VanMier_1991.

VanMier_1991.

HERON is jointly edited by:

STEVIN-LABORATORY of the faculty of Civil Engineering,

Delft University of Technology,

Delft, The Netherlands and

TNO BUILDING AND

CONSTRUCTION RESEARCH.

Rijswijk (ZH), The Netherlands

HERON contains contributions based mainly on research work performed in these laboratories on strength of materials, structures and materials science.

ISSN 0046-7316

EDITORIAL BOARD:

A. C. W. M. Vrouwenvelder,

editor in chief

R. de Borst

1. G. M. van Mier

R. Polder

J. Wardenier

Secretary:

J. G. M. van Mier

Stevinweg 1

P.O. Box 5048

2600

GA Delft, The Netherlands

Tel. 0031-15-784578

Fax 0031J 5-611465

Telex 38151 BUTUD

E vol. 36

1991 no. 4

Contents

AN EXPERIMENTAL STUDY OF SHEAR

FRACTURE AND AGGREGATE INTERLOCK

IN CEMENTBASED COMPOSITES

1. G. M. van Mier

M.

B.

Nooru-Mohamed

G. Timmers

Delft University of Technology

Department of Civil Engineering

Stevin Laboratory

Abstract

3

1 Introduction... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Mode li and mixed mode I and II fracture of concrete. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.1 Non-linearities in mode I fracture ..... 5

2.2

2.3

Mixed mode

I and

II fracture ..... . . ..

10

Does mode Ii fracture exist? . . . . . . . . .. 14

3 Experimental techniqllle . . . . . . . . . . . . . . . . . . . . .. 17

3.1 Biaxial test-rig ....................... 17

3.1.1 Loading frame. . . . . . . . . . . . . . . . . . . . . .. 17

3.1.2 Load and displacement measurements . 23

3.l.3 Test control. . . . . . . . . . . . . . . . . . . . . . . .. 27

3.1.4 Data acquisition system ...............

28

3.1.5 Experimental problems ............. "

3.1.5.1 Influence of glue platens .............

29

29

3.l.5.2 Frame rotation. . . . . . . . . . . . . . . . . . . . .. 32

3.2 Specimens and materials ............. 34

3.2.1 Plain concrete. . . . . . . . . . . . . . . . . . . . . .. 34

3.2.2 Slurry infiltrated fibre concrete

(SIFCON) .......................... 36

4 Plain concrete resuUs . . . . . . . . . . . . . . . . . . . . . . .. 40

4.1

Introduction ........................ .

40

4.2

Load-path description ............... . 42

4.2.1 Load-path 0: Uniaxial tension ........ .

42

4.2.2 Load-path 1:

4.2.3

4.2.4

Shear at constant crack opening. . . . . .. 45

Load-path 2:

Tensile shear at zero axial load. . . . . . .. 45

Load-path 3:

4.2.5

4.2.6

4.2.7

Unconfined and confined compressive shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45

Load-path 4:

Axial tension at constant shear force. " 45

Load-path 5: Axial tension at constant

....................

~

Load-path 6: Proportional loading. . . . .. 45

4.3

4.4

Influence of shear on the tensile envelope curve. . . . . . . . . . . . . . . . . . . . .. 46

Influence of crack opening on shear behaviour. . . . . . . . . . . . . . . . . . . . . . . . . .. 50

4.4.1 Tensile shear. . . . . . . . . . . . . . . . . . . . . . .. 50

4.4.2 Compressive shear. . . . . . . . . . . . . . . . . .. 52

4.5 Influence of confinement. . . . . . . . . . . .. 55

4.5.1 Confinement normal to the crack plane 56

4.5.2 Confinement in the lateral shear direction. . . . . . . . . . . . . . . . . . . . . . . . . . .. 59

4.6 Size effect under biaxial loading ...... 61

4.6.1 Size effect on strength . . . . . . . . . . . . . .. 63

4.6.2 Load-path 4 results . . . . . . . . . . . . . . . . .. 65

4.6.3 Load-path 6 results. . . . . . . . . . . . . . . . .. 67

4.7

4.8

Path-dependency. . . . . . . . . . . . . . . . . . .. 71

Summary of failure modes. . . . . . . . . . .. 72

5 Shear fracture in SiFCON .................... 74

5.1 Variables in the biaxial SIFCON

5.2

5.3

5.4

5.5 experiments ........................ 74

Strength and ductility. . . . . . . . . . . . . . .. 76

Effect of fibre type .................. 78

Effect of fibre orientation. . . . . . . . . . . .. 79

Crack patterns. . . . . . . . . . . . . . . . . . . . . .. 86

5.5.1 Shear cracks. . . . . . . . . . . . . . . . . . . . . . .. 87

5.5.2 Crack coalescence. . . . . . . . . . . . . . . . . .. 88

5.5.3 Crack closure. . . . . . . . . . . . . . . . . . . . . .. 91

6

Shear stiffness analysis. . . . . . . . . . . . . . . . . . . . . .. 92

6.1 Comparison with aggregate interlock

6.2

6.2.1

6.2.2

6.3 experiments ........................ 92

Shear stiffness reduction . . . . . . . . . . . .. 95

Plain concrete ...................... .

SIFCON ........................... .

Shear retention factor ............... .

95

95

96

7 Conclusions ........... . . . . . . . . . . . . . . . . . . . .. 98

Acknowledgement ...... . . . . . . . . . . . . . . . . . . . .. 99

Notation ................................... 99

References ................................ 101

Publication in HERON since 1970

Abstract

In the present paper the results of an

exploratory

study with the recently developed biaxial tension/shear apparatus of the Stevin Laboratory of Delft University of Technology are presented. The apparatus is unique in the sense that square double-edgenotched concrete plates up to a size of200 x 200 mm can be loaded in any combination of tension and shear in displacement control. The two loading axes are completely independent of one another. In the paper, both results of experiments on plain concrete and on slurry infiltrated fibre concrete (SIFCON) are presented.

The experiments can be divided into two main categories. In the first catagory, aggregate interlock has been studied for narrow cracks (between 10 and 400 [-tm) that can still transmit tensile loads normal to the crack plane. In the second catagory of experiments specimens were sheared off without precracking them (mode II), but in a few cases with simultaneous tensile loading (mixed mode I and II). The shear tests on specimens containing narrow cracks revealed an abundance of secondary cracking. The exact boundary conditions were very important here. Tests have been carried out with either zero confinement or with a very small confinement of - 1 kN perpendicular to the crack during shearing. Only for large crack openings, viz. larger than 200-250 [-tm, true sliding has been observed, and this seems to limit the range of applicabilty of the present aggregate interlock theories.

In the mode II tests in general a set of overlapping cracks would develop from the two notches in the specimen. This failure mode resembles the fracturing offour point shear beams with a narrow shear zone. Depending on the size of the specimen and the boundary conditions during shear, overlapping curved or straight cracks were found.

A "true macroscopic shear failure", defined as an array of short inclined tensile cracks, was found in some proportional load-path tests

(%s

= constant) on plain concrete.

Even then, this fracture mode could only develop when specimens were sufficiently small which implies that crack growth is very well confined. This type offailure was also obtained in tests on SIFCON, where shear cracks were found to develop in oriented weak planes between fibres in the specimen. The fact that distributed cracking was found in the small specimens (50 and 100 mm), but not in the larger 200 mm specimens, indicates that an unrestricted translation from results obtained in small specimens to large structures is not allowed. In fact this is the goal of many size effect laws that have been developed in the past. The biaxial test results were not in agreement with Bazant's size effect law, which may likely be explained from the shift in failure modes.

From the various load-path tests (in total 7 different load-paths were investigated), it was found that the behaviour of the specimens unde,r ~iaxialloading is path dependent.

In order to overcome the problems caused by path dependency, it is suggested to apply micro-mechanics models in order to come to a better understanding of the fracturing of the specimens and the intricate specimen/machine interactions.

3

As a number of tension shear tests were carried out on SIFCON. Several researchers have to use this material in structural engineering. The performance of the material in tension and compression is very good, leading to extremely ductile behaviour. The present tests showed however that the fracturing ofSIFCON in shear is less favourable. The shear strength is rather small about 10-20% of ice) on the main fibre orientation with respect to the shear direction. The

SIFCON is a rather these weak is material, and oriented weak planes exist. Fracturing in easy, and macroscopic shear fractures were observed. For other fibre the performance is much better, and the response of the SIFCON resembles the behaviour concrete with external confinement. The fibres can be as an internal confinement in the case of SIFCON. It is concluded that a successful structural ofSIFCON will depend to a large extent on the ability of elements with isotropic fibre orientations.

Biaxial Loading, Tension, Shear, Concrete, SIFCON, Mixed Mode

Aggregate Interlock, Mode II Fracture.

4

An experimental study of shear aggregate interlock

0

cementbased

1 Introduction

With the introduction of the Fictitious Crack Model for concrete research has been devoted to the analysis of cementbased materials tension. In a sense this is a logical development because it represents the fracture mode. However, in most structural applications pure tension much

I) is an exception and in general combined tensile/shear stress states, or stated in fracture mechanics terminology mixed mode I and II fracture, The of the sliding/friction mechanisms in concrete is a timely, but extremely difficult

Recent conferences (e.g. Shah et al. [1,2], Elfgren and Shah Van Mier et al. that many researchers are active in the field, but at the same time it is clear that the main problem remains unresolved.

In the present study, a newly developed test technique at the Stevin

University of Technology has been used in an attempt to mechanisms in various cementbased composites. Part of this work was done under an

AFOSR contract (see acknowledgement), and the present paper contains the results of the extensive set of experiments that have been carried out on mortar, normal concrete, lightweight concrete and SIFCON (Slurry Infiltrated Fibre After a short review of the literature (chapter 2), the experimental

3. The plain concrete results are the subject of a PhD the main results are included in this paper as well, chapter 4, For a better of the shear/sliding mechanism, the experiments on SIFCON were results are presented in chapters 5 and 6. Concluding remarks appear in

2 Mode I and mixed mode I and n fmctlllre of concrete

This chapter contains a brief review of the state of the art on fracture mechanics of concrete, specifically mode I and mixed mode I and n fracture. Mode results and models are included because the mixed mode situation cannot be considered j dent of the mode I fracture.

2.1 Non-/inearities in mode J fracture of concrete

The first attempts to apply fracture mechanics theories to such as concrete date back to the sixties, e.g. [6]. In these first attempts the oflinear fracture models to concrete was investigated. The main concl.usion was that the applicability of LEFM was restricted to hardened cement paste which, by its nature is a very homogeneous material the and normal concrete it was concluded that LEFM is

not

For mortar

5

Several years later, the fictitious crack model was presented by Hillerborg and coworkers

[7].

Because of the heterogeneous nature of the material it was argued that a

"zone of discontinuous micro cracking" advances in front of a visible continuous crack as depicted in Fig.

1.

This implies that the stress-redistributions do not occur conform

LEFM theory, but more energy will be dissipated in the fracture process. The fracture toughness of the material increases due to the presence of the microcracks. Petersson

[8] suggested that the best method for determining the fracture energy of heterogeneous materials such as concrete is a displacement controlled uniaxial tension test.

--a-c-r-o-c-ra-C;--k--iilil>'~~--"'''Iii--C-O-h;--e-5''''iv-e-z-o-n-e~/I>

...

I

0(6)

Fig.

1.

Classical definition of a process zone in concrete: (a) microcracks advancing a continuous macro crack, (b) and closing pressure over the cohesive zone.

Specified conditions for such a test are that the specimen should not be too large and that the test should be carried out between parallel end-platen. In Fig. 2, the tensile apparatus as available in the Stevin Laboratory is shown. In this approach it was tried to generate a uniform micro crack zone in a double notched specimen. The stress-crack width diagram obtained from a test contains all necessary information to determine the fracture energy per unit fracture surface [9].

A main problem of the Fictitious Crack Model (FCM) is that the physics of the fracture process are not taken into account in an adequate manner. In effect the assumed "zone

of discontinous microcracking in front of a macroscopic and continuous crack"

is taken

into account by assuming a fictitious crack length. The crack propagation criterion in the FCM is the exceedence ofthe tensile strength of the material. Note that LEFM has been modified along similar lines in the past few years, with the difference that the singularity at the crack tip is maintained in the LEFM based effective crack models (see for example [10]).

6

r-----oil

--vaLve

- - - actuator external

- - -- load - cell

--roller bearings

~~~-~-LVDTs

-+-+---+--speci men

T - -

:

,.jI--,........,-..lfr- -

T

:

, ,

I

-oH----internal l

I load _ cells

~

100mm

Fig. 2. Set-up for deformation controlled uniaxial tensile testing in the Stevin Laboratory.

An extensive survey of the literature by Mindess [11] showed that there is much controversy about the extent and true nature of the process zone (following the above definition) in concrete. Process zone sizes of a few micrometer to 500 mm have been reported. Furthermore, the size of the process zone seemed to depend to a large extent on the resolution of the measuring technique but also on the structural conditions under which it can develop, i.e. stress gradients. At the fracture conference in Vienna in

1988, Van Mier and Nooru-Mohamed argued that the non-linearities in the fracturing of concrete could be explained from a two stage fracture process, which depends to a large extent on the geometry of the test specimen [12]. In their tests it was shown that overlapping crack tips could explain the long stable tail of the softening diagram in the stress-crack opening diagram, see Fig. 3. This would imply that no such thing as a "zone of discontinous microcracking ahead of a continuous macro crack" would exist. In 1990

Hu and Wittmann [13] showed, by using the so-called double cutting technique developed in the field of ceramics, that the additional toughening in cracks in concrete should be explained by some process taking place in the wake of the visible crack.

However, the double cutting technique does not allow for an accurate measurement of the mechanism, and two options are possible:

(1) the crack front is non-uniform over the depth of the specimen, or (2) frictional interlock or bridging takes place in the macrocrack. The first mechanism, viz. non-uniform crack fronts, was found by Dascoul and coworkers [14J and later confirmed by others (e.g. [15, 16, 17, 18]). The non-uniform crack fronts were found by impregnating cracked specimens. The tests carried out by

7

(1) crack arrest in stress - relieved zones

(2) ligament bending

P

R

= f(h)

6 o perimeter cracking ligament bending

Fig. 3. Fracture mechanism in uniaxial tension, After [12].

Bascoul et al. and Swartz and Refai [IS] were three point bend tests. lin these experiments the specimens were impregnated under loading, and thereafter fractured completely. By using coloured dye, the shape of the crack front could easily be determined as shown in Fig. 4. Van Mier [16] used a vacuum impregnation technique to visualize cracking in prismatic specimens loaded in uniaxial tension up to a prescribed average axial crack opening. After impregnating the cracked specimen with a fluorescenting epoxy, the specimen was sawn into six slices (Fig. 5) and the internal cracking could be studied under UV light. Up to axial crack openings of 50 [lm, the crack fronts were nonuniform. At larger crack openings, the specimens were completely cracked, but still some load could be transfered. In Fig. 6 the extent of internal cracking in a specimen loaded up to 100 [lm average axial crack opening is shown. The load carrying capacity can be explained from crack face bridging, which manifests itself mostly in the form of

8

Dye

;;'-0.36

-!JJ'

0.44 fk~O.53

Fig. 4. Non-uniform crack fronts in plain concrete beams, after [15J.

z

. . , , - - - '----""7!"'---

Fig. 5. Slicing prismatic specimens for internal crack detection after loading the specimens in uniaxial tension and vacuum impregnating the cracked specimen. Identification ofinternal crack detection planes

yz

through coordinate

x,

after [16J. two overlapping crack tips with an intact ligament in between. Crack face bridging in three different concretes is shown in Fig. 7. The two overlapping crack tips shield each other, and the fracture of the ligament between the overlapping cracks is a very stable process. Recently the failure of a ligament was followed in a specimen under load [19], and a strong correlation between the size of the crack face bridges and the load carrying capacity of a concrete with a given maximum aggregate size has been found [18J.

x=22.5mm

37.4

52.3 67.3 82.1

Fig. 6. Internal cracking in a lytag specimen, loaded in tension up to an average axial deformation of 100 [J.m. The locations of the surfaces are indicated with an x-coordinate (see Fig.

5), after [16].

9

P (kN)

(a)

(b) o o

20 40 60 80 100

w(j..I.m)

~ aggregate particle w

(e)

( c)

Fig. 7. Crack face bridging at

i5

=

100 [.Lm for respectively 2 mm mortar (a), 12 mm Iytag (b),

16 mm normal concrete (c);

P-i5

diagrams (d), and bridge failure mechanism (e), after

[17, 19].

The typical shape of the crack face bridges, i.e. two overlapping crack tips, which generally develop around stiff aggregates, was recently simulated in a numerical micro-

'mechanics model for fracture of concrete, see Schlangen and Van Mier ([20] and Fig. 8).

The overlapping crack tip mode was found to be a natural consequence of the heterogeneity of the material. The individual crack branches tend to avoid each other.

Similar

results were recently also obtained by Vonk et

al.

[21].

2.2 Mixed mode I and II fracture

Most cracks in concrete structures develop under combined modes, and mixed mode I and II (tension and in-plane shear) loading seems to prevail. In LEFM criteria for mixed mode I and II fracture have been proposed, but many of the models have been developed for metals. Criteria for composites are gradually emerging, see for example

10

(d)

Fig. 8. Simulation of crack face bridging using a simple lattice model [20]. Four stages of crack growth are shown at different axial crack openings. The results are in good agreement with the experiments of Fig. 7. .

Gdoutos 1984 and Carpinteri and Swartz, 1991 [22,23]. Of course the main problem for concrete is its heterogeneity. As shown in the previous section, mode I fracture is a highly non-linear phenomenon, and this will undoubtedly have some effect on mixed mode situations as well.

Many of the attempts to develop a mixed mode criterion for concrete are in effect extensions of mixed mode criteria in LEFM. Many researchers have attempted to develop a specimen where a mode II component is present in the uncracked state, and generally the design of a specimen is based on a linear elastic analysis of the proposed geometry. An extensive review of existing geometries is given in Hordijk, Van Mier and

Reinhardt, 1989 [24], see Fig. 9a; additional geometries can be found in [4]. In many

/

Fig. 9a. Various specimen geometries and loading configurations for mixed mode I and II and mode II testing of concrete [24].

11

Fig. 9b. Mode II (shear) crack in a four point shear specimen with narrow shear zone, after [25]. cases it has been found that cracks initiate in mode I, and that a true mode II mechanism could not be obtained. This can probably be explained from the fact that cracks initiate near stress concentrations caused by the heterogeneous material structure. The draw back of designing mixed mode I and n specimens or mode II specimens on basis of linear analyses of the uncracked state is that as soon as a small crack develops severe stress-redistributions occur. The new stress state may deviate considerably from the linear state.

Mode II or shear cracking is the limit case when no tensile stresses are present. BaZant and Pfeiffer [25] claimed that they observed pure mode II fracture, defined as an array of inclined tensile cracks (Fig. 9b), in double edge notched four point shear tests of concrete. The results are considered rather controversial. For example, Ingraffea [26] suggested that the failure mode in Bazant and Pfeiffers tests is not correct and that rather a splitting type of failure must have occurred as shown in Fig. 10. Indeed, under carefully controlled conditions, the predicted failure mode by Ingraffea was observed

~------------,r----~----.~ b,

E){perim~nt

o LEFM x FC.M.

"1

CD

1

'1 n

®

e.

L

/fCD

L

Length Ilnl

Fig. 10. Primary cracking and fatal splitting crack in four point shear specimen with narrow shear zone, [27]: (a) without and (b) with axial force.

12

by Swartz and Taha [27]. Again this demonstates that it is not straightforward to obtain mode II fracture in concrete, and one may be misled when not carefully controlled experiments under pure boundary conditions are carried out.

It seems that most structural situations are governed by mode I crack initiation and propagation. If mode I fracture prevails, shear may become important only after a crack has developed. The research should then focus on the effect of friction in cracks.

Carpinteri [28) measured that a 30% increase of fracture energy occurs under mixed mode loading. These results were derived from tests on single edge notched four point shear beams. Again the effect of boundary conditions was underestimated by

Carpinteri, and Schlangen and Van Mier [29, 30] showed that the increase of fracture energy under mixed mode loading could be traced back to friction in the supports in

Carpinteri's experiments. When the four point shear beam is loaded between "true" hinges (note: Schlangen and Van Mier used pendulum bars as hinges), a mode I crack develops along a curved path. However when some frictional restraint is present in the supports, secondary cracking may occur on the other side of the specimen, Fig. 11 b. As shown in Fig. lla, the load-deformation diagram depends on the boundary conditions in the experiment: fixed supports yield a much higher descending branch than observed in a test with "true hinges". By measuring the load distribution in the pendulum bars, it could be concluded that the loading of the specimen was almost frictionless. In a carefully conducted test, the ratio

F2/Fl

in the bars should remain constant at 1110. When friction is present, smaller or larger deviations from this value would occur, and the loading of the specimen would deviate from the intented loading scheme, therefore leading to different fracture modes.

P (kN)

-

248b238 I lBBb15? II

248b237 III

I

III

I

60

40·

I,III

I

I

- -

-

-

-

0+---~--~--~--'---~--~--4 o

200 400 600

O

2

(J1.m)

(a)

(b)

Fig. 11. Effect of boundary conditions on the cracking in single-edge-notched four point shear specimens: test I with rotating supports; test II with fixed supports. (a)

P-O

diagrams, and (b) final crack patterns. After [30).

13

On the basis of all research carried out in the past, it seems that in many structural situations cracks will initiate in mode 1. The effect of shear seems restricted to deviating the cracks from a straight path. Next to this, the bridging zone in the crack may cause different stress-redistributions and it is not very clear what processes take place when shear is applied. The limit case offully openend cracks (without bridging) subjected to shear has been explored in the past, by for example Walraven [31], who developed a sophisticated grain model for the analysis of the shear stiffness of rough cracks in concrete. For small crack openings the situation is much more complicated in view of the presence of the briding stress, and it seems that the Aggregate Interlock theories are not applicable anymore in this regime. Note that most cracks in concrete structures are partly opened cracks which still allow for some stress transfer.

The lack of understanding of the behaviour of small cracks under shear is the major reason for initiating the present investigation. In most of the tests described in this report specimens were pre-cracked in mode I, whereafter a mode II (in plane shear) load was applied.

It is tried to determine the frictional characteristics of a cracked specimen, where the crack openings are very small 00-400 [lm), and where still cohesive stresses are present normal to the crack plane, see Fig. 12.

Fig. 12. Shear loading on a partially cracked specimen.

2.3 Does mode II fracture exist?

The question from the title of this paragraph is very intriguing and has been tempted many researchers to investigate the mode II (in plane shear) fracture of concrete. In the previous paragraph, reference was made already to the shear fracture tests of Bazant and Pfeiffer, which actually showed to be a curious mixed mode experiment. In effect it may be expected that (at the grain level) mode I fracture completely governs the behaviour of the specimen.

The question remains, under which conditions maya "true" mode II failure be obtained, and what is the amount of energy dissipated in the process. How do we define mode

II fracture? The "shear crack" (which may be a single crack or a conglomerate ofindividual inclined tensile cracks in a narrow band, see Fig. 9) should remain in the plane of the

14

shear loads, and no secondary cracking should occur. This is a very severe restriction, and does not seem to apply to many of the geometries shown in the previous paragraph.

A number of situations where "true" shear fractures may occur according to the above definition are (1) under dynamic loading, (2) in fiber reinforced concrete, and (3) under triaxial compression.

Recent results by Davies [32] indicate that when fracture occurs very rapidly, the cracks follow the direction of the maximum shear stress, rather than the direction of the maximum tensile stress. This phenomenon was observed in double notched and punch-through shear cubes. The stress-directions were determined from a linear elastic analysis of the un cracked specimen. These results are very interesting because they indicate that eventually mode II fracture may happen in heterogeneous materials, probably when the shear fracture energy equals the mode I fracture energy under dynamic loads.

Shear fracture, in the form of a band, has been observed in triaxially compressed concrete as well, see for example [33] (Fig. l3). The restriction should be made that the cashng surface

(a)

..A..

"Lcas ling sl.dace du,/dt

= ( ui =OJ3u',

,perpendicular to plane of drawing

_ . - BA1-5

°3101 =010

9B2-2

° 3 /°1

= O.OS

. /

.-

.-----.-

-160

-140

A. du,/dt

= ( ui

=OJ3u'" perpendicular to plane of drawing

(b)

02-U1

~03'U3 ui=

0.33ui

°2,u2

3.0 25 2.0

------- [mml

u3

15 10

.5

-20 °1'u 1 Cd.sling-

surface

-.5 -10 -15 -2.0 -25 -3.0 u1ImmJ--

( c)

Fig. 13. Shear bands in triaxially loaded concrete: (a)

u

2

=0.33 uj, 0"3=0.05

O"t;

(b)

u2=0.33

Uj,

0"3=0.10 0"]; (c) load-displacement diagrams, after [33].

15

confining stress is not too high (viz. not larger than approximately 30% ofthe maximum principal stress) to allow for brittle failure. For higher confining stresses, a more ductile behaviour is measured, and no localization in shear bands has been observed to date.

When the energy needed to obtain a stable shear band is equalled to the surface under the stress-strain curve, it is found that the mode n fracture energy might be over 100 times as large as the tensile (mode I) fracture energy, depending on the amount of confinement. The localization in compression, including boundary and size effects can be simulated with a simple numerical micromechanics model which was recently developed by V onk et al.

Secondary cracking seems to be prevented when a good confinement of those parts of the specimen outside the shear fracture zone is present. In fact several researchers have tried to design mode II fracture specimens where an optimal confinement is derived from the geometry itself, e.g. [34, 35J. In many cases, as argued before, these geometries seem to preform well at crack initiation, but as soon as a small crack grows in the specimen, severe stress redistributions have been observed to lead to secondary tensile cracking. Another possibility of confining the parts of the specimen outside the shear fracture zone is the .addition of fibres to the concrete. In this way, shear fracture in the sense of "an array of inclined tensile cracks" has recently been observed Arslan,

Hughes and Barr [35] in polypropylene and steel fibre reinforced concrete, see Fig. 14.

As earlier proposed Yin et al. [36], the fibres act as some internal confinement.

-0 o

(a.)

.0

o

(b.)

Fig. 14. Shear fracture in (a) polypropylene fibre reinforced concrete (0.10%); and (b) in steel fibre reinforced concrete (2%), after [35].

In the limit case, SIFCON, Slurry Infiltrated Fibre Concrete, may be considered. The material has extreme high steel fibre contents, viz. depending on the size and shape of the fibres up to 10-15% by volume. The structure of the material is extremely anisotropic, and weak planes may exist. Recently it was shown [37] that the shear strength of these weak layers is very low, not exceeding 10% of the compressive strength of the

16

material. The shear tractures are arrays of inclined tensile cracks, similar to the fracture shapes in ordinaryFRC. In the present study, the results of tension/shear experiments on SIFCON will be discussed in detail in chapter 5.

3 Experimental technique

In this chapter the experimental technique is explained, and specimens, materials and manufacturing procedures for the specimens are described.

3.1 Biaxial test-rig

As mentioned in the previous chapter, various specimens have been proposed for studying mixed mode fracture of concrete. In the experiments in the Stevin Laboratory it is tried to determine the shear stiffness of cracked concrete. The research focusses on small cracks when still cohesive forces are transfered over the crack. A large problem is that softening is partially a material property and partly a structural property (see [38]).

Especially just beyond the peak in a tensile stress-crack opening diagram, the crack growth is non-uniform, and part of the specimen may be cracked, whereas other parts are still uncracked. The boundary conditions of the experiment (e.g. stiffness ofthe test rig, rotating specimen boundaries, specimen size) determine to a large extent how a specimen will fracture. The effect of shear in this regime is not easy to determine. More simple is the situation again at larger crack openings, £5

>

50 to 100 [lm, when bridging is the main stress transfer mechanism between the crack faces. In this case, the shear loading of a uniform bridging zone is straightforward, and an effective shear stiffness can easily be determined. Both situations are investigated in the experimental programme.

3.1.1 Loading frame

The biaxial test-rig that was used, was developed by Reinhardt et al. [39J. The loading frame and a substantial part of the test control system, was developed and built by the

Measurement and Instrumentation group of the Stevin Laboratory, except of course the basic parts such as the SCHENCK servo-controller unit and the Personal Computer. The biaxial test-rig consists of two independent stiff square loading frames. The exploded view of the machine is shown in Fig. 15. The outer frame A is a coupled frame and it is capable of moving along the horizontal direction. The inner frame B can move along the vertical direction. The two frames A and B can move completely independent of one another. The outer frames and the inner frame are fixed to the overall frame via 8 vertical and 4 horizontal plate springs as shown in Fig. 16. When the machine was built, it was assumed that the plate springs prevent the frames from rotating (Note: in the meantime it has become clear that due to the non-uniform fracturing of a specimen, testing between non-rotating platens is almost impossible). The plate springs have a limited bending capacity

(1

N

=

1.08 [lm/m). On each side of the plate spring two strain

17

18 coupled trame A

frame

~ ~

~

~

~

.

'-...,,,-,,/

P lin.g

/

, /

/ , " ' -

<

~

/~.

,./

../'

·~raulic

loadcell A coupled frame A frame B middle

-+-If~!lI+lrvr load-cell

11 hydraulic actuator B f /':i<2~plate springs

Fig. 15. Exploded view of the biaxial test-rig. plate springs load cell A actuator A

................... :

" " , " .

"

..

"

iii

i .......... .......... .

. : ... ': .... , ... -.. : ..... : ... , ..... ', .... ,',., .. , ... : ..... ::::>:::

........

,

..............

, load cell B single frame B actuator B

Fig. 16. Assembled frames.

gauges are mounted and connected in a full Wheatstone bridge configuration (6 Volt potential) to the data acquisition system. The plate springs were instrumented because this gave the opportunity to verify ifthe loading of the specimen was indeed equal to the load measured with the load-cells that were fixed between the frames and the hydraulic actuators. Moreover, any eccentricity which may occur during a test in the frame assembly could be traced back from the plate spring readings.

Two hydraulic actuators (A, B) and two load cells (A, B) are situated outside the loading frames in order not to hinder the overall stiffness of the loading frame. The frame assembly is shown in Fig. l7.

Fig. 17. Photograph of the biaxial test-rig.

The specimen was fixed to the double and single frame using F-88 (Tridox) self curing non-epoxy plastic adhesive cement. To properly glue the specimen into the machine there must be enough space surrounding the specimen. There were two types of displacements possible in the frame. A large displacement to the frames could be inflicted via roller bearing units connected to guiding bars (Fig. 18). The roller bearing guiding unit was blocked during the execution of a test, and small displacements were possible due to the plate springs which have a limited bending capacity. To glue the specimen into the machine, a small compressive force (± 5 kN) was applied. After the specimen was properly glued to the loading platens, and the adhesive was allowed to set for approximately 90 minutes, the roller bearing units of the double and single frames

19

additional guiding bar sliding range

Fig. 18. Roller bearing guiding unit for large displacements of the frame. were fastened using bolts. Damage to the plate springs, caused for example by undesired movements of the frames, was prevented through several security devices which are made of steel plates as shown in Fig. 15.

In Figs. 19a and 19b, a sectional view of the loading frame is shown at two different stages ofloading. A 200 mm square Double-Edge-Notched (DEN) specimen was glued to the frames. As can be seen from the figures, the top of the specimen is glued to the inner frame and the bottom of the specimen to the coupled outer frame. The inner frame can slide in between the coupled frame as shown in Fig. 19a. The specimen is loaded the middle frame upward. A tensile stress develops in the concrete specimen, because the coupled outer frames are fixed in the vertical direction. A tensile crack nucleates in the notched region which is located at half height of the

DEN specimen (Fig. 19b), where crack growth can be followed at a known location.

This enables deformation controlled testing. When the specimen cracks, and the crack opening is sufficiently large, bending of the horizontal plate springs will occur as shown in Fig. 19b.

The DEN specimens are fixed to the frames via steel loading platens. For a uniaxial tensile test only two loading platens are required, however, for a biaxial test two additional loading are needed in order to apply a lateral in-plane shear load. They are glued to parts of the left and right edges of the specimen as shown in Fig. 20. Also

20

plate springs middle frame

(a.) coupled frames connecting plate tor coupled frames

Fig. 19. Sectional view ofthe biaxial test-rig in two stages: (a) before and (b) after cracking. Note the bending of the plate springs in figure (b).

B

A

C

200

2001

I

D

100

10

J

I

(b)

50 s<

I~

J

( c)

Fig. 20. Glue platen assembly for 200, 100 and 50 mm specimens.

21

shown in this figure are the complete loading platen assemblies for the three different specimen sizes tested in the present investigation. The glue platens at the edges A-B-C and D-E-F of the 200 mm specimen (Fig. 20a) are fixed to the inner frame B and the outer coupled frame A respectively. Any shear force acting at the specimen edge D-E is counter balanced by the reaction exerted at the edge A-B, since the inner frame is fixed along the horizontal direction. Some modification in the loading platen assembly is required in order to accommodate the specimens with two other sizes (l00 and 50 mm) in the test-rig. Accordingly, two different loading platen arms made of stainless steel were designed to fix the specimens into the frames as shown in Fig. 20b and c. Especially for the 50 mm specimen this results in rather slender loading platens. The influence of the loading platen arms on the specimen behaviour under biaxial loading is not yet known. The effect of boundary rotations in uniaxial tensile tests has been analysed before, see [40, 41, 42].

The assumed boundary condition for a DEN specimen is shown schematically in Fig.

21. The boundary conditions were such to allow for parallel end platen movement in the vertical and horizontal directions during a test. In principle the test resembles a shearbox experiment, frequently used in rock testing.

In the SIFCON experiments, two additional steel platens were glued to the free sides of the specimens in order to avoid glue fractures between the specimen and the loading platens. Glue fracturing was very critical when high shear loads were applied, but it was found that by using the additional glue platens the undesired glue fractures could be avoided. In the photograph of Fig. 24, where a fully instrumented SIFCON test is shown, the two additional steel platens are visible.

~ p

Fig. 21. Boundary condition for a Double-Edge-Notched specimen subjected to combined tension and shear.

22

3.1.2 Load and disp lacem en t measu remen ts

The machine contains two hydraulic actuators and two load-cells as shown in Figs. 15 and 16. The capacity of the actuators is 100 kN in compression and tension with a maximum stroke of 40 mm. The actuator is connected to the load cell via spiral washers. The capacity of the load-cells is restricted to 50 kN. The loads are measured using the calibrated load cells (40

[.Lm/m/kN

and 20 [.LV

IV IkN)

with four strain gauges in full

Wheatstone bridge configuration. The signals from the vertical and horizontal load cells were amplified via two standard amplifiers (SCHENCK MV 318) to the servo controllers. A 10 V signal corresponds to a load of 50 kN. The maximum loading capacity is restricted to 50 kN because of the limited strength ofthe plate springs that are used for fixing the loading frames.

For the vertical deformation measurements (crack opening), two or four LVDTs

(Sangamo, A6G 1) with a gauge length of 65 mm were used. The position and the number ofL VDTs varied depending on the type of tests performed. In the beginning of the investigation, in plain concrete test series 14 to 18 (the various test series are identified in section 3.2), two vertical L VDTs were placed at the middle of the specimen, one at the front and the other at the rear face of the specimen as shown in Fig. 22. Later, starting from test series 28, four L VDTs were used for test control in the vertical direction, two at each face of the specimen near the notch as shown in Fig. 23a for a 200 mm

100

200mm

---9r-J

501

I

~ n

LVOT (0,) rear face

I

-----Y-

, 65

I

~11

LVOT (0,)

.~

150

¢

-----Y-

I I

I

!

...

LVOT (0

1

I

I

~.-

Fig. 22. Locations of LVDTs for test control in test series 14 through 27: two LVDTs

(0)

for vertical control, and two

(oJ

for lateral (shear) displacement control.

23

200mm

SC~

~

+J

:g v,~

]-

~

~

F'I---"-'

~

~

51)

= /

(a)

SOmm r-t

L-r.o~'~~J5

-<r

(c)

Fig. 23. Locations of vertical and horizontal LVDTs for specimens of three different sizes, plain concrete test series 28 through 48, and SIFCON tests. specimen. Depending on the particular load-path, the fracture mode can change and quite frequently the crack would grow outside the control region when the control

L VDTs were fixed at the middle of the specimen. It proved to be better to place the

L VDTs near the notch in order to obtain a stable test. Note that this could be done for the 200 and 100 mm specimens only. For the 50 mm specimens two L VDTs with a gauge length of 35 mm were used as shown in Fig. 23c, but here no cracking could occur outside the control length simply because the specimen size would not allow this. The

L VDTs were calibrated using a device containing a Mitutoyo micro-screw (range

50 mm; accuracy 5 [lm). The L VDTs have a linear stroke of

±

1 mm with a nonlinearity of 0.3% (calibration: a 10 V signal corresponds to 400 [lm vertical/horizontal deformation). The photograph in Fig. 24 shows the front face of a fully instrumented 100 mm

(SIFCON) specimen. The L VDTs are clearly visible.

For the lateral (shear) deformation measurements two LVDTs (Sangamo, A6G 1) were used. At the front face of the 200 mm specimen one L VDT was mounted at the center

24

(b)

Fig. 24. Photograph of a fully instrumented 100 mm SIFCON specimen. of the bottom half as shown in Fig. 23a; the second L VDT was fixed in a diagonally opposite position at the rear face of the specimen. The global shear displacement b s was defined as the average displacement between the two specimen halves measured by the two horizontal LVDTs. In Figs. 23b and 23c the positions of the horizontal LVDTs for the 50 and 100 mm specimens are shown.

In addition to the L VDTs, a number of extensometers (mechanical-electrical transducers of the cantilever type of size 15 x

50 mm, developed and constructed by the

Measurements and Instrumentation group of the Stevin Laboratory), were used to measure local deformations. To convert the mechanical displacement into an electrical signal, two strain gauges were used in this extensometer as shown in Fig. 25. They were connected to the data acquisition system in a full bridge configuration with a 6 V potential. The extenso meter has a range of 0-2 mm, a resolution of

1

[lm,

and a linearity of

0.5%. The same calibration device mentioned above was used to calibrate the extensometers.

The number of extensometers used varied depending on the type of test and the size of the specimen. Six extenso meters with a gauge length of 35 mm (three extensometers at the front and the back face ofthe specimen), were used in test series

14 to 32 (plain con-

25

35mm

Fig. 25. Schematic diagram of an extensometer developed by the Measurement and Instrumentation Group of the Stevin Laboratory.

V-

200

30 ro ro

1

30

T 1

I I }

I=y

(a)

I

V-

200 so

35 35 35 35

T

I

I

I~

I

I

1= y so

(b) r -

,

15

32.5

T T

32.5

35

t1-

7

.

S

, 15

I

"I.r

I~'

'~7.5

(c) f

7.5

1"35

7.5

I

W

26

Fig. 26. Various extensometer arrangements for specimens of three different sizes. r

(d)

crete) and the SIFCON tests, see Fig. 26a. In a later test series (46-48, plain concrete), a large number of extensometers was used in order to capture the growth of overlapping cracks. This was the dominant fracture mode under the specific load-path followed and for the three different specimen sizes used in this series. As shown in Figs. 26b, 26c and

26d, the number of extensometers used for the 200, 100 and 50 mm specimens was 20, 14 and 12 respectively. In the experiments on the 50 and 100 mm specimens (for plain concrete and SIFCON), additional extensometers were placed over the glue layers in order to verify if no cracking occurred in or near the glue layer. When cracking was detected in or near the glue layer the experimental result was rejected because this would normally lead to undesired stress redistributions within the specimen. In Fig. 24, the extenso meters for monitoring glue fracture can be seen.

3.1.3 Test control

The SCHENCK hydropuls system as available in the Stevin Laboratory is an energy transmission system: the electric energy is transformed into hydraulic and mechanical energy that can be regulated. Eventually this mechanical energy can be used to load a test specimen. The loading can be applied to a specimen in a desired manner with a closed loop servo controlled system.

The hydraulic power is supplied to the loading installation through the hydraulic power unit, which consists of an electrical motor, an oil pump cooler, a filter, electrical switches etc. The hydraulic power unit regulates the oil in the main supply line at a pressure of 220 bar and a flow rate of 40 lImin. The hydraulic pressure unit and the total current is regulated by SCHENCK DU 312 and in case of an emergency this unit is capable of shutting off the hydraulic supply and the flow of current in the closed loop system. However, it is modified by the measurement group of the Stevin laboratory such that in case of an emergency only the hydraulic supply is terminated and the electrical current remains in the circuit. The purpose of this is to avoid damage to the test specimen due to the termination of the power supply. The SCHENCK steering monitor DP 317 controls the hydraulic supply from the main hydraulic line to the actuator. Also it is capable oflinking the steering monitor to external devices such as a computer. In this manner a fully automated system was built, capable of testing along pre-determined load-paths.

Tests can be performed either in load or in deformation control. But, for a stable uniaxial tensile test (stable crack growth), deformation control is essential. Two independent regulation circuits are available, and it is possible to control the vertical and horizontal deformations separately in a test. Moreover, tests can also be performed with deformation control in the vertical direction and load control in the horizontal direction and vice versa.

The average signal of the control L VDTs is amplified via a standard amplifier

(SCHENCK MV 318) to the servo controller unit. The servo controller unit consists of a two part unit, an adaptable digital controller (SCHENCK RA 311) and a standard control signal unit (SCHENCK FP 312). To this servo controller a function generator

27

was connected, which consists of two identical linear time base generators A and B. In a deformation controlled test, the average vertical deformation

(j

(in Volt) was used as the feedback signal. A comparison was made between the feedback signal and the program signal from the function generator and a control signal was supplied by the servo-controller to the servo valve (type MOOG 0-7030,

Ap

=

70 bar, flow rate

=

5 I/min) through a power amplifier (SCHENCK RL 311).

Depending on the type oftest, either the average vertical deformation

(j

or the average global shear deformation

(js

was used as the feed back signal in the closed loop servo controL Of course tests could also be carried out in load-control, and in some of the load-paths investigated a constant load was kept normal to the crack plane during shear.

In Fig. 27 the complete closed loop sytem is shown schematically. hydraulic power supply

Fig. 27. Overview of the complete biaxial loading system.

3.1.4 Data acquisition system

The measurements during a test can be divided into three categories: (1) the load cells

(vertical and horizontal), (2) the L VDTs (vertical and horizontal) and (3) the extensometers and strain gauges. All of these signals were in an analog form. First the signals from the load cells and the L VDTs were amplified to the SCHENCK regulation circuit.

The output signals corresponding to two loads and two deformations (L

28

to an HP Vectra ESI12 Personnel Computer via a 12 bit fast analog/digital converter.

Next to this, the load

P

and the vertical deformation

b

were plotted directly on a XY recorder (type HP-7046A); the shear load

P s

and the shear deformation Os were plotted on a XtY j

Y

2 recorder (type PHILIPS PM-8132), A 32 channel programmable data logger

(designed by the Measurement and Instrumentation Group of the Stevin Laboratory) was used to retrieve the data from the extensometers and strain gauges. A 6 Volt bridge power was applied to either a full, half or quarter bridge Wheastone configuration, with an internal resistance of 120

Q,

For the present data acquisition only full bridge configurations were used, The total time needed for scanning 32 channels was 976 ms, A micro-computer was required to program the data logger. Transmission of commands and data was provided by a simple RS 232 serial channeL The output from the data logger was stored on a floppy disk (0,7 MB),

Dedicated software was developed which allowed fully automatic testing, The Personal

Computer controls the datalogger, the SCHENCK regulation system, the A/D converter and the function generator as shown in Fig, 27, During a test, all measuring devices would be scanned at fixed time intervals, The load was applied continuously and no stops were made for scanning of the measuring devices, The data logger was programmed to scan every 10 seconds from the beginning of a test, with the capability of changing the scan time (usually to 30 or 60 seconds in the descending branch), The floppy could accommodate 600 scan steps, In general a change in scan time was required to include a complete test on a single floppy (0,7 ME),

A typical scan consists of signals from two loads

(p,

P

s)

[m V], two deformations

(0, bJ

[m V], six to twenty extensometers [[1. Vl, and twelve strain gauges [[1. Vl from the vertical and horizontal plate springs, During a test, the vertical and horizontal forces and deformations, the scan-number and the elapsed time were printed for each scan, All data were stored immediately on disk. Through a simple program the stored data were transformed into an advanced Symphony spread sheet format and the results of the test were obtained on the same day, Only recently, a custom built programme has been completed for plotting the results in any desired format.

3.1.5 Experimental problems

When fracture properties of materials are to be determined, it is extremely important to have the desired boundary conditions, In all the tests, the plate boundaries were kept parallel to each other (Fig, 20), With a critical mind the experimental errors in the machine were studied. Some eccentricities in the machine were already known and are discussed in [12]. For example it was found that cracking always initiated at the front left notch, As observed before, non-uniform crack opening is prevalent in heterogeneous materials such as concrete. Due to that, rotations of the frame are unavoidable even though plate springs were designed to avoid them,

3.1.5.1 Influence of glue platens

Fig, 28 shows the uniaxial

P-b

diagram for two DEN specimens (200 mm) glued

29

25 P (kN)

10~--+---+-~==~H--------r--------! o

50 100

150

200

6

(flm)

Fig. 28.

P-O

diagrams for two 200 mm specimens loaded in uniaxial tension between two or four loading platens respectively. between two and four loading platens respectively. The results indicate that the specimen 47-05 with two loading platens gave a higher tensile strength than the specimen

46-03 glued between four platens. This was consistent throughout the entire test series.

Previous analyses indicated the same trend [43]. Gluing of the lateral loading platens results in a more eccentric loading on a the specimen as compared with the case oftwo glue platens. The specimen with two platens gave a sharp peak compared to the one with four platens which gave a rounded peak. Additional eccentricities may be created when a specimen is glued between four platens.

The eccentricities related to non-uniform cracking can be observed from plots of the local deformation

OJ

versus

0

in Fig. 29. The axial load

P

was plotted in the same graph for the specimen with two loading platens. Numbers 1 to 8 correspond to 8 extensometers used for measuring local deformations at the front and rear faces. Fig. 29a, which shows the results for the specimen glued between

two

platens, indicates that the crack initiated near extenso meter 1 and subsequently at the locations of extensometers

5,2,6,3, 7 and 8 (this can be deduced from the order of the intersection points with a straight line, for example at

0

=

10 [J.m). This method for following crack growth is valid, as was found in a study where reflection photo-elasticity was used as crack detection method [12]. The eccentricity in the machine caused the crack to initiate at the leftnotch, at the location of extensometer 1. The deformation measurements demonstrate the non-uniform crack opening in uniaxial tensile tests and confirm the observations made before by Van Mier [33] and Hordijk et al. [44J. Note that correcting the machine for small eccentricities is almost impossible. The slightest non-uniformity will cause eccentric crack modes.

30

100local deformation 6d\..lm)

(a)

50

Specimen

L.7-05

(200x200x50) til

5 6 7 8

~

1 2 34

50

-2ooL-----------------~50-------------------1~0020

6 (\..lm)

100 local deformation 6.1 m)

(b)

50

-20L-----------------~------------------~-20 o 50 100

6 (\..lm)

Fig. 29. Plots oflocal deformations

0;

versus control deformation

0

for two uniaxial tensile tests with respectively two glue platens (a), and four glue platens (b). The specimen size is

200 mm.

A different phenomenon was observed in specimen 46-03 with/ouTsides glued. Fig. 29b shows the

t5 j

-t5

plot. Obviously the fracturing process is completely different to that of specimen 47-05. In Fig. 29a the largest local deformation also occurred (for example at

t5

=

10 [J.m) at extensometer 1 as discussed before, subsequently large deformations occurred at extensometers 4, 2 and 3 between the first and the second load drop. However, extenso meters 5 and 6 were in compression in this process, and it seems that out of plane bending occurred in this particular specimen.

From the above discussion it is obvious that the fracture evolution becomes different when the specimen is glued either between two or four loading platens. The effects of eccentricities in the frames seems more pronounced when four platens are glued.

31

3.1.5.2

Frame rotations

The frames in the biaxial loading rig can probably rotate in a number of ways, in spite ofthe fact that it was designed as a stiff machine where specimens are loaded between parallel travelling boundaries, see Reinhardt et a1. [39]. A possible situation is shown in

Fig. 30, where the inner frame rotates and the outer frames remain stationary. Ifihis is the case, then the lateral shear deformation measurement 6

5 defined as the relative horizontal displacement between the two frames, may include some part of the frame rotation. Therefore, at this stage it can not be concluded that 6$ is the true shear deformation. Yet, the value will be close to the true value because the machine is almost completely symmetric. In order to measure the in-plane frame rotation an independent frame of reference is required. Because of the almost perfect symmetry of the biaxial test-rig, it is assumed that the shear displacement corresponds to the true shear displacement between the two specimen halves. Future tests with an independent reference frame are planned.

A

Fig. 30. Hypothetical out-of-plane rotation of frame B with respect to frame A.

Initially, relative out-of-plane displacements of the frames were measured using four dial gauges as shown in Fig.

31.

A 100 mm specimen (46-20) was glued in the machine between four loading platens, and four dial gauges were mounted on top of the steel frames as indicated in Fig. 31. A lateral shear load

P5 was applied to the specimen in displacement control until

P

5

= -

2.5 kN; subsequently, the lateral test control was changed to load control and an axial tensile load was applied in displacement control.

3

2

32

Fig. 31. Placement of the four dial gauges for measuring out-of-plane rotations.

(This corresponds to 4 discussed in chapter Fig. 32 shows the gauge readings versus scan number for this test. In the same plot, the lateral deformation 6 s and the vertical deformation 6 are plotted. As can be seen in Fig. 32, 6 s is linear up till scan number 53. During this stage, the gauge readings were almost zero except for gauge 1. This means that there is not much out-of-plane frame movement during the first shearing regime. as soon as the axial force is activated, the gauge readings differed significantly, which suggests that much of the frame movement occurred during the initial period. The largest difference in gauge readings were recorded at scan number 100 between gauges 2 and 3. This suggests that both the coupled frames, (front and rear) were not moving by the same amount with respect to the inner frame. Moreover, at the IOOth scan the difference in local deformations on the specimen, corresponding to the of the gauges 3 and 2 were the largest. At this stage, the movements ofthe frame more or less correspond to the deformation distribution measured at the front and rear surface of the specimen.

In/act, at this stage it is not clear, whether the specimen/ollows the machine or vice versa. The above result clearly shows the intricate relationship between the specimen and the machine in a fracture test.

Note that the deformation distribution is more uniform again for larger crack openings.

At this stage of loading, as in 2, crack face bridging is the main cause of the cohesive stress transfer normal to the crack. The crack face bridges seem to be uniformly distributed over the crack area, see [17].

60 o gauge

1

1,0 x gauge 2

° gauge 3

.6 gauge

£,

20

.6

.6

0

°

}{

0 x x

X b. x

0

0

° °

.6

0

.6

)(

15

13

.6 x o~~~~~~~~--~~-===~=---~ o

I

40 scan

53

80 120

160

200

Scan

I, shear a t J

P::O tension at Ps

=_.-.=~c...:.... __

Fig. 32. Average crack opening

(b),

crack sliding (bJ and the frame displacements measured with the four dial gauges of Fig. 31.

33

3.2 Specimens and materials

When the work with the new biaxial apparatus was initiated in 1987, first a relatively large number of uniaxial experiments was carried out, see [12, 45]. This was done because some doubts were raised about the uniformity of the fracture process, as described in more detail in chapter 2. These preliminary uniaxial experiments were mainly carried out on square concrete plates of size 200 x 200 x 50 mm

3, which is the maximum size of the specimens that can be loaded in the present test set-up. This large size was chosen in order to exaggerate the structural effects caused by boundary conditions and specimen geometry. In the following paragraphs an overview of the materials and specimens used in the biaxial test-series on plain concrete and SIFCON is given.

3.2.1 Plain concrete

Most of the experiments were conducted using a mortar with 2 mm maximum aggregate size. In addition to the mortar, normal weight and lightweight high strength concrete of maximum aggregate size

d max

of 16 and 12 mm respectively were used in order to study the effect of material structure on the biaxial tension/shear behaviour. The aggregate used in the lightweight concrete was sintered fly-ash (lytag).

The different mix designs are shown in Table 1. The strength results ana the maximum aggregate size corresponding to each batch are shown in Table 2. Five plates of size

300 x 300 x 50 mm

3 were cast in a stiff wooden battery mould in the vertical direction.

Table 1. Mix design for the three concretes used in the investigation normal weight concrete

16 mm mix proportion

Portland cement water super plasticizer

(type Melment LlO) air content (%)

2mm

(kg/m3)

500

250

2.24

(kg/m3)

375

187.5

1.3

River gravel and sand

(sieve size [mm])

0.125- 0.25

0.25 - 0.50

0.50 - 1.0

1.0 - 2.0

2.0 - 4.0

4.0 - 8.0

8.0 -16.0

Lightweight aggregate

4.0 - 8.0

8.0 -12.0

303

197

515

500

128

165

202

256

256

365

457

34

Iytag

12 mm

(kg/m3)

330

110.5

5.0

3.75

158

237

158

158

79

264

484

Two days after casting the plates were demoulded and cured under water. The water basin was kept in the laboratory at an ambient temperature of approximately 18

°e.

At an age of 14 days, the plates were sawn (using a rotating diamond saw) into square

Double-Edge-Notched (DEN) specimens of size 200 x 200 x 50 mm

3 with a notch depth of 25 mm and a width of 5 mm as shown in Fig. 33a. so

1/1/

200 P

905

~ so

1/ I/V

IV

= r----

4

5

!j.25

V

IV

V

lso

Iso

~

(a)

100 so

1/1/ p4

5

~

IV I/V

V

+5 ,

1/

V

!j.25

V

j:

(b) so so

200 so

1--t--------

-<r-V

1/ /

- , - - - - - - - - - -

200 so

I

I

(c)

Fig. 33. Sawing of Double-Edge-Notched specimens from square plates of 50 mm thickness.

35

In a later test series (viz. batch nos. 46, 47 and 48) the size effect in mixed-mode fracture was studied. Each batch consisted of six plates of size 300 x 300 x 50 mm 3 and

200 x 200 x 50 mm

3.

The plates were cast in two different battery moulds and were cured as mentioned above. After 14 days, the plates were sawn into specimens of dimension 200 x 200 x 50, 100 x 100 x 50 and 50 x 50 x 50 mm

3

(each having a constant notch to depth ratio

a

I d

=

0.125) as shown in Fig. 33b, c. Directly after sawing, the specimens were placed in a fresh water basin again. At an age of28 days, the specimens were taken out of the water and left in the laboratory to dry until testing at an ambient temperature of 17-18 °C and 50% RH. Note that the drying time varied depending on the age of loading, which ranged from 42 to 216 days.

In Table 2, the 28 day cube compressive strength and the splitting tensile strength of the three materials are given. The strength results were obtained from 150 mm cubes as specified in the Dutch codes VB

74/84.

Table 2. Compressive strength, splitting tensile strength and specimen numbering for the various batches batch number of specimens

(code)

d mqx

[mm]

fcc*

[MPa] ispt

[MPa] size**

[mm]

26

27

28

29

14

15

17

IS

30

32

46

47

4S

5(14-01/05)

5(15-01/05)

5(17-01105)

5(1S-01/05)

6(26-01/06)

6(27-01/06)

6(2S-01/06)

6(29-01/06)

6(30-01/06)

6(32-01/06)

6(46-01/06)

6(46-07112)

12( 46-13/24)

6(47-01/06)

6(47-07112)

12(47-13/24)

6(

48-01/06)

6( 48-07 112)

12( 48-13/24)

2

16

12

12

2

2

2

2

16

2

2

2

2

46.59(1.37)

47.86(0.20)

46.49(1.58)

48.17(0.36)

46.68(0.48)

52.47(1.03)

49.59(0.41)

60.l7(0.35)

58.75(2.62)

46.53(0.69)

49.66(2.23)

46.19(0.32)

46.24(0.37)

3.38(0.27)

3.68(0.07)

3.95(0.24)

3.56(0.27)

3.58(0.13)

3.61(0.15)

3.16(0.lS)

4.15(0.64)

3.97(0.33)

3.47(0.2S)

3.76(0.29)

3.7S(0.23)

3.67(0.29)

200

200

200

200

100

50

200

100

50

200

100

50

200

200

200

200

200

200

200

*

Numbers between brackets denote the standard deviation in [MPa].

** Only the largest size is mentioned. The specimens are square plates with a thickness 0[50 mm.

3.2.2 Slurry Infiltrated Fibre Concrete (SIFCON)

Slurry Infiltrated Fibre CONcrete is a relatively new material. The material was first introduced by Lankard and Newell (see [46]), and applied successfully for the repair of bridge decks. the material gained considerable attention in the research community, and investigators are looking for possible structural applications. In view of

36

this, the biaxial tension/shear experiments are meaningful! as they address the shear capacity and shear stiffness of cracked SIFCON.

Crucial in testing SIFCON is the manufacturing method ofthe specimen. In the present study the SIFCON specimens were manufactured in the same battery moulds that were used for casting the plain concrete specimens. First the fibres were sprinkled in the moulds. Two types of fibres, both manufactured by Bekaert, were used: viz. the straight

OL 25/0.5 fibres and the hooked ZL 30/0.5 fibres. The numbers denote the length and the diameter (in [mm]) of the fibres respectively. Because the SIFCON plates were only

50 mm thick, the fibres would allign preferentially in horizontal directions. In Fig. 34 two photographs from a transparent plexiglass mould filled with ZL fibres are shown. In

Fig. 34a, the front view is shown. The casting direction is vertical, and it can be seen that the fibres are alligned in horizontal planes. The side view of the plexiglass mould in Fig.

34b shows that a strong wall effect is present over the thickess of the plates. The cement

(a)

Fig. 34. Alligned fibre structure (ZL fibres), front view (a) and side view (b).

(b) slurry (a normal sand/cement mix containing 978.6 kg/m

3

Portland cement type B; a w/c ratio of 0.39 (by wt.); 11.7 kg/m 3 Melment super plasticizer; and 822.4 kg/m 3 of sand with a maximum aggregate size of 125 [lm) was poured along the sides of the moulds, allowing the air to escape from the centre of the plates as shown in 35. This manufacturing method implies that the plates are filled from bottom to top. In an experiment with a mould where one of the sides was replaced by a plexiglass plate it was found that following this method all air was removed quite easily, thereby reducing the vibration times.

During casting, the battery mould (now containing four plates only) was placed on top of a vibrating table. The moulds were fixed to assure that the vibrational energy was transfered directly to the fibre mass in the moulds. This was achieved by clamping the specimens on the table via supports that were placed directly on top of the fibre mass.

37

Fig. 35. Pouring the slurry in the narrow moulds.

Two views of the fibre distribution in the specimens after pouring the slurry are shown in Fig. 36. In Fig. 36a, a saw cut has been made parallel to the main fibre direction

(a

=

0°, see Fig. 5.1), and in Fig. 36b, a section perpendicular to the main fibre direction is shown

(a

=

90°). The anisotropy of the fibre structure will be obvious.

As mentioned two different types of fibres were tested: Dramix ZL 30/0.5 and Dramix

OL 25/0.5. The ZL fibres have small hooks at the end to improve the bond between the fibres and matrix. The geometry of the fibres can be seen in Fig. 34. Because of the different shapes of the OL and ZL fibres, the mould contains different quantities: 11.47% and 9.57% (by volume) for the OL and ZL fibres respectively. The fibre volumes are the average quantities of four batches for each fibre type. The numbers indicate that - as expected - the hooked ZL fibres form a more entangled network than the straight OL fibres. The complete details, including the compressive and splitting tensile strengths, of the eight SIFCON batches are given in Table 3. Note that preceding these eight batches, several test castings were made (No. 1-9) before satisfactory results were obtained.

10

11

12

13

Table 3. SIFCON batches batch

No. fibre type

OL

OL

OL

OL fibre quantity

[% by volume]

11.00

11.75

11.25

11.88 fcc

[MPal

-

()

-

(-

)

70.2(7.66)

66.2(2.56)

/sPi

[MPa]

6.25(0.36)

6.43(0.96)

6.84(1.23)

5.57(0.75)

16

17

18

19

ZL

ZL

ZL

ZL

9.52

9.37

9.72

9.65

70.2(2.41)

70.1(0.85)

69.7(0.58)

71.8(1.56)

6.07(1.10)

6.65(0.19)

6.81(0.96)

5.96(0.49)

Note: fcc

= compressive strength and

/sPi

= splitting tensile strength from 150 mm cubes; both determined 28 days after casting. Curing under water at 20°e. The strength values are the average values of three tests, the numbers between brackets denote the standard deviation.

38

(a)

(b)

Fig. 36. Anisotropy in SIFCON specimens: sawcut at a=O°, and (b) at a=90°.

Each batch consists of four plates of size 300 x 300 x 50 mm 3 and six 150 mm cubes.

The cubes were used for the determination of the reference compressive and splitting tensile strength following the Dutch codes VB 74/84. In the test castings, the vibration times were relatively long, but by using the method of Fig. 35 could eventually be reduced to approximately 6 minutes. Two days after casting the specimens were demoulded and placed in a fresh water basin in the laboratory (ambient temperature of approximately 18 cC).

At an age of 14 days, the specimens were sawn to the required size. Two Double-Edge-Notched (DEN) specimens were sawn from each plate as shown in Fig. 37. The size of the SIFCON specimens was 100 x 100 x 50 mm 3 . This size was selected because of its ease in handeling in the biaxial machine. Because the material was extremely anisotropic (Fig. 36), the loading was applied at various angles with respect to the fibre orientation. This was achieved by simply sawing the specimens in inclined positions from the plates. Note that the sawing of the SIFCON specimens is a tedious and time consuming task. In the beginning, in many specimens fibres were partly debonded at the edges during sawing. This was later (partly) prevented by carefully clamping the specimens between wooden plates during sawing. After sawing the specimens remained under water until an age of28 days, whereafter they were allowed to dry in the laboratory atmosphere (appr. 50% RH). The age at testing was always larger than 49 days.

39

a=22S a=67S

Fig. 37. Sawing DEN specimens with inclined fibres from square plates of 50 mm thickness; example of 22.5

0

and 67.5

0

specimens.

In addition to the SIFCON specimens, two batches of plain slurry were casted. In this case no reference compressive and splitting tensile strength were determined. a number of displacement controlled uniaxial tensile tests were carried out. In contrast to the SIFCON specimens, a number of the slurry specimens were kept in the water basin up till three days before testing. This was done because previous experiments showed that plain cement paste is very sensitive to shrinkage cracking if it is allowed to dry out at early ages, see [47J.

4 Plain concrete resuJts

4.1 Introduction

Nucleation and growth of cracks under combined tensile and shear loading has been studied with the biaxial test-rig of the Stevin Laboratory. Up till now seven different load-paths have been examined in order to better understand fracture mechanisms under biaxial loading. The unique feature of the test set-up in the Stevin Laboratory is that the two loading axes can be regulated completely independent of each other. Both displacement controlled and load controlled testing is possible as de sci bed before in chapter 3.

Testing concrete under mixed-mode I and II conditions is of great practical interest.

Many existing structures are cracked, and in most cases shear stresses may be present

40

due to stress-redistributions in the cracked structure. In the past many attempts have been made to study the shear resistance of cracked concrete. As a result aggregate interlock theories have been derived for fully open cracks, see for example [31]. In the present experiments, the shear response of partially opened cracks is studied. The phrase partially opened indicates that still tensile stresses can be transferred in the direction normal to the crack plane. Of course, compared to the behaviour of fully opened cracks, the physics of the shear process will change, and next to pure sliding, secondary cracking may occur.

The early mixed-mode studies in the Stevin Laboratory were set-up with the aim of extending the Fictitious Crack Model of Hiller borg and co-workers [7] for mixed mode loading. To this end quadratic push-off type specimens were used by Reinhardt and co-workers [39]. Main goal of their study was to determine the shear characteristics of a specimen containing a uniform crack-band. As argued before in chapters 2 and 3, recent experiments have shown that uniform loading of a process-zone is impossible. The heterogeneous nature of the material will always lead to non-unifom fracturing. The push-off type specimen was selected in [39), because analyses by Watkins and Liu [48) had shown that an almost uniform state of shear stress could be obtained for specific ligament sizes. The first experiments revealed however S-shaped crack patterns, indicating that stress-rotations occur almost immediately after crack nucleation. The assumed mixed mode fracturing seems governed by the weakest link in the material: the tensile strength.

With all the problems of non-uniform fracturing, specimen/machine interactions and the dominance of tensile fracturing in heterogeneous materials as concrete, it was decided to select a more simple specimen geometry. The quadratic double-edgenotched plate was selected. The specimen size was initially taken as large as the machine could contain, in order to come to a better understanding of the intricate specimen/machine interactions. In later tests the size was reduced. Because of the dominance of the tensile stress in fracture tests on concrete it was decided to choose first load-paths where a crack was generated in tension, and subsequently shear was applied under a variety of boundary conditions. Later also the important question of the existence of mode II (shear) fracture was addressed, and several tests were carried out without pre-cracking the specimen.

In this chapter the results ofthe experiments on plain concrete are presented. First, in section 4.2 the terminology used throughout this chapter is summarised. As mentioned, seven different load-paths were studied. An overview of these load-paths is given also in section 4.2. In the following sections (4.3 through 4.6) the effect of shear on the tensile envelope curve, the influence of initial crack opening on shear resistance, the effect of confinement and specimen size are discussed. In section 4.7 the path-dependency of mixed mode fracture is debated. The shear stiffness of the cracked concrete was also studied, but these results are shown in chapter 6, together with the SIFCON shear results.

The study has a true exploratory character.

Hardly any information is available on the shear behaviour of partially cracked concrete.

41

4.2 Load-path description

Seven different biaxial load-paths were studied up till now. In many cases the specimens were precracked in deformation control, whereafter under a variety of boundary conditions shear was applied either in displacement of in load control. The simplest load-path investigated was displacement controlled uniaxial tension.

Throughout this paper the following terminology has been used:

- Compressive and tensile shear:

In classical mechanics literature shear can either be positive or negative. In the experiments on concrete usually non-planar and nonsymmetric fractures develop in the specimen. When in-plane shear is applied, the behaviour may be different depending on the direction of the shear load. Therefore tensile and compressive shear are distinguished following the definition of Fig. 38.

- Crack opening:

The total deformation measured can be subdivided in an elastic part

o

and the crack opening 0 c'

Therefore the true crack opening is the total deformation

o

corrected for the elastic contribution 0 e'

In this paper the total deformation has not been corrected for the elastic deformation.

~ITJ

I .

--

Ps

--

Ps

(a)

(b)

Fig. 38. Definition of tensile and compressive shear directions.

--

Ps

Below follows an exposure of the load-paths investigated to date. The load-paths are shown schematically in Fig. 39 in terms of P - P., P - 0 and 0 -

t

histories. The loading rates are mentioned in Fig. 39. Note that during an experiment, the loading rates (displacement control) were usually doubled two times in the post-peak regime.

4.2.1 Load-path 0: Uniaxial tension

The specimen, glued between the loading platens, is subjected to uniaxial tension. The tests are always carried out in displacement control (Fig. 39a). Two different situations are distinguished with regard to the loading platen configuration. In the simplest test, the specimen is glued at the top and bottom to two steel platens, see Fig. 40a. Because the specimen is fixed in a normal biaxial test on four sides, a number ofload-path 0 tests has also been carried out on specimens glued to four loading platens as shown in

Fig.40b.

42

p.

Load-path 0

(-)

(+)P, p.

1)

A' 8

=

1.60 Ilm/min

~----.-­ t shear 20N/s

-----> s

=

1.60 Ilm/min

Load-path 1 (a)

(-) p •

Load-path 1(b)

(-)

I.- shear 20N/s

~

! ,.....::\.-

t,

=

1.60 )lm/min

-----.~-

..

-------.. t p

Load-path 2

P t

..

8 t unloading

~

It=

I

Load-path 3(a)

softening

P

'k:: ' .

axial unloading loading

,ro~~.

t

8si / ._- .

~/min t

Fig. 39a-e. Schematic representation of load-paths 0, la, lb, 2 and 3a.

43

Load-path 3(b)

(-)

-,,~I

I

-1 kN

(+)1];

P

!

r

Load-path 4

(-)

11--

(+)P, 0, or k(!

' .

0,

= 160 flm: m1n

t axial unloading loading

!lsi

~ t

8,

=

Ii

=

1.60 flmlmin t

Load-path 5

P s ' i .

PI

(-)

~

(+)1];

8

51 ""

8

1

=

1 .60

~m/min

Load-path 6

01];1

I

-------------t>

Os

-!,----------

8

0,,0

_ 8'8

5

=1 ,2,3 v _____ _

I];

8

5 =

1,60 llm/min

Fig. 39f-i. Schematic representation of load-paths 3b, 4, 5 and 6.

44

4.2.2 Load-path 1: Shear at constant crack opening

The specimen is first loaded in axial tension up to a prescribed crack opening 50. Subsequently the crack opening 50 is kept constant, and shear is applied in load control (Fig.

39b, c). The shear load

P s

is applied at different levels of axial crack opening. In loadpath la, the shear is compressive, in load-path] b tensile shear is applied.

4.2.3 Load-path 2: Tensile shear at zero axial load

The specimen is first subjected to tension, in displacement control. After loading it to a prescribed axial crack opening, the specimen is unloaded to

P

=

O. Subsequently, the axial test control is changed to load contol, and shear is applied while maintaining

P

=

0

= constant. The shear load is applied in load control (see Fig. 39d).

4.2.4 Load-path 3: Unconfined and confined compressive shear

Again the specimen is pre cracked to a given axial crack opening 00 in displacement control. Subsequently the specimen is unloaded, either to

P

=

0 (load-path 3a, unconfined) or to

P

= -

1000 N (load-path 3b, confined), see Fig. 3ge and f respectively. As soon as the axial load is reached, shear is applied in displacement control while the axial load is kept constant. In load-path 3b, the axial confinement of -1000 N corresponds to a small confining stress of - 0.13 MPa normal to the crack plane.

4.2.5 Load-path 4: Axial tension at constant shear force

A compressive shear load is applied to the specimen in displacement control until

P,

= -

5 (load path 4a), -10 kN (load-path 4b) or

Ps,max

(load-path 4c). During shear,

P

=

0

= constant.

Ps,max is the maximum shear load the specimen can sustain. Following this, the specimen is fractured in tension, in displacement control, while maintaining

P s

= constant at one of the above loading levels (see Fig. 39g).

4.2.6 Load-path 5: Axial tension at constant shear deformation

This load-path is similar to load-path 4, except that in both directions displacement control is maintained. Again

P s

is applied until a prescribed value:

P s

= -

5 kN (Ioadpath 5a),

P s

= -

10 kN (load-path 5b) and to maximum shear (load-path During shear,

P

=

0

= constant. Subsequently the specimen is fractured in displacement control in tension, while maintaining the lateral shear displacement constant (see Fig. 39h).

4.2.7 Load-path 6: Proportional loading

A specimen is loaded such that the ratio of axial deformation 5 and shear displacement

Os

remains constant throughout the experiment. The %s ratio's for load-paths 6a, 6b and 6c are l.0, 2.0 and 3.0 respectively (see Fig. 39i).

45

r r

~p

~p

Fig. 40. Uniaxial tensile test (load-path 0) between two (a) and four loading platens (b).

4.3 Influence of shear on the tensile envelope curve

In the first experiments it was investigated whether the application of a shear load would affect the tensile softening curve. To this end two different load-paths were followed, now designated 1a and lb. In these early tests, the shear load was applied in load control, and no stable fracturing in shear could be obtained. Therefore, well before the specimen was expected to fail, it was unloaded and in several tests cyclic unloading was repeated a number of times.

Two examples of tension-compression tests on 200 mm DEN specimens are shown in

Figs. 41 through 43. In these figures the

P-O

curves (Fig. 41), the load-path

P- P s

(Fig.

20.00

P (kN)

10.00

Compressive shear at constant 6

AA

0

14-01 Lp l~aj

• D 14-02 : Lp 1 a

~---

~

0.00

-10.00

-20.00

-30.00

-25 0 25 50 75 100 125 150 175 200

46

Fig. 41.

P-O

diagrams for two compressive shear tests at

00

= constant (load-path la).

42) and one of the crack patterns after test termination (Fig. 43) are shown. Results are given of two different experiments (1401 and 1402). The changes in loading sequence are shown in the inset of Fig. 41. First a specimen was pulled, in displacement control, to a prescribed axial deformation 00' As soon as this point on the tensile softening curve was reached (A), compressive shear was applied while maintaining 00

= constant.

Because the crack was not allowed to open during shear, a compressive confinement would develop in the axial loading direction as can be seen from Fig. 41. Upon (shear) unloading at constant 00, the axial compressive load was released, and at some stage the axial softening envelope was reached again. At this moment the lateral shear was zero, and the specimen was loaded further along the envelope curve. The curves shown in

Fig. 41 indicate that the static envelope curve is reached again after the shear loading.

This would mean that at these levels of shear loading no additional damage is done to the specimen. Note that the compressive shear load

P s

could not be increased over

50 kN, which was the loading limit imposed by the design of the biaxial machine. The impression was that the specimen could carry a substantially higher shear load. As can be seen from Fig. 42, the state of stress in the specimen during application of shear is compression-compression. A rough estimate is that the specimen would fail as soon as

P

2 0 , - - - - - - - - - - - - - - - - ,

_p • (0)

_p

1 (0)

-10

-20

P, (kN)

Fig. 42. Load-paths

P-P,

for the two tests of Fig. 41. the maximum biaxial stress in the specimen was reached. Comparison with for example

Kupfer's results [49], shows that the current stress levels are still very low: approximately - 2 and - 6 MPa in the axial and lateral directions respectively. For the concrete tested, the biaxial strength is estimated above - 50 MPa on the basis of Kupfer's results.

Even if the biaxial strength envelope would be reduced due to the tensile crack that was present in the specimen, than still these stress levels are considered very low.

The two results of Fig. 41 are almost identical. Shear loading and unloading at different values of 00 does not seem t'o affect the tensile softening envelope.

47

The crack pattern traced from the specimen 1402 after test termination is shown in Fig.

43. In both experiments a single crack developed, and no additional cracking seemed to occur under shear loading. Of course this is no surprise because the stress state in the specimen changes from tension-compression to compression-compression as soon as shear is applied. front face

14-02

Fig. 43. Crack patterns for experiment 1402, load-path lao

As mentioned, the shear displacements were not measured in these pilot tests. Consequently no information on shear stiffness reduction can be obtained from these experiments.

Because of the limitations in the biaxial test-rig, the specimens could not be failed under compressive shear (load-path Therefore it was decided to carry out some experiments under tensile shear. An example of a tensile shear experiment is given in

Fig. 44. This particular specimen (1504) was loaded in displacement control to

<5

0

=

11.6

[.Lm and 23.4 [.Lm respectively. At these points, the lateral shear was applied in tension (in load-control) while maintaining

<5

0

= constant. In the first shear cycle, only moderate levels of shear-load were allowed in order to avoid premature failure of the specimen.

During the experiment crack growth was monitored using reflection photo-elasticity. A

P(kN)

20

15

SPECIMEN 15-4

DEN 25mm d max = 2 mm photoeiostic coating d= 0.25 mm

10

(a.)

5

20

15

P

(kN)

(b)

SPECIMEN 15-4

Fig. 44. P-O and P-P

s

diagrams for tensile shear test 1504 at 0

0

=

constant (load-path Ib).

48

reflective coating of photo-elastic material was glued to the specimen's surface. Under polarized light, the isochromatics changed at places where cracks developed. Although the resolution of the technique is not very high, it can be used for correlating the extent of surface cracking with the load-deflection behaviour of the specimen. The method was used successfully for monitoring crack growth in DEN specimens loaded in uniaxial tension (see [12] and [SO]). In test IS04, the first fringes were observed near the left notch when the specimen was still in the ascending branch. At b

=

10 [Lm, a complete crack traversed the specimen between the left and right notch (Fig. 4Sa), and as soon as tensile shear was applied the small diagonal crack shown in Fig. 4Sb developed. At the same moment a small diagonal crack nucleated from the top of the left notch. Under increasing shear, the crack at the left notch extended further as can be seen from the other crack patterns (Fig. 4Sc-e). Final failure was not along the left diagonal crack but through unstable extension of the diagonal crack near the right notch. The load-crack opening diagram

(p -

0)

of Fig. 44a shows that after a shear cycle, the tensile envelope curve is followed again. This illustrates that no additional cracking occurs in the plane ofthe primary (tensile) crack. Moreover, the result indicates that the shear resistance of the partially opened crack is still relatively high, and failure of the specimen through diagonal cracking prevails.

-~

(0)

(e)

Fig. 45. Cracking during test 1504. The respective stages of loading are indicated in the right upper corner of each figure, and correspond to the numbers in Fig. 44.

49

Note that the crack in the specimen nucleated at the front face. This was explained before in chapter 3. The relative in-plane and out-of-plane stiffnesses of the specimenl machine system and possibly the introduction of some additional eccentricities when the specimen is glued between four loading platens, may lead to this out-of-plane bending. During the experiment 1504, crack growth was also monitored (using the same reflection photo-elastic method) at the back side of the specimen. Here it was found that at the onset of shear loading, the axial tensile crack had developed only partly, see

[50]. The diagonal cracks at the back side developed at approximately the same locations as compared to those at the front side of the specimen.

Several load-path 1 b experiments were carried out, and three different results are given in [5]. In all cases, a diagonal tensile crack nucleated either near one of the notches, or from a sharp kink or discontinuity in the primary tensile crack. The load-deformation response for the experiments was however quite similar.

The inclination of the "shear cracks" indicates that a rotated biaxial tension/tension state of stress governs the failure of the specimen. The load-path P - P

s

(Fig. 44b) indicates that final rupture occurred in the tension-compression regime. Again this should be expected (qualitatively) on the basis of Kupfer's results [49].

4.4 Influence of crack opening on shear behaviour

The effect of crack opening 6

0 on the shear resistance and shear stiffness of cracked concrete was investigated using load-paths 2 and 3. In load-path 2, tensile shear was applied in load control after a specimen of size 200 mm was precracked to a given crack opening 60' During shear the load normal to the crack plane was kept constant at zero.

This allowed for an unrestrained opening of the crack during shear.

In load-path 3, compressive shear was applied in displacement control (note that the machine was modified in between ofthe load-path 2 and 3 experiments in order to allow for displacement controlled shear loading). Again the specimen was precracked to a given axial crack opening and unloaded to either 0 kN or to - 1 kN confinement normal to the crack plane.

The load-path 2 experiments revealed the shear resistance of concrete containing narrow cracks between 10 and 400 [lm. The load-path 3 experiments yielded information concerning the shear stiffness of the cracked concrete under confined and unconfined conditions.

4.4.1 Tensile shear

The results of the load-path 2 experiments are shown il! Figs. 46 and 47. In Fig. 46a the axial load-displacement diagrams are shown, in Fig. 47 the crack patterns for all experiments. The diagrams can best be explained by following a specific test. For example in test 1704, axial loading was applied till

0

0

=

65 [lm. At this stage the specimen was unloaded to

P

=

0, and the displacement control was changed to load control. In Fig. 46a both the loading and unloading curve are shown. Following the axial loading, lateral

50

15

P (kN)

(a)

10

.. p

5

'" 17-02 (200 IJ,m)

~:;:,.

17-05 (250 IJ,m)

'"

---...:::.:~!::::::::.::"'::::::....,-::::::;:::

... ____ 17-03 (300 IJ,m) ol-____

~----~----_===~~:::··~·~~-~~---~-~~-~--~-~-~--~-~!l~-~~~~~0~-~~0~IJ,~m~ o

50 100 150 200 250 300 350

6

(\-Lm)

2.5

(250) (275) (300)

(400)

5.0

(250)

7.5

(200)

( b.)

10.b

(150)

(65IJ,m)

( ) :"unloading - displacement" in

2 5

L -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

P s

(kN)

Fig, 46,

P-i5

(a) and

P s

-i5

plots (b) for tensile shear experiments at

P

=

0

= constant (load-path 2), shear was applied in load control, and the curve of Fig. 46b is measured. During shear, some uplift occured as can be seen from the increase of'lxial deformation. The specimen would fail as soon as the maximum shear load was reached. Fig. 46a shows that diagonal cracks developed in specimen 1704 during the shearing regime. The horizontal crack between the notches developed during the axial tensile loading. Obviously, the shear resistance of this narrow crack (note: the axial crack opening at shearing was somewhat smaller at

P

=

0, viz. 55 ttm), was relatively large and failure of the specimen occurred through diagonal cracking rather than through sliding.

The shear behaviour was consistent throughout all experiments, except that at crack openings larger than 250 ttm, the failure mode changed from diagonal cracking to sliding. This can easily be seen from the crack patterns in Fig. 47. Surprisingly the

51

front face

.......

(a)

(b) 18-01 (150 pm)

(c) front face

'-..

..

,

...

...

/

,~rE'ar facE'

17-04 (65f-lm)

(d) front face

"

;'

/~rear

face

(e)

17-02 (200 !Jm)

18-02 (225f-lm)

(g)

Ilront face

J':"'---

-------'~-~ar

face

17-05(250 f-lm)

(h)

18-04 (250 !Jm)

(i. )

B fronl face............. _ il

~

._ •..••. ""/ C rear face front face

_~--=--

'-..

.----r

C rear face

17-01 (400 pm)

Fig. 47. Crack patterns for the load-path 2 experiments of Fig. 46. change in failure modes near crack openings of 250 [lm was accompanied by a sudden decrease in maximum shear-load. Note that two duplicate tests at

00

=

250 [lm were carried out. One of the specimens failed at a relatively high shear load, whereas the other failed at a low shear loading through sliding.

4.4.2 Compressive shear

The same phenomena were investigated in the load-path 3 experiments. However, now the shear load was compressive, and three different materials were tested at different ranges of axial crack opening, see Table 4. The test scheme was considerably reduced

52

because only two or three biaxial tests could be carried out in one week. The range of crack openings for the 2 mm mortar was chosen around the transition point of 250 [.Lm in the tensile shear tests (load-path 2).

Table

4.

Compressive shear tests (load-path

3) crack opening 15

0

[[lm]

50 100

ISO

200

225 250 275 300 400 material

2 mm mortar

16

12 mm concrete mm Iytag confinement during shear

0

-I kN

0

-I kN

0

-I kN

**-

* *

* * ** * *

*-

**

* * *-

*-

**

**

**-

** *-

Note: every variable c.ombination is tested in duplicate; (-) test rejected because of too large offset 15 s during tensile loading; (*) successful test.

For the 16 mm concrete, a wider range was chosen, viz. between 200 and 400

[.Lm.

It was not certain whether a similar transition would occur at exactly the same point for the

2 and 16 mm mixes. The lytag lightweight concrete was expected to behave very brittle.

Therefore, 6

0 was chosen at relatively low levels for this material, viz. 50, 100 and

150

[.Lm.

It is now known that the lytag behaves, at least in tension, as a 4 mm mortar (see

[19] and Fig. 7). The 4 mm maximum aggregate size refers to the size of the sand in the lytag mix.

The results for the 12 mm lytag are shown in Figs. 48a, b, c. The results for unconfined shear will be discussed here, a comparison with the confined tests will be given in section 4.5. In Fig. 48a and b the P-6 and Ps-6 s curves for three lytag experiments are shown. The scatter in axial P-6 diagrams is relatively small; note that the three unloading displacements can easily be seen from Fig. 48a. The shear curves indicate that the shear resistance (maximum shear load) decreases with increasing axial crack opening, which should be expected on the basis of the load-path 2 experiments.

Because relatively large off-sets (defined as the amount of shear displacement 6$ during axial tensile loading) were measured in some of the lytag experiments, only three results were considered acceptable. The other three unconfined tests showed unacceptable large shear displacements during the application of the axial tensile load, and these results were rejected. The off-set is most likely caused by small eccentricities in the test set-up. For example small eccentricities may appear during the glueing of the specimen in the machine or when deviations occur from the exact specimen dimensions. A result was rejected when the offset was larger than 30

[.Lm,

and from the total series 10 out of36 results were not included in the analysis as can be seen from Table 4 (see also [51]).

The 6-6$ plots for the three unconfined lytag tests are shown in Fig. 48c. From this figure the following observations can be made. First, the unloading of a specimen after loading it to a certain axial crack opening is visible. This all happens along the 6$

=

0 axis. When shear is applied, 6$ increases, and generally during the first 10 [.Lm closure of

53

P (kN)

20.0

- r / i > - - - - - - - - - - - - - - ,

17.5

15.0

12.5

10.0

7.5 o o

29-06

29-01

~

50l

100

, 29-02 150 d" = 12 mm Lytag

Load-path 30

2.5

0.0

+-......

-~-"--~------I

(a)

50 100 150 200 250 300 350 400 o

Cum)

P s

(kN)

-30.0 -.-------------~ o

Cum)

2 5 0 , - - - - - - - - - - - - - - - ,

- 25.0

-20.0

5.0

29-06

~

50l

29-01 100

*

29-02 150 d a

= 12 mm Lytag

Load-path

.30

200 o o

29-01

~

50l

*

29-02 150

d"

=

12 mm Lytag

Load-path 30

150

-15.0

100

-10.0

50

- 5.0

0.0

+----'-r---~--r----;--...,.._-__l

-50 -100 -150 -200 -250 -300

(b)

O+----,-----r----,----~ o

- 50

-100

-150 - 200

Os

(fLm)

(c)

Fig. 48.

P-O

(a),

Ps-os

(b) and dilatancy plots

o-os

(c) for unconfined compressive shear tests on lytag (load-path 3a). the axial crack is observed. Subsequently, the shear displacement increases under increasing shear load, but the crack opening remains almost constant. Only when

P s

reaches its maximum value, a sudden increase of uplift is measured. Because no confinement is present normal to the crack plane, the specimen will fail as soon as uplift starts. In all unconfined tests a similar response was measured, see [5]. The crack patterns traced from the unconfined lytag experiments after failure are shown in Fig.

49. In all cases, a single crack plane was observed between the two notches.

The maximum shear loads in the unconfined tests were remarkably constant. If all experiments of the three different materials are considered, an average maximum shear load of approximately - 5 kN is measured. This value is comparable to the maximum load measured in the tensile shear tests (load-path 2), at least when failure occured through sliding (see Fig. 48b, and [5] for 2 mm mortar and 16 mm normal concrete). The

54

only exceptions are the 50 [lm and 100 [lm unconfined lytag tests (2906 and 2901, see

Fig. 48a, b), which failed at a higher shear load level. Especially the shear loading of the

50 [lm unconfined lytag test was relatively high, a level which could not be reached in the tensile shear tests for obvious reasons. The high shear load can probably be explained from the fact that the specimen was not completely cracked at the moment that shear was applied. Note that recent impregnation tests indicated that at 6

0

=

50 [lm, an intact core may be present in the specimens, see [17]. The results indicate that the sliding failure mechanism is prevalent in the unconfined compressive shear tests. Of course this remark is valid for the range of crack openings studied. In future, more experiments should be carried out at crack openings between 10 and 50 [lm.

In none of the unconfined shear tests secondary cracking was observed as can be seen from the crack patterns (Fig. 49). front face rear face

'--,

29-06 (

50~m) front face rear face

-r

front face rear face

_

-

.......

----""

-..-

29-02 (150

~m)

Fig. 49. Crack patterns for the three load-path 3a experiments of Fig. 48.

4.5 Influence of confinement

The various experiments that were carried out included tests with confinement normal to the crack plane under shear loading (load-path 3b), but also tests with "shear confinement" under axial tension (load-paths 4 and 5). In this paragraph these results will be presented. The load-path 3b results will be presented in section 4.5.1, the load-path 4 results in section 4.5.2.

55

4.5.1 Confinement normal to the crack plane

It is interesting to see how the failure of a specimen is governed by the presence of a confining stress normal to the crack plane. In the present tests a relatively low confinement acted normal to the crack, viz. - 0.13 MPa only. The confining stress was chosen at this low level in order to avoid that the specimen could not be failed in shear. Note that in the load-path la tests could not be failed in shear because of the biaxial compressive state of stress in the specimen.

In Figs. 50 and 51 results of the confined lytag tests are shown (load-path 3b). In this case all six tests were successful and these results are included in these figures. The axial load-deformation response is identical to the

P-O

behaviour measured in the unconfined experiments (Fig 48a). Clearly visible is the constant confinement of -1000 N after unloading, see Fig. 50a. Due to the application of the confining stress, the axial

20.0

P (kN)

S.O

2.S

0.0

-2.S

17.S lS.0

12.S

10.0

7.S

50

P, (kN)

- 30.0 , - - - - - - - - - - - - - - - - ,

- 25.0 o 29-03 [ 50l

i>.

29-04 100

+ 29-0S 150

d o =

12 mm Lytag

Load-path 3b

-20.0

100 o 29-03 [ SOl

6.

+

29-04 100

29-05 150 d ..

=

12 mm

Load-path 3b

Lytag

150 200

6

250

(um)

(a)

250

0

Cum)

200

0

29-05 150

de

=

12 mm Lytog

Load-path 3b

150

-15.0

100

-10.0

50

- 5.0

0.0

..---r----r----,----r---,.----1

- 50 - , 00 - 150 - 200 - 250 - 300

(b)

0, (um)

0+0-----5rO------~10rO------l~5-0-----4200

(c)

0,

().Lm)

Fig. 50. P-b (a), Ps-b s (b) and dilatancy plots b-b s

(c) for confined compressive shear tests on

Iytag (load-path 3b).

56

front face

-"~~:::? -r--------<:~-

~

29-03 {50

11m) front face

"" rear face ....

1~;:o4(100Ilm) o front face

29-05 (150

11m)

Fig. 51. Crack patterns for the three load-path 3b experiments of Fig. 50. crack opening at onset of shear application was reduced by approximately 30% when compared to the value of 60' For the tests of Fig. 50, the axial crack opening immediately before shearing was 32.6, 30.0, 65.4, 65.2, 108 and 98.6 [lm for specimen 3004

(60

=

50 [lm), 2903 (50),2904 (100), 3001 (100),3003 (150) and 2905 (150) respectively.

Again, after shear was applied, the axial crack would close slightly for very small shear displacements as shown in Fig. SOc. Following this closure, an increasing shear displacement was measured under increasing shear load, whereas the axial deformation remained almost constant. Only around peak

(ps,maJ, the axial crack opening would increase again. In comparison with the unconfined compressive shear test, this axial crack opening was controlled, and no explosive failure of the specimen would occur.

Clearly the

P s

-6 s

figures indicate that the fracturing in shear under confined conditions is more ductile, and the descending branch in the

P s

-6 s

diagrams increased with increasing axial crack opening 6

0 ,

The reason for this latter effect can perhaps best be explained from the crack modes observed in the respective experiments. The crack patterns in the duplicate test were almost identical and only three crack patterns are shown in Fig. 51. Due to the application ofthe compressive shear load, extensive crack branching was observed. The details of the branches depend strongly on the geometry ofthe axial tensile crack. For example in the 150 [lm specimen (Fig. SIc), crack A-B-C developed during the axial loading of

57

the specimen. Crack C-D nucleated as soon as shear was applied, and as will be shown in chapter 5, similar phenomena appeared in the SIFCON experiments. The branching developed either near the right notch, or somewhere from the middle of the tensile crack where a strong discontinuity or kink appeared, as for example visible in Fig. SIb.

Surprisingly, the ductility

(ps-os)

increased with increasing axial crack op~ning.

This phenomenon can most likely be explained from the mechanism of Fig. 52: depending on the local crack geometry a larger or smaller compressive strut may develop in the specimens. More or less parallel to this strut, a splitting crack will develop. If the crack patterns of Fig. 51 are studied carefully, it can be seen that the compressive strut size increases with axial crack opening. Probably this is purely accidental. On the other hand it might be argued that in the 50 [.tm specimens still axial stress was transfered through an intact core in the specimens (see [17]). In that case, the compressive shear load would be carried by the intact portion of the ligament between the notches and a more distributed cracking would prevail. In the 150 [.tm specimens, the separation ofthe crack faces was probably almost complete, and the shear resistance would depend completely on the carrying capacity caused by the local roughness of the tensile crack.

Fig. 52. Failure mechanism (schematic) in the confined compressive shear tests of Figs. 50 and 51.

The results of Fig. 50b indicate that the initial slope of the

Ps-os

curves decreases with increasing axial crack opening. This same tendency was found for the unconfined tests as well, see Fig. 48. In the confined tests on the two other materials, this tendency was present as well (see [5]). The shear stiffness analysis will be given in chapter 6.

58

4.5.2 Confinement in the lateral shear direction

Load-path 4 was the first loading sequence where specimens were not precracked. In these experiments, first a lateral shear load was applied until a given level was reached.

After this shear load level was reached, P s was kept constant and the specimen was fractured in displacement control in the axial direction. The shear load acted now as a lateral confinement, although of course this was a rather unsymmetric confinement.

The

P- 0,

P s-(5s and

(5-(\ curves for three load-path 4 experiments on 2 mm mortar are shown in Fig. 53. From Fig. 53a, the moment of application of the axial tensile load can easily be identified. The

Ps-os

curve in this figure show large non-linearities when

Ps

< -

20 kN, which is about 60% of the "shear strength" of the 200 mm DEN specimens. The definition of shear strength is somewhat dangerous, because undoubtedly

(kN)

~30.0

- , - - - - - - - - - - - - - - - - ,

·25.0

~20.0

.15.0

~10.0

·5.0 a p.

~

5 kN (LP 4aj (48-03j p. ~ -10 kN Lp 4b 47-01

p.

= max Lp 4c 47-06 do

=

2 mm

200 mm specimens

(a)

0.0

Os

Cum)

20.0

P

(kN)

17.5

15.0

12.5

10.0

7.5 a

P,

~

5 kN (LP

4aj r8-03j p. ~

P, =

-10 kN Lp

4b 47-01

max

Lp 4c

47-06

do

=

2 mm

200 mm specimens

o

Cum)

400.-----~~~---~~-,

300

200

5.0

2.5

A

0.0

-2.5

+ - - - - . - - - - - . - - - - , - - - - - - j

(b)

50 100 150 200 o

Cum)

100 o o

-100

d ..

=

2 mm

200 mm specimens

a P,

P,

~ - 5 kN

~48-03~

=

-10 kN 46-05

P,

~ max 47-06

(C)

- 200

Os

- 300

Cum)

Fig. 53.

Ps-os

(a),

P-O

(b) and dilatancy plots

0-0

5

(c) at different levels of constant lateral shear confinement (load-path 4a, b and c).

59

a somewhat rotated biaxial state of stress will be present near the notches. The extensometers showed that in the load-path 4c specimen, cracks initiated from the left notch.

Consequently, in this experiment axial deformations were measured during the shearing regime. The axial deformation that took place during shearing was relatively large as can be seen from the P-O plot for load-path 4c

in

Fig. 53b (point A). From the local deformation measurements in the load-path 4a and 4b experiments, it was evident that no tensile cracking occured in the notched region during the application of the shear loads. This is confirmed by the linear

P,-O

s curves for these two tests, see Fig. 53a.

The corresponding P-O curves of these three load-path 4 experiments are shown in

Fig. 53b. Increasing the lateral shear load from - 5 kN to -10 kN results in a decrease of front face front face

'--~~'­

"

"rear

~:~-,---load-path 4b ([,6-05) front face

60 load- path I.e

147-06)

Fig. 54. Crack patterns for the load-path 4 experiments of Fig. 53.

tensile carrying capacity of approximately 30%. Further increasing the lateral shear to

Ps,max leads to an enormous decrease of carrying capacity, and in order to stabilize crack-propagation in the load-path 4c experiments, compressive stresses were needed.

It may be concluded that the presence of a lateral compressive shear load has a significant effect on the tensile strength of the DEN specimen. Again, based on (qualitative) considerations this should be expected. The specimen is in a biaxial tensile-compressive state of stress, and Kupfer's results [49] clearly show that the failure envelope is considerably reduced under this biaxial loading.

In Fig. 54, the crack patterns traced from the specimen's surfaces after test termination are shown for the three tests of Fig. 53. The effect of a shear load on failure mode is significant: the size of the intact ligament between a set of overlapping cracks increases with increasing shear load. Note that in the case ofload-path 4c

(p s

= P s max = constant), the two overlapping crack branches developed during the application of the shear load.

During shearing, the axial load

P

was kept constant at

0 kN, and the axial deformations were unrestrained. This situation resembles the loading of a double notched fourpoint-shear-beam, as for example those tested by Bazant and Pfeiffer [25]. In [25], the development of a single shear crack was reported, but based on the present load-path 4 results, where shear is applied to failure, the findings of Bazant and Pfeiffer seem somewhat debatable. Most unfortunately a proper documentation of failure modes in

[25J is lacking, and also no efforts were undertaken to carefully monitor crack growth during the experiment. It is the author's opinion that some of curved cracks may have developed in the Bazant and Pfeiffer tests, and that explosive failure of the ligament occurred. This secondary failure might (mistakenly) be regarded as a shear fracture.

Future research is needed to further clarify this point.

4.6 Size effect under biaxial loading

Recently, the size effect on failure and localization of brittle disordered materials such as concrete has gained more interest. In conventional strength theory, the influence of the size of the structure on nominal strength (TN is neglected. In a log (Tw1og (size) plot the strength criterion appears as a horizontal line as shown in Fig.

55.

On the other hand, linear elastic fracture mechanics predicts that the structural strength is size dependent: (TN

=

C

lid,

where C is a constant and

d

is the characteristic size of the structure. In the log-log plot of Fig. 55, the LEFM criterion appears as a straight line with slope - 1/2. As argued by BaZant [52] on several occasions, the size effect is the salient property of fracture of brittle disordered materials. The fracture of reinforced concrete structures and laboratory sized samples falls normaly between the conventional strength theory and predictions based on LEFM. Non-linear fracture mechanics is introduced which gives a smooth transition between the strength criterion and LEFM as shown in Fig. 55. Bazant further argues that existing code rules should be modified, and should be based on non-linear fracture mechanics in order to allow the translation oflaboratory results to real structural sizes. Bazant proposed a size effect law as follows:

(4.1)

61

where

~

=

(d

a/

d)',

dais the maximum aggregate size, and

B,/:, r, ao,

ab ... are constants

[52]. A simplified version of equation (4.1) was also proposed:

(4.2)

This latter expression is probably sufficient for most structural applications. The size effect is caused by crack front blunting according to Bazant, which seems only a different terminology for the non-linear processes that take place around a crack in concrete as shown before in chapter 2. The size effect law suffers from two important

' " ELASTICITY OR

, PLASTICITY

f t or fr

'-

,

,

MOST EXISTING TESTS

NONLINEAR

FRACTURE

MECHANICS

LINEAR

FRACTURE

MECHANICS

LOG (SIZE d)

Fig. 55. Effect of structure size on strength, after [52].

20

15

10

25

P max

(kN) x

0 load-path

.

0

0

.

40'

40

4b

4c

.

x

0

'"

~

~

. .

0 x

0

0

·

·

25

P max

(kN)

20

0

0

c.

load-path

60

6b

6c

15

10

&

0

0 l:iI

0

0

DO

6. x

-5 a

50 100 150 200 250

I

(mm)

(a)

-5 o

50 100 150 200

250

I (mm)

(b)

Fig. 56. Variation of strength for specimens of different size: (a) load-path 0 (uniaxial tension) and load-path 4 (confined tension), and (b) load-path 6 (proportional loading).

62

restrictions. First of all it can be applied only on geometrically similar specimens. The structure is scaled proportionally in two dimensions, whereas the third dimension

(usually the thickness of the structure) must remain constant. The second restriction on the size effect law is that the load has to increase monotonically.

Using the biaxial test set-up, a number of experiments have been carried out in such a manner that verification of the size effect law is possible. Three different specimen sizes were tested, viz. double edge notched plates of size 50 x 50, 100 x 100 and

200 x 200 mm. The specimen thickness was always 50 mm. The notch to specimen size ratio was kept constant, viz.

aid

=

0.125. As explained in chapter 3, the 200 mm square plate is the maximum specimen size that the biaxial machine can contain. For the two other sizes special loading platens were manufactured as explained in chapter 3 too.

The two load-paths that could be compared with the size effect law were the uniaxial tension tests (load-path 0) and the proportional biaxial experiments (load-path 6). All other size tests (load-path 4 and 5) did not fulfil the requirement of monotonic loading.

4.6.1 Size effect on strength

In Fig. 56, the peak values measured in the load-path 4 and 6 experiments are plotted for each specimen size. On the horizontal axis the distance between the notches is plotted, on the vertical axis the maximum tensile load

P

max'

In Fig. 56a the results for the loadpaths 0 and 4a-c are shown, in Fig. 56b the results for the load-path 6a-c experiments. At first glance, an almost linear increasing peak-load is measured with increasing size.

Note that the strength decreases for the load-path 4 experiments when compared to the load-path 0 tests. This is caused by the presence of the lateral shear load at various levels. This point will be elaborated further in the next section. The results for loadpath 6 do not show any effect of the ratio

0/0

s on tensile strength. Note that this ratio

o

varied and was equal to 1.0,2.0 and 3.0 for load-path 6a, 6b and 6c respectively. The load-path 5 results are not shown here, but these were completely identical to those of load-path 4 (see [5]).

If the results of Fig. 56 are translated to stress-size plots, hardly any effect of size on strength is found. The data points are almost on a straight horizontal line. The loadpath 0 and 6a-c results have been modified in order to allow for a comparison with

Bazant's size effect law. The size effect law (equation 4.2) can be translated to a linear plot following

Y=AX+ C (4.3) where

Y

=

(f;j aN)2,

X

=

d / d a,

C

=

1/

B2 and

A

=

C

fAa.

The slope

A

and the Y-intercept

C can easily be determined from a regression analysis. This gives an estimate of the two unknown parameters in the size effect law, viz.

Band

Aa. At the same time, the errors introduced can be estimated. The coefficient of variation of the deviations from the regression line is

Wy/x

=

Sy/x/

Y,

where Sy/x is the modified standard error estimate and is equal to

!.E[Yi - YestJ2!(N - 2))112.

Y

is the mean value of the experimental

Y

data. The correlation coefficient r is given by {l-

S~/x/S~}lI2, where Sy is the standard deviation.

63

The papers published by Bazant do not give information on which values for

Wy/ x

are

r

are acceptable.

The results for load-path 0 and 6a are shown in Figs. 57 and 58 respectively. The coefficients A and C as well as the values for

Wy/ x

and

r

are plotted in the various figures. In a diagram with linear scales, the size effect law appears as a straight line. For the loadpath 0, the results are found to be in agreement with the results ofBazant. In the log-log plot of Fig. 57b, the expected tendency is retrieved. Thus, the size effect law seems to be confirmed by the present load-path 0 results.

3.00

2.00

Ut/

CJN)2

0.05

6

-0.00

6

~

6

-0.05

-0.10

-0.15 log

( CJN/8f t)

6

6

1.00

-0.20

6

6

6

6

0.00

A

=

0.014

C ~ 1.361

Wy/x

r

=

~

0.243

0.629

+ - - - - , - - - , . - - - - . . . , - - - - / o

25 50

-0.25

8 ~ 0.B57

'0

~

97.214

-0.30

+---,---,----,,---.,.---,---1

0.75 1.00 1.25 1.50 1.75 2.00 2.25 log (d/d o )

Fig. 57. Fit of size effect law to uniaxial tensile data (load-path 0).

6.0 . , - - - - - - - - - - - - - - - - - , o

0.20 - r - - - - - - - - - - - - - - - - - , o o o

0.10

4.0

0.00 o o o o

III

2.0

-0.10

A =

-0.019

C ~ 4.373

Wy/~ r

= 0.652

~ 0.42B

0.0

+ - - - - , - - - , - - - - - ; - - - - 1 o

25 50

8

~

0.478

\, ~ -230.15B

present series trial series

-0.20

+----,,---.,...--,---.,----/

0.75 1.00 1.25 1.50 1.75 2.00 log (d/d o)

Fig. 58. Fit of size effect law to biaxial results (load-path 6a,

616,

=

1.0).

64

Surprisingly, the load-path 6a results gave an opposite trend. The regression yielded a straight line with negative slope (Fig. 58a), and in a log-log plot an upward curved relationship was found. The exact reason is not known. Part may be explained from the fact that in the load-path 6a experiments a number of specimens were of slighlty higher age than the others. More important however seems the fact that the failure modes changes for the load-path 6 experiments for the three different sizes (see section 4.6.3). It is felt that a rigorous micromechanical analysis is required in order to better understand the behaviour ofthe concrete under these complex load-paths. For example the approaches from [20] and [21] could be adopted. These models gave interesting results on the fracture mechanism of concrete under uniaxial tensile or uniaxial compressive loading

(Fig.

8).

The same models can likely be used for explaining the size effect.

4.6.2 Load-path 4 results

The load-path 4 results can not be compared with the size effect law because the second condition that loading must be applied monotonically was not fulfilled. The experiments were the first that were carried out without precracking the specimen. This should give some information on mode II (shear) fracture of concrete. Some of the load-path 4 results were discussed in section 4.5.2. Here the effect of varying the specimen size is presented. The load-displacement diagrams for the load-path 4 experiments with three different sizes are shown in Fig. 59, the corresponding crack patterns for three load-path 4b experiments are shown in Fig. 60.

As can be seen from Fig. 59a, the axial peak load

P

max decreases with decreasing specimen size (see also Fig. 56a) in the presence of a lateral shear load of - 5 kN (loadpath 4a). Comparison with the uniaxial tensile results of Fig. 28 shows that the presence of the - 5 kN lateral confinement has indeed a significant effect. The post-peak

P-O

behaviour for load-path 4a did not differ significantly from the uniaxial diagram. The shape of the curve remains essentially the same, yet the impression is that the small specimens respond more ductile, but this can be a visual effect only. When the lateral confinement is increased, the peak values in the P-O diagrams are even further reduced as shown in Fig. 59b. As soon as the lateral shear load is increased to the peak value

(ps,max), controlled failure through axial loading can be obtained only when compression is applied, see Fig. 59c. Similar results were presented before in section 4.5.2. Note that the 50 mm specimens were already close to "shear-failure" in load-path 4b (Fig.

59b). For this particular 50 mm experiment also small compressive loads were needed in order to stabilize the fracturing.

It should be mentioned that the experiments on the 50 mm specimens were extremely sensitive to deviations from the exact shape and size. Eccentricities due to glueing or small geometrical deviations caused severe off-sets (see section 4.4.2, page 52) which in several cases led to glue fractures between the specimen and the loading platen, The experiments where this happened are not included in the present report.

The fracture modes for the load-path 4 experiments on specimens with different sizes are surprisingly self-similar [53]. This is shown in Fig. 60 for three load-path 4b experi-

65

P (kN)

20.0 , - - - - - - - - - - - - - - - - ,

17.5

15.0 o

200 mm

\4S-03j

50 mm 48-13

50 mm 46-15 d"

=

p.

~

2 mrn

-5 kN.

Lp 40

12.5

10.0

7.5

5.0

2.5

17.5

15.0

12.5

10.0

-2.5

- + - - - - , - - - - - , - - - , - - - - - - 1

50 100 150 200

<5

Cum)

P

(kN)

2 0 . 0 . . , . - - - - - - - - - - - - - - - - , o 200 mm \46-05j

100 mm 48-09

50 mm

47-22 d u

=

p. ~

2 mm

-10 kN. Lp 4b

P

(kN)

20.0 , - - - - - - - - - - - - - - - - - - ,

17.5

15.0

12.5

10.0 o 200

100

mm

~47-06l

50 mm

48-18

d" p.

=

2 mm

= max shear, Lp 4c

7.5

5.0

7.5

5.0

2.5

0.0

1-~============i

-2.5

- + - - - - , - - - - - , - - - , - - - - - - 1

50 100 150 200

<5

Cum)

2.5 o.o~~~~

~

-2.5

- + - - - - . - - - , - - - - - , - - - - - - - 1

50

100 150 200

Fig. 59. P-i5 response for load-path 4a, 4b and 4c for different specimen sizes. ments. Note that the 50 mm specimen is identified as load-path 4b*. In this case not the

- 10 kN lateral confinement was reached, but was maintained at - 9 kN in order to avoid premature failure of the specimen. In all cases the previously reported set of curved overlapping cracks developed in the specimens. Fig. 60 suggests that the fracture patterns scale with the scaling of the specimen. As mentioned before, the size of the intact ligament between the overlapping cracks increased with increasing lateral shear load (see Fig. 54).

Almost identical results were obtained for the load-path 5 experiments. In these tests the lateral shear confinement was changed to a constant lateral shear displacement.

Consequently, the lateral shear load varied somewhat during the application of the axial loading. As shown in [5], this has no effect on the observed behaviour. The P-O response and the failure modes were similar to those presented in Figs. 59 and 60.

66

-..---

"'

,

....

__

.....

_-

\

.....

_--

.....

rear face / -,-

----~-

4b

200x200~(50

,

\

""-,

rear face ) -

~

----~ load-path 4b(48~09)

1(0)(100)(50 load-path 4b* (41-22)

SOl,50xSO

Fig. 60. Crack patterns traced on three load-path 4b experiments on specimens of different sizes.

4.6.3 Load-path 6 results

As mentioned before several specimens were loaded following a proportional path. In this case %s was kept constant at 1.0,2.0 and 3.0 for the load-path 6a, 6b and 6c experiments respectively. Due to partial elastic unloading in the length softening, the actual ratios %s deviated somewhat from the planned values. In addition, rotations of the loading frames may have caused some deviations. These deviations were relatively small. For example for load-path 6b with

0/0

s

=

2, the a in the o-os plane should be constant and equal to 63.4°. In reality the value of a varied between 65.4 and 68.7°. Similar for load-path 6c,

a

should be to 7l.6°, but varied between 72.9 and 78.7°. For load path 6a the values were 45° and minor variations were observed.

Results for load~path

6a with

0/0

s

=

1.0 are shown in Fig. 61. In Fig. the normalised

P / P max-o plots are shown, in Fig. 61 b the corresponding

Ps-o

s curves. These latter diagrams could not be normalised because the peak shear load was not reached in all experiments (note: some ofthe 200 mm and 100 mm experiments were stopped because

67

1 . 5 o . - - - - - - - - - - - - - - -

1.00

° f~~ ~~ !~i~~!l

50

50 mm

47-15

48-15

0.50

0.00 d a

=

2 mm '[

6/6. = 1.0, Lp 60,

+--4-~"'"",,_---------_1

- 50.0

- 40.0

P,

(kN)

.--:-:c:---;-:::--:c:::----,--;;---,

~ ~gg ~~ !!~=g~l

[) , 00 mm 46-07

~

..

100 mrn 48-08

50 mm 47-15

50 mm 48-15

¢

-30.0

-0.50

-20.0

-1.00

-10.0

-1.50

-2.00

(a)

-100

-200 -300

6,

-400

(Ji-m)

(b)

Fig. 61. P / Pm,,-i5 plots (a) and

Ps-i5 s

diagrams (b) for the load-path 6a experiments

(15 /i5 s

specimens of three different sizes.

=

1.0) on

1.50

P /P mo,

- 50.0

P, (kN)

1.00

0.50

°

200 mm

ta-01

100 mm 47-08

50 mm

46-16

~ do

=

2 mm

6/6.

=

2.0, lp 6b

- 40.0

°

200 mm

ta-01

47-08

50 mm 46-16

~

d.

=

2 mm

6/6. -.; 2.0, Lp 6b

- 30.0

0.00

-0.50

-20.0

-1.00

-10.0

-1.50

-2.00

'00 200 300

6

(,um)

400

(a)

0.0

-100 - 200 -300 - 400

6,

(Ji-m)

(b)

Fig. 62.

P /Pmax-i5

plots (a) and

Ps-i5 s

diagrams (b) for the load-path 6b experiments

(15 /i5 s

specimens of three different sizes.

=

2.0) on

P,

(kN)

- 50.0 . , - - - - - - - - - - - - - - - ,

- 40.0 o

200 mm

(46-04\

100 mm 48-10

50 mm 47-17 do "" 2 mm

6/0.

= 3.0, lp Be

- 30.0

-0.50

-1.00

-1.50

-2.00 o

200 rnm

(46-04\

100 mm 48-10

50 mm

47-17

d.

=

2 mm

6/6.

= 3.0,

Lp 6e

(a)

- 20.0

-10.0

-400

(b)

-100 -200 -300

Fig. 63. P / Pmax-i5 plots (a) and

Ps-i5 s

diagrams (b) forthe load-path 6c experiments

(15 /i5 s

specimens of three different sizes.

=

3.0) on

68

the maximum capacity of the machine was reached). After a tensile peak was reached, the axial load changed from tension to compression at larger crack openings. Each test was carried out in duplicate and the results were relatively close together. In the 50 mm specimens a compressive peak was reached as well. A compressive peak would probably also have been found for the two other sizes, ifthese tests were not stopped because the maximum shear deformation of 400 [Lm was reached. Although the two 200 mm specimens gave an almost identical

P-O

response, deviations were found in the crack patterns as shown in Fig. 64a and b. In the experiment 4702 (Fig. 64a) the overlapping crack mode was observed as reported before for the load-path 4 experiments. Note that the crack branches are more straight now. In the other specimen, 4602 (Fig. 64b), the loading was completely identical but now three in stead of two cracks developed. The order of crack growth was A, Band C. The effect may be caused by an eccentricity in the specimen. The same crack patterns developed at the front and back side ofthe specimen

(see the solid and dashed crack patterns respectively). rear face

~'---~' load-path 6a(47-02)

200x200x50 front face front face load-path 6a (46-02)

200x200x50

~'--'---, load-path 6a(46-07)

100x100x50 load-path 6a(48-08)

100x100x50

front face

~ front face

~

-"---::.,,---

~ rear face load-path 6a(47-15)

50x50x50 load-path 6a(48·15)

50x50x50

Fig. 64. Crack patterns for duplicate load-path 6a experiments

(0 los

=

1.0) on

200 mm specimens

(a, b), 100 mm specimens (c, d), and 50 mm specimens (e, f).

69

The crack patterns for the 50 and 100 mm experiments are given in Figo 64c through 64f

For both sizes it was found that two identical loadings yielded different fracture patternso In two of these specimens a more distributed crack pattern was found, resembling almost the macroscopic shear crack as defined by Bazant and Pfeiffer [25]0 Perhaps these experiments are close to the transition between shear fracture and tensile fractureo They give some hope as to the possible existence of shear fractureo The use of the micromechanics models [20, 21] is considered a necessity to come to a better understanding of the observed phenomenao

In the load-path 6b and 6c experiments the effect of shear was less dominanL This can be seen from the respective

PIP

and Ps-os curves of Figs 62 and 630 In Load-path 6b, the axial stress changed from tension to compression, but obviously the effect was much smaller hereo The maximum shear load decreased considerablyo

The load-path 6 experiments can be compared with recently published test results by

Hassanzadeh at the Lund Institute of Technology [54]0 His experiments were aimed at determining the mixed mode properties of the process-zone,

in

fact similar to the present efforL In ferential groove very small specimens (size 70 x 70 x 60 mm, with a circuman effective area of 40 x 40 mm) are subjected to a combination of tension and sheaL Next to a number of parabolic load-paths, several proportional load-paths were investigated with

a

=

60 and 75°0 These values are close to the present load-path 6 experiments where

a

=

45,

63A

and 7L6°0 A comparison between the results from Lund and the 50 mm load-path 6 experiments is shown in Figo 650 Note that the results have been translated in stress-crack opening diagrams, where the

4.0 cr (Mpa)

300

0

15/15,

1

1

2

3

specimen

48-15

47-15

46-16

47-17

2.0

0

0

1.0 cr. (Mpa)

-1200 , - - - - - - - - - - - - - - - - - ,

- 1100

-1000

6/6,

specimen

1

1

2

3

48-15

47-15

46-16

47-17

- 900 a

0

~

0

-800

-700

-600

-500

000

-400

-1.0

-300

-2.0

-200

-300

(a)

- 100

",=60·

-4.0

0 100 200 300 400 500

0

Cum)

000

0 -200 -400 -600

-800 -1000 o.

Cum)

Figo 650 Comparison of the proportional load-path tests (6a, 6b and 6c) on with results from [54]: (a)

a-a

diagrams and (b) us-os diagramso

50 mm specimens

70

(nominal) stress is defined as the load divided by the net cross-section of the specimen.

Although the values of a differ, the comparison of the results in Fig. 65 shows that similar trends are found for the two different approaches. The stress changes from tension to compression in the

a-O

diagrams: the effect is most pronounced for small values of a. Deviations may occur because the experimental set-ups are different. The application of both the axial tensile and lateral shear loading is completely servo-controlled in

Delft, but must be applied manually in the shear direction in Lund. However, the Lund apparatus is supplied with an axial servo-control. Most unfortunately the circumferential notch in the tests in Lund prevented an accurate tracing of the crack patterns.

Therefore the uncertainty about the dominant failure mode in load-path 6 remains, but may likely be resolved by applying the recently developed micromechanical models as mentioned before.

4.7 Path-dependency

The experiments in Lund showed that mixed mode I and II fracture is path dependent.

This was found from a comparison between linear and parabolic crack opening paths

(O/Os)

that were tested by Hassanzadeh [54]. The present load-path tests were very extensive and can be used to confirm the path dependency observed in Lund. To this end the load-path 3b, 4, 5 and 6 experiments can be compared. All specimens that were included in the comparison are of size 200 x 200 mm, and the material is a 2 mm mortar.

In Fig. 66 the crack opening paths from four experiments are shown: load-path 3b, 4b,

5b and 6b. As can be seen, the various

o-os

diagrams intersect in one or more points. If the biaxial loading is path independent, then the same point at the

o-os

curve should correspond to the same point on the P-P

s

curve. Or stated differently, an intersection

400

0 Cum)

300

200

100

0

0

Lp 5b 47-04

Lp Sb 48-01

-50

-100 -150 -200 -250 -300

Os

(J.l.m)

(a)

20.0

P

(kN)

17.5

15.0

12.5

10.0

7.5

5.0

~

(':

I

~

I

\

!

I

~

I'

tl

2.5

0.0

Lp 5b 47-04

Lp Sb 48-01

~

-2.5

"'2.5 0.0 -2.5 -5.0 -7.5 -10.0 -12.5 -15.0 -17.5 -20.0 p.

(kN)

Fig. 66. Comparison of crack opening paths

0-0,

for load-path 3b, 4b, 5b and 6b experiments (a), and the corresponding

P-P s

diagrams (b).

(b)

71

liP (kN)

-5

..

i>

"

0

0

@>

i> i>

II

.. . 0 of' o

®~

13

i> ..

"

-10

-15

I

~

Lood-poth 6 &

51

Load-path 6

&

4

Load-path 6

&

3

-10

-5 o liP, (kN)

5

Fig. 67.

ilP-!1P

s

plot: deviations in intersection points in the

P-P s

plane. point between the

a-os

curves of two different load-path tests should correspond to an intersection of the respective

P-P s

curves. For all the load-path 3b, 4, 5 and 6, the intersections were retrieved from the data-sets, and the deviations in axial and lateral load were calculated. These loading differences were then labeled

AP

and

I:lP"

and plotted in Fig. 67. The behaviour of the specimens would be path independent if

I:lP

=

I:lP s

=

0, which is clearly not the case in the present experiments. The results confirm the findings of Hassanzadeh. Note that the maximum load

P

in a 200 mm experiment is approximately 20 kN, whereas the maximum shear load

p s•max

varies between 5 and

50 kN. This may indicate that the intersection points are significantly shifted in the

P-P s

plane.

The path dependency poses a poblem in the analysis of the results in terms of nominal stress and crack opening. The path dependency implies that the theory must contain a memory, and that the damage sustained to the specimen must be remembered at all stages.

4.8 Summary of failure modes

In Table 5, the fracture modes in the various experiments are summarized. Some general remarks can be made. First of all, the shear tests at small crack openings show that secondary cracking may occur under specific boundary conditions. This is an aspect which is completely overlooked in conventional aggregate interlock theories, e.g. [31]. In these theories sliding along crack faces has been modelled for relatively large crack openings. It is common practice to extend the range of application of the models to smaller crack widths, but the present results show that this is not unrestrictedly allowed. If a good agreement is observed between the aggregate interlock theories and the results at small crack openings this would probably be purely accidental. The

72

experiments that were used to tune the aggregate interlock models were rather rough, and the specimens were not loaded as carefully as is now possible in the newly developed biaxial apparatus. The growth of diagonal secondary cracks was observed mainly under unconfined- and confined-tensile-shear and confined-compressive-shear (viz. load-paths la, lb, 2 and 3b). The unconfined-tensile-shear-tests and the unconfinedcompressive-shear-tests showed sliding modes offailure, accompanied by uplift in the crack. The restriction for the unconfined-tensile-shear-tests in this respect is that the crack opening 15

0 should be larger than 250

!-Lm,

at least for the 2 mm mortar tested.

ABload-path 4, 5 and 6 experiments failed through the growth of a set of overlapping cracks. As shown before in paragraph 4.6, the crack shapes were similar for the three specimen sizes investigated. In the case ofload-path 4 and 5, the crack branches were curved. For load-path 6, at least for the larger sizes, straight overlapping cracks were found.

Mode II fracture from virgin specimens has not been found. An exception to this rule is that some of the smaller sized plain concrete specimens showed a more distributed

Table 5.

Overview of failure modes for plain concrete tests loadpath

0 la

Ib

2 precracked yes yes yes yes shear compr. tensile tensile boundary condition during shear

0

0

0

0

P

= constant

= constant

=

0

= constant

3a

3b yes yes compr. compr.

P

P

=

0

= constant

= -

1 kN

= constant failure mode tensile cracking could not be failed in shear secondary diagonal cracks

- secondary diagnonal cracks

(00<2S0

[lm)

- sliding

(00)2S0

[lm) sliding

- splitting cracks, lytag

- sliding, 2 mm mortar

- sliding, 16 mm concrete

4a

4b

4c

Sa

Sb

Sc

6a

6b

6c no no no no no no no no no compr. compr. compr. compr. compr. compr. compr. compr. compr.

Ps

Ps

Ps

=-

5 kN

=

= -

10 kN

= constant

=

Ps,max

= constant

Os

= constant*

Os

= constant*

Os

= constant* constant

o los

=

1

= constant

o los

=

2

= constant

o los

=

3

= constant overlapping cracks overlapping cracks overlapping cracks overlapping cracks overlapping cracks overlapping cracks overlapping cracks** overlapping cracks** overlapping cracks**

* In the load-path S experiments, a specimen was loaded in displacement control up to a prescribed lateral shear confinement of - 5 leN, -10 leN and

Ps,max

respectively, After this, the specimen was failed in axial tension while maintaining

Os

= constant.

** Some of the smaller sized load-path 6 experiments failed through the growth of a system of distributed inclined cracks. This failure mode was however not consistent throughout the complete test series.

73

crack pattern. These failure modes were however not systematic. Some other exceptions are the SIFCON tests, which will be presented in chapter 5. This observation implies that the mode

II fracture tests ofBaiant and Pfeiffer

[25] should be treated with the utmost care.

It seems that a shear crack can only develop when the neighbouring parts of the specimen are very well confined.

The present experiments may be compared with the beam tests of Bazant and Pfeiffer, but also with those of Swartz and Taha

[27].

The fracture modes ofthe unconfined beam tests (that is without prestressing normal to the potential crack plane) of Swartz and

Taha was that two overlapping curved cracks developed between the two notches in the beams, see Fig.

10.

Although the boundary conditions in the plane normal to the potential shear crack plane differed in the present experiments it is believed that the behaviour of the DEN specimens (especially the load-path 4c and 5c experiments that were first loaded in shear to the maximum shear load

Ps,max)

may be compared with the beam tests with narrow shear zone. The load-path 4 and

6 experiments show that the shape of the crack branches may differ depending on the exact boundary condition during shearing, but the essential point is that always a set of overlapping cracks develops from the two notches. Future computations are required to investigate the significance ofthe boundary conditions in these experiments.

5 Shear fracture in SIFCON

SIFCON is a relatively new construction material, and consequently only limited information is available about the mechanical properties. Recent research has focussed mainly on the properties of SIFCON under static tensile and compressive loading (see

[55, 56]). Information on the shear response of the material is almost completely lacking. Therefore, it was decided to use the biaxial test set-up for a number oftensionl shear experiments on SIFCON as well. In the following paragraphs the main results are discussed. First however the variables in the investigation are summarized in section

5.1.

5.1 Variables in the biaxial SIFCON experiments

The variables selected in the present investigation are two material parameters, and the tensile crack opening before shear was applied. Because the material is highly anisotropic, especially in the way it has been manufactured in the Stevin Laboratory, the loading direction with regard to the main fibre direction was selected as the most important variable. In Fig. 68 the fibre direction is defined through an angle a with the centre line through the two notches. It is emphasized here that the investigation has an exploratory character, and in order to limit the number of experiments only fibre inclinations between 0° and 90° have been studied. The selected angles are 0, 22.5, 45,

67.5 and 90 degrees.

The second variable in the investigation is the fibre type. Specimens were prepared with

ZL 30/0.5 and OL 25/0.5 fibres respectively. The different bond properties of the two fibre types were expected to influence the fracture behaviour of the SIFCON.

74

P t frame

B p' frame

A

Fig. 68. Orientation of fibres with respect to tensile and shear loading directions.

For comparative reasons, a number of displacement controlled uniaxial tests were carried out on the plain slurry. In these latter tests, the specimens were fixed in the biaxial machine in a similar way as the SIFCON specimens (i.e. with four sides glued, plus the additional steel platens at the free sides, see Fig. 25). Three slurry tests were carried out on specimens cured in the same manner as the SIFCON specimens as described in section 3.2. In addition, because many probles were cause by shrinkage cracking in these specimens, four additional tests on slurry specimens were carried out where the specimens remained in the water until two days before testing.

The third variable is the crack-opening before shearing. The specimens were loaded following load-path 3a (see section 4.1): shear in displacement control after the specimen was pre-loaded in tension to a prescribed axial crack opening. During shear the load normal to the crack plane was kept constant at zero. Specimens were pre-loaded to the following axial crack openings:

(5

=

10,25,50, 100,200,300 or 400 [lm. The respective loading rates for tension and shear were 1.69 and 1.57 [lm/min. In the descending branch the loading rate was normally doubled two times. From a number of preliminary tests it was found that the specimens with fibre orientations of 67.so and 90° could not be loaded up to crack openings larger than 50 [lm because the maximum loading capacity in the biaxial test-rig was reached. Therefore, a number oftests was omitted from the original test scheme. Table

4 gives the overview of all tests carried out. The letter combinations ZL/OL indicate the planned experiments. Where specimen codes appear in the table, the tests have actually been performed. Note that a number of preliminary tests have been carried out and were published in [57]. These results will not be repeated here, but only used as a reference. Furthermore it should be mentioned that by loading specimens according to load-path 3, implicitly the tensile stress-deformation response of the material is measured. Of course these results will be discussed here as well. Because the original test scheme was too time consuming, a number of tests at very small crack openings had to be omitted as well.

In the following paragraphs, the results will be presented. First the effect of the different variables on the load-displacement response in tension and shear will be discussed.

Following this exposure the fracture patterns will be shown. In a number of tests, real time crack growth was studied with a motorized high resolution long distance microscope (QUE STAR QM 100, with a resolution up to 1.1 [lm).These results will be discussed in section 5.5.

75

25

20

15

Table 6. Overview of the SIFCON test

a

[degree] 0 22.5 45 67.5 90

0

0

[fLm]

10

25

50

100

200

300

400

ZLiOL

ZLiOL

ZLiOL

160411202

ZLiOL

1702/1104

ZLiOL

190311004

ZLiOL

190411201

ZLiOL

ZLiOL

ZLiOL

ZLiOL

180111005

ZLiOL

160211103

ZLiOL

160111001

ZLiOL

170111203

ZLiOL

ZLiOL

ZLiOL

1902/1106

ZLiOL

160311006

ZLiOL

160511102

11205

ZLiOL

1901/1002

11204

ZLiOL

1703/1105

ZLiOL

1803/1101

ZLiOL

180211107*

ZLiOL

160711007

ZLiOL

1606/1003

ZLiOL

-11206

?

?

ZLiOL

ZLiOL

ZLiOL

160811108

?

?

?

?

*

Specimen code: the first two numbers denote the batch number (see Table 3), the consecutive two numbers show the sequential specimen number for the specific batch.

5.2

Strength and ductility

For

a

=

0°, the effect of crack-opening on the shear behaviour of SIFCON is shown in

Figs. 69 and 70. In each figure not only the shear-load - shear-displacement diagram

(p

s b s) is shown, but also the preceeding load-history

(p b plots). In Fig. 75 the results for ZL fibres are shown, in Fig. 70 the OL results. fibres ZL 30/5

0.=

0'

(al

-40 fibres ZL #0/5 a.

=0'

200

(b)

400

6(pm)

Fig. 69. P-O plots for experiments with ZL fibres; a

=

0° (a) and (b) Ps-os plots for the tests from

Fig. (a).

76

100 200 "300 -200

-300

Fig. 70.

P-O

plots for experiments with OL fibres;

a

=

0° (a) and (b)

Ps-os

plots for the tests from

Fig. (a). The shaded area is the range of results obtained from preliminary ZL tests (see

[57]).

The P-O diagrams (Fig. 69a and 70a) clearly show that the tensile strength of the

SIFCON is rather disappointing at fibre orientations of 0°: the average tensile strength

O"t

=

2.86 MPa and 3.09 MPa for the OL and ZL fibre specimens respectively. The strength increase is very moderate in comparison with the strength of the plain slurry

(Fig. 71). The average tensile strength of the slurry specimens cured following the normal procedure was

O"t

=

3.23 MPa (average of three tests); whereas allowing the specimens to dry only two days before testing leads to a much lower strength:

O"t

=

2.2

MPa (average offour tests). Obviously there must be a moisture gradient in these latter specimens, causing tensile eigenstresses at the surface of the specimens [58]. As shown before for normal concrete this will generally lead to a reduced strength ofthe specimen

[45, 59], even as much as 30%. The above results for plain slurry should therefore be regarded with some care. In spite of the fact that care was taken to avoid shrinkage cracking in the specimens, the angular crack patterns indicated that still shrinkage cracks appeared, and affected the tensile response. In fact, the tail of the softening diagram of the slurry is rather high, which can be explained from the resistance of the large ligament between the two overlapping cracks that developed in the specimen (see the inset of Fig. 71).

The corresponding shear curves are shown in Figs. 69b and 70b for ZL and OL fibres respectively. The first observation is the decreasing shear stiffness with increasing axial crack opening. This result is straightforward, and was expected on the basis of experiments on plain concrete. The shear strength of the material is very low. Ifthe maximum shear stress

's is calculated from the maximum values of

P s,

very low values ranging between 6.01 (5.87) and 8.64 (8.01) MPa for the OL (ZL) fibres with crack openings between 50 and 300 [Lm are found. This means that the shear strength is approximately two to three times larger than the tensile strength of the SIFCON, but in comparison to

77

20

15

10

P(kN)

3 0 , - - -

25 uniaxial tension plain slurry l00mm

Fig. 71.

P-i5

piots for four tests on plain slurry. The specimens were allowed to dry two days before testing. An example of a crack pattern is shown in the inset. the compressive strength ofthe material it is relatively low (see Table 3). The reason for this must again be sought in the anisotropy of the material as will be explained in section 5.4. The present results are too limited to draw a definite conclusion regarding the (expected) relation between shear strength and axial crack opening before shearing.

The tendency is that r s decreases with increasing axial unloading displacement

15

0,

This tendency is more pronounced for the OL tests than for the ZL tests.

5.3 Effect of fibre type

In Fig. 72 the

P-b

plots for the two types of SIFCON and the plain slurry are compared.

The post-peak behaviour of the SIFCON is very ductile when compared to the brittle behaviour of the slurry. The SIFCON results shown in Fig. 72 are for a

=

0°. The differences between the two types ofSIFCON are minor. The

P-b

curves ofthe tests on ZL fibre specimens showed a slight increase for larger crack openings in the preliminary test series (see Fig. 70a shaded area, after [57], indicating that the pull-out ofthe fibres is easier for the straight (and somewhat shorter) OL fibres. This should be expected. The more recent results (Fig. 69a) indicate that this increase in carrying capacity for large crack openings must be very small indeed.

The difference in shear response of the two SIFCON mixes is also not very large. As shown in Fig. 73, the only difference seems to be the slope of the ascending branch in the Ps-b s diagrams. The initial slope seems to increase for the ZL fibres. This point will be elaborated further in chapter 6. The results indicate that there is no effect of fibre type on maximum shear load. However, a larger test-series would be required to obtain a statistical basis for this statement.

78

25

20

!5 uniaxial tension

~ t o a=Qo

'00 200 300

Fig. 72. Comparison of

P-O

diagrams for SIFCON with OL and ZL fibres

(a

=

0°), with plain slurry.

The shear stiffness has been analysed for all experiments. These results will be discussed in chapter 6.

5.4 Effect of fibre orientation

The most important variable in the SIFCON study was the orientation ofthe fibres with respect to the biaxial loading. In Fig. 74 five results are shown of experiments loaded to an average axial crack opening of 50 [Lm, and with varying inclination of the main fibre direction (viz.

a

=

0, 22.5, 45, 67.5 and 90 degrees). The fibres were ZL 30/0.5. Both the a =0°

6

0

= 50 .. 300l-Lm

-100 -200 300

Fig. 73. Comparison of shear load-displacement

(ps-os)

response for ZL and OL specimens. The shaded areas show the range of results obtained for each fibre type.

79

P(kN)

3 0 0 ' - - - - - - - - - - - - - - - - - , fibres ZL

30/5

25

0.

=90'

(a) fibres ZL 30/.5 o,=50~m

-200 -300

Fig.

74.

Effect of fibre orientation on

P-15

(a) and

P s

-l5 s

(b) response; ZL fibres; axial unloading deformation

15

0

=

50

[.Lm.

P -

r5

(Fig. 74a) and Ps-r5s diagrams (Fig. 74b) are shown. In Fig. 75 similar results are presented for the OL 25/0.5 fibres.

The results are comparable, and indicate a similar trend. The

P-O

diagrams show a sharp increase with increasing fibre orientation

a.

The OL test with

a

=

90° (Fig. 75a) was terminated because the maximum load in the vertical axis of the biaxial machine was reached. The increase ofload

P

with increasing fibre angle

a

can easily be explained. At

a

=

0°, not many fibres are alligned with the tensile loading direction, and in fact the strength of the slurry layers in between the fibres is tested. As shown in the previous paragraph, the tensile strength

O't of the SIFCON mixes is equal to the strength of the

25

20

-r-~-~---~--

II

0.=90'

ftbres OL

25/~5

;

1

I

1/ i

. I

I

22.5 o

(a) (b) fibres OL 25/.5

0.=

50~m

Fig.

75.

Effect of fibre orientation on

P-15

(a) and

P s

-l5 s

(b) response; OL fibres; axial unloading deformation

15

0

=

50

[.Lm.

80

plain slurry. When the fibre direction rotates, an increasingly larger number of fibres intersects the potential crack plane and the strength of the specimen increases considerably. The limit value for the strength is reached for a

=

90°, when the maximum amount of fibres is alligned with the tensile loading. The effect of fibre direction on shear capacity is significant. Figs. 74b and 75b show that a low shear strength is measured for specimens with a

=

0°. This is observed both for the ZL and OL fibre systems.

At larger inclinations, it is found that the specimen can (generally) not be failed in shear anymore in the present test set-up. Either the maximum load was reached, or glue fractures would occur. For testing the SIFCON with (favourably) alligned fibres, a different test-method is required.

The effect of fibre orientation on tensile and shear behaviour of SIFCON can be deduced from the various tests on specimens pre-loaded to 100 [Lm axial crack opening as well, see Fig. 76 and 77 for the ZL and OL fibres respectively. The OL results in Fig.

77 show a similar tendency as the previous results for specimens loaded up to 50 [Lm

(Fig. 75). Again a low shear capacity is measured for the specimen with

a

=

0°, whereas the specimens with a more inclined fibre system (viz. 22.5 and 45°) could not be failed in shear. For the ZL fibre system, a somewhat different behaviour is observed, see Fig.

76a, b. In the three test results presented in this figure, first a specimen was pre-loaded to an average axial crack opening of 100 [Lm. Following this shear was applied, and surprisingly all three specimens could be failed in shear (thus irrespective of the fibre orientation). Close observation of the P-O diagrams shows that there is quite some scatter in post-peak response. In fact it is believed that the exact number of fibres that intersects the fracture plane determines the post-peak resistance, and a slight increase of the number of fibres can have a significant effect on post-peak carrying capacity. The results indicate - and in view of the number of tests that have been carried out unfortunately no more than that - that the shear capacity of the SIFCON is strongly correlated with the number of fibres that intersect the potential fracture plane. fibres Z L

30/.5

25

45

20 -40

225

15

Cl

= 45

0

22.5 o

(a)

(b) fibres ZL

5 o

=100iJ.m

301.5

200 300 400

6

(I'm)

-200

-300

Fig. 76. Effect of fibre orientation on

P-b

(a) and Ps-b s (b) response; ZL fibres; axial unloading deformation 15

0

=

100 [.tm.

81

fibres OL 25/.5

25

20

(l

=

45°

-40

-JO

22.5 o

(a)

-10

-20

/J,

<f

1

1

!

(b) fibres OL 25/.5

5

=

100 ~m

- 200 ,2,00

200 300

Fig. 77. Effect of fibre orientation on

P-o

(a) and Ps-os (b) response; OL fibres; axial unloading deformation 0

0

=

100 [lm.

It is interesting to see how the crack patterns developed in the specimens. Anticipating the microscopic observations presented in the following paragraph, global crack patterns traced from the surfaces of specimens after the tests was stopped are shown in

Fig. 78. Three different results are shown: (a) a specimen with a

=

0°, pulled in displacement control up to 50 [Lm average axial crack opening; (b) a specimen with a

=

22S

0,=

6.= 50 11m

82

Fig. 78. Global crack patterns for specimens with different fibre orientations.

loaded up to 00

=

300 [lm, and subsequently sheared to P s

=

50 kN; and (c)

a

=

45°, loaded to 00

=

300 [lm and sheared to P s

=

50 kN. The full lines are the cracks detected at the front side of the specimen, the dashed lines are the cracks at the back face.

Of these three specimens, the only one that could be failed in shear (which means that the Ps-os curve has a peak load) is the

a

=

0° specimen. Initially a set of tensile crack branches developed, more or less perpendicular to the tensile direction. These cracks developed between the notches only. Under shear the different crack branches coalesced, and a number of inclined shear cracks developed between the notches (Fig. 78a).

Note that this response resembles the recent results of Arslan et al. [35J on conventional steel fibre and polypropylene fibre reinforced cements, see Fig. 14.

The two other specimens showed that the cracks caused by the tensile loading followed more or less the direction of the steel fibres. In both specimens, inclined tensile cracks developed as shown in Figs. 78b and c. In some of the 45° specimens, the inclined cracks would propagate until they reached the specimenlloading platen interface. Further loading would then normally lead to glue fractures. Under shear, the inclined cracks were simply closed, and even with the QUEST AR long distance crack microscope, no crack initiation and growth was found under shearing. This latter observation is supported by the Ps-os curves for the 45° fibre orientations that are shown in Fig. 79. In this figure results of six 45° tests are shown. The specimens were sheared off at different

Fig. 79.

Ps-os diagrams for

45° OL specimens preloaded to different axial deformations. axial crack openings, ranging from 25 to 300 [lm. The Ps-os curve for 00

=

25 [lm is almost straight near the origin, and curves gently away from the Ps-axis. When the axial crack opening increases, an increasingly more important contact effect is observed.

Especially for the 300 [lm test, the initial run in the curve is extremely large, and is correlated to the closure of the inclined tensile cracks (Fig. 78c). The curves of Fig. 80 show that similar phenomena occured in the specimens with ZL fibres. In the ZL tests with 00

=

50 and 100 [lm, glue fracture occurred. This can be seen from Fig. 80: the respective Ps-os curves show a discontinuity at a relatively small load of - 40 kN.

83

_SOIP'(kNI

-40

-30

-20

300fl m

-l

I fibres ZL 301.5 a.= 45'

-100 -200 -300

Fig. 80. Ps-os diagrams for 45° ZL specimens preloaded to different axial deformations.

The effect of fibre orientation on the P-O response (tension, see Figs. 74 through 76) resembles the effect of external confinement in triaxially loaded concrete. In Fig. 81, results obtained by Jamet et al. [60] of displacement controlled triaxial tests on cilinders made of a microconcrete are shown. Increasing the lateral confinement leads to an increase of axial "strength" and an increased ductility. The resemblance with the current experiments is very large, and the steel fibres seem to act as an internal confinement as soon as the concrete is cracked. This was suggested earlier by Yin et al. [36] for explaining the rather ductile response of biaxially loaded conventional steel fibre concrete. The global effect seems similar, irrespective of the presence of an internal or an external confinement. Of course, the agreement is based on a global comparison only but seems promissing enough to elaborate further in future.

N

E r

M o

5--150 confining stress

02=03 = -

100

N/mm

2

-50

~

-100

E

- 25

84

-50

- - - - - 1 0

------3

O+-~r_--+_--+_--+_--o

50 75 100 axial strain El (%.)

Fig. 81. Results of displacement controlled triaxial compression tests of Jamet et al. [60].

flbresOL 25/,5

6

~

50iJ.m

300

200

(a) a. ~ 0'

~L--------'~OO~-----~2~0(-------~3~OO~----~--

Fig. 82.

a-os

plots for experiments with different fibre orientations;

00=50 ll-m;

(a) OL fibres;

(b) ZL fibres.

The resemblance between the tensile behaviour of SIFCON with inclined fibres and concrete loaded under confined conditions in compression is also observed in dilatancy plots b - b s •

The curves of Figs. 82a and b are qualitatively very much in agreement with the

Uj -

U2

and

Uj -

U3

plots observed in displacement controlled true triaxial compression tests (see Fig. 83, after [33]).

3.5

2.5

2.0

1.5

10

°1'U1

G3'U3 ~

O2'U2

tilstingsurface

J- __

°

2/0, :.33

o

-,5 -10 -15 - 2,0 - 25 - 30 - 3.5 - 4,0

displacement u1 fmmJ

Fig. 83. Dilatancy plots

(Uj-U2

and

Uj-uJ)

obtained from displacement controlled true triaxial cube tests, after [33].

u], U2

and

UJ are the displacements in the three principal loading directions.

85

5.5 Crack patterns

N ext to the global crack patterns, crack growth was monitored under load in a few tests.

To this end the recently acquired QUEST AR Remote Controlled Measurement System of the Stevin Laboratory was used. It consists of a high resolution optical microscope on a heavy stable floor stand. The microscope is fixed to a craddle which can be moved with stepper motors in three orthogonal directions. Connected to the microscope (QM-

100) is a SONY 77 -CE CCD-camera and a high resolution monitor. The CCD technique allows for digital conversion of the images. The maximum resolution is l.1 [Lm. The total set-up is shown in Fig. 84. Up till now the microscope has been used successfully in

VIDEO MONITOR

CAMERA

QM100 MKlII

~

~

/ I

~",ffim )~~

~~

I

LIGHT SOURCE

STAGES

CROSS HAIR GEN.

TILT HEAD

Q

,

22011

10 TRANSFORMER

STAGE CONTROL

86

Fig. 84. Overview of the QUESTAR long distance microscope QM 100.

monitoring crack growth in uniaxially loaded concrete specimens (see [19, 20]). More specifically the failure of crack face bridges has been observed under loading. Before viewing a specimen, it is carefully polished. The surface is lit by two flexible light sources as shown in Fig. 84. In order to identify the scan area, small markers are glued to the surface before a test. These are then used as reference points, for example for deformation measurements.

The same technique has been used for the SIFCON specimens. Not the maximum resolution was used, but rather a somewhat smaller resolution of appr. 5

[lm, which allowed a somewhat larger field of view. Several specimens were viewed under load, a summary of these tests is given in Table 7.

Table 7. Crack detection experiments specimen

No. fibre type

0

[[lm]

0502

0501

1205

1602

ZL

ZL

OL

ZL

10

150

100

100

a

[deg]

0

0

45

22.5 type of detection global near notch near notch local (4 spots) number of surface scans

2

3

3

5

The results of the first three tests are most interesting and are shown below. The fourth test confirmed the other observations.

5.5.1 Shear cracks

The first test, No. 0502, was one of the specimens of the preliminary series on ZL fibres, see [57). This particular specimen was sheared off at a very small axial crack opening of

10 [lm. The P-O and Ps-os diagrams of this experiment are shown in Fig.

85.

The loaddisplacement diagrams are compared to a similar specimen loaded monotonically to failure (0901). A large part of the specimen was scanned at two different moments: (a) at a shear deformation of - 135.9 [lm, and (b) at a shear deformation of - 261.4 [lm. The crack patterns are shown in Fig. 86. The two photoscans are near the right notch of the specimen, and each of them was assembled from 36 individual photographs. The crack patterns were traced from the photomosaic. Note that the photographs contained much more information. For example sand particles, pores and fibres could easily be identified at the surface. For the sake of clarity all this information is retained here; only the contours of fibres and pores are shown. Note that the surface was carefully polished before a test. Because ofthis polishing, even suface uplift due to cracking was observed.

In Fig. 86, the tensile loading direction is vertical. Shear was applied in the horizontal direction. Pulling the specimen to an average axial deformation of

10

[lm caused no observable cracking. The inclined cracks of Fig. 86a and b all developed during shear loading. The second steps lead to a more dense crack pattern, but the inclination of the cracks remained unchanged. In the lower part of the figures crack arrest due to steel

87

P(kNI

50

100

150

(bl

-35

fiber oriE"ntation pe-rpe-ndicular

area of scan

ZLI a.=O/6=10~m

0502

~

P=O during shear

(c)

Fig. 85.

P-O

(a) and

Ps-os

(b) plots for two ZL tests with

0

0

=

10 [.tm. In the experiment labeled

0502 cracking was monitored with the QUEST AR system. At the two points indicated in

Fig. b crack scans were made; the area of scan is given in Fig. c. fibres is observed. The lower inclined crack extended until it reached the fibre. Subsequently it propagated further in the direction of the fibre and finally extended in the original direction in the slurry.

These figures show for the first time the development of a "macroscopic shear crack" defined as an array of inclined tensile cracks in a narrow zone [25]. The presence of the fibres prevented the gowth of secondary cracking in other parts of the specimen, and the shear crack remained between the notches. Undoubtedly the redistribution of stresses caused by the fibres is the reason for this behaviour.

5.5.2 Crack coalescence

Another interesting crack mode was found in a ZL specimen loaded intension up to an average axial crack opening of 150 flm before shearing. The

P-O and Ps-os diagrams of this experiment (0501) are shown in Fig. 87. Two crack patterns are shown in Fig. 88. In

Fig. 8Sa, the specimen is loaded in displacement control to 0

=

147.3 [.Lm. At this stage a large number of tensile cracks had developed between the notches. Fig. 88a shows a number of these crack branches near the right notch of the specimen. The lower right

88

(a)

(b) o

~~

1

hL

2mm

c:d

\~

~~

Fig. 86. (a) Cracking in ZL test 0502

(0

0

=

10 [lm) after shearing to Os

=

-135.9 [lm,

0

=

136 [lm;

(b) idem after shear to 0 s

= -

261.4 [lm and 0

=

367 [lm ~

89

p (kN)

10

fiber orientation peorpendicular

"'p

(a)

fibeor orientation perpendicular

(b)

-15

-10

-5

-35

-30

-25

-20

0501 (150I-lm) ----'

0305 (150l-lm)

O~--_+---~-~--~~-~-_+--+_-~~ o

-100 -200 -300 0 s

(11m)

Fig. 87.

P-O

and

P,-os

plots for two ZL tests with

0

0

=

150 IJ-m. In the experiment labeled 0501 cracking was monitored with the QUESTAR system. crack passed through two pores. Also the figure contains a good example of crack growth along a fibre near the surface. When shear was applied (Fig. 88b), several of the tensile cracks closed, and an inclined crack developed through coalescence of the individual tensile crack branches. Several of these examples were found in the specimen. At some stage during the shearing crack closure is accompanied by sliding. The crack in Fig. 88b closed partly

(15

=

127.5

[.Lm).

This behaviour can be observed from the dilatancy plots as well. lmm

...... ..

.c

-.... -,g

(a)

Q2Ql is=1473iJ.m

~~~~-

----------------

-=- -..:...:.--'"

---_/'<-~~

"'.

(b) 0501 iSs = - 130.5 iJ.m is = 1275 iJ.m

Fig. 88. (a) Crack patterns in specimen 0501 after tensile unloading

(0

=

147.3 tJ-m); and (b) idem after shearing to

Os

=

-130 IJ-m and

0

=

127.5 IJ-m.

90

5.5.3 Crack closure

The last example of crack monitoring is shown in Fig. 89. In these three crack scans, taken at different stages ofloading, the development and closure of an inclined crack in a ZL specimen with a 45° fibre system was followed. The crack pattern of Fig. 89a was taken when the specimen was unloaded after the tensile pre-loading to 100 [lm (specimen No. 1205, the P-O and Ps-os diagrams are similar to the one presented in Fig. 76 for the 45° specimen). The other two crack graphs show the closure of the inclined crack when shear load was applied, respectively at Os

= -

49.4 and - 109.1 [lm. During this shearing absolutely no cracking was detected in other parts ofthe specimen. Note that the surface was scanned continuously with the QUE STAR during the entire test. This point is confirmed by the almost straight Ps-os diagram (Fig. 76b), indicating that no energy release due to cracking can have taken place.

(a)

0

=57 [lm

/ (b)

0=39.5 [lm os=-49.4 [lm

(c)

0

=34.4 [lm

Os=-109.1[lm

'-----'

400~m

Fig. 89. Crack growth in a ZL specimen with 45° inclined fibres (specimen

1205,0

0

= 100 [lm);

(a) after tensile unloading, 0=57 [lm; (b) after shear to os=-49.4 [lm; and (c) after shear to os=-109.1 [lm.

91

In this the first steps in analysing the shear behaviour of concrete specimens with narrow cracks is giveno The analysis is far from completeo A comparison is made between the present experimental results and conventional aggregate interlock testso

The shear stiffness results of the plain concrete and SIFCON experiments are presentand debated in relation to formulations frequently used in smeared crack analyses of concrete structureso

with aggregate interlock experiments

Shear transfer in rough cracks through aggregate interlock has been thoroughly investiin the late seventieso Shear forces can be transmitted over a tensile crack due to aggregates from the crack interfaceso A fairly large amount of has been carried out in the past, and several models have been developed which can describe the observed phenomena, eogo [31, 61]0 Several of the models were in the DIANA finite element code and tested by Feenstra et aL

One of their conclusions was that the models are in reasonable agreement with resultso However the scatter was relatively large, especially at small crack

In the conventional aggregate interlock experiments, researchers have maintained the conditions in their experiments: (1) constant restraining stiffness normal to the crack a constant restraining force normal to the crack plane, and a constant crack widtho According to Millard and Johnson [63, 64], maintaining a constant restraint stiffness normal to the crack resembles the situation in reinforced concrete structureso Conducting tests with a constant restraining force would lead to an unrealistic amount of constant crack

Also they mention that the third boundary condition, would be unrealistic because crushing of the crack interfaces in contact would Especially the cement matrix surrounding the stiff aggregate would be susceptible to crushing when the crack width is kept constant.

The present 3 experiments can be used for a comparison with the aggregate interlock tests conducted under boundary condition 20 Both plain concrete and

SIFCON double notched square plates were loaded according to load-path 30 In these tests, either a constant confinement of 0 kN or -1 kN (0013 MPa) was kept normal to the cracks before shear. The specimens were pre-cracked in displacement the shear loado The present tests provide for an important extension of the conventional aggregate interlock experimentso The main difference is that in the present experiments, extremely narrow cracks are studied that are still able of transfer of tensile stresses normal to the crack planeo In the conventional aggregate interlock [31,65], the crack was made in a rather uncontrolled manner, and the crack width was adjusted to the prescribed valueo After this splitting the exact lateral boundary condition was set, and the specimen was sheared off Results of two aggregate interlock experiments from [31] are shown in Figo 900 The before shearing is not known in detail. This part has been shown as a

92

o

Cum)

1500,--------------------------------, d max

=

16 mm fc

=

37.6 Mpa r "

1000

I I

I I

I

I

I

I

I

I

I

I I

I I

I

I omo.(?) during splitting

(Jc

=-

0.3 Mpa

(Jc

=-1.0 Mpa

500: I

Ib

I

I

I

I

I

I

O~----r---~----~----._--~;----~ o

- 500 -1000

-1500

Os

(~m)

Fig. 90. Crack opening paths for two aggregate interlock experiments with external restraining bars, after [31]. dashed loop along the 6-axis. In the experiments of Fig. 90, the confinement normal the crack plane was applied through a device with external bars. The restraint was introduced by prestressing the bars. The results of Fig. 90 indicate that sliding is accompanied by crack opening. This dilatant effect is for smaller confining stresses.

The specimens in the biaxial machine were precracked in allowed for controlled shear testing of specimens that were still in the

As discussed in chapter 4, load-path 3 experiments were carried out on three different materials. One of these materials was a 16 mm normal concrete, almost identical. to the

16 mm mix that was tested by Walraven (see Fig. 90). Therefore, a opening paths is allowed, and Fig. 91 shows the 6-6 s paths for two ments with 0 and - 0.13 MPa axial confinement respectively.

~~~H.F~' raven's experiments shows that the loading range is extremely small in the present tests.

Yet, the tensile capacity of the crack is exactly known. Note that in 'iValraven's ments no information is available at small values of shear

- 1 MPa confinement, no information regarding the crack

For the with

70 [.tm was given. This is the range which can be tested now.

The experiments of Fig. 90 showed an increase of axial crack confinement. The present load-path 3 results should therefore fall above the results

Walraven. Instead, an opposite trend was observed, which may be caused differences in shear transfer in the conventional aggregate interlock tests and the present controlled experiments. The above differences may explain Feenstra a1. found a relatively large scatter for small cracks. Clearly the conventional theories derived for larger stress free cracks (no softening), and the assumed mecha-

93

o

Cum)

1500,-----------------------------------. d mox

=

16 mm

00 400 f.J-m fc

=

49.6 Mpa

1000

28-06, a c o

Mpa

500 /

'" 28-04, a c

=

-0. 13 Mpa o

-500 -1000 -1500

Os

(J-lm)

Fig. 91. Crack opening paths

o-os

from two load-path 3 experiments on 16 mm normal concrete. nisms cannot be simply transfered to narrow cracks. For example the occurrence of splitting tensile cracks and secondary diagonal cracking are phenomena which are completely overlooked in the conventional models. Of course, the insight has increased over the years and the models must be adjusted.

400 ps/Os

(N/

J-lm)

300

200

10

0

III

III

0

..

0

..

"

2

2

16 mm

unconfined

.. a

Lytag

Lytog confined mm unconfined confined mm unconfined

16 mm confined

IIIriI

It o

III 0

t:. t:. t:.

A

..

-

III

0

C

100

0

0 100 200 300 o .

0

400

(J-lm)

Fig. 92. Decrease of shear stiffness with increasing axial crack opening for the three plain concretes tested.

94

6.2 Shear stiffness reduction

6.2.1 Plain concrete

In Fig. 92, the decrease of shear stiffness Psi

i5

s is shown as a function of the axial crack opening after unloading (denoted as i56' ). The shear stiffness is defined as the secant modulus between 10 and 30% of the maximum shear load Ps,max' Note that the

i56'

values are smaller than the

i5

0

values, which lie on the descending branch of the

Pi5

curves. In

Fig. 92, the results of all successful tests are included (see Table 4), thus irrespective of the material composition. A decreasing shear stiffness is observed with increasing crack opening. The difference between the three different materials seems not very pronounced. All tests follow the same trend, except that the secant shear modulus seems to decrease with increasing confinement normal to the crack plane, especially at larger crack openings. Part of this may be explained from the fact that the unloading displacement

i56'

decreases with an increase of confining stress. Therefore the data points for the confined tests are shifted to the right side of the graph.

6.2.2 SIFCON

For SIFCON only unconfined experiments have been carried out (load-path 3a). Note however that now fibres are present, which may be regarded as an internal confinement as argued before in chapter 5. The problem is of course to determine the level of this internal confinement. In Fig. 93, the shear stiffness is defined as

G

=

rlY

=

(p s

*

h)/(A

*

i5 sc )

(6.1) where

h

is the width of the crack band, and

i5 sc

the shear displacement ofthe crack-zone.

The shear displacement in the crack band is equal to the total shear displacement i5 s

G (MPa)

5000 •

4000

3000

2000

1000

100

150

200

300

400 oo( I-lm)

Fig. 93. Shear stiffness of SIFCON at various axial crack openings.

95

measured in the experiments minus the elastic shear deformations outside the crack band. In the present analysis, the crack band width was taken

h

=

15 mm, which corresponds to the average width of the crack zone observed in the experiments with

a

=

0°.

Note that a continuum formulation seems possible for the SIFCON, whereas this is not allowed in the case of plain concrete where cracking leads to localised deformations.

This latter point poses an extremely difficult problem for smeared crack approaches as will be discussed in section 6.3

In Fig. 93, the shear stiffnesses for all SIFCON experiments that were presented in chapter 5 are included. Note that only those results for

a

=

0° and

a

=

22.5° are included. In these experiments the notion of a crack band seemed to make some sense, whereas the specimens with higher values of a, failed through diagonal cracking (see

Fig. 78). The bold dashed line connects the data points that were obtained from the preliminary SIFCON experiments that were published in [57]. The same tendency as observed before for plain concrete is found: the shear stiffness decreases with increasing crack opening. The shear stiffness is however much higher than in the case of plain concrete, which can be explained from fibre bridging in the crack. The type of fibre (viz.

Dramix OL or ZL) had no significant effect on the shear stiffness, as was mentioned before. Fig. 93 shows clearly that this parameter has no effect. Likely, the type of fibre will be more important when fibres are pulled out c.ithe matrix. Obviously, this stage was not reached in the present experiments.

6.3 Shear retention factor

In computational models based on finite element method, often the smeared crack concept is used for analysing the behaviour of reinforced concrete structures. In these smeared models, a shear retention factor f3 is introduced to adapt the shear stiffnesss of cracked concrete. Based on the aggregate interlock experiments ofPaulay and Loeber

[66], Rots [67] derived the following expression for the shear retention factor f3:

f3

=

1/1

+

4447cnn

(6.2) where Cnn is the crack strain normal to the crack plane. This relation was derived for small shear displacements, viz. not exceeding 200 [lm. A similar equation was derived by Bazant and Gambarova [61]:

f3

=

1/(4762cnn) -1/(1346Vs:)

(6.3)

The two expressions are not very different as they were both tuned on Paulay and

Loeber's experiments.

More recently, Pruijssers [68] derived an expression for f3 which is dependent not only on the normal crack strain

Cnn, but also on the ratio cnn/y:

(6.4a) where

p

=

2500/[D~!~(0.76

-

O.l6cnn/y(l- exp (- 6Y/cnn)))]

(6.4b)

96

where

Dmax

is the maximum aggregate size. The shear retention factor according to equation (6.4) is shown in Fig. 94 for different ratios cnn/Y. For enn/Y

=

3, the formulation of Rots is retrieved.

1.0 shear retention factor

~

0.8 dmax = 19mm

---

-~-."

Enn

-v;;-;-

1

3

10

0.6

0.4

'1\

\~

,

......

"

....

I

02 o

\

.......

.

~ t=.: o

2

4 6 8 10 normal strain Enn 103

Fig. 94. Shear retention factor

fJ

for different values of Gnnly, after [68].

A direct comparison between

(3

-values predicted by the above formulations and values obtained from experiments seems however impossible. In the plain concrete experiments, a localized crack forms, which is subjected to shear. The definition of a normal crack strain e nn and a shear crack strain

Y

depends on a definition of the crack band width

h.

This value is not constant during the fracturing process as shown both experimentally, [17, 18], and numerically [20]. In continuum formulations for localized cracking, such as for example the non-local theory [69], different values of hare proposed ranging between 1.88 and 3. In view of the above formulations, any value of

(3 can be obtained by selecting a particular value of

h

(see [5]). Therefore a comparison between the present plain concrete experiments and the existing formulations of

(3 seems not very valuable.

Then what to do? The experimental technique has now been brought to a sufficiently high level. This has taken the past four years, and in order to come to a better understanding of the shear behaviour, and the development of a new theory which includes all observed phenomena, further research is required. A promising tool which can be used is the recently developed lattice model [20J. Using this model, the micromechanisms of mode I fracture (see Fig. 8), as well as the growth of curved mixed mode cracks can be simulated very well (see [30]). Problems encountered in conventional smeared crack models are circumvented and it would be interesting to extend the existing formulation for shear friction. The model, if successfully extended, could well be used for developing a macroscopic theory for aggregate interlock, and perhaps also for shear fracture. This latter aspect can likely be handeled because at a lower level shear fracture seems merely a mode I problem.

97

7 Conclusions

Biaxial tension/shear experiments have been carried out on plain concrete and

SIFCON mixes. The experiments were conducted on square plates with a constant thickness of 50 mm, but with varying dimensions. A unique feature of the test technique is that specimens can be loaded independently in displacement control both in the tensile and shear direction in the biaxial machine. The experiments can broadly be subdivided into two catagories. First, experiments have been carried out on specimens that were carefully precracked in displacement control. This allowed for the determination of the shear stiffness of concrete containing narrow cracks that were still capable of transferring tensile stresses normal to the crack. The second catagory are experiments where a combination of shear and tension is applied to uncracked specimens. These latter experiments were carried out in order to come to a better understanding of mode

II (shear) fracture in concrete. The following conclusions can be drawn.

1.

The complicated testing technique has been developed to a sufficient level where reliable results are obtained.

2. The shear experiments on plain concrete specimens containing narrow cracks showed the occurrence of secondary diagonal cracking and splitting under a variety of boundary conditions. True sliding has been observed only in a number of tests where both the crack width was sufficiently large

(15

=

250 !J.m) and where no confinement was present normal to the crack plane. These results show that the conventional aggregate interlock theories developed in the late seventies, cannot be used anymore in this regime. This conclusion is supported by recent numerical analyses by Feenstra et a!. [62].

3. The shear experiments on uncracked plain concrete showed that no true shear failure defined as an array of short inclined cracks can be obtained in the larger specimens. Reducing the specimen size seemed to have a significant effect on the failure mode of the specimen, and in several proportional load-path tests

(15 /15

0

= constant) distributed cracking as defined above was observed. These results indicate that an intricate relationship between fracture mode and specimen geometry exists.

4. The dominant failure mode in specimens where shear was applied first was the growth of a set of overlapping (curved) cracks from the two notches. This failure mode occurred probably also in the shear fracture tests of Baiant and Pfeiffer, but can only be found under very well controlled conditions.

5. The shear stiffness of the material decreases with increasing crack opening. The effect seemed independent on the type of material tested: 2 mm mortar, 12 mm lytag and 16 mm normal concrete. The effect of confinement on the shear stiffness of a partly open crack was minimal, at least for the range investigated.

6. The fracturing of plain concrete and mortar under biaxial tension and shear is path dependent.

7. The material structure of the SIFCON was highly ansisotropic. Consequently, shear tests were carried out on specimens with fibre systems that were oriented at various angles to the biaxial loading. True shear failure (defined as an array of short

98

inclined tensile cracks) has been observed in SIFCON specimens where the fibres are oriented parallel to the shear direction. The shear fractures could develop here because the anisotropic material structure contained oriented weak planes.

8. When the orientation of the fibres is changed, no sliding failures could be obtained in the SIFCON, but rather a set of diagonal cracks would develop from the notches in the main fibre direction. In general these specimens could not be failed in shear in the present experimental set-up.

9. A similar shear stiffness reduction as found for plain concrete was observed for

SIFCON. A rapid decrease of shear stiffness is observed for narrow cracks, whereas the decrease diminishes at larger crack openings. The shear stiffness is somewhat higher than that for plain concrete, which may be explained from the fibre bridging.

10. The tensile strength and the shear strength of SIFCON vary significantly with varying fibre orientation. The highest tensile strength is found when the fibres are oriented parallel to the tensile direction; the lowest tensile strength (approximately equal to the tensile strength of the slurry) when the fibres are oriented perpendicular to the tensile loading. The highest shear strength is measured in specimens containing fibres prependicular to the shear loading, a much lower shear strength

(appr. 10-12% of

ice)

is measured when the fibres are alligned with the shear load.

11. The SIFCON behaves considerably more ductile than the plain slurry or plain concrete. The fibres can be regarded as an internal confinement, and the response resembles the behaviour of confined plain concrete.

12. The results for SIFCON show that all effort should be stored in obtaining randomly oriented fibres in the material. As mentioned in the previous paragraph, the increase in strength in the weakest direction is nil or only moderate in comparison with plain concrete.

13. For further interpretation of the results at small crack openings, and verification and extension of existing aggregate interlock theories, further research is required.

Numerical micro mechanics [20, 21] seems a useful tool for further developing these macroscopic theories. Main advantage is that machine/specimen interactions can be taken into account in a very simple and straightforward manner.

Acknowledgement

This research was sponsored by the Air Force Office of Scientific Research (AFSC) under contract number F49620-88-C-013S. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon. The support of AFSC is gratefully acknowledged.

Notation

a

notch depth

d

specimen size

icc

compressive strength (1S0 mm cubes)

99

hpj

G

P

splitting tensile strength (150 mm cubes) shear modulus axial load

P5

shear load

a

main fibre orientation in SIFCON

f3

shear retention factor

6 global average crack opening (65 mm gauge length)

6 i

6

5

C nn

y

local crack opening (35 mm gauge length) global shear displacement normal crack strain shear crack strain

100

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104

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