
discussed in Section 10.7 for the case of an F/A- 18 aileron hinge. Here the use of an
optimal rework prior to reinforcing has the double benefit of keeping the surface
stresses to their initial un-cracked and un-reworked values and reducing adhesive
stresses when the reinforcement is applied. It is important to note that a 2mm deep
rework of some form was required for crack removal and the use of a standard
circular shaped rework would have significantly raised the peak surface stress, as
compared to the optimal rework.
Investigation of repair in-plane shaping in Section 10.8 has led to the conclusion
that the standard rectangular shape is good if not optimal for the typical repair
aspect ratios of 2: 1 or higher. The exception is for unusually wide patches where an
elliptical shape gives better results for the stress concentration in the repaired
component. Hence for such wide patches the opportunity exists to apply numerical
procedures to determine the optimal shapes. It is expected that future work will
need to be directed at the inclusion of temperature curing effects as part of the
optimisation process.
314
Advances in the bonded composite repair of metallic aircraft structure
References
1. Rose, L.F.R. (1988). Theoretical analysis of crack patching, in Chapter 5 - Bonded repair of aircraft
structures (A.A. Baker and R. Jones, eds.), Martinus Nijhoff.
2. Zienkiewicz, O.C. and Taylor, R.L. (1991). The Finite Element Method (4th ed.), New York,
McGraw-Hill.
3. Bathe, K.J. (1982). The Element Procedures in Engineering Analysis. New Jersey, Prentice-Hall.
4. Spyrakos, C.C. and Raftoyiannis, J. (1997). Linear and Non-Linear Finite Element Analysis, Algor
Publ. Div., Pittsburgh, PA.
5. Rockey, K.C., Evans, H.R., Grifiths, D.W., et a/. (1983). The Finite Element Method (2nd ed.),
John Willey & Sons, New York.
6. Kaye, R. and Heller, M. (1997). Structural Shape Optimisation by Iterative Finite Element Solution,
DSTO-RR-0105, Defence Science and Technology Organisation, Department of Defence, Australia,
June.
7. Heller, M., Kaye, R. and Rose, L.R.F. (1999). A gradientless finite element procedure for shape
optimisation. J. Strain Analysis, 34(5), pp. 323-336.
8. Kaye, R. and Heller, M. (2000). Design of life extension options for an F/A-18 bulkhead using shape
optimisation. J. of Strain Analysis, 35(6), pp. 493-505.
9. Waldman, W. and Heller, M. (1999). Shape optimisation of PC9/A lower wing skin rework in
vicinity of undercarriage bay door up-lock mechanism mounting holes, Defence Science and
Technology Organisation, Department of Defence, Australia, File B2/129, April.
10. Heller, M., Mcdondld, M. and Burchill, M.(2001). Shape optimisation of critical stiffener run-outs
in the F-111 Wing pivot fitting. DSTO-TR-I 119, Defence Science and Technology Organisation,
Department of Defence, Australia, April.
11. Heller, M., Kaye, R., Whitehead, S., e f al. (1999). Design and Stress Analysis, Chapter 3 - Life
extension of F/A- 18 inboard aileron hinges by shape optimisation and composite reinforcement
(Editor R. Chester,), Defence Science and Technology Organisation, Australian Department of
Defence, DSTO-TR-0699.
12. Hart-Smith, L.J. (1973). Adhesive Double Lap Joints, NASA CR-112235.
13. Chalkley, P.D. (1993). Mathematical Modelling of Bonded Fibre-Composite Repairs to Aircraft,
Defence Science and Technology Organisation, Australian Department of Defence, Aeronautical
Research Laboratory, Research Report, ARL-RR-7.
14. Tran-Cong, T. and Heller, M. (1997). Reduction in Adhesive Shear Strains at the Ends of Bonded
Reinforcements, Defence Science and Technology Organisation, Australian Department of Defence,
DSTO-RR-0115, September.
15. Chester, R.J., Walker, K.F. and Chalkley, P.D. (1999). Adhesively bonded repairs to primary
aircraft structure. In?. J. of Adhesion and Adhesives, 19,pp. 1-8.
16. Bartholomeusz, R., Searl, A., Baker, A., et al. (1999). Bonded composite repair of F/A-18 Y470.5
bulkhead - applications with through-thickness stresses. Proc. ofthe Inf. Aerospace Congress (IAC
97), 1, Sydney, February, pp. 24-21.
17. Ojalvo, I.U. (1985). Optimisation of bonded joints. AIAA J., 23(10), January, pp. 1578-1582.
18. Groth, H.L. and Norlund, P. (1991). Shape optimisation of bonded joints, Int. J. of Adhesion and
Adhesives, 11(4), pp. 2W212.
19. Kaye, R. and Heller, M. (2001). Through thickness shape optimisation of bonded repairs and lapjoints, Znt. J. of Adhesion and Adhesives, Vol 22, pp. 7-21.
20. Rees, D. and Molent, L. (1993). Analysis of Candidate Bonded Repairs for Cracks in Weep Holes of
USAF C141 Aircraft, Defence Science and Technology Organisation, Australian Department of
Defence, Aeronautical Research Laboratory, Technical Note, ARL-TN-62.
21. Goland, M. and Reissner, E. (1999). The stresses in cemented joints. J. of Applied Mec., 7 , A17.
22. Volkerson, 0. Die Nietkraftverteilung in Zugbeanspruchten Nietverbindungen mit Konstanten
Laschenguerschnitten, Luftfahrtforschung, 15, pp. 4147.
23. Anon. (1995). Composite Materials and Adhesive Bonded Repairs, RAAF Engineering Standard,
No. C5033, Issue I , Department of Defence, Australia.
Chapter IO. Shape optimisation for bonded repairs
315
24. Boykett, R. and Walker, K. (1996). F-1IlC Lower Wing Skin Bonded Composite Repair
Subsantiation Testing, Technical Report, DSTO-TR-0480.
25. Wang, C.H., Heller, M. and Rose, L.R.F. (1998). Substrate stress concentrations in bonded lap
joints. J. of Strain Analysis, 33(5), pp. 331-346.
26. Shah, L.P., Heller, M., Wang, C.H., et al. (1997). Reduction of plate stress concentration factors due
to bonded reinforcements. Int. Aero. ConJ, 2.
27. Adams, R.D., Comyn, J. and Wake, W.C. (1997). Structural Adhesive Joints in Engineering,
Chapman and Hall, (2nd ed.).
28. Moore, G.J. (1994). Design Sensitivity and Optimisation, The MacNeal-SchwendlerCorporation.
29. Martin, P. (1995). ECP 365 Y470 bulkhead beef-up, SES DI 0942, Defence Systems Division,
Canadair Group, Bombardier Inc.
30. Kaye, R. and Heller, M. (2000). Comparative Assessment of Local Adhesive and adherend Stress
Concentrations for Full 3D Bonded Repairs (in preparation).
Chapter 1 1
THERMAL STRESS ANALYSIS
R.J. CALLINAN
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
11.1. Introduction
Accurate computational thermal stress analysis is particularly important for
assessment of the viability of bonded repairs to aircraft. Thermal stresses arise due
to the different coefficients of thermal expansion of the plate and patch involved
and may be significant at the extremes of the operating temperatures of these
aircraft. Furthermore the bonding process involves heating to approximately
100 "C for several hours before curing and cooling to room temperature. The
resulting residual thermal stresses due to the bonding process may be significant in
affecting fatigue crack growth rate. In this section closed form solutions are
considered and verified using F.E. analysis. In particular, 1D closed form solutions
[1,2,3] and 2D solutions [4,5,6,7,8]for circular repairs on circular plates are
considered. This involves computation of thermal stresses due to heating and
thermal stress in both isotropic and orthotropic repairs, and have been found to be
accurate in comparison to F.E. results. Both thermal and residual stresses are
considered in this analysis. It is found that this solution can be used for bonded
repairs to large structures such as aircraft wings provided that a suitable edge
restraint factor is applied. A relatively simple closed form solution is applied for the
thermal analysis of one dimensional strip joints. A simplification of the problem is
made by assuming that bending is restrained as shown in Figure 11.1. This
assumption is applicable to integral stiffened skins or thick skins supported by
multiple spars. The approach to the residual stress problem involves a two stage
process, firstly heating the structure up to the curing temperature, and secondly
cooling down to ambient temperature.
317
Baker, A.A., Rose. L.R.F. and Jones, R. (eds.).
Advances in the Bonded Composite Repairs of Metallic Airerast Structure
Crown Copyright (0 2002 Published by Elsevier Science Ltd. All rights reserved.
318
Advances in the bonded composite repair of metallic aircraft structure
Bending restraint
Fig. 11.1. Bending restraint provided to repaired skin.
11.2. Analytical expression for initial stresses in a circular plate due to heating
Circular repairs on circular plates are useful for the derivation of a closed form
solution which contains a bi-axial stress/strain field and has relevance for actual
repairs. Consider now a circular plate shown in Figure 1 1.2. This plate is uniformly
heated within a radius r = Ri equal to a temperature Ti, while the temperature at
the boundary is To. The temperature solution given in [5] which satisfies the
Laplacian operator:
V2T=0,
(11.1)
Fig. 1 I .2. Circular plate, definition of temperatures and radii.
Chapter 11. Thermal stress analysis
319
is given by:
(11.2)
for r 5 RI
T=Tl,
For this temperature distribution, the following differential equation is applicable
for the elastic displacement, assuming plane stress:
-(-)-=a(l+v)d 1 d(m)
dr
dr r
ddrT
,
(11.3)
where:
r is the radius
u is the radial displacement
v is Poisson's ratio
2 is the coefficient of thermal expansion
T is the temperature.
For the case of plane stress, and fixed edges the strain can be defined as:
er
= aeff( TI - TU) 9
(11.4)
where aeffis the effective coefficient of thermal expansion and is given by:
(11.5)
The explicit solution given by [5] for the case of fixed edges for r 5 RI is:
(11.6)
As expected, the expression is dependent on the geometry only and not
temperature.
As mentioned in 191 the calculation of the effective coefficient of expansion in a
structure is important in determining the residual stresses in a bonded structure.
The effective coefficient of expansion of the plate structure is very much lower than
the value a in the asymptotic limit RI/Ro = 0, i.e.
a& =
a( 1
~
+ v)
2
(11.7)
From Eq. (1 1.6) the asymptotic value for an aluminium plate is 14.95 x
while
the 1D value is 23 x 10-6/oC. The lower value of the coefficient of thermal
expansion, in this example, is firstly due to the circumferential restraints applied to
the edge of the plate and secondly is the result of the resistance of the surrounding
Advances in the bonded composite repair of metallic aircraft structure
320
colder structure. This occurs, for example, in the bonding of a high strength repair
to the wing of an aircraft in which a high temperature, over a local area, is required
to cure the adhesive.
In this section the derivation of an expression for residual stresses essentially
follows that given by [5,6]. In a bonded repair both the patch and plate are heated
to the cure temperature T. In the case of a plate in which the edges are restrained,
the heating gives rise to an initial stress in the plate before curing of the adhesive
and cooling takes place. In the case of the patch no restraint exists and the initial
stress is negligible. To compute the initial stress in the plate we have the following
expressions for displacement, obtained by integrating Eq. (1 1.3), and radial stress
from [lo]:
(11.8)
(11.9)
from the boundary condition that u = 0 at r = Ro we obtain the integration
constant C . From this the general form for the radial displacements and stresses is:
u=
{?[ -&
RO+'I
1
,
(1 1.10)
(1 - v ) R ~ Trdr)
(11.11)
Trdr
'+'
Trdr}
/
Specifically for r = RI the displacement is given by:
(11.12)
Specifically for r 5 RI we have a constant state of stress given by:
(1 1.13)
Equation (11.13) gives the required initial stress. The second part to the solution of
residual stresses involves the analysis of the plate and patch. We require the state of
stress corresponding to a cooling of the plate and patch. If we start at a temperature
0 "C corresponding to zero initial stress, then cooling to a negative temperature
equal in magnitude to the cure temperature (-T)will give the required stress
components. A summation with the initial stresses will give the residual stress state.
Chapter 1 I . Thermal stress analysis
32 1
In this analysis, the adhesive will not be considered, and the patch is assumed to
be rigidly connected to the plate. Radial stresses and displacements will be obtained
for the skin and patch. The skin is hereafter referred to as the plate. Consider a plate
shown in Figure 11.3, which has properties El,al,t l for r 2 R, and overall
properties E,, a,,to for r I R I . Again the temperature boundary conditions are
given by T, being constant for r I RJ and T = TOat r = Ro. The displacements are
given by:
(1 1.14)
T
E2. t2,
m
Ei.fi, ai
Fig. 11.3. Idealised bonded repair.
Advances in the bonded composite repair of metallic aircraft structure
322
uo =
+
r
1
Trdr + Clr
(11.15)
0
The stresses are given by:
for r 2 RI
( 11.16)
co = --
r2
/
(11.17)
T r d r Eo
+ m Cl(1 + v )
0
The solution of these equations must satisfy the following conditions:
(a) The displacement u1 and uo is equal at r = RI, hence from Eqs. (1 1.14) and
(11.15):
(1 1.18)
(b) Equilibrium must be maintained across the boundary at r = Rl, using
Eqs. (11.16) and (11.17):
3
1= -Rr2
aoEoto
/
RI
Trdr+- Eo t o
(1 - VIC1
(11.19)
0
(c) Also we have the further boundary condition that at r = Ro:
u1=0=
a1(l+v)
RO
J" Trdr + C ~ R O+ c
3
RI
RO
(1 1.20)
At this stage we have enough information for the evaluation of the constants C1, C2
and C3.
It is more convenient to have the equations in the form that represent a patch
over the plate for r 5 RI as shown in Figure 11.3. As before, the plate has the
properties El, t l ,011 while the patch has the properties E2, t2, a2. It is necessary to
Chapter 1 I . Thermal stress analysis
derive an expression for
considerations we have:
E,
323
in terms of these quantities. From equilibrium
hence:
(11.22)
where:
(1 1.23)
The expression for the stress state in the plate just outside the patch is given by
Eq. (11.16) for r = RI:
1
c
2
o = E l --
[(I - v )
(1 +v)R;
c3
( 1 1.24)
We will now derive the expressions for the stress state in the plate beneath the patch
and in the patch. From Eq. (1 1.15) with r 5 R I , under a uniform temperature, the
displacement is given by:
(11.25)
Since the displacement is the same in both the patch and plate we have:
(1 + V)QTI
2
( 1 + v)a2TI
+
-
U
I-RI
U
+c2=-
RI
’
’
(11.26)
(11.27)
where the displacement u corresponds to the location r = RI.
The radial stresses for the plate and patch are given by:
(1 1.28)
(11.29)
Using Eqs. (1 1.26-1 1.29) we have the expressions for the radial stresses in the plate
324
Advances in the bonded composite repair of metallic aircraft structure
beneath the patch and in the patch:
(11.30)
(11.31)
To obtain the residual stress in the plate beneath the patch it is necessary to sum
Eqs. (11.13) and (11.30), but with TI = -TI in Eq. (11.30). Hence the final
expression for the residual stress beneath the patch is:
( 11.32)
Since the initial stress in the patch is zero, then the residual stress in the patch is
given by Eq. (11.31), but again with TI = -TIhence:
(11.33)
and the final expression for the residual stress just outside the patch is given by the
summation of Eqs. (11.13) and (11.24), hence:
( 11.34)
These equations now give the residual stress in terms of the cure temperature T .
The displacement u at r = RI for Eqs. (11.17, 11.18) and integration constants C2,
C3 are given in the appendix.
These equations now give the residual stress in terms of the cure temperature T.
For operating temperatures different from room temperature, Eqs. (11.24), (11.30)
and (1 1.31) can be used to calculate the stresses. In this case TI= TO= uniform
temperature change from room to operating temperature. The final stresses are
obtained by superimposing these stresses on the residual stresses.
11.2.1. Comparison of F.E. and analytic results
The solution of these equations has been carried out for AT = lOO"C,and the
following quantities have been evaluated for the comparison with F.E. results, the
mesh is shown in Figure 11.4:
1. residual stress just outside the patch at r = RI
Chapter 11. Thermal stress analysis
325
Fig. 11.4. Finite element mesh of circular patch on circular plate. Here RI = 162 mm and
Ro = 500 mm.
2. residual stress in the skin beneath the patch (01)
3. residual stress in the patch ( 0 2 )
As an example a circular patch and plate are considered whose mechanical
properties are shown in Table 11.1. These properties are representative of a quasiisotropic boron patch reinforcement of an aluminium plate (although the value of a
used here for boron corresponds to uni-directional boron and should have been
Table 11.1
Material properties used for study of circular repairs on circular plates, A T = 100°C.
Component
Thickness
(mm)
Young's
modulus
(MPa)
Poisson's
ratio
Plate(A1uminium)
Patch(boron)
*Adhesive (FM300)
1.O
0.5
0.254
71016
156000
3460
0.3
0.3
0.35
Coefficient of
thermalexpansion
(1°C)
23 x IOs6
**4.1 x 10-6
Conductivity
(J/ms"C)
13.2
0.294
* Only used for a 3D run.
** In this instance the value for the laminate is taken to be equal to the unidirectional value.
326
Advances in the bonded composite repair of metallic aircraft structure
3.76 x [email protected] for the laminate). While this is not a perfect representation of an actual
repair it is acceptable for estimating residual stresses. Also this assumes that
bending is restrained, e.g. by stiffeners or thick plates, and also the edge restraint
exists when the repair is bounded by structural elements such as spars and ribs.
Consider the case in which the plate edge is restrained in the radial direction. Firstly
consider the heating up process to the cure temperature, given by Eq. (11.13) and
shown in Figure 11.5. The comparison between theory and F.E. results is in
agreement to four significant figures. In the case of no edge restraint the initial
stresses would be zero.
The second stage of the process involves cooling down from the cooling
temperature alone. The analytical and F.E. results are shown in Figure 11.6 where
the curves are from Eqs. (11.24), (11.30) and (11.31), and the points on the curves
are F.E. results. In all cases very good agreement between analytical and F.E.
results are obtained, (to four significant figures). The final solution for the residual
stresses is given by Eqs. (1 1.32-1 1.34) in Figure 11.7 with the corresponding F.E.
results. Again very good agreement between analytical and F.E. results is obtained.
Note that the residual stresses in the plate shown in Figure 11.7 are significantly
lower than those during the cooling process, Figure 1 1.6. This is simply due to the
lack of initial stresses which arise as a result of the restrained edges of the plate
when heated up to the cure temperature. The assumption of edge restraints is
important. Typically a repair to an aircraft wing plate can be considered as fully
restrained in the radial direction if the repair is bounded by significant structural
elements such as spars and ribs.
Returning to the residual stresses shown in Figure 11.7. It is evident that for large
values of R o / R , asymtotic values occur for all stress components and may be
considered as limiting values.
-100,
-105-110-
2
-115-
5
cn
-120-
A
cn
a,
3
F.E.
-125-
- 1 4 5 ( .
0
,
5
.
I
10
I
I
.
15
,
20
.
,
25
.
,
30
RdRi
Fig. 11.5. Initial stresses in plate due to heating to cure temperature.
,
I
35
Chapter 1 1. Thermal stress analysis
327
1
501
Stress in plate beneath patch,Theory/F.E.
Stress in patch,Theory/F.E.
0
0
Stress in plate just outside patch, Theory/F.E.
-504
0
5
15
10
20
25
30
35
R,IRi
Fig. 1 1.6. Comparison of theory and F.E. results for cooling down process only.
0rr
-200
-40-
n
0
Stress in plate outside patch,Theory/F.E.
Stress in patch, Theory/F.E.
-60-
So far, the adhesive has not been considered in the analysis. However F.E. results
have been obtained in which the patch and plate have been coupled using 3D
adhesive elements. To make a useful comparison with the previous analytical work
the bending of the plate has had to be restrained. The introduction of the adhesive has
328
Advances in the bonded composite repair of metallic aircraft structure
Table 11.2
2 D isotropic circular plate, patch and 3D adhesive elements. Residual displacements and
stresses, al = 23 x 10-6/"C, a2 = 4.1 x 10-6/"C (analytic values in parenthesis), [5].
Residual stress
Displacement at
just outside patch
Ro (mm) edge of patch (mm) (MPa)
Residual stress in
skin beneath patch
(MW
Residual stress
in patch (MPa)
500
161.91
(1 6 1.33)
- 65.532
(-66.813)
- 0.1 1551
(-0.1 1499)
128.31
(127.92)
resulted in an error of only 2%in direct stresses, shown in Table 11.2, and indicates
that the use of a closed form solution is sufficiently accurate for patch design.
The main concern in this chapter is the equations for direct stresses in the repair.
It is important to know the direct stress in the plate beneath the patch in order to
predict crack growth rate or simply the residual strength of the repaired structure.
The adhesive itself has no effect on the maximum value of the direct stresses.
Some F.E. programs have the capability in which the material properties can be
temperature/time dependent. In this case a simulation of the bonding process can
be carried out. The adhesive properties change during the curing process. At the
end of the curing process the adhesive has developed a shear stiffness and as the
repair is cooled to room temperature residual stresses develop. If the simulation
capability is available, then residual stresses are directly obtained from the analysis.
If this capability is not available then a superposition procedure can be used. The
analysis is carried out in two steps. The first analysis is equivalent to heating up of
the plate to the curing temperature (without the patch, since the adhesive has no
stiffness at this stage). Secondly, another analysis is carried out with the patch
included, subject to a cooling temperature equal to the cure temperature.
(TI= -TI). In the work presented here this two stage procedure has been shown
to be very accurate. The superposition of these two analyses gives the residual
stresses in the repair. Since the adhesive shear modulus is temperature dependent,
an arithmetic average value of the shear modulus should be used during the cooling
process.
I I .2.2. Orthotropic solution
Recent work by [7,8] has extended the analysis of residual stresses to circular
orthotropic patches on isotropic plates. The solution of this problem is based on an
inclusion analogy, which refers to the inner region of the repair where r 5 RI in
which equivalent properties of the inclusion can be made without altering the stress
or displacement state. Exact solutions are presented for both residual stresses and
thermal coefficients of expansion.
Results of this work are shown in Figures 11.8 and 11.9 for stresses due to
cooling only. For plate stresses beneath the patch both oXxand oYYare predicted, as
shown in Figure 11.8 and correspond to clamped edge conditions. As a
comparison, the isotropic solution is included and gives close results when
Chapter 1 1. Thermal stress anaIysis
.
.
.
,
.
.
.
,
.
.
.
,
.
.
.
I
.
.
.
329
I
.
.
.
clamped edge
1.4
Q
.
4
o
FEresults
Equivalent isotropic patch
1.2
a
c
.e
1.o
0.8
0.6
1
3
5
7
9
I1
13
Ratio of outer radius to inner radius RJR,
Fig. 11.8. A circular patch over a concentric plate with outer edge being clamped: cooling induced
stresses in the plate. [7]
1.o
F
W
0
0
6
w
g
0.5
FEresults
Equivalent isotropic patch
E
P
.*
2
....c
v)
2
E
-
t
0
s
b
-0.5
1
3
5
7
9
Ratio of outer radius to inner radius Mi
I1
Fig. 11.9. A circular patch over a concentric plate with outer edge being clamped: cooling induced
stresses in the orthotropic reinforcement. [7]
Advances in the bonded composite repair of metallic aircraft structure
330
compared with oxxstresses, however the isotropic solution predicts oxx= oyywhere
in fact oyy< oxx.
In the case of the reinforcement shown in Figure 11.9, the isotropic stress is
slightly higher than the owx stress, but while the isotropic solution predicts
oxx = oyy,where in fact the absolute value of the stresses, Joyy(
< (oxx(.Note that
for Ro/RI 2 1.5 the sign of the oyystress is opposite in sign to the o, stress. For
the cases of both the plate and reinforcement stresses, the isotropic solution is
conservative.
1 I .2.3. Thermal stresses in a one-dimensional strip
11.2.3.1. Shear stresses. In a bonded joint in which two materials are bonded
together, thermal stresses may develop as a result of the difference in thermal
coefficients of expansion. The following equations will be given for a simple double
overlap joint whose geometry is given in Figure 11.10 together with the location of
the origin of the x axis. It is assumed that all the load transferred by the lap joint is
by adhesive shear. Also, in this symmetrical joint it is assumed that no bending
takes place [5].
The constitutive equations are:
(11.35)
where:
u1 and u2 are the displacements in the components of the joint
a1 and a2 are the thermal coefficients of expansion
E1 and E2 are the Young’s moduli of the two materials
AT is the change of temperature = TC - TA
Tc is the cure temperature
TA is the initial temperature
6 1 and 0 2 are the stresses in the components of the joint.
The equilibrium equations are:
(1 1.36)
where:
r 1 , t2
are the different thicknesses of the two components and
z is the shear stress in the adhesive.
Compatibility requires that the shear stress is given by:
Ga
z=-(u2-u,),
ta
where:
t , is the thickness of the adhesive
(11.37)
Chapter 1 1. Thermal stress analysis
33 1
Reinforcement
A.
-x
Adhesive
2tl
/!
I
/
w
h
t
1
OZ
+-
1
t
i
t
L
Deformation of adhesive
Fig. 11.10. One dimensional equation, definition of parameters.
G, is the shear modulus of the adhesive.
From these equations the result is obtained:
(11.38)
Advances in the bonded composite repair of metallic aircrafi structure
332
where:
(1 1.39)
For thermal stresses only crA = 0 and:
T = -Gaz
(E1
- a2)ATe-X/'
(1 1.40)
fa
The direct stress for component 1 given by:
(1 1.41)
At x = 0, ul = 0, and 01 rises to a maximum value when x is large which is given by:
(1 1.42)
If we consider a single lap joint in which bending is restrained and if the thickness
of the skin is ts, then tl = t,.
I I .2.4. Peel stresses
Comparisons of the F.E. are made with the d.e. expression, given by [ll]. This
expression can be used for a single lap joint but with no bending and is a function
of the shear stress T:
u p = -woEc/ta
>
(1 1.43)
where
(1 1.44)
where
x = (Ec/(4Dta))0'25
A = ( z ( t a / 2 ~sinxZ/2)/x3
)
B = +(ta/2q COS X1/2)/X3
E, =effective tensile modulus of the adhesive
z = shear stress (normally taken to be the plastic value zp)
D = E0tz/12(1 - v2) and is the bending stiffness of boron
In this case the location of the coordinate system is at the midpoint of the joint,
and x = k112 corresponds to the ends of the joint.
Chapter 11. Thermal stress analysis
333
11.2.5. CoefJicients of thermal expansion of a laminate
The material properties of the basic unidirectional laminate of boron/epoxy used
in the 3D analysis are given in Table 11.8. For a thermal analysis of a multi-ply
laminate it is necessary to compute the effective coefficients of thermal expansion in
the material symmetry axes. Usually manufacturers’ data will provide the
longitudinal (al) and transverse (az) coefficient of thermal expansion for a
unidirectional laminate. In this case the longitudinal coefficient of thermal
expansion is a measure of the fibre property while the transverse coefficient is a
measure of the resin property. The starting point for the derivation of overall
coefficients of thermal expansion in a laminate is the well known stiffness matrices
corresponding to in-plane stiffness, bending stiffness and coupling between in-plane
and bending respectively:
(1 1.45)
(1 1.46)
[Q](z:- . z3 ~ - ~ ) (bending)
[D]=
(11.47)
;=I
where
[Q] is the reduced stiffness matrix of the laminate
zi- zi-lis the thickness of each ply
k is the total number of plies in the laminate
If the analysis is restricted to symmetric laminates then it can be shown that the
coefficient of thermal expansion is restricted to in-plane extensional stiffness only
with no bending effects. The expression for the overall thermal expansion of the
laminate is given by [ 121 as:
(11.48)
[ax]= -
where:
/
h
{NT}=
o,dz
(1 1.49)
-h
where the thermal contribution is given by:
(1 1 S O )
Advances in the bonded composite repair of metallic aircraft structure
334
where
[e]is a 3 x 3 transformation
matrix defined by:
where x denotes the laminate axis and I the ply axis. The individual terms are given
by: 811 = m2, 812 = n2, 813 = -2mn, 821 = n2, 822 = m2, 623 = 2mn, 831 = mn,
832 = -mn, 833 = m2 - n2, m = cos 8 , n = sin8 The angle 8 is from the laminate
axis to the ply axis.
where [Q] is a 3 x 3 elasticity matrix defined by:
where x refers to the laminate axis and I to the ply axis. The individual terms are
given by:
QII = E
e
1
3
2
I / (~ v E2/E1)
,QIZ
= ~12E2/(1- v2&/Ei)
= Q23 = Q31 = Q32 = 0 Q22 = E2/(1
where{ccr}T = { a l , a 2 , 0 } ,
= Q21
,
- v2E2/Ei)
( 1 1.53)
finally integrating through the thickness:
(11.54)
Hence substituting in Eq. (1 1.48) gives the overall laminate coefficient of thermal
expansion.
In order to demonstrate the effect of ply lay-up on the effective coefficient of
thermal expansion, an angle ply has been considered in which the + 8 plies have
been varied from 0 to f 90 The value of ax is shown in Figure 11.11. Starting
from a value of zero degrees a, continually reduces until approximately 33 degrees,
after which it continually increases to a maximum at 90 degrees. This corresponds
to 19.1 x 10-6/oC which is the transverse value for the unidirectional laminate. The
resulting shape of the curve is dependent on both Poisson’s ratio effects (that are
continuously changing), and plies values of a1.
The coefficients of thermal expansion, a1 and a2, are the effective coefficients of
thermal expansion for a unidirectional laminate. For a 3 D laminate the out of
plane coefficient of thermal expansion may be taken as being equal to the value a2
in the unidirectional lay-up.
In Table 11.3 a comparison has been made between the coefficients of thermal
expansion for a unidirectional laminate and a lay-up consisting of [02, &45,03],.
The overall effect of the Poisson’s ratio and the lay-up is to produce an effective
)
than the unidirectional lay-up
coefficient in the longitudinal direction ( a ~higher
)
than the unidirectional lay-up.
and a transverse coefficient ( a ~ lower
O.
Chapter 11. Thermal stress analysis
pc
335
-Boron cross ply laminate
20-1
x
c
.-0
co
S
m
n
X
m
Q
i
s
c
0
I
0
20
I
I
I
40
60
Laminate angle degrees
80
Fig. 11.11. Cross ply laminate coefficient of thermal expansion. a,, versus laminate angle.
11.3. Finite element thermal stress analysis
As a result of the increasing trend towards computational stress analysis it is
worthwhile looking at the equations used by F.E. analysis. A thermal stress
analysis is usually carried out with the intention to calculate thermally induced
stresses, strains or displacements. Thermal stresses may arise, for example, in a
bonded joint consisting of materials with different thermal coefficients of thermal
expansion. Thermal stresses may occur in a heated structure which is rigidly
constrained, and also in a structure with temperature gradients. As previously
mentioned, a thermal stress analysis is usually carried out in two steps, the first
being the thermal analysis which will calculate temperatures at each node, and the
second to calculate the corresponding stresses and displacements.
The governing equation for heat flow problems is:
(11.55)
V=T=Q,
where Q is the heat flux.
Table 11.3
Thermal expansion coefficients for unidirectional boron/epoxy,
and values computed for a Boron/epoxy laminate.
Coefficient of expansion
U L (longitudinal)
E-/-
(transverse)
Unidirectional [I91
4.1 x
19.1 x
[02,
+45, O&
3.76 x low6
12.29 x
Advances in the bonded composite repair of metallic aircraft structure
336
For F.E. analysis the equations that govern the non-linear heat transfer analysis
are given in matrix form by [13]:
[CI{T) + [RI{T + TABS)= { Q ) + I N )
>
(11.56)
where:
[C]is the conductivity matrix
[R]is the radiation exchange matrix
{ T} is the nodal temperature vector
is the heat flux vector
{N} is the non-linear heat flux vector that depends on temperature
T is the temperature
TASsis the absolute temperature
For steady state conduction and where the radiation losses are insignificant the
equations are linear and reduce to:
{e}
The boundary conditions may be specified as temperatures or heat flux at nodes. A
partitioning of Eq. (1 1.57) is carried out into unknown and known temperatures. If
the heat flux is known at a node, then the temperature is treated as being unknown
at that node. The thermal solution carried out by NASTRAN, PAFEC and
ABAQUS use elements whose properties are dependent on the geometry and
thermal conductivity for that material. This analysis solves for the temperature
vector and writes it to an output file for use in the structural analysis that follows.
The static structural solution involves the matrix equations:
[Kl{4 = {P)+ CPT)
9
(11.58)
where:
[K] is the structure stiffness matrix
{d} is the displacement vector
{P} is the applied load
{ P T } is the thermal load vector and is given by:
(11.59)
where:
[B] relates strains to displacements
[D]is the elasticity matrix
[a] are the coefficients of expansion
[TI is the temperature vector from the thermal solution
dv integration is taken over the volume.
The thermal load vector is added to any applied loads that exist, and the usual
displacement solution is obtained. This corresponds to the second NASTRAN,
Chapter 11. Thermal stress analysis
337
PAFEC and ABAQUS run in which the previously calculated temperatures in the
output file are read back in.
I I .3.1. Two-dimensional strip joints
A 2D F.E. (plane stress) analysis has been carried out for a bonded joint whose
geometry is shown in Figure 11.10. Only 2D isotropic, 8 noded quadrilateral
elements are used in the analysis, and all lie in the xy plane. While Figure 11.12 is a
diagram only, the area which is refined is indicated. The temperature throughout
the joint is set at 100°C with a reference temperature of 0°C. The relevant
coefficients of thermal expansion are shown in Table 11.5, which may be derived
from figures in Tables 11.3 and 11.4.
In the structural analysis that follows, the corresponding structural properties
used, are shown in Table 11.6. While the adhesive also has a coefficient of thermal
\Fine
mesh
\. -f t z
IL
Table 11.4
Properties of unidirectional Boron/epoxy, [ 141.
207000
10.89
0.21
4800
Table 11.5
Thermal properties in 2D isotropicjoint.
Component
Coefficiant of thermal expansion PC
a1 (Aluminium)
a2 (Boron laminate)
23 x
3.76 x
Table 11.6
Mechanical properties of 2D strip.
3.6
1.778
0.254
0.3
0.3
0.35
71016.0
156000.0
842.0
t,
Advances in the bonded composite repair of metallic aircraft structure
338
expansion it is neglected in order to make the best comparison with the 1D d.e.
given by Eq. (1 1.a).
In the analysis the restraints used are:
1. restraints are used in the x direction for all nodes located on component 1 with
co-ordinates of x = 0
2. restraint in the y direction for all nodes in component 1 with the co-ordinate of
y=o.
The restraints in the y direction have been applied to prevent bending of
component 1, so that a direct comparison can be made with the 1D d.e. The d.e.
results are based on Eq. (1 1.40). Also in this analysis no non-thermal loads have
been applied.
A comparison of the shear stress is made on the basis of shear stress taken
directly from the F.E. results corresponding to the midplane of the adhesive are
shown in Figure 11.13. The F.E. results for the 2D isotropic case are about 2.5%
lower than the 1D d.e.
Overall the difference in results between the 2D F.E. and 1D d.e. do not
necessarily indicate the existence of an error in either solution. Factors that may
influence results are firstly the Poisson's ratio effect which is not considered in the
1D d.e. Secondly, in the F.E. analysis shear deformation occurs in all components
of the joint, while in the 1D d.e. it only occurs in the adhesive. Furthermore, the
F.E. analysis of bonded repairs in general shows a considerable variation in shear
stress from the patch/adhesive interface to the plate/adhesive interface as shown in
Figure 11.13.
To achieve good results in the F.E. analysis a very fine mesh of 0.05mm
increments has been required to pick up the rise from z = 0 to a maximum at up to
3530h
g
z_
g
25-
20-
0
c
u)
15-
-0-
Lower interface
-A-
Midplane
-0-
Upper interface
-0-
D.E.
W
c
&-
10-
50-
".
l
0.0
-
l
0.2
.
l
0.4
.
l
.
0.6
,
0.8
.
,
1.o
Distancefrom start of joint (mm)
Fig. 11.13. Thermal adhesive shear stresses in 2D bonded strip joint.
.
,
1.2
Chapter 1 1. Thermal stress analysis
339
0.25 mm away from the end of the joint. This distance is approximately equal to the
thickness of the adhesive. In the case of the d.e. the formulation is such that the
maximum value occurs at the end of the joint. Also the decay of the F.E. and d.e.
results are the same.
In the case just considered the F.E. analysis was confined to the analysis of
isotropic materials. Now consider the case in which component 2 has orthotropic
properties. Composite materials are orthotropic and bonded joints are often
comprised of such materials. In the repair of cracked metallic structures, materials
such as boron/epoxy laminates are used as reinforcement. Consider a 2D analysis
in which EX is the major modulus of the laminate and E y represents the modulus
perpendicular to the laminate. In this case the shear modulus is taken as that for a
unidirectional layer of boron/epoxy. Using typical properties for the boron/epoxy
and making a comparison with the 1D d.e. on the basis of E2 = EX gives the results
shown in Figure 11.13. The isotropic solution was found to give almost identical
results and have has not been plotted. Comparison of the shear stresses obtained by
the F.E. and ID d.e. show that the midplane 2D orthotropic results are about 2.5%
lower than the 1D d.e.
I I .3.2. Three-dimensional strip joints
A 3D F.E. thermal analysis, using 20 noded brick elements, has been carried out
for the structure defined in Figure 11.14, which is fully restrained at the right hand
end. Also, bending in the y direction has been restrained. To simplify matters the
[02, +45",03] laminate is assumed to be homogenous orthotropic, where the
principal material symmetry axis is in the x direction. The mechanical properties of
the laminate are derived from the uni-directional properties in Table 11.3 and are
shown in Table 11.7. The coefficients of thermal expansion are calculated using
Eqs. (1 1.48) and (1 1.54) and are also shown in Table 11.3. The mesh used for the
width of the patch involves 0.05mm increments at both the free edge and
centreline. The overall effect of the Poisson's ratio and angle ply layup is to produce
an effective coefficient in the longitudinal direction (a=) lower than the unidirectional lay-up and transverse coefficient ( E T ) also lower than the uni-directional
lay-up. The value used by the 1D d.e. is E L .
This joint is subject to a uniform temperature of 100 "C. The resulting ZXY shear
stresses have been evaluated at points A and B which are located as shown in
Figure 11.14. It was found that the Z X Y shear stresses were 13% higher at location A
than location B and these are plotted in Figure 11.15. The 3D results are the most
accurate computation of the shear stresses and exceed that predicted by the d.e. by
15%. Again shear stresses considered are those in the midplane of the adhesive.
Although results are not presented, if transverse coefficients of thermal expansion
are ignored and set to zero, this may result in 8% higher shear stresses. It is evident
that an interaction is occurring between the Poisson's ratio effect and the two
coefficients of thermal expansion. Clearly a 3D analysis is significantly different to
a 1D analysis when both longitudinal and transverse coefficients of thermal
expansion exist. While the 1D d.e., Eq. (11.40), provides a close estimate shear
Advances in the bonded composite repair of metallic aircraft sfructure
340
b-Lp-,yaesiv;+
Boron patch
tl
Plate
I
x
E
ta
t1
Fig. 11.14. Three dimensional bonded joint subject to uniform temperature change.
Table 11.7
Overall properties of the Boron patch for patch lay-up of [02, f45,03],.
EYY = 29781.
Exx = 156107.
~ x=
y 0.574884
vyx = 0.109675
40 -
-
35 3025-
v
3
a,
5
g
c
.
Free edge.z,
Centrehe,z,
20-
-A-
15-
-v-
10-
-0- Free edge,.c,
50-
-5
,
~,
,
,
,
,
,
,
,
,
Gxy = 190651.
Chapter 11. Thermal stress anaIysis
34 1
stresses at the free edge it under-predicted the maximum value by 15%. Note that at
the free edge a ZZY shear stress component exists with maximum value of 6 MPa,
Figure 11.15.
11.4. Application of analysis to large repairs of aircraft wings
The object of this section is to determine the applicability of a closed form
solution to the large repair of an aircraft wing, whose cross section is shown in
Figure 11.16. In this case the repair covers one spar and two of the cells. While the
application of closed form solutions to repairs bounded by spars and ribs is
reasonable, the application of closed form solutions to large repairs presents
difficulties. In this section a simplified multi-spar wing FE model is considered and
has properties at the repaired site similar to an F-111 wing. The wing is only
constrained at the wing root and a repair is considered over the middle spar. A
similar repair has been carried out on an F-11 I wing, [15]. In this case the repair
considered was rectangular of size 450 mm in the spanwise direction and 300 mm in
the chordwise direction with the repair centred over the forward auxiliary spar,
rather than the middle spar. Since heat losses to the surrounding air will occur due
to convection, the actual temperature distribution was determined during a
simulation of the curing cycle, [16], and are shown in Figures 11.17 and 11.18. This
has been adjusted for a cure cycle of 100 "Cand a room temperature of 25 "C and
will be applied to the FE wing model. The alternative procedure is to specify a
convection heat transfer coefficient, h, in the thermal analysis, in which the rate of
Fig. 11.16. Cross-section of multi-spar wing (up-side down), flanges not shown.
342
Advances in the bonded composite repair of metallic aircraft structure
90P
80-
9
9?
c
2
70-
rn
Inboard temperature distribution
60-
o
Outboard temperature distribution
(IJ
L
50E
40-
30-
-v
20I
I
90-
80-
2
f
c
7060-
2
'
E
Q
J
5040-
30I
0
400
600
Distance from spar (mm)
200
9
-
800
Fig. 11 .IS. Chordwise variation of temperature for simulated curing.
heat transfer is, in its simplest form, given by [17] as:
Q = hA(Ts -)'7
(1 1.60)
(This is also known as heat flux, as shown in Eq. (1 1.56))
where
TS is the temperature of the surface
Tf is the air temperature
where h is the heat transfer coefficient and needs to be experimentally
determined.
This wing model is idealised using shell elements for the skins (plates) and spar
webs, and rod elements for the spar flanges. The dimensions are shown in Table
11.8. Also the adhesive has been ignored and the boron fibre patch is considered to
be welded to the plate, i.e. composite shell elements overlay the plate. In other
words, it is assumed that bending is fully restrained. In this analysis we will
Chapter 11. Thermal stress analvsis
343
Table 11.8
Dimensions of wing box in mm.
Overall length
Distance of patch centre to wing tip
WP
dw
W,
tup
fLP
tW
lP
fR
Flange areas
4300.0
2300.0
800.0
185.0
400.0
3.6
3.6
2.5
400.0
1.778
200.0 mm2
consider a repair using both a uni-directional boron laminate and an angle ply
laminate.
I I .4.I . F.E. analysis
The first step in the F.E. analysis is to determine the initial stresseswith no repair. In
this case the temperature distribution is determinedin the complete structure. Known
temperatures are input into the model and the unknown temperatures are found
during the thermal analysis as shown in Figure 11.19. The corresponding structural
analysis then determines the distribution of initial stresses throughout the F.E. model
as shown in Figure 11.20. These stresses are spanwise components. Note that tensile
stresseson the edge of the wing box exist to restore the equilibrium.The next step in the
analysis involves the cooling down of the F.E. model which in this case also contains
the boron patch. In this case the sign of the temperatures is changed (Figure 11.21),
and the thermal and corresponding structural analysis is run, with results shown in
Figures 11.22and 11.23. In Figure 11.22the spanwisestressesin the plate of a repaired
wing are shown, while Figure 11.23shows the spanwisestressesin the patch, and plate
outside the repair. Significant variations of stress occur from the centre and edges of
the repair, and also plate stresses beneath the repair. The stresses shown in the patch
are the final residual stresses, while the residual stresses in the plate are a sum of the
initial stresses and stresses due to cooling. In both Figures 11.22 and 11.23 stresses
exist on the top edges of the wing box to restore equilibrium.Initially, only the stresses
in the centre of the plate and patch are considered, Tables 11.9 and 11.10.
For the heating up of the F.E. model spanwise displacements have been
computed in the area that is to be repaired. From these results it is possible to
compute the effective coefficient of thermal of expansion of the aluminium wing in
this region. A slight variation occurs across the patch in a chordwise direction and
an average spanwise value of 16.76 x lop6/ "C is obtained. This is comparable with
Eq. (1 1.7) where c t e ~= 14.95 x
"C for a bi-axial stress state in a circular repair
on a circular plate, fully restrained at the edges.
The F.E. results for the [02,f45, 03Is and [07Islaminates are contained within
Tables 11.9 and 11.10 respectively. These tables contain results corresponding to
344
Advances in the bonded composite repair of metallic aircraft structure
Fig. 11.19. Distribution of temperature for heating process only. The repair is closest to the wing tip, the
wing being completely restrained at the root end only.
the initial stresses, stresses due to cooling and residual stresses for both F.E. and
closed form solutions.
The first closed form solution is that from [2]. In this case the residual stresses are
obtained directly. The first equation for the residual stress under the patch is given
by:
(1 1.61)
The equation for the residual stress in the patch is given by:
(1 1.62)
The results for these equations are based on the direct value of c11 = 23 x
"C.
The results over predict the residual stress in the plate, but does give a close value
for the residual stress in the patch. Although not shown, results based on a1 =
Chapter 1 1. Thermal stress analysis
345
2 3k01
n
r’;
9.8%
64A
-7 2
Fig. 11.20. Spanwise stresses corresponding to thermal loading as a result of heating. (This model does
not include the patch). Note the tension stresses on the top edge of the wing.
14.95 x 10-6/oC do more accurately predict the residual stress in the plate but
significantly under predict the stress in the patch.
The 2D closed form solutions derived from circular patches on circular plates
will now be considered, the first being the isotropic solution and the second the
orthotropic solution. Application of a closed form solution to the repair of an
aircraft wing requires an assumption of the value of Ro to be used. Previous results
have shown limiting stress values are obtained for large Ro/R, ratios, hence these
are the results shown in Tables 11.9 and 11.10.
Consider now the residual stresses predicted by the 2D isotropic solution. From
both Tables 11.9 and 11.10 these values show conservative agreement for residual
stresses in the plate beneath the patch, slightly un-conservative stresses in the patch
and un-conservative values in the plate just outside the patch.
The 2D orthotropic solution, shown in Table 11.9, gives much the same results as
the 2D isotropic solution except that it can predict both stress components for the
orthotropic patch material. However the stress perpendicular to the spanwise axis
has been found to be much lower than the spanwise component and hence is not as
important.
346
Advances in the bonded composite repair of metallic aircraft structure
-2.004.'
-2.5%~
-3.O(kl
Fig. 11.21. Distribution of temperature for cooling down process only. The repair is closest to the wing
tip, the wing being completely restrained at the root end only.
Overall the 1D solution compares more favourably with the F.E. than 2D
sohtions, since with the wing tip unrestrained the problem is closer to a 1D problem.
The main reason for the difference of 2D and FE solutions is that the analytical
models do not take into account the stiffness and temperature distributions of the
spar webs and upper skin structure. It is clear that for accurate thermal stress analysis
of a large repair to a wing structure the FE method is the most suitable.
11.4.2. Edge restraint factor
If a suitable edge restraint factor, k, can be found, see Figure 11.1, then it may be
possible to more accurately predict stresses in the wing using 2D closed form
solutions. Returning to Eq. (1 1.13) if the boundary condition u = 0 at r = Ro is
changed to u = ii then Eq. (11.13) can be written as:
This represents the initial stress as a result of displacement of the outer edge of the
plate which has stiffness k.
Chapter 11. Thermal stress analysis
347
4
A
LFig. 11.22. Spanwise stresses, shown in the plate only, corresponding to a cooling thermal loading. The
repair lay-up is [02,+45,03],. Note the compressive stresses on the top edge of the wingbox.
r.ss+ml
3.i&cm
,31+
I
72,
11
.%
1 Y+
.lot
24+
52+
Fig. 11.23. Spanwise stresses in boron patch and stresses in plate surrounding the repair. corresponding
to a cooling thermal loading for a repair with a lay-up of [02,+45,03],.
Table 11.9
Stresses predicted in wing box corresponding to a geometric symmetric repair; layup [02, f45,O& boron repair AT = 75°C.
Centre of plate under repair (MPa)
Thermal
loading
Heating
Cooling
Residual
Centre of patch (MPa)
Plate just in/outboard of patch (MPa)
b
4
F.E.
1D
2D (iso.)
- 11.6
-
- 68.6
111.0
42.4
67.3
55.7
-
46.5
2D (orth.)
F.E.
ID
0
- 113.0 - 113.0 -94.2
2D (iso.)
0
-64.3
-64.3
2D (orth.)
-63.3
-63.3
F.E.
2D (isot.)
- 11.6
- 68.6
9.2
- 2.4
- 11.0
57.6
$
2
g.
E
B
E
9
b
-.E
F
9
Table 11.10
Stresses predicted in wing box corresponding to a geometric symmetric repair;
Thermal
loading
Heating
Cooling
Residual
3
2
Q
[014]
Centre of plate under repair (MPa)
Centre of patch (MPa)
F.E.
ID
2D (iso.)
F.E.
- 11.6
-
- 68.6
95.0
26 .4
58.4*
46.8*
52.8
2D (orth.)
1D
2D (iso.)
-107.0
0
-91.9
-91.9
0
- 131.0
-131.0
3
boron repair. AT = 75 "C.
2D (orth.)
-
E
?.
Plate just inloutboard of patch (MPa)
3
F.E.
2D (isot.)
9
- 11.6
- 68.6
50.7
- 17.9
13.6
1.8
E
r.
E
m'
Chapter 1 1. Thermal stress analysis
349
Table 11.11
Stresses predicted in wing box correspondingto a geometric symmetric repair; layup
[Oz. f45,03], boron repair. AT = 75 "C,k = 4.42 x IO6 N/mm.
~~~~~~~~
Plate under repair (MPa)
Patch (MPa)
Thermal loading
F.E. (centre/edge)
2D (iso)
F.E. (centre/edge)
2D(iso)
Heating
- 11.6/-13.2
54.?/67.8
43.1p 4 . 6
- 9.7
- 113.0,'- 139.7
- 113.0/-139.7
- 154.0
- 154.0
Cooling
Residual
65.8
56.1
Also Eq. (1 1.20) becomes:
(11.64)
at r = Ro the stresses due to cooling at the boundary are given by Eq. (11.16):
(11.65)
The constants of integration C, and C3 are now found from the solution of
Eqs. (11.18, 11.19, 11.63). If the edge restraint factor is denoted by k then the
displacement U is given by:
U =~ITRo~~cJR/~.
(11.66)
Furthermore if Ro is chosen to be approximately 2000mm on the basis of
temperature measurements, then it is possible to choose a value k which when
incorporated in the analysis will give better agreement, as shown in Table 1 1 . 1 1 .
However it is clear that these results still involve some error, and as a result F.E.
analysis is still recommended. Also as mentioned previously the F.E. method has
also shown some variation, see Table 1 1 . 1 1 , of stress under the patch and in the
patch where in both cases the closed form solution predicts uniform stress. In Table
1 1.11 the edge of the plate is defined by the following. Consider the axis system
shown in Figure 11.23 to be translated to the centre of the patch. The particular
edge considered is defined by x = 0, y = f200 mm.
11.5. Conclusions
In this chapter some proposed closed form solutions for direct residual stresses in
bonded repairs have been considered. 2D solutions considered are for direct
stresses in the plate beneath the repair, stresses in the repair and stresses in the plate
just outside the repair. These solutions are restricted to steady state heat
conduction, and are for both isotropic and orthotropic circular patches on circular
350
Advances in the bonded composite repair of metallic aircraft structure
plates. Validation of these solutions has been carried out using F.E. analysis. The
applicability of these equations is restricted to repairs which are bounded by
structural members such as spars or ribs.
Adhesive shear stresses have been evaluated in I D strip joints subject to a
uniform temperature. In this case results have been considered from the simple
differential equation, and also 2D and 3D F.E. models. It has been found that the
simple d.e. gives results which exceed 7.5% of the results given by 3D F.E.
A multi-spar wing box containing a very large repair in which bending is
restrained has also been considered. In this case the temperature field was based on
a simulation cure on a F-1 11 wing. The results have been obtained using a F.E.
model in which the repair site is similar to an F - I l l wing. Comparison with
predictions using 1D and 2D closed form solutions have shown that 1D solutions
give better agreement than 2D solutions. However when an appropriate edge
restraint factor is used then the 2D solution improves. Only small differences occur
between the 2D isotropic and orthotropic results, except that isotropic solution will
over-predict the stresses in the minor material symmetry axis.
While the effective coefficient of thermal expansion used for biaxial stress state
has given good agreement with the geometrically symmetric multi-spar wing repair,
the asymmetric repair results in lateral bending and an average effective coefficient
of expansion which exceeds the closed solution value. It is evident that more
analytical work is required in this area.
Acknowledgment
The author would like to thank Mr S. Sanderson for assistance with the F.E.
work carried out in this chapter.
References
1. Baker, A.A., Hawkes, G.A. and Lumley, E.J. (1978). Fibre composite reinforcement of cracked
structures - thermal - stress and thermal fatigue studies. ICCM2 Proceedings of the 1978 In?. Conf
on Composite Materials (B. Noton, R. Sigorelli, K. Street, eds.). April, Toronta, Canada.
2. Rose, L.R.F. (1982). A cracked plate repaired by bonded reinforcements. fnt. J. Fracture, 18,
pp. 135-144.
3. Baker, A.A. (1988). Crack patching: experimental studies, practical applications. Bonded Repair of
Aircraft Structures edited by (A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers,
Dordrecht, pp. 107-173.
4. Rose, L.R.F. (1988). Theoretical analysis of crack patching. Bonded Repair of Aircraft Structures
(A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, Dordrecht, pp. 77-106.
5. Callinan, R.J., Sanderson, S., Tran-Cong, T., e f al. (1997). Development and validation of a Finite
element based method to determine thermally induced stresses in bonded joint of dissimilar
materials, DSTO RR-0109, Aeronautical and Maritime Research Laboratory, Melbourne,
Australia.
-
Chapter 1 1. Thermal stress analysis
35 I
6. Callinan, R.J., Ton Tran-Cong, Sanderson, S., et al. (1998). Development of an Analytical
Expression and a Finite Element Procedure to Determine the Residual Stresses in Bonded Repairs.
Paper A98-31608 21st ICAS Congress, 13-18 Sept. Melbourne, Australia.
7. Wang, C.H.. Rose, L.R.F., Callinan, R.J., et al. (2000). Thermal stresses in a plate with circular
reinforcement. Int. J. Sol. and Structures, 37, pp. 45774599,
8. Wang, C.H. and Erjavec, D. (2000). Geometrically linear analysis of the thermal stresses in one sided
composite repairs. Journal of thermal stresses, 23, pp. 833-852.
9. Jones, R. and Callinan. R.J. (1981). Thermal considerations in the patching of metal sheets with
composite overlaps. J. of Structural Mechanics, 8.
10. Timoshenko, S.P. and Goodier, J.N. (1970). Theory of EIasticity, Third edition, McCraw-Hill.
1 I. Hart-Smith, L.J. (1973). Adhesive-Bonded Double-Lap Joints. NASA CR 112235, January.
12. Humphreys, E.A. and Rosen, B.W. Properties analysis of laminates. Composite Materiub and
Design, pp. 218-230.
13. Blakely. MSC/NASTRAN, basic dynamics analysis, user’s guide. The MacNeal-Schwendler
Corporation, Dec. 1993.
14. Hadcock, R.N. (1969). Table 24.3, Boron-Epoxy Aircraft Structures Handbook of Fibreglass and
Advanced Plastic Composites. Editor G.Lubin,Van Nostrand Reinhold Company.
15. Callinan, R.J., Sanderson, S. and Keeley, D. (1997). Finite element analysis of an F-1 I I Lower Wing
Skin Crack Repair. DSTO-TN-0067, January.
16. Mirabelia, L. and Callinan, R.J. Temperature Simulation of Boron/epoxy Patch Repair Site on a F1 I 1 Outer Lower Wing Skin. Draft report.
17. Rohsenow, W.M., Hartnett, J.P. and Cho, Y.1. (1998). Handbook of Heat Transfer, McGraw-Hill.
Appendix
The displacement at r = Rr is given by:
The integration constants are given by:
where
Advances in the bonded composite repair of metallic aircraft structure
352
and
(1+v) 2
Fi +F2
c, = 4 R1 2Ri + s(1 f v)(Ri
where
and
-
R!)
Chapter 12
FATIGUE CRACK GROWTH ANALYSIS OF
REPAIRED STRUCTURES
C.H. WANG
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, VIC 3207, Australia
12.1. Introduction
The primary function of composite repairs is to restore or improve the damage
tolerance of the repaired structure. To this end, it is essential to demonstrate by
analysis and/or test that the repair can meet the residual strength and damage
tolerance requirements. This means that the stress-intensity factor after repair has
been sufficiently reduced so that (i) the residual strength has been restored to an
acceptable level, and (ii) the growth rate of the crack under fatigue condition is
sufficiently slow to ensure an acceptable residual life, or inspection interval. In this
regard, theoretical and numerical analyses of repair efficiency are respectively
discussed in Chapters 7 and 9, while experimental investigations of the fatigue
crack growth are described in Chapter 13. The aim of this chapter is to present an
analytical method for predicting the growth rates of patched cracks, and hence the
residual life or inspection interval. Emphasis will be given to the modelling of the
crack closure behaviour of patched cracks under constant amplitude and variable
amplitude loading. Comparison with experimental results will be made whenever
possible to validate the proposed methodology.
Extensive experimental studies, see Chapter 13 of this book and References [l-31,
have demonstrated the effectiveness of bonded repairs as a cost-effective means of
repairing cracked structures, in terms of restoring the residual strength to the
design level and significantly reducing fatigue crack growth rate. However, it
remains a challenging task to predict the growth rate of patched cracks using the
crack growth data obtained from un-patched specimens, especially under spectrum
loading. For un-patched cracks, it is now possible to obtain satisfactory predictions
of the effects of stress ratio and variable amplitude loading on fatigue crack growth
rate using crack-closure models [4]. The aim of this chapter is to establish a
353
Baker, A.A.. Rose, L.R.F. and Jones, R. (eds.).
Advances in the Bonded Composite Repairs of Metallic Aircrafi Structure
Crown Copyright 02002 Published by Elsevier Science Ltd. All rights reserved.
354
Advances in the bonded composite repair of metallic aircraft structure
correspondence principle between patched cracks and un-patched cracks, with
particular emphasis on the crack-closure behaviour under steady-state (constant
amplitude loading) and transient conditions (spectrum loading). The effect of
thermal residual stress resulting from the mismatch between the coefficients of
thermal expansion for the composite patch and the parent metallic material will
also be considered.
A repaired crack can be viewed as being bridged by a series of distributed springs
sprang between the crack faces [5,6]. Under fatigue loading, these springs restrain
the opening of the crack, and thus reducing the stress-intensity factor. To analyse
the effect of this bridging mechanism on the residual plastic wake behind the crack
tip, the crack bridging theory [6] is employed together with a crack-closure model
[7] to analyse the steady-state closure of patched cracks subjected to constant
amplitude loading. The analytical consideration proves that under small-scale
yielding condition (the applied stress is far smaller than the material’s yield stress),
the steady-state crack closure level depends only on the applied stress ratio and is
almost identical to that corresponding to un-repaired cracks subjected to the same
applied stress ratio. This finding has been verified by a finite element analysis.
Furthermore, the transient crack closure behaviour following an overload, which is
the main mechanism responsible for crack growth retardation, has also been
investigated by the finite element method. The results reveal that patched cracks
exhibit the same transient decrease/increase in the crack-closure stress as unpatched cracks. Based on these findings, a correspondence principle relating the
transient crack-closure behaviour of patched cracks to that of un-patched cracks is
proposed. It is finally shown that predictions based on this method are in good
agreement with the experimental results obtained using two aircraft loading
spectra.
12.2. Crack-closure analysis of repaired cracks
12.2.1. Small-scale yielding
A schematic of a patch repair is shown in Figure 12.1, where it is assumed for
simplicity that the cracked plate is restrained from out-of-plane deflection. The
problem to be considered is a cracked plate repaired by a patch adhesively bonded
on one side of the cracked plate. The plate, which has a thickness of t p , contains a
through crack of length 2a. The thickness of the patch and the adhesive layer are
respectively t~ and t A . The front view in the xy plane and the cross-section in the yz
plane are depicted in Figure 12.l(a) and (b). The Young’s modulus and the
Poisson’s ratio of each individual layer are denoted as E and v; here and in the
following subscripts P , R, and A will be used to distinguish properties pertaining
respectively to the plate, the reinforcement and the adhesive layer.
As discussed in Chapter 7, the elastic problem has been analysed using a crack
bridging model [5,6], and an integral equation method [8,9]. For isotropic
reinforcement having the same Poisson’s ratio as the cracked plate, the stress-
Chapter 12. Fatigue crack growth analysis of repaired structures
355
IS-
‘ T T T T T T T T
Fig. 12.1. Repair configuration: (a) plan view, (b) cross-section along centre line.
intensity factor range can be expressed as [9], assuming that the adhesive remains
elastic,
AK = Aao&F(nka, S )
,
(12.1)
where the parameter Aao denotes the stress range which would prevail at the
prospective location of the crack for a patched but un-cracked plate, which can be
related to the remotely applied stress AoW [lo],
AGO= 4Agw
,
(12.2)
where the factor 4 depends on several non-dimensional parameters for an elliptical
reinforcement having the same Poisson’s ratio as the plate; see Chapter 7 for
details. The parameters k and S denote respectively the spring stiffness and stiffness
ratio.
k=
PS
(1 - v 2 ) ( 1 + S )
(12.3)
’
+
and S = E R t R / E p t p . The
where P = [ G A / t A (( 1 - v $ ) / E p t p ( 1 - V i ) / E R t R ) ]
function F can be well approximated (within an error less than 0.5%) by
(12.4)
where the parameter B(S) has been obtained by curve fitting the numerical solution
of integral equation [8,9] representing patch repairs, e.g. B = 0.3 for balanced
repairs ( S = 1) and B = 0.1 for thick patch ( S + 00).
356
Advances m the bonded composite repair of metallic aircraft structure
In the long crack limit (zku b l), the stress intensity factor of patched cracks (see
Eq. 12.4) asymptotes to the following upper limit, in the absence of disbonding and
plastic deformation in the adhesive layer,
(
7
t
hB
1)
(12.5)
This near constant stress-intensity factor suggests that under constant amplitude
loading, a patched crack would grow at an approximately constant rate, indicating
a steady-state condition. In this case, it is not unreasonable to postulate that
patched cracks ought to experience the same crack-closure as un-patched cracks
subjected to the same stress ratio (as the amplitude of the stress-intensity factor
does affect crack closure, provided small-scale yielding prevails at the crack tip). In
this case the plastic zone size and the crack-tip opening displacement are given by
the following well-known relationship,
(12.6)
(12.7)
where GOK and CTODK denote the plastic zone size and the crack-tip opening
displacement estimated based on stress-intensity factor K.
The fatigue crack growth rate can be correlated using the effective stress intensity
factor,
AK,a=-(lAK
I-R
-“>
,
(12.8)
Cmax
where R denotes the applied stress ratio (= O,in/Omax), which is strongly influenced
by the thermal residual stresses [11,121 present in the plate induced by curing;
further in discussion will be presented later in Section 4 . The crack-opening stress
oOp
can be obtained by simplifying the expressions constructed by Newman [13],
+ A2R2 + A3R3
R<0
R >0 ’
(12.9)
where the constants Ao, A2, A3 are
A0 0.825 - 0.3401+ 0.05a2 ,
A2=2-3&,
A3 = 2Ao - 1
(12.10)
The pIastic constraint factor a depends parametrically on only one non-
Chapter 12. Fatigue crack growth analysis of repaired structures
351
dimensional parameter: the ratio of plastic zone size to plate thickness [14],
a=
+
+
1 O.64([ o K / ~ P ]1/2 ~ [ w K / ~ P ] ~ )
1 - 2v o.54([wK/tp]1/2 2[WK/tp]2)’
+
(12.11)
+
which is illustrated in Figure 12.2 together with the finite element results obtained
by Newman, et al. [15].
12.2.2. Large-scale yielding solution for a stationary crack
The above method is valid in the limiting case of small-scale yielding, i.e., the
applied stress is far smaller than the material’s yield stress, the plastic zone size is
far smaller than the crack size and the plate thickness. In practice, however, such
conditions are not always met, especially when repairs are applied to fatigue cracks
in highly stress regions. To evaluate the range of the validity of the method
presented in the previous section, the influences of large-scale yielding on the cracktip plastic deformation and plasticity-induced crack closure will now be addressed.
To this end, a model for patched cracks will be presented, which extends the
complex function method of Budiansky and Hutchinson [7] to include crack
bridging effect.
For simplicity, let us consider the long crack limit, i.e. nka 2 1, so that the stressintensity factor under maximum load can be considered as approximately constant.
Since the crack-tip opening displacement (CTOD) is proportional to the square of
the stress-intensity factor, the residual plastic stretch attached to the crack faces
would be approximately constant in thickness. A simple schematic of the deformed
2.5
t;
2.0
1.5
Symbols: data from Newman et a2 1995
1.o
0.01
0.1
1
10
Normalisedplastic zone size w/$
Fig. 12.2. Constraint factor versus normalised plastic zone size.
Advances in the bonded composite repair of metallic aireraft strueture
358
X
(a)
0
-a
-C
a
C
u=um
-c
-d
-a
-h
0
h
a
d
e
Fig. 12.3. Crack closure model for short cracks.
profile of a bridged crack at maximum stress is shown in Figure 12.3(a), while the
boundary conditions upon unloading to the minimum stress are shown in
Figure 12.3(b). Here the difference between a patched crack and an un-repaired
crack is that the crack faces of a patched crack are bridged by a series of distributed
springs. As will be seen later, this bridging mechanism will affect the plastic
deformation ahead of the crack tip.
Adopting the Dugdale model, plastic deformation ahead of the crack tip is
assumed to occur within the region a < 1x1 < c, where c = a u). Here u) denotes
the plastic zone size. The problem depicted in Figure 12.3(a) can be mathematically
+
Chapter 12. Fatigue crack growth analysis of repaired structures
359
expressed as [6]
(12.12)
where u denotes the crack face displacement, cy the material’s yield stress, and cx
the plastic constraint factor discussed in Section 12.2.1. The first term in the lefthand side of Eq. (12.12) represents the resistance of material to crack opening and
the send term represents the resistance of springs.
The above hyper-singular integral equation can be solved using a Galerkin
method: the unknown crack-face displacement u is expanded in terms of Chebyshev
polynomials [6]. The plastic zone size o is determined so that the stress just outside
the plastic zone x = c+ is non-singular, i.e.,
K = lim
.Y-C’
EPfi
~
4x1
2
(12.13)
which furnishes the necessary condition for determining the plastic zone for a given
applied stress. Solution of o can be determined by iteration: Eq. (12.12) is first
solved for a trial o,then check whether Eq. (12.13) is satisfied. If this is the case,
then convergence is achieved. The numerical results are presented in Figure 12.4. It
is evident that provided the prospective stress is less than 40% of the material’s yield
stress, the plastic zone size is approximately equal to the estimate by the stressintensity factor. At high stress levels, the prospective stress has a significant effect
on the plastic zone size. As shown in Figure 12.3(a), the ratio of the plastic zone size
for large-scale yielding to the values from K solution can be well approximated by
the following expression,
(12.14)
where the coefficient A is determined by a least square method, A = 0.4272. By
contrast, the crack-tip opening displacement remains the same as that estimated
based on the stress-intensity factor, for prospective stress up to 70% of the yield
stress. Furthermore, it is interesting to note that the normalised plastic stretch
variation ahead of the crack tip, as shown in Figure 12.4(b) seems to be reasonably
insensitive to the level of applied stress. Therefore the plastic stretch variation is
approximately given by a universal relation identical to that pertaining to unpatched cracks under small-scale yielding conditions. This is best illustrated by the
ratio of the crack opening displacement to the maximum opening at the crack tip,
CTODK
=g(x/w)
,
(12.15)
360
Advances in the bonded composite repair of metallic aircraft structure
0
0.1
0.2
0.3
0.4 0.5
0.6
0.7
0.8
Ratio of prospective stress to yield stress u&u
1.o
0.8
0.6
0.4
0.2
0
0
co)
0.25
0.50
0.75
1.oo
Normalised distance ahead of crack tip r/rp
Fig. 12.4. Inhence of applied stress on (a) plastic zone size and (b) crack-tip opening displacement.
where the function g is [7]
(12.16)
Chapter 12. Fatigue crack growth analysis of repaired structures
361
This important result provides a basis to extend existing crack closure model for
un-patched cracks to analyse patched cracks.
12.2.3. Plasticity induced crack closure under large-scale yielding solutions
Having now determined the crack-tip plastic deformation at the maximum
applied stress, it is now possible to characterise the plasticity-induced crack closure.
Denote the crack opening at the maximum stress at 6~ and the crack opening at
the minimum stress at 6,. Upon unloading to the minimum stress, referring to
crack surface contact is assumed to occur within the intervals A < 1x1 < a, where 1
denotes the as-yet-unknown size of the contact-free region. The upper and lower
crack surfaces are now attached with a layer of plastically stretched material of asyet-unknown size 61112. There is also a region ahead of the crack tip, of unknown
length d - a, that has gone into reverse plastic flow, leading to a total crack-tip
residual stretch equal to 6 ~Here
. d denotes the coordinate of reversed plastic zone.
Between x = d and x = c the plastic stretch is equal to the plastic stretch that
existed at the maximum stress that remains unchanged. The boundary-value
problem depicted in Figure 12.2(b) can be analysed using the complex function
method [7,16,17]. In particular, the boundary conditions can be expressed as,
k
(12.17)
For low prospective stress, we have, noting 6~ 5 CTOD and Eq. (12.5),
(12.18)
therefore the term k E 6 ~ / 2 o can
~ be neglected without appreciable loss of
accuracy. In this case the boundary conditions for the minimum stress can be
reduced to those corresponding to un-bridged cracks. The resulting equations can
be solved in a manner similar to that employed by Wang and Rose [17].
Consequently the known solutions for un-repaired cracks, as described in Section
12.2.1, can be extended without modifications to bridged cracks.
12.3. Overload effect and validation using finite element method
To verify the above analytical solutions, a finite element analysis was performed.
The finite element model will also be employed to investigate the transient crackclosure behaviour of patched and un-patched cracks subjected to variable
362
Advances in the bonded composite repair of metallic aircraft structure
(a)
(b)
(c)
Fig. 12.5. Spring elements (a) attached to one node, constitutive relations for (b) bi-linear spring S1, and
(c) tension-only spring S2.
amplitude loading. The fatigue crack opening and closure stresses were obtained
using a spring element release method, which involves introducing two sets of bilinear spring elements along the crack plane, as illustrated in Figure 12.5(a). One set
of spring elements, which are attached to all the nodes, are used to simulate the
patch in restraining the opening of the crack as well as to maintain the zero
displacement condition under compression. This series of spring elements have a
force-displacement relationship to give the spring constant given by Eq. (12.3), and
an almost infinite compressive stiffness, as illustrated in Figure 12.5(b). For an
element of width h, The force-displacement of this bi-linear spring attached to a
corner node is
F = (k.h.E)u ,
(12.19)
where I; and u are the force and displacement pertaining to the spring element, and
E is the Young’s modulus of the parent plate material. In addition, a series of
tension-only spring elements are also attached to each node ahead of the crack tip
to maintain the zero displacement condition ahead of the crack tip under tension,
see Figure 12.5(c). Crack-growth was simulated by releasing, at the maximum load,
one tension-only spring-element every two cycles. The emphasis here is to
determine the stabilised crack-closure stress, assuming that the crack will take
many cycles to grow one element distance.
The finite element model was developed using a general-purpose finite element
code, ABAQUS. A quarter model of centre-crack panel is modelled using planestress quadrilateral elements; the size of the initial crack, ai,was 5 mm. The material
is assumed to have Young’s modulus of 72 GPa, a Poisson’s ratio of 0.3, and a yield
stress of 400 MPa, typifying an aluminium alloy. The half panel width was 101 mm.
For the patched crack, the spring elements are chosen to simulate a spring constant
of k = 120m-’, and the applied stress is repeated tension with a maximum value of
150 MPa. For the un-patched centre-crack, the applied stress is also repeated tension
but with a maximum value of 100MPa to ensure the patched crack and the unpatched crack are subjected to approximately the same stress intensity factor.
Shown in Figure 12.6 are the contours of the y-stress plotted on the deformed
geometry of the patched crack after the crack has grown 0.8mm under constant
Chapter 12. Fatigue crack growth analysis of repaired structures
363
in o f initial crack
Tip of initial crack
Crack tip
Crack tip
(b)
(a)
Fig. 12.6. Finite element solution of a patched crack growing under constant amplitude loading with
R = 0; (a) at the maximum stress showing the residual plastic stretch and (b) at minimum stress showing
crack surface closure.
amplitude loading. As it can been seen in the figure, the residual plastic stretch at the
crack tip caused the crack surface to close before the minimum stress is reached,
similar to that observed in un-repaired cracks. In fact, the crack-closure stresses
correspond to the patched crack and the unpatched crack agree well with each other,
and are in close correlation with the theoretical solution [7] of un-repaired cracks
subjected to the same stress ratio. Therefore, under constant amplitude loading, the
crack-closure stress of patched cracks can be determined from the known results of
un-repaired cracks. It is also noted that under steady-state condition, the crackclosure stress depends solely on the applied stress ratio, and is independent of the
level of the applied stress intensity factor. As discussed later, this is in sharp contrast
with the transient crack closure under variable amplitude loading.
The same finite element model has been used to further investigate the transient
crack closure behaviour of patched cracks subjected to variable amplitude loading,
with a view to identifying an equivalence between patched cracks and un-patched
cracks. A simple overload sequence as shown in Figure 12.7 is applied to both an
un-repaired crack and a patched crack. The maximum stress of the overload is
about 30% higher than that of the background constant loading (150MPa for
patched crack and 100 MPa for un-patched crack). The patched crack experienced
the same stress-intensity factor history as the un-repaired crack. Figure 12.8 shows
4
Stress
Fig. 12.7. A single overload superimposed on a constant amplitude loading sequence.
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Advances in the bonded composite repair of metallic aircraft structure
i
(a)
(b)
Fig. 12.8. Plastic wake induced by an overload for (a) an un-patched crack and (b) a patched crack
subjected to approximately the same stress-intensity factor history.
the plastic wake created by the overload for an un-patched crack and a patched
crack. It is evident that there is no discernible difference between the patched crack
and the un-patched crack. A fundamental difference between the crack closure
behaviour under steady-state condition (see Figure 12.6) and variable amplitude
loading is that the crack-closure stress is independent of the magnitude of the
residual plastic stretch under steady-state condition. By contrast, the transient
crack-closure behaviour after an overload is dictated by the residual stretch created
by the overload relative to that induced by prior constant amplitude loading. A
schematic of the residual plastic wake associated with a single overload is shown in
Figure 12.9. The ratios of the crack-closure stress (and crack-opening stress) to the
maximum stress are calculated from the finite element results and shown in Figure
12.10, for both the patched and the un-patched crack. The crack advance is
normalised by the distance between the plastic zone boundaries for the overload
and the constant amplitude loading. Two important observations can be made
from the results shown in Figure 12.10. First, following the overload, an initial
Plast
Wak
Fig. 12.9. Schematic of transient crack closure for a single overload.
Chapter 12. Fatigue crack growsth analysb of repaired structures
365
......... ..:................. .... ...... ...__._....__
.........._...
....
open symbbls: un-patched
filled sym$ols: patkhed
n
" l . . . . l.
-0.2
0
i
. . ,I . . , . l , . . . I . . . . I ,
0.4
0.6
Crack advance Aa/(r,-r,)
0.2
:
0.8
1.0
Fig. 12.10. Effect of overload on the crack-closure stress of patched and un-patched crack.
sharp drop occurred in the crack-closure and crack-opening stresses, for both the
patched and un-patched cracks. After the initial drop, the crack-closure stress
attained a higher value and it was only after considerable crack growth did the
crack-closure stress return to the same level as prior to the overload. The fact that
the higher (than steady-state value) crack-closure stress occurred over a crack
advance greater than that over which the lower crack-closure stress occurred is a
clear indication of net retardation in fatigue crack growth rates. Secondly, and
more importantly, there is little difference between the transient evolution of the
crack-closure stress for the patched crack and the un-patched crack. This implies
that the crack closure behaviour of patched crack can be well approximated by that
corresponding to an un-patched crack subjected to the same stress intensity factor.
Therefore, the crack-closure behaviour of a patched crack can be obtained by
analysing an un-patched, centre crack subjected to the same stress-intensity factor
history as the patched crack, or the equivalent crack method [IS]. In this regard, it
is worth noting that the under-prediction of the fatigue crack growth rates of
patched crack as reported in [ 181 is due to ignorance of the thermal residual stress in
the earlier analysis, an issue to be discussed in more detail in the next section.
12.4. Thermal residual stresses and comparison with experimental results
12.4.1. Thermal residual stresses
Since composite patches generally have a lower thermal expansion coefficient
than the metallic component to be repaired, thermal residual stresses would occur
upon cooling the fully cured repair from elevated temperature (typically around
80-120 "C for structural adhesives) to either the ambient temperature or the
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Advances in the bonded composite repair of metallic aircraft structure
operating temperature. In particular, the residual stress in the metallic plate is
generally positive, which may enhance fatigue crack growth rate due to increased
stress ratio. Other complicating factors affecting fatigue crack propagation include
possible changes in the patching efficiency resulting from adhesive plastic yielding
(referring to Chapter 7 for more details) and debonding (referring to Chapter 13 for
more details). In the following, we will focus our attention on the influence of
thermal residual stress only.
For an orthotropic composite patch bonded to an isotropic plate, the resulting
thermal residual stresses can be determined using the method developed in [l 13. For
a patched specimen being cured in a uniform temperature field (e.g. an oven), an
approximate solution of the thermal stress in the plate can be derived by treating
the patch as isotropic [l 11,
(12.20)
where a,E, v denote the coefficient of thermal expansion, Young's modulus and
Poisson's ratio. As before, the subscript R is used to distinguish parameters
pertaining to the patch. The temperature change is given by AT. For a typical
balanced repair with S = 1 and v = vR = 0.3, the above equation yields a thermal
stress about 12.6% higher than that estimated based on 1D idealisation [l].
In practical applications to actual aircraft structures, bonding a composite patch
requires a localised heating of the repair area followed by cooling to the ambient
temperature (or the operating temperature). In this case the constraint imparted by
the surrounding structure induces additional thermal residual stresses. Upon
heating of a circular region in an infinite plate from the room temperature T, to the
curing temperature T,, the following compressive thermal residual stress C T
develops in the structure when the adhesive is being cured [l 13,
0;
1
2
= - - aE( T,- T,)
(12.2 1)
Cooling of the patched structure to the operating temperature To,which may be the
same as the room temperature, results in a tensile thermal residual stress,:a
(12.22)
Consequently the total thermal residual stress
above two stresses,
in the plate is the sum of the
which is generally a tensile stress for Boron patches with a coefficient of thermal
expansion being far smaller than that of the metallic material O I R< a.
~
Chapter 12. Fatigue crack growth anaIysis of repaired structures
367
For a constant amplitude loading, the presence of the residual thermal stress
implies that the patched crack experiences a stress intensity factor Rtip different
from the applied stress ratio,
(12.24)
where R denotes the ratio of the applied stress R = tsZn/ozax.Since 00'2 0, the
actual stress intensity factor ratio is higher than the applied stress ratio. This
difference needs to be considered when comparing the fatigue crack growth rates of
patched and un-patched cracks. In this regard, a rational approach would be to
adopt the effective stress intensity factor as the correlating parameter for fatigue
crack growth. Take the example of aluminium alloy 2024-T3, the fatigue crackgrowth rates obtained using an un-patched, edge cracked panel are plotted in
Figure 12.1l(a) against the applied stress-intensity factor range. It is evident that
the stress ratio has a considerable effect on the crack-growth rates for a given
applied stress-intensity factor range. By re-plotting the crack growth rates against
the effective stress-intensity factor range determined using Eq. (12.8), as shown in
Figure 12.1l(b), the crack-growth rate data corresponding to three different stress
ratios fall within a narrow band (kloo%), consistent with the crack growth rates
independently obtained for the same material [19]. The plastic constraint factor a
employed in the analysis is equal to 1.8. The following expression provides the best
fit to all the experimental data,
(12.25)
where C = 2.234 x
and m = 3.135, in SI unit.
12.4.2. Experimental results under spectrum loading
In light of the above success in correlating the crack-growth rates of the unpatched cracks, the experimental results of patched cracks reported in [12] are reanalysed, taking into account of the residual thermal stress. The results are shown
in Figure 12.12. It can be seen that the experimental results of patched cracks also
fall within the same band as the un-patched cracks. Here the stress-intensity factors
for the patched cracks are calculated using Eq. (12.1), assuming that the adhesive
remains elastic. With the actual stress ratio being determined from Eq. (12.24), the
crack-opening stress is evaluated by Eq. (12.9), and the effective stress-intensity
factor range is calculated via Eq. (12.8). The good correlation between the patched
and un-patched cracks as observed in Figure 12.12 confirms that growth rates of
patched cracks and un-patched cracks are uniquely characterised by the effective
stress-intensity factor range. Therefore, the growth behaviour of patched cracks
and un-patched cracks, under constant amplitude loading, can be successfully
rationalised by the concept of fatigue crack closure. This enables the crack growth
rates of patched cracks to be predicted using the growth rates of un-patched cracks.
Advances in the bonded composite repair of metallic aircraft structure
368
un-patched data
h
aJ
5
lo"
-2
v
lo4
5
6
7
8 910
14
20
30
Stress-intensity factor range AK (MPadm)
1o - ~
aJ
*
E
1o-8
Effective stress-intensity factor AK& (MPadm)
tb)
Fig. 12.11. Fatigue crack growth rates in 2024-T3 aluminium alloy (un-repaired) plotted against (a) the
applied stress-intensity factor range AK and (b) the effective stress-intensity factor range AI&.
Under variable amplitude or spectrum loading, it is important to analyse the
transient crack closure, especially the retardationeffects associated with overloads.
As already discussed in the previous section, after the application of an overload, a
patched crack experiences nearly the same transient crack closure behaviour as un-
Chapter 12. Fatigue crack growth analysis of repaired structures
t
3
-‘
1
I
4
369
5
6
7
8
15
9 1 0
Effective stress-intensity factor AKm(MPadm)
Fig. 12.12. Growth rates of patched and unpatched cracks under constant amplitude loading with
various stress ratios.
patched crack subjected to the same stress intensity factor. Therefore the crack
closure of patched cracks can be determined by analysing the crack closure of a
centre-cracked panel subjected to a reference stress, as illustrated in Figure 12.13.
The reference that the centre-cracked panel is subjected to is determined to ensure
c7 -(t)
’TTTTtTTT
plate
t
Y
Plastic wake
Fig. 12.13. Correspondence between a patched crack and an un-patched crack subject to an equivalent
stress.
370
Advances in the bonded composite repair of metallic aircraft structure
that the stress intensity factor is the same as the patched crack, viz,
+
a * ( t ) f i = [40CC)(t)c$]fiF(nku,
S)
,
(12.26)
which leads to
+
u*(t) = [ Q S P ( t ) 4 ] F ( . k a , S )
(12.27)
Since the factor F decreases as the crack size increases, the equivalent stress a*(t)
would become a progressively smaller fraction of the applied stress, to ensure that
the cyclic plastic deformation at the tip of the equivalent crack remain the same as
that for the patched crack.
A comparison with some experimental results [20] is shown in Figure 12.14. The
test specimens, which were made of 2024-TS51 aluminium alloy panels having a
thickness of 3.7mm, were repaired with a boron composite patch after being precracked to give a half crack size equal to 20mm. Patches were made from Boron/
Epoxy pre-preg fibre composites to form a 14-ply laminate; the lay-up is [Os, &45],.
The patched specimens were subjected to a load spectrum (to be denoted as F-1 11)
consisting of 36273 turning points per block, with the ratio of the minimum to the
maximum equal to -0.278. The maximum applied stress, as listed in Table 12.1,
was equal to 217MPa, giving rise to a maximum plate stress (in a block) about
112 MPa. The geometry and material properties of the patched specimen (denoted
as F111) are summaries in Tables 12.1 and 12.2. The patches were bonded to the
plate using a FM-73 adhesive and cured at 80°C, resulting in a thermal residual
stress of 67.35 MPa. The base-line fatigue crack-growth data for the material were
taken from the literature [21], which were then converted to obtain the crackgrowth rate against effective stress-intensity factor range relationship. This allows
Fig. 12.14. Comparison between experimental and predicted growth behaviour of patched cracks under
F-111 spectrum. Symbols denote experimental data.
Chapter 12. Fatigue crack growth analysis of repaired structures
37 1
Table 12.1
Geometry and material properties of specimens.
Specimen
EpGPa Tpmm
F-111
FALSTAFF
72
72
3.7
3.14
E R G P ~t R m m
GA GPa t ~ m m 4
156
200
0.57
0.54
1.82
0.91
0.25
0.2
k l/m
0.52 58.0
0.55 65.5
u&
MPa
217
248
Table 12.2
Thermal properties and temperature change.
Specimen
z (plate)
aR (patch)
AT ( “C)
ul (MPa)
F-111
FALSTAFF
2.40E-05
2.40E-05
4.00E-06
4.00E-06
60
100
67.35
70.67
the experimental results from various stress-ratio tests to be collapsed within a
single scatter band. The converted data can be well correlated using the standard
Paris relationship, giving rise to the following constants C = 7.4 x
and
pyt = 2.93. As seen in Figure 12.14, the predictions based on the equivalent crack
method are in good agreement with the experimental results. It is also interesting to
note that, due to the increased mean stress resulting from the thermal residual
stress, simple predictions based on simply integrating the crack growth equation on
a cycle-by-cycle basis, using the steady-state crack opening stress given by
Eq. (12.9), are slightly conservative. This implies that the retardation effect of the
loading spectrum is also not very significant due to the high mean stress. Also
shown in Figure 12.14 are the predictions based on the crack closure model,
without considering the thermal residual stress. It is evident that the calculated
crack growth rate is far lower than the experimental results, demonstrating the
importance of the thermal residual stress in enhancing the fatigue crack-growth
rates. This also highlights the need to minimise the thermal residual stress.
The experimental results of another series of tests involving FALSTAFF
spectrum [3] are plotted in Figure 12.15, together with predictions made using
equivalent crack method. The test specimens, which were made from 3.2 mm thick
2024-T3 aluminium sheets, were first fatigue pre-cracked under constant amplitude
loading to two prescribed crack lengths: 5 mm and 25 mm. The test panels were
then repaired with boron/epoxy using three different adhesive systems. Two edgecracked face-sheets were bonded to an aluminium honeycomb core to form a
sandwich panel to avoid out-of-plane bending. A total of six such panels were
tested. The thermal residual stress, as listed in Table 12.2, was estimated based on
Eq. (12.20) to be approximately 70.67 MPa. This thermal residual stress is
significant as the maximum plate stress q50mis about 136 MPa. The spectrum used
was a “clipped” FALSTAFF spectrum, in which the negative loading has been
removed. As seen in the figure, the predictions based on the crack closure model,
when thermal residual stress is taken into account, are in good correlation with the
experimental data. As indicated by the dashed lines in Figure 12.15, predictions
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Advances in the bonded composite repair of metallic aircrafi structure
75
65
25
15
5
0
50
100
150
200
250
Number of FALSTAFF (clipped) Blocks
Fig. 12.15. Comparison between experimental and predicted growth behaviour of patched cracks under
FALSTAFF spectrum.
made by integrating the crack growth rate equation, with the crack-opening stress
for each reversal being taken to be the steady-state value, are slightly on the
conservative side. Similar to the results shown in Figure 12.14, this behaviour
indicates that, due to the high thermal residual stress, the spectrum loading does
not have a strong retardation effect. Also plotted in Figure 12.15 are the
predictions made by neglecting the thermal residual stress. Again, much slower
crack-growth rates are predicted. This confirms the observations made earlier
regarding the importance of the thermal residual stresses and the need to minimise
residual stresses in order to achieve lower crack-growth rates. It should be noted
that the effects of disbond and adhesive plasticity have not been considered in this
chapter. Further work is required to account for the interaction between of fatigue
crack growth and disbond.
12.5. Conclusions
It has been shown that under constant amplitude loading with the prospective
stress much lower than the material yield stress, the closure behaviour of repaired
cracks is nearly identical to that corresponding to un-patched cracks subjected to
steady-state loading. Under variable amplitude loading, the crack closure
behaviour of a patched crack has also been shown to be identical to that
corresponding to an un-patched crack subjected to the same stress-intensity factor
history.
Chapter 12. Fatigue crack growth analysis of repaired structures
373
An equivalent crack method has been developed, which enables the fatigue crack
closure of patched cracks to be determined by analysing a centre-cracked panel
subjected to an equivalent stress given by
+ o;]F(nku,S)
o * ( t ) = [+o"0(t)
(12.28)
Predictions based on this method have been found to correlate well the
experimental results obtained under two aircraft loading spectra. It has also been
found that the ignorance of the thermal residual stress would lead to significant
under-predication of the crack growth rate.
References
I . Baker, A.A. (1988). Crack patching: experimental studies, practical Applications, Chapter 6. in
Bonded Repair of Aircruji Structures, (A.A Baker and R. Jones, eds.), Martinus Nijhoff, pp. 107173.
2. Baker, A.A. (I 993). Repair efficiency in fatigue-cracked panels reinforced with boron/epoxy patches.
Fatigue and Fracture of Engineering Materials and Structures, 16, pp. 753-765.
3. Raizenne, M.D., Heath, J.B.R. and Benak, T. (1988). TTCP PTP-4 Collaborative test program variable amplitude loading of thin metallic materials repaired with composite patches, Laboratory
Technical Report, LTR-ST-I 662, National Aeronautical Establishment, Ottawa, Canada.
4. Newman, J.C. Jr. (1992). FASTRANII - A fatigue crack growth structural analysis program,
NASA Technical Memorandum 104195, NASA Langley Research Centre.
5. Rose, L.R.F. (1988). Crack reinforcement by distributed springs. Journal of Mechanics and Physics
of Solids, 35, pp. 383-405.
6. Wang, C.H. and Rose, L.R.F. (1999). A crack bridging model for bonded plates subjected to tension
and bending. Int. J. of Solids and Structures, 36, pp. 1985-2014.
7. Budiansky, B. and Hutchinson, J.W. (1978). Analysis of closure in fatigue crack growth. J. o f
Applied mechanics, 45, pp. 261-215.
8. Keer, L.M., Lin, C.T. and Mura, T. (1976). Fracture analysis of adhesively bonded sheets. J. of
Applied Mechanics, 98(4), pp. 652-656.
9. Wang, C.H. and Rose, L.F.R. (1998). Bonded repair of cracks under mixed mode loading, Int.
Solids and Structures, 35(21), pp. 2749-2773.
10. Rose, L.R.F. (1981). An application of the inclusion analogy for bonded reinforcements. Int. J.
Solids Structures, 17, pp. 827-838.
11. Wang, C.H., Rose, L.R.F., Callinan, R.,et al. (1999). Thermal stresses in a plate with a circular
reinforcement. Int. J. of Solids and Structures, 37, pp. 4577-4599.
12. Baker, A.A. (1996). Fatigue studies related to certification of composite crack patching for primary
metallic structure. Proc. of the FAAINASA Symposium on Continued Airworthiness of Aircraft
Structures, Atlanta, USA, pp. 313-330.
13. Newman, J.C., Jr. (1984). A crack-opening stress equation for fatigue crack growth. Int. J. of
Fracture, 24, pp. R131-Rl35.
14. Guo, W., Wang, C.H. and Rose, L.R.F. (1998). On the influence of cross sectional thickness on
fatigue crack growth. Fatigue and Fracture of Engineering Materials and Technology, 22, pp. 437444.
15. Newman, J.C. Jr., Crews, J.H. Jr., Biglew, C.A., et al. (1995). Variations of a global constraint factor
in cracked bodies under tension and bending loading, Constraint Effects in Fracture Theory and
Applications: Second Volume, ASTM STP 1244, M. Kirk and A. Bakker, eds., American Society for
Testing and Materials, Philadelphia.
374
Advances in the bonded composite repair of metallic aircraft structure
16. Tanaka, K. and Nakai, Y. (1983). Mechanics of growth threshold of small fatigue cracks, Fatigue
Crack Growth Threshold Concepts, (D.L. Davidson and S. Suresh, eds.). The Metallurgical Society of
AIME, pp. 497-516.
17. Wang, C.H. and Rose, L.R.F. (2001). Closure analysis of small fatigue cracks with a self-similar
plastic wake. J. of the Mechanics and Physics of Solids, 49, pp. 401-429.
18. Wang, C.H., Rose, L.R.F. and Baker, A.A. (1998). Modelling of the fatigue growth behaviour of
patched cracks. Int. J . of Fracture, 88, pp. L6SL70.
19. Edwards, P.R. and Newman, J.C. Jr. (1990). An AGARD supplemental test programme on the
behaviour of short cracks under constant amplitude and aircraft spectrum loading, AGARD Report
767.
20. Boykett, R.and Walker, K. (1996). F-ll1C lower wing skin bonded composite repair substantiation
testing, DSTO-TR-0480, Aeronautical and Maritime Research Laboratory, Melbourne, Australia.
21. DTDH (1972). Damage Tolerant Design Handbook, a compilation of fracture and crack-growth
data for high-strength alloys, Metals and Ceramics Information Centre, MCIC-HB-01.
Chapter 13
BORON/EPOXY PATCHING EFFICIENCY STUDIES
A.A. BAKER
Defence Science and Technology Organisation, Air Vehicles Division, Fishermans
Bend, Victoria 3207, Australia
13.1. Introduction
As discussed in Chapters 1 and 2, the fibre-composite boron/epoxy (b/ep) is well
suited for use as a patching or reinforcing material for metallic structures. Briefly
the attributes of b/ep include:
0 High Youngs modulus (three x aluminium for unidirectional b/ep) and static
and fatigue strength, which minimises the required patch thickness
0 Good formability, which allows formation of complex shapes
0 Low electrical conductivity, which facilitates use of eddy-current non destructive
inspection for monitoring the patched cracks and eliminates concerns with
galvanic corrosion.
However, b/ep is not suited for repairs of regions with small radius of curvature,
because of the large diameter of the boron fibres (125 micrometres compared to 8
micrometres for graphite). Graphite/epoxy (gr/ep) would be chosen for such
applications.
Because of its attributes, b/ep was chosen for most Australian [1,2] bonded
composite repair applications. The patches are generally bonded with an aerospacegrade structural epoxy-nitrile film adhesive, currently [email protected] FM 73 a 120°C
curing adhesive. This adhesive has the additional advantage that it can be cured at
temperatures as low as 80°C. However, FM 73 is limited to applications below
about 80 "Cso Cytec FM 300-2, a 120 "Ccuring adhesive is chosen for applications
at over 80°C to around 100°C. A modified acrylic, such as Flexon 241, is chosen
for applications below 50°C where curing temperatures even as low as 80°C are
not acceptable.
To develop a capability to predict patching efficiency of b/ep patched fatigue
cracks, studies were made to assess the effect of important variables on crack-
315
Baker, A.A., Rose, L.R.F. and Jones, R . (eds.).
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 0 2002 Published by Elsevier Science Ltd. All rights reserved.
376
Advances in the bonded composite repair of metallic aircraft structure
growth rate under constant amplitude fatigue. The variables studied included (a)
patch disbond size, (b) applied stress, (c) patch thickness, (d) stress ratio R (e) test
temperature and (f) panel thickness variation. The parameter used to assess crackgrowth behaviour is the stress intensity K . This study is based on estimations of K
using Rose’s [3] analysis for patched cracks.
13.2. Stress intensity analysis of patched cracks
One important aim in the analysis of patch repairs is to estimate the stress
intensity of the patched crack as a function of the various geometrical, physical and
stress parameters.
The parameters other than applied stress o, in determining K for a patched
crack are:
0 Metallic structure: thickness t,,, Youngs modulus E,,, shear modulus Gp and
thermal expansion coefficient E,,
0 Reinforcement: thickness t R , Youngs modulus ER, and thermal expansion
coefficient K R
0 Adhesive: thickness tA, shear modulus G A ,shear yield stress ,z
, under the service
conditions of temperature, humidity and loading rate.
0 Disbonds (if any) over the cracked region: length normal to the crack, 2b.
13.2.1. Model for estimating stress intensity
In the model developed by Rose [3] in the patched crack a two-step approach is
used to estimate stress intensity, as illustrated in Figure 13.1.
Briefly, in step 1, Figure 13.1, the patch is modelled as an inclusion in a large
panel and the presence of the crack (assumed to be relatively very small) is
neglected. The stress in the metallic component in the prospective region of the
crack is then given by +om, where I$ is a factor which accounts for the stiffness and
shape of the patch. Because the patch attracts load, the stress reduction may be
significantly less than predicted simply on the basis of ratio of patch stiffness to
plate stiffness. Calculation of is described in reference [l].
For full width reinforcement 4 is given by (1 ERrR/Epfp)-’.For the patch and
plate properties used here, assuming full width reinforcement 4 = 0.6, while for a
circular patch as used in these experiments 4 = 0.68, estimated from inclusion
theory.
In step 2, Figure 13.1 the crack is assumed to be semi-infinite and fully covered
by the patch. The stress in the panel containing the crack is bo,. The upper-bound
stress intensity Koc is then as given by:
+
+
( 13.1a)
where 6 is the “crack” opening displacement; 6 is estimated from the overlap joint
Chapter 13. Boronlepoxy patching efficiencystudies
26
+
+
Step 1 Inclusion effect
+ +
1
Step 2 Crack Reinforcement
Fig. 13.1. Schematic illustration of the analytical approach to crack patching. The dotted parallel lines
represent a disbond, width 26.
that would be obtained by cutting a strip through the panel normal to the crack.
Equation (13.la) is strictly correct only for linear behaviour (no yielding of the
adhesive) but provides a reasonable estimate of AKm provided yielding of the
adhesive is small.
The use of Km to assess the stress intensity in the cracked component allows
considerable simplification in crack-growth analysis, since as seen in Eq. (13.la) K x
is independent of crack length a.
The use of Km is justified in Figure 13.2, which plots K R the predicted stress
intensity (based on Rose’s model and the more recent Rose-Wang model [4])versus
a. The parameters used are those of the b/ep patched panels tested in these studies,
described in Section 13.3. This plot shows that K R becomes close to Ko0 for crack
lengths above 20 mm. Thus at least to a good first approximation, the assumption
that KR is equal to Ko0 for a above 20mm is reasonable for these specimens.
Experiments to measure KR for comparison with the predicted KR are described in
Chapter 18. The results of these experiments provide some confidence in the model
and in particular the use of Km as the key patch design parameter.
Under the cyclic stress range Aom the stress-intensity range AKm is given by:
(1 3.1b)
The displacement range A6 is dependent on the thicknesses and stiffnesses of the
patch and of the cracked component, and on the thickness, shear modulus and
effective shear yield stress of the adhesive. It is important to note that the adhesive
Advances in the bonded composite repair of metallic aircraft structure
378
-,
7.5
d
3.51.
0
'
'
"
'
'
"
"
10
20
.I.
'
'
.
"
"
40
30
'
'
'
"
'
'
50
"
60
Crack length a mm
Fig. 13.2. Plot of predicted variation of stress intensity of the patched crack KR versus crack length,
based on Rose's model and the more recent Rose-Wang model. K m is the upper bound estimate used in
these studies.
properties are highly temperature- and strain-dependent and strain-rate dependent
and also dependent on the amount of absorbed moisture. The displacement A8 is
also dependent on the residual stress, cT,resulting from the difference in thermal
expansion coefficient between the patch and parent structure, since this affects the
level of external stress at which the adhesive will yield. The estimation of 6 is as
described in reference [l]; for the elastic adhesive case it is given by the following
relationship:
(13.1~)
where
=
{ (?)(A
+
112
A)}
(13.1d)
'
p is the exponent of the elastic shear strain distribution
(/?-I
is called the
characteristic load transfer length).
13.2.2. Use of model to estimate crack growth
It is assumed for simplicity that, as for unpatched cracks, a Paris-type
relationship holds:
da
dN
-=f ( A K ,R ) = A R A K " ~,
(1 3.2)
where a is crack size, N is the number of constant amplitude cycles and AR and n R
are assumed to be constants for a given minimum to maximum stress ratio R.
Chapter 13. Boronlepoxy patching efficiency studies
379
If this assumption is reasonable (for practical purposes) a should be found
experimentally to be linearly related to N, at least to a reasonable first
approximation. This is found to be the case, as shown later.
Finally, the relationship between crack length a and the number of cycles N can
be obtained from:
N
(13.3)
0
As A K , is constant, it can be moved outside of the integration sign; however, A K ,
is not constant where disbonding occurs, as discussed in the next section.
13.2.3. Extension of the model for growth of disbond damage
Experimentally and practically it is found that local disbonds develop in the high
shear-stress regions around the crack in the parent structure. It is thus necessary to
modify the model to account for this behaviour.
It is assumed for a simple extension to the basic model [5] that a parallel disbond,
size 2b, traverses the specimen, as illustrated in Figure 13.1.
Then the opening of the gap is increased by 2be, where e is the estimated strain in
the reinforcement.
Equation (13.la) then becomes:
(13.4)
If it is assumed as a first approximation (based on early fatigue tests on doubleoverlap joints 161) that db/dN is a constant for given stressing conditions, then:
b = N($)
(13.5)
Thus, the effect of disbond growth on crack-growth behaviour can be estimated
approximately using Eq. (1 3.4). Because of the disbond growth AK, then no longer
remains constant but follows a square-root relationship as a function of b. Finally,
from Eqs (13.3) and (13.4) a non-linear relationship between a and N is predicted.
13.3. Experimental approach
Fatigue crack propagation tests were conducted on 2024 T3 specimens 3.14 mm
thick having starting cracks about 5 mm long repaired with unidirectional boron/
epoxy (Textron 5521/4) patches which (unless otherwise mentioned) were 7 plies
(0.9 mm) thick. In most studies a layer of FM 73 adhesive was first cocured onto the
boron/epoxy-bonding surface. This is current Australian practice since patches
380
Advances in the bonded composite repair of metallic aircraft structure
with the cocured layer of adhesive are much less prone to disbond damage during
fatigue and the adhesive provides a less sensitive surface for grit blasting. However,
in some specimens representative of our previous practice (in the disbond study) to
encourage the growth of disbonds, the cocured layer was not used.
The patches were then bonded with adhesive FM 73 at 120 "C,following surface
treatment of the metal using the silane process [ 1,7] and the boron/epoxy patches by
blasting with alumina grit, either directly onto boron/epoxy or onto the cocured
adhesive layer.
In the fatigue tests, two similar panels are simultaneously tested, joined together
as a honeycomb sandwich panel, as shown in Figure 13.3. There are two reasons
for using this configuration. The first is to minimise bending curvature following
patching due to the residual stress cTwhich, as mentioned earlier, arises from the
mismatch in thermal expansion coefficient between the patch material and
the metal panel. Thus, the patches were bonded to the panels at the same time
as the panels were bonded to the honeycomb core. The second reason is to
minimise the secondary bending of the panels, which would otherwise occur during
testing. The bending moments arise from the displacement of the neutral plane by
the patch. The resistance to bending resulting from the honeycomb core
(substantial but not perfect) is considered a reasonable simulation of the level of
support that would be provided by typical military aircraft structure. In almost all
tests, similar rates of crack growth were observed for the two panels in the
combination.
A L U Y
iQ24-n3.2 mm
7-PLYBoKti
IBRE PATCH
CORE lYmn
I
= 1.30
I
Fig. 13.3. Illustration of the test configuration used to evaluate patching efficiency in patched panels.
Note that two cracked-patched panels are tested simultaneously in this configuration. A 7 ply patch is
standard but 4 and 10 ply patches were also evaluated. The table provides properties assumed in the
calculations based on Cytec short-overlap shear data.
Chapter 13. Boronlepoxy parching efficiency siudies
38 1
Tests were conducted under constant amplitude stressing to a maximum of
240 MPa at a range of temperatures up to 100 "C and applied R values to 0.64.
However, a stress of 138 MPa and an applied R of 0.1 and ambient temperature
were the standard conditions. The length of the crack under the patch was
measured within about & 0.5 mm using standard eddy-current NDI.
After testing, the patches were heated to 190 "Cfor 2 h and stripped from the test
specimen (at the elevated temperature). This process discolours any disbonded
regions by oxidation, making them clearly visible.
13.4. Fatigue studies
13.4.1. Disbond damage in the patch system
In these studies [2] the aim was to evaluate the effect of disbonds on the rate of
crack growth. A series of specimens was made with artificial disbonds (using thin
PTFE sheet inserts) of length 26 ranging from lOmm to 60mm. Tests were
conducted at the standard conditions of 138 MPa and R=0.1. The crack-growth
results, Figure 13.4(a), show that, as expected, patching efficiency falls dramatically
with increasing disbond size.
Tests were also conducted on patched specimens having a single adhesive layer,
which are more prone to disbond growth. However, in all specimens, disbonds if
they occur propagate almost totally within the surface layer of the boron/epoxy,
which consists of a very light scrim of glass cloth, impregnated with the matrix
epoxy resin. The locus of failure is in the matrix resin between the scrim and the
boron fibre surface.
60
-
Zb (mm.)
. a
/
E
/o
E
Zb (mm.)
experimental
m o
40
30
-
10
A
Am
30
+ 40
10mm
0
0
50
I00
150
ZOO
Thousands of cycles N
(a)
250
300
0
50
100
150
200
250
300
Thousands of cycles N
(b)
Fig. 13.4. (a) Plot of crack length (a) versus cycles (N) for a patched specimen having artificial disbonds
of various lengths; solid lines are theoretical estimates, based on estimated A R and nR. (b) Plot of crack
length (a) versus cycles (N) for patched panels tested at a peak stress of 138MPa and nominal R=0.1.
382
Advances in the bonded composite repair of metallic aircraft structure
Figure 13.4(b) plots crack length a versus N at a peak stress of 138MPa and
R = 0.1 for three test panels. The observed final disbond shapes (2b) are shown inset
in the figure. As seen in Figure 13.4(b), the greater the final disbond size the greater
the crack-growth rate and the more strongly parabolic the curve of a versus N.
These observations are in qualitative agreement with predictions of the patching
model described in Section 13.2.3.
Figure 13.4(b) also shows, as solid curves labelled a to c, the predicted behaviour
based on the analysis in Section 13.4 assuming disbond growth rates, db/dN,
respectively of 0, 6 x lop5 and 20 x 10-5mm/cycle. To produce these curves an
Excel spreadsheet was developed to estimate da/dN and thus a versus N based on
Eqs (13.2-13.5); where A R and nR for Eq. (13.2) were determined from the
experiments on patched panels with artificial disbonds.
The approach used to find A R and nR was:
0 Estimate the theoretical value for the ratio R K ~
the relative rates of crack
propagation for disbonded and no disbond at the various disbond sizes 2b. This
is defined as:
(1 3.6)
Then find an experimental value for
nR
using the measured crack growth ratio
RKe:
(da/dN),
RKe =
0
[(da/dN),,=,l
flR
'
(13.7)
where the da/dN values are determined from the crack-growth rates for different
disbond rates in the specimen with the artificial disbonds. Assuming R K t = R K e ,
the value of nR was found to be around 3.
Finally, the experimental value for A R was obtained from:
(13.8)
Using this approach A R was thus found to be around 5 x lo-", which with nR of
around 3 is reasonable for 2024 T3 compared with unpatched results at similar AK
levels.
Estimates for the disbond growth rates, db/dN, for use in Eq. (13.5) were
obtained from the observed maximum disbond size observed in the tests divided by
N.
On the basis of the results provided here, the tentative conclusion reached is that
the model outlined in Section 13.2.3 can reasonably account for the influence of
disbond growth in the patch system on patching efficiency.
A major input to this model is the relationship between db/dN and cyclic stress or
strain level. This relationship can be obtained empirically from tests on equivalent
double-overlap joint specimens representing the repair configuration, Chapter 5.
383
Chapter 13. Boronlepoxy patching efficiency studies
However, to estimate db/dN generically from repair design data, stress patch
geometry etc. a suitable damage criterion for the adhesive is required. In the
preliminary tests on representative joints [ 11, the effective shear-strain range in the
adhesive (AyA)was used as the damage criterion. An alternative criteria based on
strain energy release rate is discussed in Chapter 5.
13.4.2. Influence of stress range
Figure 13.5(a) plots the results for a versus N for a 7 ply specimen for R = 0.1 at
IT,,,levels ranging from 80 to 244MPa. The highest stress level corresponds to
typical design limit load capability (DLL) for this alloy. This stress level is
nominally experienced only once in the life of an aircraft.
The plots in Figure 13.5 at the low stress levels are quite linear, suggesting that
the experimental value of KR is effectively constant. The increase in K R with a at
small crack lengths as expected from the predictions plotted in Figure 13.2 may be
too small to show up in these experiments.
The change from an approximately linear relationship to a more parabolic
relationship occurs above nmax= 138 MPa and results from the development of
disbond damage in the bond layer, indicated as a 2b value in the figure. For the
standard 138MPa stress level, damage in the adhesive system is negligible so, as
expected, patching efficiency is comparable to the best of the previous series,
Figure 13.4.
A linear least-squares fit was used to obtain da/dN for all the stress levels, despite
the disbond damage found at the two highest stresses. The high stress values at
-580
0 ‘0
-600
-
-620
.
540
$
-660
-
480
-
I
5
T1
E?
A
-7w
.
-720
-
-?40
-
-760
-
-7.80
i
0.90
110
130
150
244 MPa
1 70
1
200 MPa
180 MPa
140 MPa
’
-,-8QMPa
12OMPa
lop d M N = aq
*-
10 1
J
Fig. 13.5. (a) Plots of crack length a versus cycles N for a standard 7-ply patched specimen for applied
R = 0 . 1 . (b) Plot of log da/dN versus log AK, for the results in (a).
384
Advances in the bonded composite repair of metallic aircraft structure
log M YPa main
1.OEd6
5.80
-
9.OE-07
4.00
-
8.OE-07
-6.20.
7DE-07
Y
5
-
3
-6.60-
$
-6.80-
4.OE-07
:
-
-..
v
2
-6.40
10 Ply
e
5.OE-07
6.OE-07
0
-
-
-7.00
0
3.OE-03
-7.20
-
2.OE-Oi
4 ply
dddN = 3.6bg aK-10.6
l.OE-0i
RR =0.27 to 0.47
-7.60
0 OE+M
-
I
---
Fig. 13.6. Plots (a) of da/dN versus A o and (b) log da/dN versus log AK,,,for test panels having 4-, 7- or
IO-ply patches. R is 0.1. RR is as indicated on (b) and t R is about 0.5mm.
small crack lengths are included since they fit well with the other results; however, if
only the large crack da/dN values at these high stresses are considered, these lie well
to the left of the curve, as expected for damage. Using these results, Figure 13.5(b)
plots log da/dN versus log AKm for these test specimens. The relationship thus
obtained is da/dN = 7.9 x lo-" AKL m/cycle, which is reasonably close to the
results for the damage series mentioned in the previous section.
13.4.3. Influence of patch thickness
Figure 13.6 plots log da/dN versus log A K , for test panels with 4-, 7- or IO-ply
thick patches, at an R value of 0.1. The results for the 7-ply panel are as plotted in
Figure 13.5(b); the results for the 4- and 10-ply panels were obtained from single
test panels stressed at several levels.
It can be seen from Figure 13.6 that the model using the da/dN relationship for
the 7-ply panel would have given quite reasonable predictions for the 4- and IO-ply
panels. However, the values obtained are 4 ply: n R = 3.6, A R= 2.3 x lo-"; 7 ply:
n R 3, AR = 7.7 X lo-"; 10 ply: nR = 3.12, A R = 5 X lo-".
13.4.4. Influence of R ratio
For an unpatched specimen R = oZin/crgaax,
whereas for a patched specimen due
to residual stress RR the effective ratio is given by:
(13.9)
Chapter 13. Boronlepoxy patching efficiencystudies
385
log AK YPa m"112
-5.80-1
0.90
-
1.10
30
-6.40.-
$ -6.60-
z
2 -6.80-
e
v
~
-7.00.-
0I
5--
0-=80 MPa
R=O.l, R ~ = 0 . 5 8
da/dN=0.25E 7
-
-7.40.-
R.0.55 R ~ z 0 . 7 2
R=0.4 RR=0.66
-7.6s- 8
R=0.1 RR=o.58
Fig. 13.7. (a) Plot of a versus N for R values as shown for a standard 7-ply test specimen and (b) Plot of
log da/dN versus log AKm for the data from the 7-ply specimen (R=O.I) of Fig. 13.6(b), including, as
solid data points the corresponding results for different R ratios from (a).
where oT is the thermal residual stress, which has a maximum value OF:
bT =
tREREpAT(ap - E R )
(tpEp
+~RER)
7
( 13.10)
where AT = (adhesive cure temperature - operating temperature).
Thus RR > R and varies with stress level for a constant R.For the standard 7-ply
patched panel at omax=138MPa and R=0.1, R R z 0 . 5 8 .
To evaluate the effect of R , standard 7-ply panel tests were conducted at R values
of 0. I (standard), 0.4, 0.55 and 0.64 at Ao = 72 MPa. Stresses were kept fairly low
to avoid adhesive damage, which would have complicated the outcome of the tests.
Figure 13.8 shows the results of (a) a versus N and (b) log da/dN versus log AK,.
As seen in Figure 13.7(b), the data points for R > 0 fall close to the curve for
R = 0.1. This is unexpected since a higher crack-growth rate would be expected at
the higher R level so that these data points should lie to the left of the curve.
However, earlier studies at low temperatures [2] (-40°C) where RR is very high,
( 0 . 5 5 ) showed no observable change in crack-growth rate compared to ambient,
which also suggests an insensitivity to R.
A possible explanation is that the crack does not experience closure due to the
presence of high tensile residual stresses in the patched panel so that the effective
AK is insensitive to mean stress.
If the behaviour of composite patched cracks turns out to be insensitive to R,
prediction of crack-growth behaviour under spectrum loading will be greatly
simplified.
Advances in the bonded composite repair of metallic aircraft structure
386
40
IOO'C
35
--
30
--
25
--
E
f
20
Temp. ('C)
20
60
80
100
'I
daldN (dCycle)
0.139 E-6
0.237 E-6
0.341 E-6
O."O
-5.20 --
-5.40
--
-5.60
--
0.90
1.10
1.30
1.50
1.70
I IO
IW C RR=0.2
--
J
al
&
u
e
15--
10
,
'
m.
5L
0 10
30
50
70
90
110
Cycles, N (~1000)
Fig. 13.8. (a) Plot of a versus N at various temperatures and (b) Plot of log da/dN versus log AK, for
the data from the standard 7-ply specimen of Fig. 13.6 (R=O.l at 20°C), including, as separate data
points, the corresponding results from (a).
13.4.5. Influence of temperature
The influence of temperature on crack propagation behaviour in patched
specimens is quite complex [2] since several changes occur including:
0 A change in R since residual stress reduces as temperature increases
e A change in patching efficiency:
- AKm is increased as temperature increases because of a decrease in adhesive
shear modulus GA and shear yield stress zp,
- AKm is increased if the rate of disbond damage increases with increasing
temperature.
0 A change in the crack propagation properties of the aluminium alloy panel.
To investigate the influence of temperature, tests were conducted on a standard
7-ply specimen at a stress level of 138 MPa at 20, 60, 80 and 100 "C. Estimations
of AKm for the log plots against da/dN were based on the temperature values of
GA and zp provided in the table with Figure 13.3. Figure 13.8 shows the results of
(a) a versus N and (b) log da/dN versus log AKm.
Based on these approximate values Figure 13.8(b) shows that the data points for
temperatures up to 80°C lie below those for the standard 7-ply specimen,
suggesting that the patching model or the input data is in error. The main difficulty
with the model is to know what values to take for the adhesive properties at
elevated temperature because both temperature and strain rate have to be taken
into account; the values used (Table in Figure 13.3) for GA and zp were based on
Chapter 13. Boronlepoxy patching efficiency studies
0
10
5
387
15
20
25
Length mm
30
35
40
Fig. 13.9. (a) Geometry and (b) profile of the grind-out region.
static measurements and so will be low compared to dynamic values appropriate to
the fatigue test conditions.
13.4.6. Influence of panel thickness variation
In these experiments [8] to simulate repair after the removal of corrosion
damage, a ground-out region was produced, as shown in Figure 13.9(a), having the
profile shown in Figure 13.9(b). Fatigue tests were conducted under constant
amplitude stressing to a maximum of 120 MPa and nominal R of 0.1 and ambient
temperature. Plots of crack growth versus cycles are shown in Figure 13.10.
35.00 -
.*
.**
30.00 ..
.**
25.00 --
**...****
E 20.M) _'.. . . . . . . . . . . . . . . . . . . . + w e * . * ..*?.'.
*+.*.***
E
m
15.00--
.. .. . . .. . .. .
*.++
****
. . .. . . . . , . . . . .. . . . . . . , . .
.*
10.00---
5.00 ..
0.00 .(
Fig. 13.10. Plot of crack length versus cycles for the specimen with the grind-out.
388
Advances in the bonded composiie repair of metallic aircraft structure
35
E
15
10
5 -.
Fig. 13.11. Plots of crack size a versus cycles N for both the standard and the specimen with the
simulated corrosion grind out. The predicted curves for both cases are shown as solid lines.
In contrast to the standard panels, the crack-growth behaviour of the panel with
the simulated corrosion grind out is highly non-linear. However, once the crack
emerges from the grind-out region growth becomes reasonably linear.
The main reasons for this are that over the grind-out zone (a) there is a reduction
in patching efficiency (even though the patch is relatively stiffer), due to the
increased adhesive thickness and (b) there is an increased stress, due to the local
thinning. Thus AK, varies along the grind-out region.
To simplify the analysis, the increased stress in the grind-out zone is assumed to
be simply due to the thinning of the panel, with zero stress concentration factor
assumed because of the large grind-out radius. Also the panel was arbitrarily
divided into 2-mm wide slices normal to the crack (in which tp is assumed
constant), each considered as a separate joint with constant load equal to that for
the full 3.14 mm thickness.
The parameters A R and nR used to estimate crack growth were obtained from the
study on crack propagation in the standard panels at varying stress levels, Figure
13.4.
The predicted curves of a versus N are shown superimposed on the
experimental curves in Figure 13.11 where it can be seen that, as expected, the
predicted behaviour over the constant thickness zone appears in good agreement
with the experimental observations. Although agreement over the grind-out zone
is only fair, it seems reasonable considering the highly simplified approach taken.
The model predicts a smoothed out version of the actual behaviour. However, the
rather complex crack-growth behaviour observed, particularly near the edge of the
grind-out is difficult to explain and would not expected to be matched by this
simple patching model.
Chapter 13. Boronlepoxy patching efJiciency studies
389
500
400
2
z
t
PATCHED a=30mm
OU
300
u)
u)
E
z
200
100
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Micro Strain
Fig. 13.12. Plot of stress versus strain to failure for (a) a fatigue cracked unpatched panel and (b) a panel
initially fatigue cracked unpatched and then patched; strain readings are taken from the gauge position
indicated.
13.4.7. Residual strength of patched panels
No prior fatigue
Figure 13.12 plots the stress-strain behaviour to failure of (a) unpatched and (b)
patched panels [9]. The strain plotted is measured from the strain gauge shown on
the diagram inset. In this test the residual strength in the patched panel exceeded
the nominal yield stress o,,of 2024T3 (B allowable value, Mil Handbook 5C),
indicated on Figure 13.12. .However, significant yielding was observed at a higher
stress level, as shown by the stress at departure from linearity.
Failure of the patched panel, shown schematically in Figure 13.12 inset, occurred
as a fracture through the patch above the crack with no evidence of any disbond.
This mode of failure could be caused by either:
(a) exceeding the strain capacity of the patch when the crack grew under the patch,
or
(b) exceeding the strain capacity of the patch over the existing crack.
Stress intensity analysis
The first mechanism requires that the critical stress intensity Kcrit of the crack
under the patch be exceeded. From the failure stress CT, of unpatched panel, Kc,it
can be obtained using the standard relationship for an edge-cracked panel
390
Advances in the bonded composite repair of metallic aircraft structure
(assumed to apply for this specimen configuration):
(13.11)
Since, from Figure 13.12, omax
is around 160 MPa and a is 33 mm, Kcdt is estimated
to be about 56 MPam'/2. Similar results for
were obtained from several other
unpatched panels. These values for &
I are in reasonable agreement with published
values for 2024T3 panels of this thickness.
For the patched panel, patching theory suggests that K, is approximately
53MPam1/*. Although Ko0 is fairly close to Grit,the former is an upper-bound
estimate of stress intensity so it is tentatively concluded that crack propagation in
the metal was not the cause of the failure.
Strain capacity analysis
A direct estimate, using joint theory, of net strain in the patch over the crack
indicates a value of 7100 microstrain. However, if the extra load attracted to the
patch (as a result of the inclusion effect) is considered, the strain could be as high as
9500 microstrain. Since strain capacity of the boron/epoxy is measured to be about
7300 microstrain, the conclusion is that failure was probably a result of initial
failure of the patch.
Furthermore, as discussed in reference [11 for the patch configuration employed,
the ratio (inner-surface strain)/(outer-surface strain) in the patch is significantly
greater than unity. In this case it is estimated to be about 2.5. On this basis the inner
strain could have exceeded 12 000 microstrain; however, the strain elevation would
be very localised.
The conclusion is thus reached that failure in the patched panels resulted from
initial failure of the patch, possibly associated with the strain concentration at its
inner surface.
This failure mode may change where significant disbond growth occurs during
fatigue cycling for two reasons:
0 Stress intensity K, may exceed Ltallowing the crack to grow catastrophically
under the patch.
0 The strain concentration in the patch over the crack will be reduced if even minor
disbonding occurs.
Thus, for a small disbond, say a fewmm, residual strength is likely to increase
because of the reduced stress concentration in the patch.
Increasing the thickness of the patch, say to nine layers (the current patch is
seven layers), should provide some increase in residual strength. However, at higher
stress levels, plastic yielding of the metal around the patch (exacerbated by stress
concentrations at the ends of the patch) will limit this increase. The failure mode is
then expected to change from patch failure to disbonding from at the ends of the
patch.
Chapter 13. Boronlepoxy patching efficiency studies
450
...............................................................................
400
bI
391
-
........ .... ...................
350
5 300
m
-m
250
I.,
;200
u)
2
150
100
50
0
:onstant Amplitude a=%
Standard Boron
I
FALSTAFF a=39 mm
Standard Boron
I
F l l l a = 3 8 mm No Fatigue a=30 mm
Standard Boron
Standard Boron
No Fatigue a=33 mm
Unpatched
Fig. 13.13. Histogram showing residual strengths for patched panels with or without prior fatigue
testing and for an unpatched panel. The results for the panels with no prior fatigue are plotted in
Figure 13.12.
Residual strength following fatigue testing
Tests were also conducted on panels after fatigue testing under (a) constant
amplitude, (b) F-111 spectrum loading-representative of the F-1 11 lower wing skin
or (c) FALSTAFF spectrum, representative of a standard fighter lower wing skin.
Figure 13.13 depicts the results together with those patched after fatigue
cracking. Thermographic NDI was used in an attempt to detect disbond damage
over the crack region in the fatigue-tested specimen; however, damage could only
be detected in the FALSTAFF specimen as a relatively small -2mm ellipse
centred on the crack. This does not imply that the other specimens had not suffered
damage, only that the disbonds were probably smaller or for some reason less
detectable by thermography.
The first conclusion is that the residual strength has not been reduced by cyclic
loading for cracks in the 30-40mm range. Indeed the strength may have actually
increased due to the reduction of stress concentration around the crack caused by
any local disbonding. In the case of the 56-mm crack residual strength was clearly
reduced compared to the others. Since this crack is approaching the boundary of
the patch, it is possible that in this case the critical stress intensity for the crack in
the panel was exceeded, rather than the failure stress of the boron/epoxy. In all test
panels the strength equalled or exceeded oy- although, with no margin in the case
of the panel with the 56-mm crack.
As discussed later, there is a case for equating oJ, with DUL. If this case is
accepted it can be concluded that the patched panels had adequate residual strength
to satisfy most certification requirements.
Advances in the bonded composite repair of metallic aircraft structure
392
13.5. An approach to b/ep patch design
13.5.1. Cyclic loading
Assuming that environmental degradation of the adhesive is not an issue
(through good quality control), the margin of safety, efficiency and durability of a
repair to a cracked component can be assessed from estimates of the following:
(a) The stress intensity range AK and R in the repaired region. This determines
patching efficiency through the crack-growth parameters AR and nR.
(b) The tensile strain e R in the b/ep patch which allows estimation of the margin of
safety for failure of the patch. It is assumed for a composite patch that fatigue
is not an issue; if it were then the range of strain AeRand R ratio would have to
be considered.
(c) A (validated) damage parameter in the adhesive system (including the
composite interface). Possible parameters are the shear strain range Ay or
Mode I1 energy release rate AGII. This allows estimation of the fatigue
durability of the adhesive system. It is best, if feasible, to design the repair so
that the damage threshold of the adhesive system over the crack is not
exceeded; however, if it is not feasible the disbond growth rate, db/dN (Section
13.2.3) must be included in the analysis, using Eq. (4).Limited disbond growth
over the crack is acceptable, however, and within limits will not dramatically
reduce patching efficiency.
Another important factor needed for design of the repair system is the length L*
available for the patch between obstructions (Figure 13.14), since this can limit the
allowable patch thickness. The length LR required for efficient load transfer
depends on the patch and adhesive parameters (Figure 13.3) including patch
thickness tp and the taper rate at the outer ends of the patch.
Assuming largely elastic conditions in the adhesive (as required to avoid patch
system fatigue), a conservative estimate of the patch length [l] is given by:
6
LR = -
D
+ length of the taper ,
(13.12)
where /3 is given by Eq. (Id), The taper rate for b/ep we use is around 3 mm per ply.
Finally, the residual stress oT, resulting from patch and component thermal
expansion mismatch, must be included in the analysis, since this influences Ay, eR
and RR. Residual stress CT depends on A T = (Toperating temperature - Tcure temperature),
typically 100 "C for a 120 "C curing adhesive and, Aa = (@pat& - acomponent). The
length between thermal expansion constraints in the component structure (see
which for full constraint is 0.5 aP.
Figure 13.13) influences acomponent
Based on Rose's analysis described earlier, the author [l] developed a simple
algorithm for estimating the minimum thickness patch that could be applied within
the installation constraints that would survive the external cyclic loading.
It is generally desired to use the thinnest patch feasible for several reasons,
including (a) to minimise the residual stress problems, (b) to maintain aerodynamic
Chapter 13. Boronlepoxy patching eficiency studies
393
Patch
Craack
PARAMETERS
FIRST CYCLE FOR MIN THICKNESS
PATCH
Fig. 13.14. Outline of algorithm for designing the minimum thickness patch.
acceptability, for example to minimise disturbance to the airflow when repairs are
made to an external surface, (c) to minimise balance problems; for example, when
repairs are made to a control surface, and (d) to comply with installation restraints,
for example, not to exceed available fastener lengths when fasteners must pass
through the patch for system requirements, or to maintain clearance between
moving surfaces.
The logic for the design approach is shown in flow chart form in Figure 13.14,
which is based on comparison of the following, as the patch is increased in
thickness one ply at a time:
0 The computed patch length LR with the allowable (available) length L*
0 The computed styin in the patch compared with the experimentally determined
allowable strain e,; a value of 5000 microstrain was found to be reasonable for b/
eP.
0 The computed shear-strain range compared with experimentally determined
allowable A?* = 0.18 was originally used for FM73, but current work suggests
that 0.10 may be more appropriate for long life repairs.
These patch and adhesive allowables were obtained from tests on representative
bonded joints. Increasing patch thickness increases LR but reduces eR and Ay.
Assuming constant amplitude fatigue at Bo, and R, Figure 13.15, shows the
outcome of a calculation based on the parameters listed.
394
Advances in the bonded composite repair of metallic aircraft structure
EXAMPLE
~ ~ 1 3R 8
z 0,. 1
7 plies blep
2024T3
eR
AT=IOO”C
FREE EDGES
25 mm
L* = 80 mm
~0.18
A?*.
e*R=
= 3x1o3
ATA ~ 0 . 1 6
5x1O3
A K, = 12.5 MNm’”
t . = 0.1 9 m m
A K, = 40 MNm’”
uT=67 MPa
-
3 mm
LR=
57 mm
Fig. 13.15. Outcome of an analysis for the minimum patch thickness, AKa is the stress intensity for the
unpatched case.
Once AK, is estimated the inspection interval N can be determined from
Eq. (13.2) and (la) or (if disbonding is a consideration) from Eq. (13.4) as:
(13.13)
where ai is the initial crack size and ax is the size chosen for inspection. Typically ax
would be less than one third patch width to provide at least three chances of finding
the crack before it grows out from under the patch.
As shown in Figure 13.14, if the inspection interval is too short, (the AK
reduction is inadequate) there is an option to increase the thickness of the patch
providing it can still fit within the allowable length.
13.5.2. Spectrum loading
Crack-growth analysis is significantly more complex under spectrum loading. It
is feasible to assess crack growth for the cracked component and damage growth in
the adhesive system on a cycle-by-cycle basis for the various values of effective
AKo, and R .
Chapter 13. Boronlepoxy patching efJiciency studies
395
If the spectrum is unknown, design can be based on a standard spectrum:
FALSTAFF or TWIST for fighter or large transport aircraft respectively. If the
peak stress in the spectrum (the design limit stress, CTDLL) is unknown, an estimate
can be made based on the material yield stress o,,as described in the next section.
The patch length LRcan then be estimated for the estimated patch thickness t,, to
obtain the required K reduction. However, this may be over-conservative since by
definition DDLL is expected to occur only once (although in fighter aircraft it can
occur many times) in the life of the aircraft. Thus LR could be based on say 0.5 or
0.6 CJDLL - and still provide acceptable residual strength at say 1.2 x ODLL (see final
section).
A simplified estimate of patching efficiency could be obtained by increasing
stresses in all cycles in the spectrum above the thresholdfor crack growth to the peak
stress CJDLL. As this is a severe assumption for both the cracked component and
patch system, it provides an over-conservative estimate. A complication with using
this approach is that the threshold stress will reduce with disbond growth.
13.5.2.1. Estimating the design limit stress
There are several options to estimate the CDLL:
(a) The most conservative is to equate it with material yield o,,.Thus the nominal
stress at the design ultimate load DUL is 1.50,,, which marginally exceeds the
material ultimate strength ou. For example for 2024T3 and 7075T6,
respectively, ou/o,,= 1.4 and 1.3.
(b) A less conservative but (in the author’s opinion) more reasonable assumption
[2] is to equate the stress at DUL with o,,.Thus in accord with the requirements
for DLL, where limited yielding is allowed at stress concentrations but no
large-scale yielding leading to permanent deformation. As an example, Table
13.1 provides cDLL and o,,values for the F-1 11 lower wing skin, which is made
of aluminium alloy 2024 T581. This shows that the ratio CT,,/ODLL exceeds 1.5,
as required. Use of approach A would result in a 3040% overdesign.
(c) By direct strain measurement, either from a static calibration or in flight.
(d) From a knowledge of the external aerodynamic loads and the availability of a
full F-E model of the aircraft and local region to estimate internal loads.
Table 13.1
Data on design limit stress UDLL for F-111 for several (DADTA) data points in the lower
wing made of aluminium alloy 2024 T581, compared with the yield stress uy
67
70
70a
78
154
194
202.9
167.0
204.2
149.7
171.8
165.6
400.2
400.2
400.2
400.2
400.2
400.2
462.3
462.3
462.3
462.3
462.3
462.3
1.2
1.2
1.2
1.2
1.2
1.2
266.8
266.8
266.8
266.8
266.8
266.8
1.97
2.40
1.96
2.67
2.33
2.42
2.28
2.77
2.26
3.09
2.69
2.79
396
Advances in the bonded composite repair of metallic aircraft structure
Approach (c) is very time consuming and likely to be prohibitively expensive in
most repairs. Approach (d) depends on having the loads and F-E model available,
and even then will be costly and time consuming. However, this is the preferred
approach for critical repairs and was the procedure adopted in a bonded composite
repair developed for the F-111 lower wing skin [lo].
Of the two simple approaches the result of assuming approach (a) is that a thick
repair would be designed resulting, in the case of composite patches, in large
residual stresses and in large parasitic stress concentrations. This is not a major
concern for thin-skin components (skin thickness <2 mm) where approach (a) is
probably quite acceptable.
13.5.3. Check on residual strength
It is most important to check that residual strength of the repaired region will
exceed oDLL by an acceptable factor F generally between 1.2 and 1.5 x (the latter
being the design ultimate). If this is not the case the thickness of the patch will need
to be increased beyond that required for the fatigue stress level.
The residual strength of the patched cracked component appears to be dependent
on the strain capability of the reinforcement (including strain concentration) and
the adhesive rather than on the stress intensity in the patched crack. However, a
first test should be made to check that at F x ODLL, KR < Ke the effective critical
stress intensity for the cracked material. If this is not the case then the patch
thickness must be increased.
The main test check is to ensure that the patch static-strength allowables,
obtained from tests on representative bonded joints, are not exceeded. For the
adhesive the allowable shear strain will be greatly increased (for FM73, Ay* = 0.5);
however, the allowable patch strain eR* is unchanged, since for b/ep the static
strength allowable is the about same as the fatigue allowable.
At the ultimateload the adhesive yield shear stress will be greatly exceeded so, in
principle, a much longer length than predicted by Eq. (13.12) would be required.
However, since the ultimate load case is a check load (where large-scale yielding in
both the metallic structure and adhesive is acceptable, as long as failure does not
occur) the length given by Eq. (13.12) for the fatigue case should still provide an
adequate strength margin.
References
1. Baker. A.A. (1988). Crack patching: Experimental studies, practical applications. Chapter 6 in
Bonded Repair of Aircraft Structures, (A.A. Baker and R. Jones, eds.) Martinus Nijhoff, pp. 107173.
2. Baker, A.A. (1994). Bonded composite repair of metallic aircraft components, Paper 1 in AGARDCP-550 Composite Repair of Military Aircraft Structures.
3. Rose, L.R.F. (1988). Theoretical analysis of crack patching. Chapter 5 in Bonded Repair ofAircraft
Structures, (A.A. Baker and R. Jones, eds.), Martinus Nijhoff, pp. 107-173.
Chapter 13. Boronlepoxy patching efficiency studies
397
4. Wang, C.H. and Rose. L.R.F. (1998). Bonded repair of cracks under mixed mode loading. Int. J . of
Solids, 35, pp. 2148-2113.
5. Baker, A.A. (1 993). Repair efficiency in fatigue-cracked panels reinforced with boron/epoxy patches.
Fatigue and Fracture of Engineering Materials and Structures, 16, pp. 753-765.
6. Chalkley, P.D. and Baker, A.A. (1999). Development of a generic repair joint for certification of
bonded composite repairs. Int. J. Adhesion and Adhesives 19, pp. 121-132.
7. Baker, A.A. and Chester, R.J. (1992). Minimum surface treatments for adhesively bonded repairs.
Int. J . of’ Adhesives and Adhesion, 12,pp. 13-18.
8. Baker, A.A. and Beninati, 0. (1997) Repair efficiency in composite patched panels after removal of
corrosion damage. Proc. of Int. Aerospace Conf. 1997, Sydney, Australia, pp. 53-60.
9. Baker, A.A. (1997). On the certification of bonded composite repairs to primary aircraft structure.
Proc. of ICCM II, Gold Coast Australia, July, Volume 1, pp. 1-24.
10. Baker, A.A., Rose, L.R. and Walker, K.F. (1999). Repair substantiation for a bonded composite
repair to F-I11 lower wing skin, Applied Composite Materials, 6, pp. 251-267.
Chapter 14
GLARE PATCHING EFFICIENCY STUDIES
R. FREDELL
and C. GUIJT
Department of Engineering Mechanics, Center for Aircraft Structural Life
Extension, US Air Force Academy
14.1 Introduction
Most bonded composite crack patching has been accomplished on small areas of
thick structures using high-modulus boron/epoxy composites. Extending the lives
of aging transport fuselage structures, however, may involve repairs to large areas
of thin fuselage skins and lap joints. These structures often see their highest
mechanical stresses (due to pressurization) at the low temperatures encountered at
cruise altitude. Hence, more attention to the thermal properties of composite
materials may be needed when fuselage structures are being repaired.
This chapter presents the results of detailed parametric studies of thermal effects
on bonded repairs to cracked pressurized transport fuselage structures. The hybrid
glass/epoxy/ aluminum materials known as GLARE are offered as an alternative to
boron/epoxy for this special crack patching application. Experiments performed at
room temperature, and at the low temperatures encountered at high altitudes, show
that bonded GLARE 2 patches can out-perform boron-epoxy in selected repairs to
thin skins. These results are discussed with the conclusion that, under certain
circumstances, thermal compatibility can be the driving factor in repair material
selection in pressurized fuselage skin repairs.
14.1.1. Overview and background of jibre metal laminates
The Fiber metal laminate (FML) GLARE 2 is a hybrid material of moderate
modulus, combining 2024-T3 aluminum with high-strength unidirectional S-glass/
epoxy composite in a sheet like laminate [2-31. It is known for its excellent fatigue
resistance due to the “crack-bridging” effect of the fibers and its high residual
399
Baker, A.A.. Rose, L.R.F. and Jones, R. (eds.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Published by Elsevier Science Ltd.
Advances in the bonded composite repair of nietallic uireraft struetirre
--atuminfum alloy
Fig. 14.1. Schematic of glass/epoxy/aluminum laminate GLARE 2.
strength. Figure 14.1 shows a schematic of GLARE 2 with a crack in the aluminum
layers and "crack-bridging'' fibers.
GLARE and the ARALL family of FMLs were developed by Delft University,
the Netherlands, with the support of AKZO and Alcoa. FMLs have the high
strength and excellent fatigue resistance of advanced composite materials, while
retaining the machinability and cold-formability of aluminum alloys. In addition,
the GLARE laminates approach the performance of titanium alloys as fire barrier
materials. Fiber metal laminates are in service on the C-17 Globemaster I11 (aft
cargo door), Boeing 777 (cargo floors and liners) aircraft, and as bonded repairs on
a USAF C-5A. Airbus Industrie will use GLARE as a fuselage skin material for the
A-380 aircraft.
14.2. Parametric studies of various patch materials
When one focuses on pressurized fuselage skin repairs, the following special
conditions must be considered:
0 The damaged structure is relatively thin (up to 2 mm/0.079"). An extremely stiff
patch is not required, or even desireable, as load attraction to the repaired region
could cause secondary damage to the relatively thin skin.
0 The adhesive is cured at a temperature ranging from 80 to 120 "C (180 to 250 OF),
and the fuselage sees service temperatures ranging from perhaps 60 "C (140 OF)
Chapter 14. GLARE patching efficiency studies
40 1
(unloaded, hot day on the ground) to -54°C (-65°F) (maximum internal
pressure, temperature at cruise altitude). This increases the likelihood of thermal
mismatch problems.
Because the transport fuselage experiences its greatest internal pressure loads at its
minimum service temperature, thermally-induced stresses in a fuselage bonded
repair can be a more significant consideration than in, say, a fighter wing skin
repair.
Reduction in stress intensity factor, K, to slow or stop crack growth, is not the
only design criterion for effective crack patching. The significant variables to be
considered in a crack patching design include (see Figure 14.2):
0 slow down or stop crack growth
0 acceptably low stresses in the patch to avoid patch failure
0 avoidance of excessively high stresses in the skin adjacent to the repair to
preclude new fatigue problems in the skin
0 tolerably low peel and shear stresses in the bond line
0 prevention of adhesive bond line shear yielding to ensure patch and bondline
durability
By varying the patch material and dimensions, the adhesive, and the curing
temperature, the repair designer may be able to produce a patch meeting all of these
8
0
b
8
0
\ m e
0
\
O
\
O
@
0
b
0
8
o o
0
o e 0 o o o
@
8
Q
Q
0
e o o o o o
1
Patch strength
Patch durability 8
creep anchor
8
0
8
@
Fig. 14.2. Failure modes for bonded repairs.
0
0
8
0
8
0
0
0
8
8
@
1
0
1
402
Advances in the bonded composite repair of metallic aircraft structure
goals for successful patching. However, in an operational maintenance environment, the design and analysis of bonded repairs must be able to be accomplished
quickly, often without a detailed knowledge of the precise stress state in the cracked
panel.
This section describes the results of detailed parametric studies performed on
various repair designs based on the Rose model of crack patching [&8]. It considers
an infinite, center-cracked, isotropic plate loaded by a remote biaxial stress with a
bonded orthotropic elliptical patch on one side of the plate. Several writers have
published studies comparing various finite element-based crack patching models
[9-111 with the Rose model.
Tarn and Shek [9] performed a detailed finite element analysis to compare the
crack-bridging efficiency predicted by various elastic models of boron/epoxy patch
repair of cracked aluminum sheets. Material responses were assumed to be linear
elastic, and thermal effects were ignored.
With increased loading, inelastic material behavior is first observed in the
adhesive layer. Therefore, to consider linearly elastic material behavior only, the
adhesive in the Rose model was given an artificially high shear yield strength. In the
elastic case shown in Figure 14.3, the reduction in K of Rose (shown as the
“CalcuRep” result) matches well with the more complex finite element models from
the literature. The maximum difference between Rose and [9] occurred when the
repair patch was eight plies thick. Here Rose overestimated the K reduction by no
more than 5%.
The assumption of various authors that the adhesive will behave elastically is
questionable, especially when the patch extensional stiffness is roughly equal with
10 --
Fig. 14.3. Comparison of reduction in stress intensity factor for bonded boron/epoxy patches, elastic
and elastic-plastic models of adhesive behavior.
Chapter 14. GLARE patching efficiency studies
403
the cracked plate stiffness. Thin patches experience large normal strains over the
crack and induce large shear strains in the adhesive as well.
The lowest line in Figure 14.3 represents the Rose model’s results when elasticplastic adhesive behavior was allowed around the crack tip. The differences
between the models are striking. With the elastic model, adhesive shear stresses are
able to reach unrealistically high levels so thin patches appear to be quite effective
at reducing K . However, including inelastic material effects in the model shows that
when patch thicknesses are relatively low, the reduction in K is not nearly as
significant. This is due to the patch strains being quite high, which can lead to early
adhesive yielding and delamination, reducing crack-patching effectiveness. Therefore, it can be said that a realistic constitutive model of the adhesive is important,
since the avoidance of large-scale adhesive yielding can be important for effective
crack patching and good patch durability.
This result is consistent with the work of Marissen [ 121 and Roebroeks [ 131, who
found that low fiber/metal ratios (Le. low patch/plate stiffness ratios) resulted in
poor crack-bridging efficiency for fiber metal laminates. The elastic results converge
with the elastic-plastic model only when six boron plies are used. At this point, the
extensional stiffness of the boron patch approaches that of the plate.
These results allowed sufficient confidence in Rose’s basic approach to proceed
with the parametric analysis, outlined in the following section. The study assesses
the thermal considerations to be accounted for in the selection of patch materials.
Crack patching of aircraft usually involves local heating of the repair area.
During the curing process, the unheated structure surrounding the repair area
constrains the thermal expansion of the heated area. But the patch, which is entirely
inside the heated region, expands freely. In stiffened structures, the “effective”
coefficient of thermal expansion (CTE) of the constrained structure is much less
than the material CTE. Figure 14.4 illustrates this effect.
After cooling to room temperature, the bondline for patch materials with
relatively low CTE, like boron- or carbon-fiber composites, is relatively stress free.
This has been pointed out by various writers [7,11,14-161. Moderate- to high-CTE
patches actually place the crack in compression at room temperature. This reduces
the stress intensity near the crack tip and decreases or even stops crack growth.
Figure 14.5 shows the effect of cooling to room temperature for high- and low-CTE
materials, respectively.
The blue arrows indicate the compressive stress in the skin acting on the crack.
The additional tensile stress in the patch is less significant if composite patch
materials are used with a higher fatigue threshold.
When a transport aircraft climbs to cruising altitude, its fuselage is cooled
uniformly to the outside air temperature (-54 “C at 10 km). The structure cools and
contracts uniformly, but a low thermal expansion composite patch would not
contract nearly as much.
For example, a boron-epoxy patch shrinks only about 1/6 as much as the nowunconstrained aluminum fuselage. This induces an additional cyclic tensile (crackopening) load on the crack tip at a time when the pressure-induced stress is highest.
Further, the adhesive that was ductile and relatively flexible at room temperature is
404
Advances in the bonded composite repair of metallic aircraft structure
High CTE patch (e.g., GLARE)
Low CTE patch (e.g., boron-epoxy)
Fig. 14.4. Thermal effects in skin and patch, due to the elevated temperature during bonding.
High CTE patch (e.g., GLARE)
Low CTE patch (e.g., boron-epoxy)
Fig. 14.5. Thermal effects in skin and patch at room temperature.
substantially stiffer and more brittle at -54 "C.The additional tensile load due to
these effects occurs every flight. On the other hand, a patch material with a moderate
or high CTE, such as GLARE 2 will still cause some crack-closing compression in
the skin. (GLARE 2 has a CTE of approximately two-thirds that of aluminum.)
Figure 14.6 compares the patching efficiency of two potential fuselage patch
materials, boron-epoxy and [email protected] 2. The patching efficiency is defined as the
reduction of the stress intensity factor, K, at the crack tip. A sufficient reduction of
these stresses will slow down or even stop further crack growth. The stresses near
Chapter 14. GLARE patching ef$ciency studies
E
120
AI 2024-T3
110
h o o p = IOOMPa
dong = 5OMpa
2a
= 51mm
Altitude = IOOOOm
100
Y
.-
go
I A.
Boron
-I?
405
Glare 2
Thermal effect
\
.*...- -A- - - - - A Glare
-.
No thermal
U
I2
80
0
'
0
**.----
Thermal effects
_ *
0.5
1
1.5
patch thickness [mm]
2
2.5
Fig. 14.6. Comparison of reduction in stress intensity factor for bonded GLARE 2 and boron patches,
with and without considering thermal effects [5].
the crack tip are described with the stress intensity factor K . A 100% reduction in K
means no crack opening. Higher than 100% means that the crack is still in
compression at the given load due to the residual thermal stresses.
The comparison shown, using the Rose-model, was done for the case of a
narrow-body fuselage at a cruising altitude of 10 km. In the 2024-T3 Aluminum
skin of 1mm thickness, a crack of 51 mm is modeled. The patch dimensions were
the same for both materials. The patch length (perpendicular to the crack) was
140mm, the patch width was 102mm. To bond the patch over the crack, the
adhesive AF-163-2K of 3M was used. The Shear Modulus, G, and the Yield
Strength, Tyield, of this material (modeled as elastic-perfectly plastic material) were
corrected for the cruising temperature. The manufacturer-recommended cure
temperature of 120 "C was used. A biaxial stress field of 100 MPa (hoop tension)
and 50 MPa (longitudinal tension) was applied.
When thermal effects are ignored, the much stiffer boron/epoxy patch seems to
do a better job closing the crack. However, when the complexities of constraint
during bonding, and free thermal contraction during cruise flight are considered,
GLARE 2 is predicted to be the more effective patch. At an often used stiffness
ratio (Epatch
* tpatch / Eskin* &kin) of roughly one, the thickness of the Glare patch is
1.1mm and the thickness for boron is 0.39 mm. The K-reduction is 100% for Glare
and 78% for boron.
Thermal effects also change the situation with regard to skin stresses at the edge
of the patch: Any thermal residual K reduction at the crack tip, gained by using a
high-CTE patch, occurs at the expense of additional tension in the skin at the patch
tip. The designer/analyst must strike the proper balance.
406
Advances in the bonded composite repair of metallic aircraft structure
The choice of adhesive cure temperature can also affect the results. When repairs
are performed on or near structures containing absorbed moisture (e.g. honeycomb
core materials), cure temperatures under 100 “C are desired to prevent damage
from evolved steam. Furthermore, a lower cure temperature can reduce thermal
buckling problems. Moreover, cure temperatures are limited by equipment
capabilities, which in turn are driven by the size, material(s), structure, and
substructure (which can act as an effective heat sink) of the repair area.
When materials of different coefficients of thermal expansion are bonded, cure
temperature can affect residual stress states as well. Baker [17] recommends curing
at “the lowest possible temperature” to minimize residual thermal stresses. If a
patch has a higher effective coefficient of thermal expansion than the substrate,
cooling from the cure temperature results in residual compression at the crack tip.
As pointed out before, this should by itself be beneficial for fatigue crack
retardation. If the patch’s effective thermal expansion coefficient is lower than the
substrate’s, a residual tensile (crack-opening) load will exist at the crack tip.
However, the change in cure cycle could (adversely) affect the adhesive properties.
Figure 14.7 shows the effect of various cure temperatures on the patching
effectiveness of GLARE 2 and boron/epoxy patches in the Rose model at the cruise
altitude situation described before. In the analyzed case, the effective expansion
coefficient of the stiffened fuselage structure is approximately equal to that of
boron/epoxy during the cure cycle of the adhesive (local heating). Thus, in fuselage
skin repairs, boron/epoxy is not substantially affected by a change in the cure
temperature. The large thermal effects with boron/epoxy occur in the cooling from
room to cruise temperature of the complete structure, now the CTE of the structure
AI 2024-T3
105
Altitude = 10000 rn
-c
t= 1.05rnm
100 --
95 --
Y
.c
5
.-
90
--
I
a
V
2
“;I
85.-
75
70
Glare 2
Boron
I
1
0
20
40
60
Cure Temperature [‘C]
80
100
Fig. 14.7. Influence of adhesive cure temperature on patch effectiveness.
120
Chapter 14. GLARE patching efjciency studies
407
0.07 1
0.06 -
I
Boron
.
3 plies, t=0.38rnrn
0.05 -
.9
0.04 -
-. yield12
%
Jz
0.03
~
E
?-
0.020.01
.
I
0 -
-0.01
0
20
40
60
80
100
120
Cure Temperature ["C]
Fig. 14.8. Influence of adhesive cure temperature on maximum adhesive shear strain
is higher since there is no local constraint and will be roughly equal to the CTE of
aluminum.
Thermal effects have yet another significant impact on patch selection. The high
adhesive shear strains experienced with some low CTE patches cannot be reduced
significantly by curing at a lower temperature, as shown in Figure 14.8, generated
using the Rose model under the same conditions as before.
With [email protected] 2, the effect is reversed due to the higher CTE of the patch
during the cure cycle: A cure temperature of 100 to 120°C actually benefits the
bond by reducing adhesive shear strains at low operating temperatures.
Furthermore, as can be seen in this figure, the global adhesive shear strains with
the boron/epoxy patch remain above half the adhesive yield strain. Half the yield
strain is a design limit for typical operating loads. Because of both effects
mentioned, the bonded GLARE 2 patch repair will have a better durability. Also, a
higher resistance against delamination might be expected.
A series of analyses were performed using the same narrow-body fuselage case at
various cruise altitudes corresponding to different operating temperatures.
Figure 14.9 shows the influence of the operating (cruise) temperature on the four
significant crack patching design parameters. Again, the shear modulus and yield
strength of the adhesive were corrected for the various temperatures.
The boron/epoxy patch is strongly influenced by the warmer temperatures at
lower altitudes, while the more thermally compatible GLARE 2 patch is less
sensitive to temperature variations. The skin stresses adjacent to the boron/epoxy
patches were consistently lower.
Advances in the bonded composite repair of metallic aircraft strueiure
408
Influence of cruise temperature on
Adhesive Shear Strain
Influence of cruise temperature on
maximum stress in the skin
-
210
200 ..
.,
Glare 2 (t=0.85mm)
g 190”
z
180..
140
7 3 0 1 : : :
-60
-50 -40
10
-60
20
Influence of cruise temperature on
Patch Effectiveness
1053
-E
0
Cruise Temperature [‘C]
-30 -20 - 1 0
400
-50 -40
.
’
,
:
0
Cruise Temperature [‘C]
-30
-20 -10
10
20
Influence of cruise temperature on
maximum stress in the patch
,
.
100..Glare 2 (t=0.85mm)
95..
C
5
$
90..
250
U
f
75.
:
:
:
:
-60 -50 -40 -30 -20 -10 0
Cruise Temperature [“C]
10
20
..
150
Glare 2 (t=0.85)
..
100..
-60 -50
:
-40
:
.
-30 - 2 0
:
:
:
-10
0
10
20
Cruise Temperature [“C]
Fig. 14.9. Influence of cruise temperature on crack-patching design parameters.
14.3. Experimental results
Experimental results tended to bear out the analytical predictions: Both
constant- and variable-amplitude fatigue testing was performed at room- and
low-temperature conditions [ 181.
In experiments with single-sided bonded repairs to pre-cracked thin aluminum
sheets, GLARE 2 patches always gave longer lives than equivalent (in terms of
patch stiffness) boron/epoxy repairs. The largest difference was in the time to crack
growth re-initiation after repair, see Figure 14.10. The aluminum panels were precracked to 25 mm at different stress levels; 60, 80, and 120 MPa. After the patches
were applied the fatigue tests were continued at 120MPa, and
t ~ , , , j ~ / c ~ , , , ~ = R = 0.05. These experiments were performed to investigate the effect
of the pre-crack level and the plastic zone on crack-growth rates after patching. The
fact that the crack growth rates after patching are lower for the Glare patches
indicates a lower K-repaired, just as predicted by the Rose-model. At a pre-crack
level of 120MPa, the plastic zone formed stops crack growth for roughly 250000
cycles after the Glare patch was applied, obviously AK is low enough to stop the
crack from growing through the plastic zone immediately. The scatter in this period
can be very large. Periods of 50000 up to 400000 cycles of no crack-growth are
observed in similar specimens [ 191.
Chapter 14. GLARE patching efficiency studies
409
Pre-crack tests
0
50000
I00000
150000
200000
250000
300000
350000
400000
Number of cycles N
Fig. 14.10. Effect of pre-crack stress level and plastic zone on crack growth behavior after patching.
Previous research [1] has indicated that the 120"C cure cycle temperature is the
dominant mechanism in determining the retardation period. Baker found that the
cure cycle of the adhesive does affect the plastic zone created in the material before
patching. These recent experiments appear to indicate that the CTE match between
patch and substrate is another important feature in retardation of crack growth
after patching.
In other experiments, the influence of overloads in variable amplitude fatigue
testing of repairs was observed to be muted in comparison to unrepaired fatigue
crack growth experience. An example of this behavior is given in Figure 14.11.
Overload experiments with patches specimens showed the classical fatigue
behavior, an overload slows down the crack growth due to the plastic zone formed
during the overload. The effect is smaller than with unpatched-cracked panels since
the K is lower due to the patch. When testing different spectra, see Figure 14.11,
this behavior was confirmed. The spectra used were derived from Lockheed stress
data for the C-5A, see Chapter 3 1. The unfiltered spectrum contained all the loads,
the filtered spectrum had less loads and allowed shorter testing times. The crack
growth under the patch was the same for both spectra, however, the crack-growth
rate of an unpatched crack was different for the filtered and the unfiltered spectra.
This indicates again that some load cycles are less significant if a patched crack is
Advances in the bonded composite repair of metallic aircruft structure
410
Spectrum test results
60Filteredspectrum unpatched (01)
70 ..
patched
tFilteredspectrun
S3 patched
--t
Full spectrum 06
unpatched
+Filtered spectrun
01 unpatched
*O
t
I
lo/
0
0
10
20
30
40
50
60
70
80
Number of blocks
Fig. 14.11. Effect of spectrum loads.
tested. If all failure modes, for example a crack at the patch tip due to (high) skin
stresses, are considered, the (filtered) spectrum must be used which results in the
same unpatched crack growth rate.
At low temperatures, a mismatch in CTE between the patch and the skin can
cause higher stresses in both the adhesive and at the crack tip. However,
experiments show a surprising result. In Figure 14.12 the results of crack-growth
experiments are shown for boron and Glare patches at -40°C. At the lower
temperatures, the crack-growth rates for both patch materials are lower. There are
two possible explanations for this behaviour:
1. Although the residual thermal stresses might be higher, the low temperature
increases the shear modulus, G, of the adhesive. This can reduce crack opening
and therefore reduce the crack-growth rate.
2. Aluminum has slower crack growth rates at low temperatures due to the lower
humidity at the low temperatures. This explains the fact that both Glare and
boron perform better at lower temperatures despite the increased thermal
stresses.
14.4. Discussion
The analytical and experimental results clearly show the strong influence of the
differential CTE effects on the stress intensity reduction and subsequent crack
41 1
Chapter 14. GLARE patching ef$ciency studies
Low temperature tests
0
50000
100000
150000
200000
Number of cycles N
250000
300000
Fig. 14.12. Effect of low temperatures on crack-growth rates of patched panels.
growth. When the thermal effects are considered, boron/epoxy patches are less
effective than the fiber metal laminate GLARE 2 at operating temperatures below
the cure temperature of the adhesive.
Furthermore, the effect of the cure temperature can have a significant positive
influence on the effectiveness of the GLARE 2 patch, while the boron/epoxy patch
is only slightly influenced (Figure 14.7). In Figure 14.8, one can see the positive
influence of an increasing cure temperature on the decreasing shear strain in the
GLARE 2 patch, while the strains in the bond line of the boron/epoxy patch
remain above the design limit for typical operating loads.
Figure 14.9 shows the influence of the operating temperature on the most
significant crack patching design parameters. More thermally compatible
composite patches are less sensitive to temperature variations. This results in
better patching effectiveness at high- altitude/low-temperature cruise conditions,
while keeping the adhesive shear strain in the bond line acceptably low. However,
better crack closure comes at the expense of higher skin stresses at the edges of the
repair. This increases risk of a new fatigue crack nucleating at the boundary of the
patch, and must be considered in design.
The experiments show the same trends as predicted by the Rose-model: A closer
CTE-match between the patch and the skin can result in more efficient patches for
412
Advances in the bonded composite repair of metallic aircraft structure
a typical fuselage skin thickness (1 mm). Both the pre-crack stress level and the
patch material used affect the re-initiation period of the crack after patching. If the
same stress level is applied before and after patching, the Glare patches can result in
significant retardation periods. This retardation period is not affected by the curecycle of the adhesive.
Overloads and spectrum loading does affect crack growth under patches in the
same way as it does for unpatched cracks. However, the absolute effect is smaller
due to the reduced K after patching. When testing bonded repairs under spectrum
loading, the spectrum has to be verified on unpatched cracks.
The low temperature tests show that although the thermal stresses might
increase, the crack-growth rate decreases. This is not what the models predict,
therefore the change in crack-growth behavior of aluminium at low temperatures/
humidities must be more dominant than the increase in thermal stresses under the
repair. A higher G of the adhesive, might also contribute to the slower crackgrowth rates.
This combination of analyses and experiments tends to indicate various niches
where various candidate crack patching materials appear to be best suited. The
high-modulus, low-CTE boron/epoxy composite excels in the repair of relatively
thick cracked structures where peak flight loads are encountered at moderate to
high service temperatures. In these cases, low patch volume could be critical for
aerodynamic reasons, and CTE mismatch-related problems are minimal. Good
examples of boron/epoxy applications include lower wing skins, wing/fuselage
attachments, and fuselage keels beams.
In contrast, the moderate-modulus. high-CTE GLARE 2 patches appear to be
best suited for repair of thin fuselage skins. The high stresses in these structures due
to the maximum pressure level at low cruise temperature are increased by the
additional temperature-related stresses. In repairs to thin-skinned fuselage
structures, the slightly greater patch thickness associated with GLARE 2 is usually
negligible. With the superior reductions in K and accompanying low adhesive shear
strains, GLARE 2 patches promise superior durability, resistance against
delamination, and excellent damage tolerance.
14.5. Summary and conclusions
The results of more than 20 years of experience with repairs of relatively thick
cracked aircraft structures have shown boron/epoxy to be an excellent patch
material. Peak flight loads at moderate to high service temperatures can be
sustained by the high-modulus material, without demanding high patch volumes
(thickness). Because of the thick structures, mismatch problems due to the curing
temperature are minimal.
When the transition is made to the repair of cracked fuselage structures, thermal
considerations become paramount. The fuselage will see its highest stress levels at
low temperatures.
Chapter 14. GLARE patching ejficiency studies
41 3
Detailed parametric studies were performed to calculate thermal effects.
Variation of the patch thickness, cure temperature and cruising temperature for
two competing patch materials, the fiber metal laminate [email protected] 2 and the
traditional composite boron/epoxy, gave a good opportunity to compare those
materials for a fuselage crack patching situation.
Experimental work was performed in constant- and variable-amplitude fatigue a
room and low temperatures. The results showed several advantages of GLARE 2
over boron/epoxy patches in fuselage skin repairs due to improved thermal
expansion compatibility between GLARE 2 and aluminum. The results predict
GLARE 2 to be an effective, damage-tolerant fuselage repair material.
References
I. Baker, A.A. and Jones. R. (1988). Bonded Repair of Aircraft Structures (A.A. Baker and R. Jones.
eds.). Boston: Martinus Nijhoff Publishers.
2. Fredell, R. and Gunnink, J. (1992). Fiber metal laminates for improved structural integrity. Proc. o/the Int. Workshop on Structural Integrity of Ageing Aircraft, Atlanta. Georgia, April, pp. 362-375.
3. Fredell, R., Vlot, A. and Roebroeks, R. (1994). Fiber metal laminates: New frontiers in damage
tolerance. Proc. qf the 15th Int. European Conference of the Society for the Advancement qf‘ Material
and Process Engineering. Toulouse, France, June, pp. 3 19-328.
4. Fredell, R. (1994). Damage Tolerant Repair Techniques for Pressurized Aircraft Fuselages. WL-TR94-3 134, Wright-Patterson Air Force Base Ohio, June.
5. Fredell, R., van Barneveld, W. and Vlot, A. (1994). Analysis of composite crack patching of fuselage
structures: High patch elastic modulus isn’t the whole story. Proc. qf the 39th hf.S A M P E
Symposium and Exhibition, Anaheim, California, April, pp. 610-623.
6. Rose, L.R.F. (1981). An application of the inclusion analogy. Int. J . S0lid.s and Structures. 17.
pp. 827-838.
7. Rose, L.R.F. (1988). Theoretical Analysis of Crack Patching, in Bonded Repair of Aircraft
Structures, (Baker, Jones, eds.). Dordrecht: Kluwer Academic Publishers, pp. 77-106.
8. Muki, R. and Sternberg, E. Int. J . Solids and Structures, 4, pp. 75-94.
9. Tarn, J.Q. and Shek, K.L. (1991). Analysis of cracked plates with a bonded patch. Enginwring
Fracture Mechunics, 40(6), pp. 1055-1065.
10. Chu. R.C. and KO, T.C. (1989). Isoparametric shear spring element applied to crack patching and
instability. Theoretical and Applied Fracture Mechanics, 11, pp. 93-102.
1 1 . Jones, R. and Callinan, R.J. (1980). J . Structural Mechanics, 8(2), pp. 143-149.
12. Marissen, R. Fatigue Crack Growth in ARALL, Ph.D. thesis, Department of Aerospace
Engineering, Delft University of Technology, Delft, the Netherlands,
13. Roebroeks, G.H.J.J. (1991). Towards GLARE The Development of a Fatigue Insensitive and
Damage Tolerant Material, Ph.D. thesis, Department of Aerospace Engineering, Delft University of
Technology, Delft, the Netherlands, December.
14. Rose, L.R.F. (1988). Residual Thermal Stresses, in Bonded Repair of Aircraft Structures (Baker.
Jones, eds.). Dordrecht: Kluwer Academic Publishers, pp. 90-91.
15. Baker, A.A., Davis, M.J. and Hawkes, G.A. (1979) Proc. 10th Int. Symp. qf’the Int. Comm. on
Aeronautical Fatigue, paper 4.3.
16. Rose, L.R.F. (1982). Int. J . Fracture, 18, pp. 135-144.
17. Baker, A.A. (1988). Crack Patching: Experimental Studies, Practical Applications, from Bonded
Repair of Aircraft Structures (Baker, Jones, eds.). Dordrecht: Kluwer Academic Publishers, pp. 107.172.
414
Advances in the bonded composite repair of metallic aircraft structure
18. Verhoeven, S. (1988). In Service Effects on Crack Growth Under Bonded Composite Repairs.
Masters thesis, Department of Aerospace Engineering, Delft University of Technology, Delft, the
Netherlands, July.
19. Guijt, C. and Fredell, R. (1996). Delamination Effects in Fuselage Crack Patching, SAMPE
Anaheim.
Chapter 15
GRAPHITE/EPOXY PATCHING EFFICIENCY
STUDIES
P. POOLE
Structural Materials Centre, Defence Evaluation and Research Agency,
Farnborough, €€ants, UK
15.1. Introduction
Theoretical and experimental research on adhesively bonded graphite/epoxy
patch repair of cracked metallic structures has been in progress at DERA for many
years. The early experimental work [ 1 4 ] concerned the repair of central fatigue
cracks in thin aluminium alloy panels and the influence of repair variables on the
effectiveness of the patches in retarding crack growth, while the early theoretical
work [5-71 involved the development of collocation [strip patch and isotropic disc
patch] and 2D boundary element models, and their application to cracked sheet
repairs. Graphite/epoxy patches were used for the initial investigations because
various forms of woven cloth and prepreg were readily available, and because wet
layup of graphite cloth had shown considerable promise for battle damage repair.
Since that time, repairs to stiffened panels and thick sections containing fatigue
cracks, and thin panels containing simulated battle damage, have been investigated,
and a 3D boundary element/finite element computer program for the analysis of
bonded patch repairs has been developed. In addition, the performance of graphite/
epoxy [gr/ep] and boron/epoxy [b/ep] patch repairs have been compared and the
effects of bondline defects and in-service variables on patch efficiency have been
studied.
This chapter reviews DERA research on bonded composite patch repair of
aluminium alloy structures; it contains nine main sections covering repair of thin
skin components, repair of thick sections, gr/ep versus b/ep patches, effect of
bondline defects, effect of impact damage, effect of service temperature, effect of
exposure to hot-wet environments, repair of battle damage and future work.
415
Baker, A.A., Rose, L.R.F. and Jones, R. ( e d s . ) ,
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Q 2002 Elsevier Science Ltd. All rights reserved.
Advances in the bonded composite repair of metallic aircruft structure
416
15.2. Repair of thin skin components
Initial studies at DERA involved the use of adhesively bonded gr/ep patches to
repair 1.6 mm thick aluminium alloy panels containing central fatigue cracks.
Precured patches were manufactured from woven or unidirectional gr/ep prepreg
[e.g. XAS/9 141 and adhesively bonded to cracked test panels in an autoclave,
usually with a 120°C curing epoxy film adhesive such as Redux 31215. Constant
amplitude fatigue tests were carried out to establish the effectiveness of the patches
in retarding fatigue crack growth and patch efficiency was expressed in terms of the
reduction in stress intensity factor range due to patching [AKP/AKu].Figure 15.1
shows typical crack growth rate data obtained for R = 0.1 fatigue testing of patched
and unpatched panels, and illustrates the method that was used to determine AKP
and hence A K P / A K u . It can be seen that for a normalised crack length of
a/ W = 0.5, the effective stress intensity factor range experienced by the crack in the
patched specimen is just over 10 MPam1/2,compared to about 22 MPam'/2 for the
unpatched panel, i.e. AKP/AKU 0.45.
Fatigue tests were carried out to study the effects of a wide range of repair and
test variables on patch efficiency. The variables investigated included type of
prepreg, layup, thickness, size and shape of patch, thickness, modulus and cure
temperature of adhesive, surface treatment of aluminium alloy panels, pre-exposure
to a warm, moist environment, type of fatigue loading and crack length. Most
-
R=0.1, alternating stress An=54 MPa
J
-
I
I
I
IO-^
m
-
m
.
!
.
.
.
.
Chapter 15. Graphitelepoxy patching efficiency studies
417
panels were patched on one side only, but a limited number were patched on both
sides and in these cases crack arrest occurred. Some of the important conclusions
from this work are summarised below:
(a) The rate of crack growth after patching depended on the loading conditions
used for precracking prior to patching. Thus, load shedding during precracking
was recommended in order to ensure that the plastic zones associated with the
final stages of precracking do not cause crack growth retardation when fatigue
loading commences after patching.
(b) In the case of asymmetric single-sided patch repairs, patch efficiency was
improved by the use of anti-buckling plates which restricted out-of-planebending. For such repairs, the use of appropriate anti-buckling devices was
recommended in order to avoid unrealistic pessimistic test results.
(c) In general, patch efficiency improved with increasing crack length and patch
stiffness, and with decreasing adhesive thickness. Varying the adhesive
thickness had a relatively small effect. For example, in the case of repairs
involving woven patches of stiffness approximately 55% that of the aluminium
alloy panels, AK'IAK" increased from 0.57 to 0.64 when the adhesive
thickness was increased from 0.13 mm to 0.76mm [3].
(d) Tests on panels repaired with adhesives cured at room temperature, 120 "C and
175 "C indicated that patch efficiency was affected adversely by residual
thermal stresses arising from differential thermal contraction of patch and
aluminium alloy on cooling from the adhesive cure temperature.
(e) Boeing wedge tests in 50 "C/96% RH indicated that the environmental
durability of adhesively bonded aluminium alloy joints was improved
markedly if a grit blast/silane swab pretreatment was used instead of grit
blasting only. However, when panels were pretreated by various processes,
including grit blasting only, no significant increase in A K p / A K c was observed
following exposure of patched panels to 70 "C/84%RH for 2150 h [3].
(f) Although the results of early theoretical studies at DERA were consistent with
experimental observations concerning the general effects of patch and adhesive
variables on A K P / A K u , the models were unable to predict accurately the
effects of repair variables on the rate of fatigue crack growth. This was not
surprising since these preliminary models did not take into account the effects
of debonding, residual stresses and out-of-plane bending.
The work on patch repair of fatigue cracked thin sheet was extended to stiffened
panels through a contract with British Aerospace [SI. In this programme stiffened
and unstiffened 1.6 mm thick aluminium alloy sheets containing centre cracks were
repaired with precured woven and unidirectional gr/ep patches of equivalent stiffness. For the stiffened panel the initial design represented a two-bay fuselage panel
with a central riveted U-section stiffener. However, owing to fatigue failures at the
first fastener hole it was necessary to redesign the panel with the working section
reduced to a width of 100 mm. Panels were precracked with load shedding, to give a
25 mm crack at the centre fastener hole, and 50 mm wide patches were applied using
a 120°C curing epoxy film adhesive. Constant amplitude [R=0.1. urnax=
80 MPa] fatigue tests demonstrated that both unidirectional and woven gr/ep
418
Advances in the bonded composite repair of metallic aircraft struciure
patches reduced the rate of fatigue crack growth by a factor of 10, when cracks
were grown from 25 mm to 70 mm. It was confirmed that crack growth under the
gr/ep patches could be monitored effectively using an eddy current technique.
Finite element analysis resulted in unconservative predictions, i.e. the predicted
values of A K P / A K Uwere lower than those indicated by the measured crack growth
rate data.
15.3. Repair of thick sections
Initial work at DERA on repair of thick sections [9] was carried out in
collaboration with AMRL, who supplied patched and unpatched specimens for
testing. Figure 15.2 shows the main features of these symmetric specimens, which
comprised two 11.2 mm thick 2024-T4 aluminium alloy plates containing centrally
located surface flaws of surface length 40mm and maximum depth 5.7mm. Each
plate was subjected to constant amplitude fatigue loading until cracking occurred
at the base of the flaw. Ten-ply unidirectional b/ep patches were manufactured
Dimensions in mm
Fig. 15.2. Patched surface flaw specimen.
Chapter 15. Graphitelepoxy patching efJiciencj1 studies
419
from 5521/4 prepreg, and FM73M adhesive was used to simultaneously bond the
patches to cracked plates and the plates to aluminium honeycomb.
Table 15.1 summarises the fatigue life data obtained for patched and unpatched
specimens tested under FALSTAFF [peak stress 137.8MPa] and constant
amplitude [R = 0.1, gmax= 65.5 MPa] loading. These results show that, for
FALSTAFF loading, patching increased fatigue life by a factor of 5.8, which
was much lower than the life improvement factor of 22 reported by AMRL for
constant amplitude loading. When the remaining two specimens were tested under
constant amplitude conditions similar to those used by AMRL, patching increased
fatigue life by a factor of 28, which is in reasonable agreement with the AMRL
results. The effect of patching on the growth of fatigue cracks was also studied at
DERA [9], and examination of fracture surfaces showed that cracks grew through
the plates before any surface crack growth was detected. The growth of surface
cracks was monitored for patched and unpatched specimens, and Figure 15.3
shows crack growth rate data obtained for FALSTAFF loading. For some
specimens, ultrasonic and SPATE techniques were used to monitor debonding of
patches during fatigue testing. Extensive debonding was observed in the case of
FALSTAFF loading, as illustrated in Figure 15.4, but no significant debonding
was detected in the case of the patched specimen tested under constant amplitude
loading. This observation is consistent with the fatigue life and crack growth data
which indicated that patching was more efficient for constant amplitude loading
than for FALSTAFF loading.
A second series of fatigue tests on similar thick section specimens was carried out
at DERA using the same loading spectra and stress levels [lo]. However, in this
case, surface flaws in 12.4mm thick aluminium alloy plates were repaired by
bonding gr/ep [XAS/914] patches to the plates with a 120°C curing epoxy film
adhesive [Redux 3 12/51. In agreement with the previous tests, the increases in
Table 15.1
Effect of patching on fatigue life.
Loading sequence
Patched/unpatched
Specimen
Cycles to failure
Unpatched
9/22U
5/6U
3/4u
7/8U
344039
326056
41 1595
334778
Mean
3541 17
14/15P
18/19P
16/17P
12/13P
1954783
2699351
1923680
1632406
Mean
2052557
1/2u
20/21P
31681
1041557
~~
FALSTAFF
Patched
Constant amplitude
Unpatched
Patched
420
Advances in the bonded composite repair of mefallic &rcra$ structure
Ixlo-br
i
da
dN
mmlcyclc
SXIO-~
/
-
Patched
L
t o m -Fractography
1x106
0.3
0.L
0.7
0.5
0.6
Normalized Crack length I:[
0.8
0.9
Fig. 15.3. Effect of patching on rate of growth of through-thicknesscracks during FALSTAFF loading.
Debond
FALSTAFF cycles
.oo x I O 6
.25 x
50 x
.75 x
.88x
IO6
IO6
IO6
IO6
Fig. 15.4. Development of debond during FALSTAFF loading (specimen 16/17P).
Chapter 15. Graphitelepoxy patching efficiency studies
42 1
fatigue lives and reductions in crack growth rates due to patching were much more
pronounced for constant amplitude loading than for FALSTAFF loading, and
debonding was observed for FALSTAFF loading only. The size and shape of the
debonds indicated by ultrasonic inspection were in excellent agreement with the
debonds observed following specimen failure. In general, the debonds were
elliptical in shape, with the length of the major axis corresponding approximately
to the crack length and the ratio of minor axis to major axis about 0.7, particularly
at relatively long crack lengths. It is possible that fatigue damage of the adhesive
and patch debonding were caused by the relatively high adhesive shear strains
associated with high FALSTAFF loads. It should be noted that these high loads
were selected for the thick section repairs in order to study patch repair efficiency
when the adhesive is subjected to extremely demanding cyclic loading conditions.
Additional fatigue tests showed that the extent of debonding was reduced by either
doubling the adhesive thickness or increasing patch thickness by 50%, but a
significant improvement in fatigue performance was only observed when patch
thickness was increased.
A 2D boundary element model [6] was used to analyse the above thick section
repairs after a through crack had developed from the surface flaw. The model was
used to predict the effects of crack length, debonding, stress level, patch thickness
and adhesive thickness on patch efficiency. In general, the predicted values of
AK'IAK" tended to be lower than the corresponding values determined from
fatigue crack growth rate data, even when debonding was taken into account.
However, reasonable agreement was obtained when a factor wds applied to account
for residual thermal stresses [lo].
It was recognised that a 3D model was required to enable repairs to thick
sections containing surfxe flaws to be analysed in detail and the effectiveness of
patches in retarding crack growth to be predicted accurately. Thus, a 3D boundary
element/finite element model was developed at DERA, where the cracked plate was
modelled using the boundary element method and the composite patch was
modelled using a partially mixed stress-displacement finite element method [ 1 11.
The mixed finite element formulation enabled direct coupling with the boundary
element system in terms of displacement and traction compatibility conditions on
the adhesion surfaces. The adhesive layer could have been included as one of the
patch layers [i.e. a 3D elastic continuum] but for reasons of computational
economy it was treated as a continuous spring mechanism, the properties of which
were absorbed into the adhesion compatibility conditions. This simplified spring
representation allows an efficient consideration of an elastoplastic adhesive layer.
Residual stresses arising from differential thermal contraction of composite patch
and metallic substrate are taken into account in the model.
Since 3D analysis is expensive and time consuming, it was decided to compare
the values of A K Pf AKU predicted by the 3D model with corresponding values
predicted by analytical formulae and a 2D boundary element model. The study was
confined to double sided repairs of the type shown in Figure 15.5, where
unidirectional gr/ep patches are bonded to both sides of an aluminium alloy sheet
containing a central through crack. It was assumed that the patches were bonded
422
Advances in the bonded composite repair of metallic aircraft structure
I
\
E
E
0
0
m
Q
\
Fig. 15.5. Double-sided patched specimen.
with a 120"C curing adhesive and that the patch fibres were aligned perpendicular
to the crack. Five repairs were studied where the sheet thickness [2h-) was 1.55, 3.1,
6.2, 12.4 or 24.8mm and the patch thickness [PIvaried with sheet thickness
according to W=0.1645hS,i.e. the ratio of patch stiffness to sheet stiffness was
constant. The non-linear stress-strain behaviour of the adhesive was assumed to be
consistent with the experimental behaviour reported in the literature for Redux 3 12
adhesive; it was found that this behaviour could be described accurately by the
Ramberg-Osgood equation for pure shear y = t/G" + A ( z / t c ) " with parameters
n = 14.26, z,=40 MPa and A = 0.041 17 for the range 0 < y 5 0.15.
The 3D model was used to study the variation in stress intensity factor range AK
through the thickness of patched and unpatched sheets subjected to constant
amplitude loading [R = 0.1, omax
= 65.5 MPa]. These data were used to determine
root mean square values of AKp and AKU, and hence A K P / A K U .The variation of
Chapter 15. Graphitelepoxy patching efficiency studies
425
by using patches with a layer of glass/epoxy on the surface to be bonded, while
ingress of moisture can be minimised by sealing edges of patches and cracks and by
wet assembly of any fasteners passing through the patches. Theoretical work at
DERA has established that patch efficiency is only slightly affected by the presence
of one ply of woven glass/epoxy on the patch surface. For example, for the repair
configuration described in Section 15.5 and a crack length of 15 mm, the 3D BE/FE
model predicted that A K P / A K u would be increased from 0.24 to 0.25 by the
presence of a single ply of glass/epoxy.
The coefficient of thermal expansion for unidirectional b/ep is about 4.5 x lo-'
("C)-' compared to 0.4 x
("C)-' for gr/ep and 23 x 10-6("C)-* for
aluminium alloy. This means that the residual stresses arising from differential
thermal contraction of patch and aluminium alloy on cooling from the adhesive
cure temperature will be greater for gr/ep than for b/ep. However, it is difficult to
estimate the precise improvement in resistance to fatigue crack growth that will be
achieved by using b/ep rather than g/ep patches of the same stiffness, and thus the
work outlined below was undertaken at DERA [13].
Single and double-side patch repairs were carried out on 12.4mm thick, 108mm
wide L97 aluminium alloy test pieces containing central through-thickness fatigue
cracks [20 mm or 40 mm long]. 1.34 mm thick b/ep and 1.65 mm thick gr/ep patches
were manufactured from Textron 5521 and Ciba-Geigy T800/924 prepregs,
respectively. These thicknesses were selected in order to produce b/ep and gr/ep
patches of similar stiffness, assuming Young's modulus was 208 GPa for 5521 and
168 GPa for T800/924. In addition, it was estimated that these thicknesses would
result in measureable rates of crack growth and not cause crack arrest. The patches
were 180mm long, including 30mm tapered portions at either end, and 108mm
wide; these patch sizes were selected to provide large residual stress effects.
Following grit blast/silane treatment of the aluminium alloy surfaces, patches were
applied using a 120°C curing epoxy film adhesive [Redux 312/5]. Constant
amplitude [ R = 0.1, omax
= 55 MPa] fatigue tests were carried out on six patched
and three unpatched specimens; Figure 15.8 summarises the crack growth rate data
obtained. It can be seen that the rate of crack growth was reduced by a factor of
about two in the case of single-side repairs, and by a factor greater than ten in the
case of double-side repairs, and that b/ep patches were slightly more effective than
gr/ep patches in retarding crack growth.
The DERA 3D BE/FE computer program was used to predict A K P / A K " for
both single and double-side repairs. Predicted values of A K P / A K u are shown in
Table 15.2 for crack lengths [2a]of 50 mm and 70 mm. The computer program was
also used to predict the effect of residual thermal stresses on K,,,/K,,,,, [R-ratio] for
patched specimens subjected to R = 0.1, omax= 55 MPa remote loading. For
a = 25 mm, the predicted values of Kmin/Kmaxwere 0.64 and 0.68 for double-sided
repairs with b/ep and gr/ep, respectively, and 0.33 and 0.36 for single-sided repairs
with b/ep and gr/ep, respectively.
Values of AKP/AKC' were determined from the crack growth rate data
summarised in Figure 15.8 and that determined for unpatched specimens loaded
at R = 0.33,0.36,0.64 and 0.68. For example, in the case of double-sided b/ep patch
Advances in the bonded composite repair of metaltic aircrafz structure
426
-E
I . . , , I , , . , I , , , . I , , . , I .
18
0
I0
I
I
I
I
.
9
I
. I . . , . I . , . . I . .
28
30
H a l f c r a c k l e n g t h a Lmm)
40
,
I
SO
Fig. 15.8. Effect of patching on rate of crack growth (R=0.1, urnax
= 55MPa).
repair and a half crack length of 25 mm, daldN = 2.35 x IO-' m/cycle was obtained
directly from Figure 15.8 and the value of AK corresponding to this da/dN in da/
dN-AK data for R = 0.64 loading was assumed to be AKp [4.6 MPam'/2]. Thus, for
this particular repair it was estimated that AKp =4.6 MPam'j2 and
A K P / A K U= 0.27. Values of A K p / A K u determined in this way from experimental
Table 15.2
Comparison of theoretical and experimental values of AKP/AKU.
AKP/AKu
Half crack length, a(mm)
Single/double
Patch type
Theory
Expt
B/ep
Gr/eP
0.66
S
0.70
0.71
D
B/ep
GrieP
0.27
0.29
0.28
S
Grh
0.61
0.61
0.66
0.67
D
B/ep
GrIep
0.20
0.20
0.20
0.21
25
35
0.66
0.27
Chapter 15. Graphitelepoxy patching efficiency studies
423
0.3 AKP
-
AK"
0.2
-
0.1
-
Fig. 15.6. Effect of analysis method and sheet thickness on AKp/AKC (a= 20 mm).
A K P / A K u with sheet thickness predicted by the 3D model for a half crack length
[a] of 20mm is shown in Figure 15.6, together with corresponding A K P / A K L 'data
predicted by analyical formulae and a 2D boundary element model. It is evident
that for hs 2 3.1 mm the values of A K P / A K U predicted by the 3D model are
significantly higher than those predicted by the other models. Thus, it is
recommended that a 3D model should be used for the analysis of relatively thick
sections, since it appears that the other methods will predict erroneous low rates of
fatigue crack growth following patching. Relatively small differences in predicted
values of A K P / A K U were observed for the other two models; these have been
discussed in detail elsewhere [l 11. The 3D and 2D models were used to predict the
effects of elliptical debonds, assuming that the major axis of the debond was
equivalent to the crack length and the ratio of major axis to minor axis was 0.7.
Typical data are shown in Figure 15.7 for repairs to thick plate [h"= 12.4mml; it
can be seen that both models predicted marked increases in A K p / A K u with
debonding and that the difference between the values of AKP/AKU predicted by
the two models was less pronounced when debonding was present.
The values of A K p / A K u predicted by the 3D model were in excellent agreement
with corresponding values determined from experimental crack growth data
obtained for centre cracked 12.4mm thick plate specimens [see Section 15.41 and
edge cracked 4.0mm thick sheet specimens [see Section 15.51. In addition, patch
surface stress distributions determined from SPATE [stress pattern analysis by
thermal emission] and strain gauge measurements were in good agreement with
distributions predicted by the 3D model, but in poor agreement with those
predicted by the 2D model.
424
Adwnces in the bonded composite repair of metallic aircraft structure
30
U 2D
Debond
d l a = 0.7
I
20
I
30
a.mm
I
I
40
50
Fig. 15.7. Effect of analysis method, debonding and crack length on AKP/AK" (h'= 12.4mm)
15.4. Graphitelepoxy versus boronlepoxy
Gr/ep materials were selected for bonded composite patch research at DERA
because, compared to b/ep, a wide range of materials were readily available from
various sources and because they were cheaper, easier to handle and more suitable
for curved surfaces. Furthermore, 120 "C curing prepregs were available which
would allow repairs to thin skins to be carried out efficiently by co-cure of adhesive
and prepreg. Other researchers [12] have stated that they prefer b/ep, rather than
gr/ep, for patch repairs because it offers (i) a superior combination of strength and
stiffness, (ii) low electrical conductivity, and (iii) a higher coefficient of thermal
expansion. These three advantages are considered separately below.
Although recent advances with gr/ep materials have resulted in tensile strength
and stiffness properties which approach those of b/ep, it is recognised that b/ep still
offers a stiffness advantage which will enable slightly thinner patches to be used for
some repairs. This may be important for repairs to control surfaces if aerodynamic
considerations dictate the use of minimum thickness patches.
It has been stated that the low electrical conductivity of boron is advantageous
because it avoids the danger of galvanic corrosion associated with the use of gr/ep
and allows the use of simple eddy current techniques to detect and monitor cracks
under patches. However, work at British Aerospace, DERA and the RAF has
shown that the growth of fatigue cracks under gr/ep patches can be monitored
successfully using eddy current techniques. Furthermore, the author considers that
potential corrosion problems associated with the use of gr/ep can be avoided or
minimised by appropriate protection measures. Galvanic contact may be avoided
Chapter 15. Graphitelepoxy patching ef'jciency studies
425
by using patches with a layer of glass/epoxy on the surface to be bonded, while
ingress of moisture can be minimised by sealing edges of patches and cracks and by
wet assembly of any fasteners passing through the patches. Theoretical work at
DERA has established that patch efficiency is only slightly affected by the presence
of one ply of woven glass/epoxy on the patch surface. For example, for the repair
configuration described in Section 15.5 and a crack length of 15mm, the 3D BE/FE
model predicted that A K P / A K U would be increased from 0.24 to 0.25 by the
presence of a single ply of glass/epoxy.
The coefficient of thermal expansion for unidirectional b/ep is about 4.5 x
("C)-' compared to 0.4 x lop6 ("C)-' for gr/ep and 23 x 10-6("C)-' for
aluminium alloy. This means that the residual stresses arising from differential
thermal contraction of patch and aluminium alloy on cooling from the adhesive
cure temperature will be greater for gr/ep than for b/ep. However, it is difficult to
estimate the precise improvement in resistance to fatigue crack growth that will be
achieved by using b/ep rather than g/ep patches of the same stiffness, and thus the
work outlined below was undertaken at DERA [13].
Single and double-side patch repairs were carried out on 12.4mm thick, 108mm
wide L97 aluminium alloy test pieces containing central through-thickness fatigue
cracks [20 mm or 40 mm long]. 1.34mm thick b/ep and 1.65mm thick gr/ep patches
were manufactured from Textron 5521 and Ciba-Geigy T800/924 prepregs,
respectively. These thicknesses were selected in order to produce b/ep and gr/ep
patches of similar stiffness, assuming Young's modulus was 208 GPa for 5521 and
168 GPa for T800/924. In addition, it was estimated that these thicknesses would
result in measureable rates of crack growth and not cause crack arrest. The patches
were 180mm long, including 30mm tapered portions at either end, and 108mm
wide; these patch sizes were selected to provide large residual stress effects.
Following grit blast/silane treatment of the aluminium alloy surfaces, patches were
applied using a 120°C curing epoxy film adhesive [Redux 312/5]. Constant
amplitude [R = 0.1,,,,rc
= 55 MPa] fatigue tests were carried out on six patched
and three unpatched specimens; Figure 15.8 summarises the crack growth rate data
obtained. It can be seen that the rate of crack growth was reduced by a factor of
about two in the case of single-side repairs, and by a factor greater than ten in the
case of double-side repairs, and that b/ep patches were slightly more effective than
gr/ep patches in retarding crack growth.
The DERA 3D BE/FE computer program was used to predict A K P / A K u for
both single and double-side repairs. Predicted values of A K P / A K U are shown in
Table 15.2 for crack lengths [2a] of 50 mm and 70 mm. The computer program was
also used to predict the effect of residual thermal stresses on Kmin/Kmax
[R-ratio] for
patched specimens subjected to R = 0.1, omax
= 55 MPa remote loading. For
a = 25 mm, the predicted values of Kmin/Kmaxwere 0.64 and 0.68 for double-sided
repairs with b/ep and gr/ep, respectively, and 0.33 and 0.36 for single-sided repairs
with b/ep and gr/ep, respectively.
Values of A K p / A K u were determined from the crack growth rate data
summarised in Figure 15.8 and that determined for unpatched specimens loaded
at R = 0.33,0.36,0.64 and 0.68. For example, in the case of double-sided b/ep patch
Advances in the bonded composite repair of metallic aircraft structure
426
-s
10
I ' ' ' ' I " ' ' I " " I " " 1 ' ' " 1 " " I " " I ' ' ' ' I ' " '
o
*
x
+
-8-
-
Grlep
wep
Unpatched
i
-6
0
16
0
7
c
0
6
\
E
Single patch
Y
-
z
U
\
---
-7
10
D o u b l e patch
-8
-e
I0
' . . . . l . . , . l . * . , r . . . . I . . . , I . . . . I . . . . I . . . . I . . . . I . . . * '
25
35
0.66
0.66
0.70
0.71
0.27
0.27
0.29
0.28
0.61
0.61
0.66
0.67
0.20
0.20
0.20
0.21
Chapter 15. Graphitelepoxy parching ef$cieney studies
427
crack growth data are shown in Table 15.2 together with corresponding theoretical
values predicted by the 3D BE/FE program. It is evident that excellent agreement
between experimental and theoretical values of A K P / A K Uwas obtained in the case
of double-sided repairs, where large differences in crack growth rates were observed
for patched and unpatched specimens. In the case of single-sided repairs, the
predicted values of A K P / A K u were lower than than those determined experimentally. This observation may be associated with debonding, which would be more
likely to occur in the case of the asymmetric single-sided repairs. This suggestion is
consistent with the increase in crack growth rate with crack length observed for the
single-sided repairs. Unfortunately, debonding was not monitored during this
investigation because none had been detected in earlier work when symmetric
patched thick section specimens were subjected to similar constant amplitude
loading.
The investigation outlined above showed that the lower coefficient of thermal
expansion of b/ep patches resulted in only slightly better performance than for gr/
ep patches, even though the patch size had been selected to produce a large residual
stress effect. In practise, the effect of residual thermal stresses will be less
pronounced due to the restraint provided by surrounding structure, and therefore
the use of b/ep rather than gr/ep patches will generally result in only very small
improvements in fatigue performance due to reduced residual stresses.
For many applications it appears that efficient, durable repairs can be achieved
using either b/ep or gr/ep patches. However, b/ep may be more suitable for some
repairs [eg where maximum stiffness/minimum thickness patches are required] and
gr/ep for others [e.g. where patches have to be applied to sharply curved surfaces].
Although this section has been confined to a comparison of b/ep and gr/ep patches,
it should be noted that GLARE patches may be attractive for some applications,
such as transport aircraft fuselage skins, because they offer improved fatigue
performance due to reduced residual stress effects. The use of GLARE patches is
considered in detail in Chapter 14.
15.5. Effect of bondline defects
Research at DERA on thick section repairs [see Section 15.3 above] showed that
patch efficiency depended on the extent to which debonding developed during
fatigue loading. However, it is possible that bondline defects may form during
patching and it is essential that the effects of such defects on repair performance
can be predicted accurately, since this will enable the acceptability of specific
defects to be assessed and critical defect sizes to be defined. Thus, the research
programme outlined below was undertaken to investigate the significance of a
range of bondline defects on the performance of patch repairs to panels containing
edge cracks [14].
145mm wide panels, containing a 5 mm long single edge notch, were machined
from 4.0 mm thick 2024-T3 aluminium alloy sheet. 2.5 mm long fatigue cracks were
grown from the 5 mm slots under load shedding conditions, with the final 0.5 mm of
428
Advances in the bonded composite repair of metallic uircraft structure
growth achieved by loading at R = 0.05, omax= 55 MPa. Two cracked panels were
bonded to aluminium alloy honeycomb and aluminium alloy end spacers to
produce symmetric unpatched specimens.
Twelve ply unidirectional b/ep [5521] patches were supplied by AMRL,
Melbourn for this programme. In addition, sixteen ply unidirectional gr/ep
[T800/924] patches were manufactured. The average measured thicknesses of the
patches were 1.645mm for b/ep and 2.00mm for gr/ep. These patch thicknesses
were selected so that the b/ep and gr/ep patches would have similar stiffnesses,
assuming Young’s modulus was 208 GPa for 5521 and 168 MPa for T800/924. The
patches were 132mm long, including 30 mm or 33 mm tapered portions at either
end, and 70 mm wide. The tapered portions of the b/ep patches consisted of eleven
3 mm steps, compared with fifteen 2 mm steps in the case of gr/ep patches. Prior to
adhesive bonding, patch surfaces were lightly grit blasted while aluminium alloy
surfaces were subjected to a grit blast/silane swab treatment. Redux 312/5 adhesive
was used to bond gr/ep or b/ep patches to both sides of specimens at the same time
as skin/honeycomb and skin/spacer bonding. For selected specimens, small
[8mm x lOmm] pieces of Teflon film were placed on the pretreated aluminium
alloy surface prior to adhesive bonding, in order to produce bondline defects at the
locations shown in Figure 15.9. These locations were selected because they were
considered most likely to have a significant effect on the performance of patched
specimens.
Unpatched and patched specimens were tested under R = 0.05, omax
= 110 MPa
constant amplitude loading. For patched specimens, crack length was monitored
using an eddy current technique [Elotest B 11, while debonding was monitored using
a pulse-echo ultrasonic technique, which involved a hand-held 10 MHz transducer.
The fatigue lives of patched specimens were at least 70 times greater than for
unpatched specimens, and were reduced by about 14% due to the presence of small
[8mm x lOmm] bondline defects at the onset of fatigue testing. Figure 15.10 shows
that patching was very effective in reducing the rate of crack growth, and that the
initial bondline defects resulted in relatively small effects. Although there is some
overlap of data for patched specimens, it can be seen that b/ep patches without
defects were most effective in reducing the rate of crack growth while gr/ep patches
with defects were least effective. Ultrasonic inspection established that debonds
developed from the initial defects located adjacent to the crack. Typical debond
growth is illustrated in Figure 15.11, where the tip of the debond corresponds
approximately to the crack tip position. In the absence of initial defects, debonds of
similar shape developed although they tended to be narrower and the tip of the
debond was located behind the crack tip. No debond growth was detected for
defects located at the tapered edge of patches, [see defect X in Figure 15.111.
Repairs were analysed using the 3D BE/FE computer program, assuming rigid
grips with displacement boundary conditions on the leading edges. Figure 15.12
shows the variation in Kmin/Kmax
[R-ratio] with crack length predicted for patched
specimens subjected to R = 0.05, cmax
= 110 MPa loading, while Figure 15.13
indicates the effects of defects and debonding on predicted values of A K P / A K u for
both gr/ep and b/ep patch repairs. Table 15.3 compares predicted values of
Chapter IS. Gruphitelepoxy patching efficiency studies
I
I
II
I
429
I
la
I
Fig. 15.9. Dimensions and locations of patches and bondline defects
AK'IAK" with corresponding values determined from crack growth rate data,
where residual stress effects were taken into account by determining AK' from da/
dN-AK data for R-ratios predicted for patched specimens [as described in section
15.4 above]. It can be seen that there is excellent agreement between the predicted
values of AK'IAK" and those determined from experimental data, providing the
effect of debonds and defects are taken into account in the analytical model. For
ease of modelling, it was assumed that the shape of the debond relative to the initial
defect and crack was as shown in Figure 15.14, i.e. the debond was as wide as the
initial defect and extended to the crack tip. In general, the measured debonds were
smaller than this, and therefore the values of AKP/AKC'predicted for defects and
debonds were greater than those determined from experimental data. The only
exception concerned gr/ep and a crack length of 60 mm, when the measured debond
was slightly larger than that assumed for modelling purposes. The slightly better
crack growth performance observed for b/ep patches, compared to gr/ep patches,
[Figure 15.101 may be explained in terms of the lower R-ratio for b/ep [Figure
15.121, due to reduced residual stresses.
Advances in the bonded composite repair of metallic uircruft structure
430
-a
I0
-4
1E
-
6
P
-5
m
e
u
10
-
P
P
-
x
.\"
-
-6
E 10
-
A
P
z
a
-
x
+o
Y
U
.
10-7
o
-0
+
+
x
10
-9
10
-
*
BFRP
BFRP
+
defects
CFRP
CFRP + d e f e c t s
Unpatchad
-
1....1....1...~1...1(1...(1.111....1.(1.l....l....l~..~l~...l...~
Fig. 15.10, Effect of patch type and defects on rate of fatigue crack growth (R= 0.05, om,, = 110 MPa).
I
~
Cycles
280000
410000
-__-
490000
550000
590000
No debond growth at x
Fig. 15.1 1. Growth of debond from bondline defect in gr/ep patched specimen.
Chapter 15. Graphitelepoxy patching efficiency studies
43 1
1.o
1
0.5
CFRP
w:
Lu:
(3:
a:
0:
0:
W-
BFRP
w:
I:
t:
2;
LL:
0:
I--.
a:
w:
a
0:
0.0
0
Fig. 15.12. Variation of K,,,,,/K,,,,, with crack length for b/ep and gr/ep patched specimens.
0.5
0.4
7: DEFECTS
0.3
DEFECTS + DEBONDING
3
Y
3
3 0.2
w :
a
:
n:
W :
0.1
I-:
0 :
w:
LI'
w:
c3j
0
145
0
a [mml
Fig. 15.13. Variation of AKP/AKUwith crack length, defects and debonding.
Advances in the bonded composite repair of metallic aircraft structure
432
Table 15.3
Comparison of values of A K p / A p determined from experimental crack growth rate data
with those predicted by analytical model.
AKp/AKu (Theoretical)
Patch type
a, mm
AK'IAK"
WP
15
30
60
15
30
60
Gr/ep
+ defects
(Expt)
No defectldebond
Defect and debond
0.25
0.20
0.17
0.24
0.18
0.28
0.22
0.15
0.17
0.27
0.21
0.19
0.24
0.18
0.28
0.22
0.17
0.1s
The analytical model was used to predict the effect of increasing the size of the
initial bondline defect. Table 15.4 shows that, for a crack length of 15mm,
A K P / A K u increased from 0.24 in the absence of bondline defects to 0.26 with a
10 mm x 8 mm defect, and to 0.35 with a 20 mm x 16mm defect. It follows that the
20mm x 16mm defect would have a significant effect on the rate of fatigue crack
growth, while the lOmm x 8mm defect would have little effect and would
probably be acceptable. However, any assessment of bondline defects must take
account of the load spectra which may be experienced in service.
Fig. 15.14. Shape and size of debond region assumed in theoretical study.
Chapter 15. Graphitelepoxy patching efficiency studies
433
Table 15.4
Effect of initial defect size on AKp/AKU ( a = 15 mm).
Patch
B/ep
WeP
Defect size
AK
N o defect
lOmm x Xmm
15mm x 12mm
20mm x 16mm
0.24
0.26
0.32
0.35
No defect
lOmm x 8mm
15mm x 12mm
20mm x 16mm
0.24
0.26
0.32
0.35
1AK
15.6. Effect of impact damage
For many bonded composite patch repairs, particularly those on external
surfaces, there is a risk that impact damage may occur in service. Thus, research
was undertaken at DERA to investigate the influence of impact damage on the
effectiveness of bonded patches in retarding the growth of fatigue cracks [15].
12.4 mm thick aluminium alloy specimens containing 40 mm long central throughthickness cracks were repaired on both sides by bonding b/ep, gr/ep or gr/ep + gl/ep
patches with Redux 31215 adhesive. The gr/ep gl/ep patches were manufactured
using 13 plies of unidirectional gr/ep prepreg [T800/924] and 1 ply of woven gl/ep
prepreg [9246/37%/7781]. Impact damage was introduced at sites 5 mm in front of
the underlying fatigue cracks, using a Rosand impact machine with a 16mm
diameter hemispherical impacter. The impact energy was either 9 Joules [typical of
impact involving a dropped tool] or 45 Joules [typical of impact with runway
debris]. For patches subjected to low energy [9 Joules] impact, small areas of
surface damage were visible and C-scans indicated that the damaged area was less
than 5 mm diameter. This level of damage did not result in a significant increase in
the rate of crack growth, i.e. patch efficiency was not reduced. In contrast, high
energy [45 Joules] impact resulted in severe damage and subsequent acceleration of
crack growth, as illustrated in Figure 15.15 for specimens repaired on both sides
with gr/ep + gl/ep patches. Visual examination of the patches revealed extensive
splitting, delamination and fibre breakage, with some damage present at the
bonded surface of the patch. In most cases the damage appeared to be contained by
an area approximately 12 mm wide and 50 mm long, located with its 50 mm length
edges 18 mm and 30 mm from the centre of the patch.
The 3D BE/FE computer program was used to predict the effect of impact
damage on patch efficiency. Since the precise nature of the damage was difficult to
quantify, a worst case was assumed where two 12mm wide, 50mm long, full
thickness portions of the patch were completely removed. This simulated damage
was referred to as full damage. The effect of removing similar portions of patch, but
of half thickness only, was also studied. This form of simulated damage, where the
patch is of half thickness in the two 12mm x 50mm areas, was referred to as ha!f
+
Advances in the bonded composite repair of metallic aircruft structure
434
l.0E4
._
1
- .
.. .
I
A Without impact damage
!
1.OE-5 .. -
1 A With impact damage
.
I
I
I
.
I
c
2
I
1 OE-7
0
I
1
10
5
0
15
20
25
30
35
40
45
50
55
a (mm)
Fig. 15.15. Effect of high energy impact on rate of crack growth [double-sided repair with gr/ep+ gl/ep
patches].
damage. For comparison, the effect of two 12mm x 50mm debonds at the patch/
metal interface was investigated. The predicted effect of these different simulated
damages on AKP/AK" is shown in Figure 15.16. It can be seen that the values of
[email protected]/AK"
0.5
I
I
1
I
I
I
0.4
0.3
0.2
0.1
x Debond
0.0
0
10
20
30
40
50
Fig. 15.16. Variation of AKP/AK" with crack length for various damage scenarios.
a
Chapter 15. Graphitelepoxy patching efficiency studies
435
AK'IAK" for the full damage case exceed those for the no damage case by about
21% at a = 20 mm [i.e. when the crack tips are just inside the damage area], rising to
a maximum of about 45% as the crack tips approach a = 30 mm, before tailing off
to 27% at a=42mm. It is interesting to note that for the half damage case at
a = 24mm, AKP/AKU is only 8% higher than for the no damage case, compared to
34% for ,full damage and 16% for the debonds.
Crack growth rates for patched specimens were predicted from the theoretical
values of AK'IAK' and RP,and experimental da/dN-AK data for 2024-T3 alloy at
various R-ratios, as described previously. In the absence of impact damage, the
predicted and measured crack growth rates were in good agreement. However, the
crack growth rates predicted for full damage were faster than those observed
following high energy impact. This was expected because the .full darnage case was
deliberately selected to represent more severe damage than that resulting from high
energy impact.
The observed effects of impact damage on patch performance, and the C-scan
evidence that growth of damage did not occur during fatigue testing, indicate that
impact damage is unlikely to present serious in-service problems. Furthermore, it
appears that visual examination of the patch surface will enable significant impact
damage to be detected readily, and that an estimate of the maximum extent of such
damage will allow a conservative estimate of its effect on patch efficiency.
15.7. Effect of service temperature
Accurate prediction of the influence of service temperature on the effectiveness of
patch repairs in retarding fatigue crack growth is not straightforward because
temperature may affect residual stresses, adhesive properties and resistance to
fatigue crack growth. Recent research at DERA on the effect of test temperature on
patch efficiency involved 12.4mm thick specimens similar to those used for the
impact damage investigation [ 151. Theoretical and experimental work was carried
out to investigate the effect of varying the test temperature in the range -55 "C to
70 "C. Fatigue testing demonstrated that increasing the test temperature from
ambient to 70°C resdted in very small reductions in crack growth rate for
specimens repaired on one side with b/ep or gr/ep patches. This observation was
consistent with theoretical analysis which predicted that the opposing effects of
reduced residual stresses and reduced adhesive modulus would result in a small
reduction in crack growth rate. In contrast, for double-sided repairs, a small
increase in crack growth rate was predicted.
Theoretical analysis predicted that reducing the test temperature to -55 "C
would result in an increase in crack growth rate for patched specimens, owing to
increased residual stresses having a greater effect than any likely accompanying
increase in adhesive shear modulus. Fatigue testing at -55°C to determine the
magnitude of this effect has not yet been carried out. However, when a single sided
gr/ep patched specimen was tested at -2O"C, rather than at ambient laboratory
conditions, a significant decrease in crack growth rate was observed. This
436
Advances in the bonded composiie repair of metallic aircraft structure
behaviour may be explained in terms of an increase in the crack growth resistance
of 2024-T3 alloy, due to removal of moisture from the test environment at a
temperature of -20 "C. Fatigue tests on unpatched specimens confirmed that crack
growth rates were significantly lower at -20 "C than at room temperature. Thus,
from the results of the DERA investigation [15] it appears that, for gr/ep patches
bonded with a 120 "C curing adhesive, patch efficiency under ambient conditions
will not be reduced significantly by varying the service temperature in the range
-55°C to 70°C. However, further work is required to establish the effect of
increasing the temperature to 70 "C following long term exposure to hot-wet
conditions [see next section], and to confirm performance at -55 "C.
15.8. Effect of exposure to hot-wet environments
The effectiveness of adhesively bonded composite patches in retarding fatigue
crack growth in aluminium alloy structures may be affected adversely by long-term
exposure to hot-wet environments, due to moisture causing reduced strength and
stiffness of the adhesive, loss of adhesion at the aluminium alloy/adhesive interface
and/or corrosion under the patch. Research has been carried out at DERA [16] to
investigate the extent to which bonded gr/ep patch repairs are degraded when they
are exposed to various hot-wet environments. In one programme, 1.6mm thick,
150 mm wide aluminium alloy panels containing 38 mm long central fatigue cracks
were repaired on one side with various patchladhesive systems. Panel surfaces were
subjected to a grit blast/silane swab treatment prior to bonding; an adhesive
bonding primer was not used. Following patching, fatigue testing was carried out
to grow cracks by approximately 4 mm and thereby enable the effect of patching on
crack growth rate to be determined. These panels were then transported to
Australia where they were exposed under load at Pin Gin Hill hot-wet cleared
jungle site or Cowley Beach marine site for up to six years. After exposure for one
or six years, panels were placed in sealed polyethylene bags and returned to DERA
for fatigue testing. Thus, for each panel, fatigue crack growth rate data [for R = 0.1,
omax
= 60 MPa loading] were obtained before patching, immediately after patching,
and after exposure for one or six years. The main results of this investigation are
summarised below:
i For panels repaired by bonding precured patches with a 120°C curing film
adhesive [Redux 312/5], exposure at the jungle or marine sites for one or six
years had no significant effect on crack growth rate, i.e. patch efficiency was
not affected. This is illustrated in Figure 15.17 by the crack growth rate data
obtained for a patched panel exposed at the jungle site for six years.
ii For panels repaired by bonding precured patches with a paste adhesive
[Araldite 20051, crack growth rate data exhibited greater variability but again
exposure appeared to have no significant effect on patch efficiency.
iii In contrast, for panels repaired with wet laminated patches, exposure at the
marine site for six years resulted in extensive debonding and almost no
retardation of fatigue crack growth. This behaviour was attributed to
431
Chapter 15. Graphite/epo.xy patching ef$ciency studies
1 .E-03
-a2
0
.
5r
0
.
.*
1
/
Unpatchecl
.
.
Patchec
1.E-04
pW%@
Exposed
a2
c
E
c
2
$
1.E-05
Y
0
~
... . Control unpatched
E
0
1 .E-06
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
a/ W
Fig. 15.17. Effect of exposure at jungle site for six years on fatigue crack growth rate for panel repaired
with precured patch and Redux 31215 adhesive.
corrosion under the patch, caused by high levels of salinity in the atmosphere
and the galvanic action of the gr/ep patch. [No effort was made during patch
application to avoid electrical contact between the graphite cloth and the
aluminium panel, i.e. a layer of woven glass was not used to separate the
graphite from the aluminium].
iv In the case of panels repaired with wet laminated patches and exposed at the
jungle site, patch efficiency improved as exposure time increased. This
unexpected but consistent observation was attributed to additional curing of
the wet laminated resin during exposure. Corrosion was not detected at/under
the edges of the patches, which was not surprising since there was no salinity at
the jungle site.
When similar panels were repaired with precured patches and a 120 "C curing film
adhesive, exposed to 70 "C/84%RH for up to 408 days, and then fatigue tested, only
very small increases in fatigue crack growth rate were observed. Other panels were
exposed to a hot-wet-freeze cycle, comprising cooling from +50 "C to -55 "C over
70min, dwell at -55°C for 30min, heating to +50"C over 35min, and dwell at
50°C/96%RH for 585min. Exposure to this cycle for up to 696 days, and then to
50 "C/96%RH for up to 720 days, resulted in small increases in crack growth rate,
i.e. prolonged exposure to these relatively severe conditions had little effect on
patch efficiency.
In another DERA study [16], 12.4mm thick specimens were repaired on both
sides, using T800/924 patches and Redux 312/5 adhesive, and exposed to 70"C/
84%RH for about one year. Recent fatigue testing under ambient laboratory
conditions indicated that this exposure had little effect on crack growth rate.
However, higher crack growth rates were observed when exposed, patched
438
Advances in the bonded composite repair of metallic aircraft structure
specimens were fatigue tested in an environmental cabinet at 70 “C/84%RH.
Further work is in progress to confirm and explain this behaviour.
In general, the research outlined above indicates that the effectiveness of
adhesively bonded composite patch repairs to aluminium alloy structures will not
be affected significantly by long-term exposure to hot-wet environments, providing
appropriate surface treatments, adhesives, patches and bonding processes are used.
This general conclusion is supported by the excellent long-term service experience
reported in this book for a wide range of repairs.
15.9. Repair of battle damage
Theoretical and experimental research has been carried out at DERA to assess
the potential of adhesively bonded gr/ep patches for the “permanent” repair of
battle damage. Work to date has concerned the repair of simulated battle damage
in 3.175mm thick, 160mm wide 2024-T3 aluminium alloy test panels, where the
damage consisted of holes with defects at various locations round the edges of the
holes. Several damage configurations have been investigated, including those based
on 5 mm or 40 mm diameter central holes with either [a] two slots at opposite sides
of the holes and perpendicular to the loading axis, [b] one slot perpendicular to the
loading axis, or [c] four slots at 45” to the loading axis. All test panels were fatigue
loaded until a crack of specified length, e.g. 1 mm, developed at the end of each slot.
Repairs were carried out using precured gr/ep [T800/924] patches and a 120°C
curing epoxy film adhesive [Redux 312/5].
A 3D boundary element/finite element model was used to study patch repair of
various forms of damage, and to predict the influence of patch, adhesive and
loading variables on repair efficiency. The through thickness variation of K was
studied and root mean square values were determined for the entire crack front.
Similar values of K were obtained if the crack front was assumed to be at 45” to, or
perpendicular to, the patch plane, i.e. crack front shape had only a small effect on
K, and therefore perpendicular cracks were assumed for the remainder of the study.
In general, significant improvements in fatigue performance were predicted for
single-sided patch repair of various forms of damage, with better performance
predicted for thicker patches but only a small improvement predicted when
adhesive thickness was reduced from 0.3 mm to 0.05 mm. Less efficient repairs were
predicted for larger holes; for example, in the case of two cracks at opposite sides of
the hole and a half crack length of 30mm [measured from centre of hole],
A K P / A K Uwas about 0.48 for a 40 mm diameter hole compared to 0.42 for a 5 mm
diameter hole. When panels containing four slots at 45” to the loading axis were
fatigue loaded, cracks tended to grow perpendicular to the loading axis to produce
kinked cracks of the type shown in Figure 15.18. When repair of this type of
damage was compared with that of “equivalent” damage in the form of two cracks
at opposite sides of a hole [see Figure 15.181, more efficient repairs were predicted
in the case of the four kinked cracks, as illustrated in Table 15.5. In the case of the
four kinked cracks, values of ICI, ICIKrr
and KIIIwere determined and it was shown
Chapter 15. Graphite/epo.xypatching eficiency studies
439
Fig. 15.18. Different damage configurations of "equivalent" width
that the combined contribution of Kl,and KIIrto the effective stress intensity factor
was less than 8% for the configurations studied.
Fatigue testing confirmed that various forms of damage could be repaired
effectively with single patches. For example, the fatigue lives of panels containing
40mm diameter holes and either single cracks or four 45 kinked cracks were
improved by factors of 5.1 and > 15, respectively, by single-sided repairs with a
1 mm thick patch [80 mm x 80mml. The measured fatigue crack growth rates were
Table 15.5
Comparison of stress intensity factor ranges for four 45" kinked cracks
and two diametrically opposite cracks, with tips at x, =4Omm and hole
radius = 20 mm ( R = 0.1, omrx= 65 MPa).
Crack configuration
Patch thickness,mm
4 x 45" kinked
cracks
2 x diam. opposite
cracks
AKP
AKu
AKp/AKL'
2.0
1 .o
6.0
8.8
22.3
22.3
0.30
0.39
2.0
1.o
11.3
13.7
27.7
27.7
0.41
0.49
440
Advances in the bonded composite repair of metallic aircraft structure
in good general agreement with theoretical predictions. For example, the mean
crack growth rate of 9 x 10~9m/cycle
measured for four kinked cracks at a half
crack length of 35mm during R = 0 . 1 , am,,=41.25MPa loading, was in good
agreement with predicted values of AKp= 5.7 MPam’I2 and Kmin/Kmax
= 0.51, and
da/dN-AK data for 2024-T351 aluminium alloy sheet. Furthermore, the observed
crack paths indicated little effect due to Mode I1 loading. In the case of a 40mm
hole and two cracks, double sided patching resulted in crack arrest, in agreement
with theoretical predictions. Work is in progress to determine the effectiveness of
patch repairs for other damage configurations.
15.10. Future work
Although adhesively bonded gr/ep patch repair of cracked metallic structures has
been studied extensively and service experience with repairs has been good, it
appears that further work is required to address some remaining problems and to
assess the full potential of the repair technique. Specific research objectives include
the following:
(a) To investigate the effect of variable amplitude loading spectra on patch
debonding and hence on patch efficiency. There is a clear requirement for a
model to predict debonding, and for incorporation of this in a general model,
which will enable the effect of patching on fatigue crack growth to be predicted
for a wide range of loading spectra.
(b) To assess the influence of hot-wet fatigue test environments on patch efficiency,
and the effect of long-term pre-exposure to hot-wet environments on such
behaviour.
(c) To establish the advantages and limitations of repairs carried out by co-cure of
prepreg and adhesive.
(d) To develop and assess bonded patch repair schemes for applications involving
elevated service temperatures.
(e) To investigate the effectiveness of bonded patches for the repair of various
forms of corrosion damage and battle damage in aluminium alloy structures.
( f ) To develop and assess patch repairs for applications involving bonding over
fasteners.
(g) To assess the potential of bonded patches for the repair of SPF/DB titanium
alloy structures, and to develop optimum repair schemes.
(h) To develop “Smart” patches for monitoring repair performance in service, and
improved NDE techniques for (i) inspecting pretreated surfaces prior to
bonding, and (ii) assessing the strength and durability bonded patch repairs.
15.11 Acknowledgements
0British Crown Copyright 2001. Published with the permission of the Defence
Evaluation and Research Agency on behalf of the Controller of HMSO.
Chapter 15. Graphitelepoxy patching efficiency studies
44 1
References
I . Kemp, R.M.J., Murphy, D.J., Butt, R.I., et al. (1983). RAE Technical Report TR 83005.
2. Sutton, G.R., Stone, M.H., Poole, P. et a/. (1984). In: Repair and Reclamation, The Metals Society;
pp. 17.1-17.6.
3. Poole, P., Stone, M.H.. Sutton, G.R., et al. (1986). In: The Repair of Aircraft Structures Involving
Composite Materials, AGARD-CP-402, pp. 9.1-9.21.
4. Sutton, G.R. and Stone, M.H. (1989). RAE Technical Report TR 89034.
5. Dowrick, G., Cartwright, D.J. and Rooke, D.P. (1980). RAE Technical Report TR 80098.
6. Young, A,, Cartwright, D.J. and Rooke, D.P. (1988). Aeronautical J., pp. 41&421.
7. Young, A,, Rooke, D.P. and Cartwright, D.J. (1989). Aeronautical J., pp. 327-332.
8. Ball, A S . (1993). MOD Contract SLS 41B/2093, Final Report BAe-KDD-FCP-0104.
9. Poole, P., Brown, K. and Young, A. (1990). RAE Technical Report TR 90055.
10. Poole, P., Lock, D.S. and Young, A. (1991). In: Aircraft Damage Assessment and Repair. The
Institution of Engineers, Australia, pp. 85-91.
11. Poole, P. and Young, A. (1992). In: Theoretical concepts and Numerical Analysis of Fatigue [A.F.
Blom and C.J. Beevers, eds.], EMAS, pp. 421438.
12. Baker, A.A. (1988). In: Bonded Repair of Aircraft Structures (A.A. Baker and R. Jones, eds.),
Martinus Nijhoff, pp. 107-173.
13. Poole, P., Young, A. and Ball, A S . (1994). In: Composite Repair of Military Aircraft, AGARDCP-550, pp. 3.1-3.12.
14. Poole, P., Lock. D.S. and Young, A. (1997). In: Proc. of 1997 USAF Aircrufi Structural Infqrit.)’
Conf., USAF.
15. Poole, P., Brown, K., Lock, D.S.. et a/. (1999). In: Proc. of I W 9 USAF Aircruft Structural Infegrit?,
ConA, USAF.
16. Poole, P., Stone, M.H., Sutton, G.R., el al. (2000). In: Proc. of 2000 USAF Aircraft Structural
Integrity Conf., USAF.
Chapter 16
REPAIR OF MULTI-SITE DAMAGE
R. JONESand L. MOLENT"
Defence Science and Technology Organisation, Air Vehicles Division, Monash
University, Wellington Rd, CEayton, Victoria 3168, Australia
16.1. Introduction
The phenomenon of multi-site damage (MSD) in aircraft has been under
examination in recent years by many in the aviation industry. This section
investigates the feasibility of applying advanced bonding technology to commercial
aviation structures containing MSD. The validity of this technology has already
been proven in its application to fatigue and stress corrosion in military aircraft, as
described in other chapters of this book.
The consequence of the undetected presence of MSD was dramatically illustrated
through the in-flight failure of a fuselage lap joint on an Aloha Airlines B-737
aircraft on April 28, 1988. Essentially this failure occurred due to numerous small
cracks along a fastener line linking together, causing the residual strength of the
fuselage to be exceeded under pressurization. A test programme was conducted to
reproduce this type of failure, and an adhesively bonded boron/epoxy doubler for
use as a repair or preventative measure has been developed.
This chapter presents the results of a fatigue test programme, which also
considers environmental and damage tolerance aspects, conducted using specimens
representative of wide-bodied commercial aircraft fuselage lap joints. This work
was reported in detail in [l-lo].
Two separate generic specimens were considered, one representative of Boeing
Commercial Aircraft Company (Boeing) and the other of Deutsche Airbus GmbH
(Airbus) aircraft fuselage lap joints.
* Air
Frames and Engines Divbion, Aeronautical and Maritime Research Laboratory, Fishermum Bend,
Virtoriu 3207. Australia.
443
Baker, A . A . , Rose, L.R.F. and Jones, R. (ea's.),
Advances in the Bonded Composite Repairs of Metallic Aircraft Structure
Crown Copyright 0 2002 Published by Elsevier Science Ltd. All rights reserved.
444
Advances in the bonded composite repair of metallic uircraft structure
Following the development of a bonded-composite repair for MSD in the
fuselage lap-joint of wide bodied transport aircraft a number of full scale
demonstration repair/reinforcements were undertaken.
16.2. Specimen and loading
16.2.1. Boeing lap joints
Figure 16.1 details a typical configuration of a modern Boeing wide bodied
aircraft pressurized fuselage construction. For the purpose of this work attention is
focused on the lap joint area. Local details of this location vary depending on the
age of the aircraft and specific manufacturers’ details.
It should he noted that, in many cases, in addition to fasteners, the lap joints are
bonded together, either using hot or cold setting adhesives. This is done for the
purpose of increasing the fatigue life of the joint. In service, environmental
degradation may cause this bond to become ineffective, and corrosion of the
mating skins could accelerate the onset of MSD (as was the case in the Aloha
incident). For these reasons bonded lap joints are not considered in this work.
In the present investigation a worst-case scenario was assumed, viz: a nonbonded, full depth, upper plate, counter-sunk configuration as shown in
Figure 16.2(a). Here the counter-sunk rivet hole, if accompanied by improper
rivet head seating, leads to a phenomenon known as “knife-edging’’ (i.e. the tip of
the counter-sunk in the top plate “cutting” into the lower plate). This in turn leads
to a reduction in the fatigue life of the joint, relative to the case where the countersunk does not fully penetrate the plate, due to the sharp corners accelerating the
initiation of cracks.
The basic specimen used in this investigation (referred to as the “Boeing” type)
consisted of two 2024-T3 clad aluminium alloy sheets 1.016mm (0.04 inch) thick,
fastened with three rows of BACR15CE-5, 100” shear head counter-sunk rivets,
3.968 mm (5/32 inch) diameter, as shown in Figure 16.3. The width of the specimen
was chosen to coincide with the typical distance between tear straps of a B-737
aircraft.
The upper row of rivet holes contained crack initiation sites, induced by means of
an electrical spark erosion technique, on either side, nominally 1.2mm long. This
length was chosen so that the defect was obscured by the fastener head, which is
representative of possible undetectable flaws. These flaws were achieved by drilling
the rivet holes undersize (3.85mm diameter), spark eroding the initiation sites to
1.225 mm, and then machining the counter-sunk (4.039 mm) to achieve the required
hole diameter. The accuracy to which the latter was performed determined the final
configuration of the defects. In some cases the defects only remained on one side of
the hole, the other being removed by the tool. Following this the fasteners were
inserted.
The specimens were manufactured by the then Australian Airlines (now
QANTAS), from material supplied by them, to aircraft standards. End tabs were
Chapter 16. Repair of multi-site damage
445
Frame
station
Fig. 16. I , Typical wide body fuselage construction (from Boeing).
bonded to the base specimen to ensure failure would not initiate from the specimen
ends (see Figure 16.3).
Since the amount of out-of-plane bending due to fuselage curvature in a typical
fuselage joint was unknown, the local bending was prevented by testing the
specimens bonded back-to-back and separated by a 12.5 mm thick honeycomb
446
Advances in the bonded composite repair of metallic aircraft structure
Joint description configuration
(a)
Base line
3 rows - 5/32’ Csk. Rivets
1.13” space
.wto .w
(b) 2 rows - 5/32 Csk. Rivets
1 row -3/16 Universal
.04to .04
(c)
-
3 rows 3/16 Universal
0.04to 0.04
(d) 3 rows - 3/16 Csk. Rivets
0.02 Bonded Doublers
0.04to 0.04
(e) 3 rows - 3/16 Csk. Rivets
1.30 space
0.056to 0.056
(9
-
3 rows 3/16 Csk. Rivets
External Doubler
0.04to 0.04
(9) 3 rows - 5/32 Csk. Rivets
Hot Bonded 0.02 Doubler
0.04to 0.04
Bond
Fig. 16.2. Various fuselage lap joint configurations (from Boeing).
Chapter 16. Repair of multi-site damage
447
2024-T3 plate
thickness = 0.040in
End tab
3.0
5I. 0 L
I
Dimensionsin inches
End tabs to be bonded
Fig. 16.3. Uniaxial "Boeing" type lap joint specimen. Note rivet numbering used in this chapter.
core. Details of the procedure used to construct the test specimens can be found in
[2]. In this configuration strain gauge results indicated no global bending or
parasitic stiffening due to the honeycomb.
One drawback of this method of testing is that the failure of one face (i.e. the
base specimen) terminates further testing of the other. The over-riding advantage of
this technique is that due to symmetry, a heat cured repair can be applied to the
base specimens without inducing extensive bending due to the thermal expansion
mismatch of the parent material and that of the repair. A view of the assembled test
specimen is given in Figure 16.4.
The specimens were tested in various capacity servo-hydraulic test machines. The
specimens were loaded in tension to give a remote plate stress of 92 MPa (13.4 ksi).
This figure was determined from operational data obtained for the US DOT MSD
Committee Review Board, see Table 16.1 (from [ll]), for the B-737 aircraft.
448
Advances in the bonded composite repair of nietallic aircraft structure
Fig. 16.4. Back to back bonded lap joint specimens.
Table 16.1
MSD committee review results [l 11.
Typical maximum normal operating stresses for Boeing 727 and 737 fuselage splices
Primary skin stress is pressure hoop stress
Aircraft
B727
B737
PR/T
At frames
15900
16100
psi
10000
9800
Actual
highest
Comment
13200
Midway between frames
13400
Middle of waffle strap area
10400
Midway between frames
Maximum applied shear stresses are less than 25% of the 13000 psi hoop stresses
Maximum principal stresses are:
Tension less than 110% of hoop stress
Shear - less than 60% of hoop stress
~
Chapter 16. Repair of multi-site damage
449
The applied constant amplitude loading used was:
P,,,
P,,,,
= 40.0 kN
= 21 kN
Pmin= 2 k N
,
at a frequency range between 2.5 and 3 Hz. This loading represents the hoop stress
induced in the fuselage skin due to pressurization.
Pre-cracking of some specimens were conducted using the following loading:
P,,,
P,,,,
= 50.0 kN
26 kN
Pmin= 1.2kN
=
,
at a frequency of 2.5 Hz. With this loading, cracks were initiated within 5000 cycles.
For the unreinforced specimen crack growth was monitored optically using a
travelling microscope, with a magnification factor of 40.
For the unreinforced specimen the tests were terminated when the upper row of
fasteners had completely failed (i.e. all cracks linked). For the reinforced specimens,
eddy current techniques (see [2]) were used to check for crack growth beneath the
doubler.
16.2.2. Airbus lap joints
Initial work had concentrated on the development of a bonded composite repair
for MSD in joints similar to those encountered in Boeing aircraft. After discussions
with Airbus, four “generic” specimens typical of current (7050-T73) fuselage
construction were provided by Airbus for repair and testing. This work was
reported in detail in reference [SI. The specimens had previously been fatigue tested
to failure and each specimen had failed in the first row of rivets in the upper skin.
On average the life to failure of the unrepaired specimens ranged from between
77200 to 2175600 cycles, depending on the test load which ranged from 80 MPa for
the former to 43.7MPa for the latter. The specimens were 115mm wide and
(nominally) 420mm long. Two of the specimens had also failed at the ends of the
specimen near the edge of the change of thickness at the joint. The skin thickness
varied from 2.3mm near the joint, to 1.6mm elsewhere (see Figure 16.5).
In an attempt to reproduce the level of local constraint, as seen in service aircraft.
the specimens were “paired” and mounted back to back on a 25.4mm thick
aluminium honeycomb core (this has negligible stiffness in the direction of the load,
as demonstrated for the “Boeing” specimens).
Whilst these specimens had failed at the first row of rivets in the upper skin, the
third row of rivets in the lower skin is also a potential failure location. To simulate
cracking at this location a saw cut was inserted between the middle rivets in the
lower skin of each of the four specimens (Figure 16.5). The specimens, along with
the aluminium honeycomb and end tabs, were then assembled and bonded together
450
Advances in the bonded composite repair
of
metallic aircruft structure
I
Dimmims m mm
-
1.6
...................x.( .................................
2.2-
250
.......*..-....
I
1
Y
~~
I
-,--
I
- 8
.............
"'it""r
Y . Y. V....
I
I
/.
,
117
I
- - I - -
Machined slot in lowerskm
(==
w.
................ .....................................
Possible cracksite
1
Fig. 16.5. "Airbus" lap joint specimen [8].
using an epoxy-nitrile structural thin-film adhesive which was cured at 120 "C in an
autoclave.
The repaired specimens were fatigue tested under constant amplitude loading,
with a maximum load of 47.49 kN and a minimum load of 4.83 kN. These loads
correspond to a remote stress in the skin, suggested by Airbus, of 128.9MPa and
13.1 MPa respectively.
16.3. Repairs
Conventional repair methods for detected cracking in fuselage lap joints involve
removing the damaged material and the use of a riveted scab patch, see Figure 16.6.
Chapter 16. Repair of multi-site damage
45 1
Fig. 16.6. Typical lap joint fastened repair
The concern here is that this introduces further stress concentrations, due to the
increase in fastener holes, and that the close proximity of these repairs may lead to
a compromise in the damage tolerance of the structure. The objective of this
investigation was to evaluate a possible bonded repair or life enhancement for
mechanically fastened fuselage lap joints.
I6.3.1. Repair philosophy
In 1990, with the support of the then Australian Civil Aviation Authority (CAA,
now Civil Aviation Safety Authority), a world wide study into the commercial
application of bonded repair technology was performed [12]. Thirty four
organisations in eight countries, including ten manufacturers and seven Regulatory
Authorities were consulted. The following proposed design rules and procedures
were subsequently adopted by the CAA; viz:
1. Designs shall be substantiated against the Damage Tolerance provisions of the
United States Federal Aviation Regulations (FAR) Part 25.57 1 at Amendment
45.
452
Advances in the bonded conyosite repair of metallic aircraft structure
2. The repair of any structural component which contains damage sufficient to
reduce the aircraft structure to below design limit load residual strength shall
not normally be attempted.
3. Service time degradation, environmental and impact damage substantiation
evidence shall be provided for the composite material and the structural bond,
as appropriate to the design. This should include sufficient work to enable the
composite repair to meet the intent of the damage tolerance requirements.
4. Quality control consideration should include, for all critical areas, wedge testing
of bond strips produced during the repair process.
In the CAA Airworthiness Advisory Circular it was stated that:
" . . . civil requirements do not mandate an initial flaw approach. However, it is
often convenient to do so and this may reduce the threshold fatigue testing
requirement. This may be in recognition of leaving the initial crack in the metal
unchanged but also may cover the presence of an un-bonded region in the joint."
The bonded repairs/reinforcements described below were designed and tested to
fulfil the above requirements.
16.3.2. Repair details
A boron fibrelepoxy composite was chosen for the repair applications because of
its high stiffness, relatively high coefficient of thermal expansion, low void content
and the environmental resistance of the cured epoxy resin. The specimens were
surface treated prior to doubler application using the standard AMRL pre-bonding
surface treatment, which includes a thorough degrease, mechanical abrade and
application of an aqueous silane solution. The boron/epoxy laminate was cured in
an autoclave to form the composite doubler and the repair was bonded to the
specimens with the same epoxy-nitrile structural thin-film adhesive (FM73, Wayne,
New Jersey) as described in other chapters, in an oven using mechanical pressure.
-
16.3.2.1. Boeing specimens
The bonded doubler used in this investigation was a multi-segmented
unidirectional boron/epoxy laminate, containing ten plies at the greatest thickness.
The laminate (203.2 mm long by 203.2 mm wide), was bonded over the joint, with
one segment butting up against the skin step, to provide an alternative load path
for each row of fasteners, see Figure 16.7, similar to the concept used in the F-111
'
a
Composite I= I
Adhesive
Lap-joint
Crack
3
2
1
-
A
A
Rivet
I
0
0
Fig. 16.7. Section through lap-joint and doubler showing areas of potential high stress concentration
( 1 4 PI.
Chapter 16. Repair of multi-site damage
453
wing pivot fitting upper plate repair [13]. The doubler was applied after the
specimens had been pre-cracked. In order to evaluate the fail-safe nature of the
repair, two specimens were also repaired following complete failure of the upper
row of fasteners.
In addition to the hot-curing adhesive (FM-73), a cold-setting adhesive (Flexon
241, Victoria, Australia) was also investigated.
The doublers were applied both as a reinforcement (specimens with short cracks
emanating from rivet heads) and as a repair (specimens completely cracked
through).
In one specimen pair (A9/A10) the stiffness of the doubler (upper section) was
reduced by a third, in order to investigate the optimum thickness or stiffness
required.
16.3.2.2. Airbus Specimens
To restore structural strength to the damaged Airbus lap joint specimens a
0.76 mm thick doubler was required. The dimensions of the doubler were 115 mm
by 285 mm [8], similar to that described above for the Boeing lap joint specimen.
16.4. Stress analyses
Before implementing or considering a given repair it is best if the stress state and
the failure mechanisms of the existing structure are understood. To that end, both
thermo-elastic and finite element analyses of the specimen were undertaken to
investigate the stress distribution of the lap joint.
16.4.1. Therrno-elastic analysis
An unreinforced “Boeing” specimen was placed in an Instron 500kN
electrohydraulic fatigue testing machine and cycled at 8Hz with a load range of
13 kN to 2kN, proportionally representative of the hoop stresses due to
pressurisation, and thermal emission scans of various regions were then performed
using a SPATE 8000 infrared camera located approximately 50cm from the
specimen. (Thermal emission techniques rely on the coupling between thermal and
mechanical energies [ 141. Under adiabatic conditions the observed signal is
proportional to the sum of the three principal stresses, often referred to as the bulk
stress. Since, in this case, the stress normal to the surface is zero, the bulk stress on
the surface is equal to the sum of the principal in-plane stresses).
The three regions scanned were as follows, viz:
1. Region 1. A scan encompassing all three rows of rivets and regions of both the
upper and lower skins. The area scanned was 113mm by 98mm. The scan
generated an array of 114 by 105 data points.
2. Region 2. A scan encompassing three rivets in the first (Le. critical) row of rivets.
The area of the specimen scanned was 88 mm by 47 mm generating an array of
116 by 67 data points.
454
Advances in the bonded composite repair of metallic aircraft structure
Fig. 16.8. Location of SPATE regions.
3. Region 3. A scan of a rivet in the first row. The area of the specimen scanned
was 15 mm by 15 mm generating an array of 82 by 80 data points, each data
point corresponding to a region approximately 0.2 mm square.
In each case the scan region was sprayed matt black to achieve a uniformly high
infrared emissivity. The location of these regions are shown in Figure 16.8 and the
resultant scans, in uncalibrated stress units, of regions 1-3 were shown in [6]. The
SPATE scan for region 1 is shown in Figure 16.9.
16.4.1. I . Discussion of results
Figure 16.9 clearly shows the load path taken in the specimen. There are three
distinct zones, in each of which the bulk stress is relatively uniform. The first zone is
the region up to and including the first row of rivets. At the line of the rivets there is
a rapid decrease in the bulk stress to a second relatively constant value. This
decrease in the bulk stress reflects the load transferred at the first line of rivets. An
analysis of this data reveals that approximately 45% of the load is transferred by
this row of rivets.
The bulk stress undergoes another decrease at the second line of rivets. At this scale
the stress concentration, in the bulk stress, at the first row of rivets, was not apparent.
A more detailed view of the bulk stress field around the first row of rivets was
taken for region 2 [6]. This confirmed the rapid decay in the load at the first row of
rivets, due to load transfer to the lower skin. Again a t this scale, the stress
concentration in the bulk stress was not apparent. This also illustrated the rapid
decay of the stress concentration on the upper surface of the upper skin, However,
we know that, in the fatigue test program outlined in Section 16.5.1, cracks always
Chapter 16. Repair of multi-site damage
455
P
Fig. 16.9. SPATE scan of region 1.
initiated at the first row of fasteners. This highlights the role that the full depth
counter-sunk plays in creating a fracture critical location at the lower surface.
Unfortunately this surface is not observable via standard thermal emission
techniques.
An even more detailed picture of the stress field around a fastener in the first row
of rivets was taken for region 3 [6]. The concentration in the bulk stress at the upper
surface of the upper skin was now visible. However, it was seen that this stress
concentration, which is quite small, was very localised.
From these scans it was apparent that the lack of a bond between the upper and
lower skins results in the major load transfer occurring at the first row of rivets.
This will exacerbate the stress concentration effect of the full depth counter-sunk
holes at the lower surface of the upper plate even though the stress concentration at
the upper surface is particularly localised.
Had the upper and lower skins been bonded, a substantial proportion of the load
would have been transferred prior to the first row of fasteners. The boron/epoxy
doubler, described in Section 16.3.2.1, uses this concept to increase the damage
tolerance of the joint. In this approach a boron/epoxy laminate is bonded to the
456
Advances in the honiied composite repair of metallic aircraft structure
external surface of the joint so as to provide an alternate load path, from the upper
to the lower skin, thus by-passing the critical row of fasteners.
16.4.2. Finite element analyses
A three dimensional finite element analysis of the specimen was undertaken to
confirm the above results. The model contained 4296 nodes and had 10680 degrees
of freedom with the counter-sunk rivets modelled separately as three dimensional
isoparametric elements, see Figure 16.10. This analysis confirmed the rapid decay
of the stress concentration in the bulk stress. The load transfer at the first row of
rivets was also consistent with experimental measurements.
To confirm the low stress concentration at the rivet hole, the “Boeing” specimen
was extensively strain gauged. A strip of ten micro-gauges was located on the
surface of the upper skin adjacent to a rivet in the first row. The resultant strains for
a remote stress of 92MPa (13.4ksi) are given in Table 16.2. These results confirm
the results of the previous investigation, and yields a localised strain concentration,
at the hole, of approximately 1.45.
16.4.2.1. Elastic-plastic analysis
As will be described in Section 16.5.1.1 it was noted in the fatigue tests performed
on these “Boeing” specimens, that the linking of adjacent cracks appeared to occur
when the remaining distance between the crack tips was approximately 2 mm. To
examine this phenomenon a 3D elastic-plastic finite element analysis was
performed. A main objective of this analysis was to determine if this “failure”
was due to net section failure of the remaining 2mm ligament, between the crack
tips, or due to ductile fracture. The basic finite element model used is as described
in Section 16.4.2.
CRACK
IJNJFORM
CRACK
STRESS
TIPS
FIELD
92 MPa
CRACK
REGION OF
INTEREST
Fig. 16.10. Finite element model of cracked lap joint.
Chapter 16. Repair of multi-sire damage
451
Table 16.2
Surface strains.
Distance from edge
of rivet head (mm)
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
Hoop strain (w)
1911
1612
1464
1388
1351
1335
1315
1312
1324
1368
This model was significantly refined about the rivets and includes two equal
length cracks approaching each other from two adjacent fastener holes, see
Figure 16.10. The elastic-plastic stress-strain curve for the material was taken from
the MIL-Handbook-SE.
For mechanically fastened structures with multiple load paths, the commonly
used J integral is path dependent, even for monotonic loading. To overcome this
shortcoming the path independent r* integral, see [15] for more details, was
calculated along a number of separate paths for a remote stress of 92 MPa, which
was the maximum stress applied to the specimens in the fatigue tests. At the peak
load the equivalent stress intensity factor K , which was defined, as in linear elastic
fracture, in terms of r“ and E ( Young’s modulus) as:
K =
ET* ,
was found to be approximately 23.9 MPam’” which is well below the fracture
toughness of the material. However, the von Mises equivalent stress was found to
exceed its ultimate permissible value for more than 0.5 mm of the 2.0 mm between
the crack tips. This implies that failure of the ligament, which was a precursor to
the total failure of the specimens, was due to net section failure. This result is
consistent with experimental work (see [1,2] and Section 16.5.1) where it was found
that, regardless of the length of the cracks emanating from two adjacent fastener
holes, linking of these cracks was always observed when the remaining ligament
was approximately 2 mm.
Whilst repairs to MSD in the first row of rivets has received considerable
attention, and the fundamental mechanisms underpinning this technique determined, the ability of an external bonded doubler to repair cracks in the third row of
rivets in the lower (hidden) skin has not previously been investigated analytically.
To address this problem the lap joint described in Section 16.2.2 was also modelled,
using two-dimensional eight-noded iso-parametric elements, with a 75 mm edge
458
Advances in the bonded composite repair of metallic aircraft structure
vvvvvvvvvv
to
loaded
129MPa
Fig. 16.11. Schematic of FEM lap joint with edge crack [8].
crack in the lower skin at the third row of rivets (Figure 16.11) [8]. In this analysis a
remote stress of 129 MPa was applied to the aluminium skins and the mechanical
properties used for the composite, adhesive and aluminium alloy are given in Table
16.3.
Table 16.3
Material properties used for the numerical analysis.
Composite boron/epoxy
E,,=208.116
x 10'MPa
E,,,,.=Ezz=25.440
x 103MPa
G,. = G,; = G).== 7.240 x lo3 MPa
= 0.17
v).== 0.25
v;, = 0.02
, s = 1520 MPa
s,~).= a,= = 150 MPa
T . ~ )=
, 97 MPa
Adhesive
Aluminium alloy 7050-T73
G.ry= 750 MPa
v = 0.35
7,). = 30 MPa
E.yx=70.1 x 103MPa
v = 0.33
V.y.v
E= Tensile Modulus, G = Shear Modulus, v =Poisson's Ratio, s = Tensile Strength and t = Shear
Strength
Chapter 16. Repair of multi-site damage
459
Table 16.4
Critical composite and adhesive stresses (see Fig. 16.7) [8].
Composite
Adhesive
Location
1
2
3
4
1
2
3
C7X.Y
280.2
0.61
9.23
425.5
17.90
8.62
158.8
2.67
7.13
138.8
0.40
-7.75
4.53
2.08
7.75
25.4
21.7
21.5
6.73
1.74
1.98
CYY
T.yY
4
2.77
1.65
-8.00
The stress intensity factor K was calculated, for both the unrepaired and repaired
“Airbus” cases, using Eq. 16.1, see [16]:
K=”J4
1 ( 12n
-f)
for plane stress
(16.1)
Here v is the crack opening displacement at a distance 1 behind the crack tip and
a is the half-crack length. For the unrepaired case K was calculated to be
47.1 MPam”*, and for the repaired case K reduced to 6.89MPam‘’2 which is
approximately the fatigue threshold value for this material.
The stresses at each of the critical points, see Figure 16.7, are given in Table 16.4
and were found to be beneath the design allowables. The adhesive shear stress was
also found to be beneath the endurance limit of 25MPa [17]. This implies that,
during fatigue testing, crack growth should be very slow, the adhesive should
exhibit adequate damage tolerance with minimal degradation in its performance
and that delamination should not occur.
16.5. Specimen fatigue test results
16.5.1. Unreinforced baseline fuselage lap joint specimens
Only the “Boeing” type fuselage lap joint specimens were tested in this program.
Ten unreinforced specimens were tested (see Table 16.5). It should be noted that
in the initial process used to bond specimens Al-A4 to the honeycomb, adhesive
flowed between the two aluminium sheets and across the upper row of fasteners.
This was detected subsequent to the failure of specimens Al/A2. This, in effect,
enhanced the fatigue life of the upper row of fasteners, as can be seen from Table
16.5. This specimen failed within 140000 cycles of the last inspection, at which no
damage had been detected. The failure of A2, although probably influenced by the
final failure of AI, occurred through the inner plate at the lower fastener row, in
contrast to all other specimens. This may indicate a possible danger in lap joint
modifications which consider only the upper row. This is of concern, since damage
occurring at the lower fastener is only detectable from the interior of the aircraft.
Advances in the bonded composite repair of metallic aircraji structure
460
Table 16.5
"Boeing" fuselage lap joint fatigue program.
Specimen
Status
Al*
A2*
A3*
A4*
A3
A4
A5
A6
AS+
A6/2"
A5/2'"!
A6/2""
A7
A8
A7
A8
A9
A10
A9/2'"
A 10/2'"'
A1 1
A12
A13
A14
Unreinforced
Unreinforced
Reinforced
Reinforced
Conditionede
Conditioned
Unreinforced
Unreinforced
Unreinforced
Reinforced
Reinforced
Reinforced
Reinforced
Reinforced
Conditioned
Conditioned
Unreinforced
Unreinforced
Reinforced'
Reinforced'
Unreinforced
Unreinforced
Unreinforced
Unreinforced
Precrdcking
cycles at
17.8 ksi
Cycles to
failure at
13.4ksi
-
977600"
977600a
>[email protected]
>[email protected]
[email protected]
32179509
-
178400
178400
-
5000
5000
n/a
n/a
n/a
n/a
5000
5000
-
-
25000
4 I400
see below
> 1300000d
> 1316400
>[email protected]
>[email protected]
>[email protected]
>[email protected]
-
n/a
n/a
105700
1000000
I 1 11000
-
-
-
67000
57370
-
-
-
Ligaments joined
(top row)
Yes
Nob
-
No
No
No
Yes
Yes
prior
prior
prior
-
No
No
No
Yes
prior
prior
No
Yes
Yes
No
Longest
crack
mm
-
9.0
4.5
~
~
~
1.8
~
-
1 .o
1.O
-
7.1
-
2.4
-
0.7
* Adhesive seepage occurred across top fastener row (enhanced fatigue life).
No crack detected at 837000 cycles.
Failed lower fastener row.
Patch stiffness decreased by a third.
Failed in grip area of A5.
e Environmentally conditioned.
Continuation of specimen test.
(?
' Repaired after complete failure, using room temperature curing adhesive (Flexon 241).
@ Testing not completed.
a
+
To rectify the seepage of adhesive into the lap joint, a teflon strip was placed over
the skin step.
During the cycling of the unreinforced specimens periodic crack measurements
were made. A mean life to failure of approximately 59000 cycles was obtained. It
was observed that, in each case, the initial linking of two adjacent cracks occurred
when the remaining ligament was approximately 2 mm long.
Figure 16.12 presents typical crack growth data for specimen A6 which suffered
total failure.
Chapter 16. Repair
of multi-site damage
sp.~tmen M cirm a
46 1
m oats
8
7
04
0
5000
15000
10000
20wo
25000
Cy&.
Fig. 16.12. Specimen A6 crack growth data.
Figure 16.13 presents a view of a failure surface. By referring to Figure 16.14
(from [18]) it is seen that these failures reflect the nature of in-service crack growth.
In Figure 16.15, a comparison of crack growth data for the two most prominent
cracks for a number of specimen was plotted, from the same common initial crack
length as used in data given by Boeing (see Figure 16.16). In these figures only data
for the most significant cracks occurring on a specimen were plotted. In each figure
the two curves corresponding to the least number of cycles, were the cracks which
first linked.
Comparison of the experimentally obtained crack growth rates to the crack
growth rates obtained from fleet data, shows good agreement. The experimental
crack growth data are bounded, above and below, by the crack growth data
obtained from service aircraft. This agreement implied that this specimen geometry
could be used to study the repair of fuselage lap joints.
16.5.I.1. Discussion
It was observed that the variation in the fatigue lives of the unreinforced
specimens was partly due to the nature of the cracking. In general, the shortest life
occurred when the largest cracks in a specimen grew towards each other from
adjacent fastener holes. A longer life occurred when cracks initiated and grew from
widely separated holes.
462
Advances in the bonded composite repair of nietallic aircraft structure
Fig. 16.13. Failure of specimen A12.
Even though, due to manufacturing tolerance, some notches were visible to one
side of a fastener (i.e. notch larger than had been intended), this did not necessarily
facilitate the initiation of the most prominent crack in a specimen. The “knifeedging” phenomenon was felt to be the dominant factor determining crack
initiation.
-Yeer d mgwfschre 1981
-HgM hours rot a d a b l e
-FibhiC&le8 39,523
o o o o *
0
- 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
STA 960
STAS80
Fig. 16.14. Example of in-service cracking.
Stringer 4R
463
Chapter 16. Repair of multi-site damage
I
250
A9 nn16
-a
-
T
fj
md5
.
A
9
300 -
A10 weld
-42
mnll
-A12
nn15
200.
-I
% 150-
e
100-
00 4
0
40000
20000
Boo00
Tstt cvtlst
8MoO
100000
1 2 m
Fig. 16.15. Crack growth curve.
550
500
-
450.
f 400
5
-
C 350c
f
.x
5
300250-
F”
200s
f?
150-
100 50 00
.I
0
20000
40000
60000
FflgMCycler
80000
Fig. 16.16. Fleet crack growth data.
I00000
lMWO
464
Advunces in the bonded composite repair of metallic aircraft structure
It was observed that before initial failure (Le. two cracks linking) of a specimen,
the remaining ligament length was consistently of the order of 2mm.
In each case the number of cycles required to achieve initial failure did not differ
significantly from that to final failure of the specimen.
16.5.2. Reinforced baseline fuselage lap joint specimens
16.5.2.1. Boeing specimens
From Table 16.5, it can be seen that the use of a bonded boronlepoxy doubler
leads to an order of magnitude increase in the fatigue life of the basic specimens.
Even the reduced stiffness specimens (A9/A 10) experienced over 1000000 cycles
without failure.
Once failure of A6 occurred, it was repaired using a boron/epoxy doubler, and
testing continued until failure of specimen A5 occurred. Because of the increased
stiffness due to the repair, the loading was increased in order to maintain a 92 MPa
stress range for A5 [see 21. Subsequent to the failure of A5, it was also repaired with
a doubler and fatigue testing continued. As symmetrical conditions now applied,
the loading reverted to that of Section 16.2.
Damage beneath the doublers was monitored using eddy current techniques. The
results of periodic monitoring of the reinforced specimens was presented in [2]. None
of the reinforced or repaired specimens experienced failure in the test section under
fatigue loading. Given the large number of cycles experienced, this implies that the
reinforcement also sufficiently suppresses the failure mode in the lower skin.
This investigation also showed that a bonded boron/epoxy doubler was capable
of restoring the fatigue performance of a representative fuselage lap-joint
containing MSD.
16.5.2.2. Airbus specimens
The repaired “Airbus” specimens were also fatigue tested, under constant
amplitude loading, with a maximum load of 47.49 kN and a minimum load of
4.83 kN. These loads correspond to a remote stress in the skin, suggested by Airbus,
of 128.9MPa and 13.1 MPa respectively. After 365000 cycles the first pair of
specimens failed in the aluminium outside the doubler. At this stage the doubler
showed no sign of degradation. The second pair of specimens were subsequently
tested to 100000 cycles without failure or degradation in the doublers.
This investigation again showed that a bonded boron/epoxy doubler was capable
of restoring the fatigue performance of a representative fuselage lap joint
containing MSD. The experimental program showed that after at least 100000
cycles the bonded-composite doubler was capable of withstanding the imposed
fatigue loading. Also, the cracks (cut) in the lower (hidden) row had not grown.
16.5.3. Environmental evaluation of repairs
The initial testing of the reinforced and unreinforced specimens demonstrated
that the bonded composite reinforcement significantly increased the fatigue life of
Chapter 16. Repair q / multi-site damage
465
Table 16.6
Fuselage lap joint environmental fatigue programme.
Test
Temperature
("C)
Specimen
Pre-condition
Additional cycles
at 92.4 MPa
A3"
A4"
No
No
> 2155550
> 2155550
20
20
A3
A4
Water for 7 days
at 60°C
> 522000b
> 522000'
60
60
A3
A4
5% NaCl for
7 days at 60°C
> 5500OOc
> 550O0Oc
60
60
A7
A8
No
No
> 400 1000
> 4001000
20
20
A7
A8
Water for 7 days
at 60°C
> 503000b
> 503000'
60
60
A7
A8
5% NaCl for
10 days at 60°C
> 1000000"
> 1000000"
60
60
'' Adhesive seepage occurred across top fastener row (enhanced fatigue life).
Specimen failed in grip area. Testing continued with grips repaired.
Test stopped. All specimens are reinforced. Total cycles for each specimen on completion of
environmental test programme are: specimens A3/A4,3217950 cycle (intact); specimens A7iA8, 5504590
cycles (intact).
fuselage lap joints with MSD. As can be seen in Table 16.5, all "Boeing" reinforced
specimens did in excess of one million cycles with no patch degradation, and one
specimen (A7/A8) did in excess of four million cycles without failure of either the
boron patch or the adhesive bond.
To further demonstrate the validity of the bonded repair scheme, environmental
conditioning of the reinforced specimens was conducted. Table 16.6 details the
processes applied to each specimen. Only the "Boeing" type fuselage lap joint
specimens were tested in the AMRL environmental program.
16.5.4. Hotlwet
Specimens A3/A4 and A7/A8 were first soaked in a water bath for a minimum of
seven days, with the temperature held constant at 60 "C. Although tap water was
used, on removal the specimens showed signs of extensive corrosion of the
aluminium. One week was considered sufficient time to thoroughly soak the boron
doubler and the adhesive. Water temperature was continuously monitored
throughout this time.
466
Advances in the bonded composite repair of metallic aircraft structure
Fig. 16.17. Reinforced lap joint specimen sealed to retain moisture (note corrosion of aluminium ends).
On removal from the water bath the specimens were wrapped in plastic and sealed
to retain their moisture content, see Figure 16.17. They were then immediately
placed in the testing machine and wrapped in 250 mm x 250 mm heater blankets, see
Figure 16.18. The blankets were fixed directly to each side of the specimen, then
covered with insulating material. Temperature was controlled by a single
thermocouple, and monitored by another four thermocouples. The temperature
controller was an ETHER "Digi", which maintained a uniform temperature
distribution of 60 f 4 "C over the specimen test area throughout the test.
Specimens were then cycled at the stated load levels, for a minimum of 500000
cycles, without failure and with no visible damage to the doubler system (see Table
16.5).
16.5.5. NaCl aqueous
Following testing under hot/wet conditions, the specimens were then exposed to
a more corrosive environment. They were wrapped in aluminium tape to minimise
corrosion in the grip area, and placed in a water bath containing a 5% NaCl
aqueous solution. The temperature was maintained at 60 "C, and specimens were
immersed for a minimum of seven days. Figure 16.17 shows the typical condition of
the specimen after removal from the salt bath.
Chapter 16. Repair of multi-site damage
461
Fig. 16.18. Environmental fatigue test set-up.
Testing was then continued, under the conditions described above, with the
temperature maintained at 60 "C, and the moisture content retained, see Table 16.5
(Conditioned).
Specimens A3/A4 and A7/A8 were then examined, prior to environmental
testing, using eddy current techniques, with the results detailed in [4]. Specimen A3
had small cracks emanating from some rivets, while A4 had no detectable cracking.
It is interesting to note that A3 also had a crack emanating from a rivet in the
second row. There was significant crack growth in specimens A7/A8. However, it
must be noted that these specimens had experienced more than 4000000 cycles.
Each specimen then experienced a very large number of additional cycles under
adverse conditions without failure of either the specimen or the repair. In the case
468
Advances in the bonded composite repair of metallic aircraft struelure
of specimens A7 and A8 the crack lengths were such that, unrepaired, the
specimens would have failed after a very few additional cycles.
Following the environmental conditioning and testing, the specimens were reexamined. No growth was detected for specimens A3/A4, however, crack growth
had occurred in specimens A7/A8 [4]. In both specimens the left hand side (LHS)
crack from rivet 2 (R2) had increased significantly in length. The cracks from R3
and R4 had joined, as had those from R7 and R8. All cracks had joined in
specimen A8, except those from R1 and R2. If cycling had continued it could be
expected that these specimens would have cracked completely through the
aluminium section. However, as has been demonstrated previously, the doubler
is more than capable of carrying the entire load. Testing was continued for both
specimens (see below), with the cracks being periodically monitored. None of the
reinforced or repaired specimens has experienced failure in the test section.
After more than 550000 cycles of testing in a hot/wet salt environment the
doublers showed no sign of degradation or failure. This is in contrast to an average
fatigue life of 59000 cycles for failure of the unreinforced specimens. Therefore
environmental degradation is not considered a significant factor when using these
repairs.
16.6. Damage tolerant evaluation of specimens
Six “Boeing” type specimens were used to investigate the damage tolerance of
the proposed repair scheme. A summary of the specimen histories, prior to damage
tolerance testing, is given in Table 16.5. Specimens A3, A4 and A5 had experienced
a large number of fatigue cycles prior to the application of the impact damage.
Specimens A3, A4 and A5 only contained impact damage, whilst specimen A6
contained both impact damage and adhesive disbonds, and specimens A9 and A10
contained adhesive disbonds only, see Figure 16.19.
16.6.1. Adhesive disbonds
In specimen A6 the adhesive disbonds were simulated by inserting teflon release
film between the aluminium sheet and adhesive during bonding of the doubler
(repair). The size and the location of these inserts is shown in Figure 16.20.
For specimens A9 and A10 a deliberate attempt was made to produce a poor
quality bond (see Figure 16.19). In this case the low temperature curing adhesive
Flexon 241, which has an inferior durability performance to FM73 was used [17].
These specimens also contained areas in which the patch was not bonded. The
extent of these disbonds was not known until the patches were removed after
testing had been completed. The disbonded area in specimen A9 was approximately
five percent of the total patch area, whilst for specimen A10 approximately twenty
percent of the patch area was disbonded, see [9]. The adhesive thickness was also
very uneven, varying from “zero” to approximately 1 mm.
Chapter 16. Repair of multi-sire damage
469
-1
Fig. 16.19. Specimen A10 with doubler removed.
16.6.2. Impact damage
Specimens A3, A4, A5 and A6 were subjected to low velocity impact damage
using a 9.5mm diameter impactor, of varying mass, dropped from a height of
1.3 m. A special impact test rig was used to record the absorbed impact energy. The
rig consisted of a laser which was triggered by the impactor both before and after
impact, producing initial and rebound pulses which were recorded on a digital
oscilloscope (NICOLET 2090 MODEL 207) and analysed on a HP9816 computer.
From these results the kinetic energy of the impactor before and after impact was
determined. The impact site locations are shown in Figure 16.21, and the impact
energies are summarised in Table 16.7.
Fatigue testing was conducted in a 1 MN Instron servo-hydraulic test machine.
The damaged specimens were subjected to a constant amplitude tensile fatigue
loading with R = 0.05, a load amplitude of 38 kN, and a frequency of 2.5 Hz. This
loading represents the hoop stress in the fuselage skin due to pressurization, as
described previously. Testing was continued until failure of the specimen occurred,
or a sufficient number of cycles had been accumulated to demonstrate the
effectiveness of the repair.
The condition of the impacted specimens was monitored throughout the test
using the shadow-Moire technique. A detailed description of this technique and its
application to monitoring damage growth is given in [19]. The patches were coated
470
Advances in the bonded composite repair of metallic aircrafi structure
i
1
BORCN/EPOXY
PATCH
,
STEP
-
37.5
I
25 I
Fig. 16.20. Insert details for specimen A6.
with a white matte paint and two l00mm by 125mm glass plates with ljl000 inch
grid lines were placed directly over the area containing the damage. A collimated
light source was then directed at the specimen at an angle of approximately 45" to
the surface. The resulting Moire fringe pattern was monitored visually and also
photographed at various stages during the test, thus enabling a qualitative
assessment of patch disbonding to be made.
The number of fatigue cycles applied to each of the specimens (in addition to
those demonstrated by Table 16.5) are shown in Table 16.8.
None of the repairs showed any significant sign of failure or degradation (no
delamination growth) during the tests. This contrasts with an average life of 59000
cycles (discounting A 1/A2 due to adhesive seepage) for the unrepaired specimens,
refer Table 16.5.
Chapter 16. Repair
of multi-site damage
47 I
wA6
MIA4
n
--SPmEnA3
0 -rnlmIAs
0
-SPESPEQlENM
+
-~fpEclnENM
Fig. 16.21. Impact site locations.
More than 1000000 cycles were applied to specimens A9 and A10 without failure
of the repairs (recall these specimens had reduced stiffness). It should be noted that
for these specimens, prior to repair, the cracks at the first row of rivets had
propagated across the entire width of the specimen (i.e. the specimen had failed).
Despite the deliberate poor quality of these repairs and in particular the large
disbond area in specimen A10, the composite doubler was able to carry the load
without further degradation.
Specimen A6 withstood more than 1400000 cycles without failure or apparent
disbond growth.
After impacting, specimens A3 and A4 were subjected to in excess of 450000
cycles. These failed by fatigue crack growth in the aluminium sheet outside the
repair. It should be noted that these specimens had accumulated a total of more
than 3000000 load cycles during previous testing. There was no sign of degradation
472
Advances in the bonded composite repair of rneiallic uircruft structure
Table 16.7
Impact results.
Specimen no.
Impactor
mass (g)
A3
200
A4
200
Impact site
1
2
3
1
2
3”
4
A5
400
A6
400
a
1
2
1
2
Impact
energy (J)
1.6
1.7
1.2
1.7
2.0
-
1.4
4.0
3.7
4.0
4.2
impact energy not recorded
Table 16.8
Damage tolerance testing results
Specimen No.
Type of Damage
Fatigue Cycles
(additional)
impact
impact
impact
disbond
impact
disbond
disbond
454670
454670
180000
13 16470
180000
1000000
1004330
~
A3“
A4“
A5
A6
A9
A10
a
specimen failed by fatigue in aluminium sheet outside repair area.
or failure of the repair. An eddy current inspection of the specimens was conducted
to determine the extent of crack growth since impacting. It was found that no
further crack growth had occurred during this test program.
Specimens A5 and A6 withstood 180000 cycles after impacting, again with no
apparent degradation or failure. The Moire fringe pattern for these specimens, i.e.
A3-A6, revealed that there had been no delamination growth, see [9] and Figure
16.22 (see Figure 16.21 location A6-1).
16.6.3. Tension testing
On completion of these fatigue tests four specimens, namely A3/A4 and A9/A10,
were loaded to failure in tension in order to determine the strength of the
“damaged” repair. For the purpose of comparison an undamaged and unrepaired,
i.e. “as new”, lap joint specimen pair was also tested. Specimens A5/A6 were also
Chapter 16. Repair of multi-site damage
473
Fig. 6.22. Views of specimen A6 Moire ringes.
loaded above normal limit load. In each case load was applied at a rate of 37.5 kN/
min.
The specimen pair A3/A4, which had previously failed outside of the patched
region, was repaired to enable the tensile test to be conducted, see [9]. The tension
474
Advances in the bonded composite repair of metallic aircraft structure
Table 16.9
Tensile static test results.
Specimen
Undamaged Lap Joint
A3/A4
~ 5 i
A6
A9/A10
*
Total fatigue
cycles
Static failure load
0
3672570
1480070
1496470
11 10030
116
161
> 54*
(W
121
test terminated, no sign of failure.
test results are shown in Table 16.9. The repaired specimens exceeded the strength
of the “as new” lap joint specimen. Specimens A3/A4 failed in the aluminium sheet
outside the repair area, while specimens A9/A10 failed by debonding and tearing of
the composite doublers. The significantly lower strength of specimens A9/AIO was
expected due to the poor quality of the bond and the reduced stiffness. Despite this,
the strength of these fatigued specimens still exceeded the strength of the standard,
“as new” lap joint.
After the second pair of “Airbus” specimens were tested to 100000 cycles without
failure or degradation in the doubler, they were then removed from the test
machine and the doublers were subjected to low energy impact damage in the
regions directly over the upper row of rivets and above the step between the upper
and the lower skins. The impact damage was inflicted using a 1 kg mass from a
height of 813 mm. This is equivalent to the “Mil Spec” standard 7.98 J impact test.
In each case a rebound height of approximately 250mm was recorded together with
an absorbed energy of approximately 5.5 J. The specimens were then subjected to a
further 100000 cycles, for a total of 200000 cycles, without failure and with the
doubler showing no signs of degradation or damage growth.
This test program demonstrated that the presence of adhesive disbonds and
damage due to low velocity impacts does not degrade the boron/epoxy lap joint
repairs, even after the repairs had experienced significant fatigue cycles. This was
shown by demonstrating that the fatigue life of the repaired specimens, containing
damage, far exceeds that of an unrepaired lap joint specimen. Inspection of the
specimens during and after testing revealed no damage growth and that the MSD
beneath the repair did not grow. It was also shown that the static strength of the
damaged repairs exceeds that of an uncracked lap joint specimen.
16.7. Full scale repair demonstrators
16.7.1. Airbus A330lA340 fatigue test article
On demonstration of the repair schemes’ capability to restore strength and
fatigue life to generic “Airbus” lap-joint specimens it was considered important to
Chapter 16. Repair of multi-site damage
475
examine the fatigue performance of the scheme under realistic loading conditions.
To this end two doublers were applied to an Airbus A330/A340 full-scale fatiguetest article [8,20]. In-service loading conditions was used throughout the test
program, including both representative short range and medium range mission
profiles. A total of 80000 flight cycles was applied to the test article and the load
spectrum included pressurisation, flight, gust, landing, take-off and ground loads.
Two simulated damage locations were considered:
(a) a 220mm crack in the top row of rivets in the outer skin of the lap-joint
(b) a 170mm crack in the bottom row of rivets in the inner skin of the lap-joint.
Airbus introduced this damage to the test article at stringer location P31 between
stations C26.2, C26.3 and C26.4, C27 respectively by the use of a saw cut (see
Figure 16.23).
During doubler application excessive heating of a region can cause local buckling
of the parent structure that must be avoided as this can induce thermal stresses in
the adhesive bondline. This is a common problem when heating thin skins with no
stiffeners in the region to stop out-of-plane deformation. Prior to each hot-bond
application a thermal survey was carried out to ensure that the cure temperature
could be achieved and that the skin would not buckle excessively. The survey
showed that the temperature varied from 120 "C at the centre of the repair to 80 "C
at the edges and no buckling of the skin was observed. The application time was
extended to eight hours to ensure complete cure of the adhesive and doubler.
The two cracks, representative of MSD, were repaired using two identical
composite doublers bonded with an epoxy-nitrile structural film adhesive. The
doublers were made from boron/epoxy pre-preg tape and measured 300 mm by
285 mm. As mentioned previously, the epoxy is an elevated temperature curing
Bonded co'mplosite repairs
Fig. 16.23. Location of lap joint doublers on airbus fatigue test article [8].
Chapter 16. Repair of multi-site damage
477
12285 cycles in December 1992. At the completion of the test, 67715 flight cycles
had been applied to the doublers with no deterioration of the doublers being
observed. No crack growth in the saw cuts was detected, and the strain surveys
revealed no strain redistribution during the testing.
16.7.2. Boeing 727, 747 und 767 in-flight demonstrators
As part of a demonstration program, nine bonded composite doublers were
applied to a Boeing 747-300 aircraft in service with QANTAS Airways Limited
[9,21,22 and Chapter 371. The aim was to demonstrate the environmental durability
of this type of repair, and thus the doublers were not applied to any damaged
locations.
Important work in the area of bonded repair has also involved collaborative
programs with commercial aircraft manufacturers and operators, including a series
of demonstration programs to assess the durability of bonded-composite repairs.
AMRL and Boeing have participated in such programs with the aim of allowing
aircraft manufacturers, operators and the various regulatory authorities to gain
confidence in the technology.
The first demonstration program was in March 1989, when the application of a
boron/epoxy reinforcement to an aircraft in service with Ansett Airlines, B767-200
VH-RMF, restored stiffness in a (7150-T6511) keel beam damaged by multi-site
corrosion [see 3,23 & Chapter 371. This repair is shown in Figure 16.25. A similar,
KEEL BEAM 767
\
BORON PATCH
12 LAYERS
W E FM 73
\
\
CORROSIONGROUND OUT
;
--..__30
I
Fig. 16.25. Schematic of 767 keel beam repair to MSD corrosion.
478
Advances in the bonded composite repair of metallic aircraft structure
but shorter, doubler was also applied to an non-damaged section of the keel beam
using a cold setting acrylic adhesive. The second was in November 1989, when a
boron/epoxy doubler was applied to a lap joint of an aircraft in service with
Australian Airlines (now QANTAS), B727-200 VH-TBM [24]. In the second
program there was no prior damage, the application was simply to demonstrate the
feasibility of doubler application and its durability. This re