FRANC2D/L: A Crack Propagation Simulator for Plane Layered

FRANC2D/L: A Crack Propagation Simulator for Plane Layered
FRANC2D/L: A Crack Propagation
Simulator for Plane Layered Structures
Version 1.4 User's Guide
Daniel Swenson and Mark James
Kansas State University • Manhattan, Kansas
FRANC2D/L User's Guide
Table of Contents
ii
Table of Contents
Introduction ............................................................................................1
Basics of Implementation..................................................................2
Data Structure .................................................................................2
Finite Elements................................................................................4
Layers ..............................................................................................6
Fracture ...........................................................................................7
Remeshing During Crack Growth.....................................................7
Solution Procedures..........................................................................7
Computer Graphics ..........................................................................7
FRANC2D/L Files ....................................................................................9
CASCA and Input Files......................................................................9
CASCA *.csc Files.............................................................................9
Input *.inp Files ...............................................................................9
FRANC2D/L Restart Files..................................................................9
*.wdb Files .......................................................................................10
*.rsp Files.........................................................................................10
FRANC2D/L Output Files..................................................................10
*.grf Files .........................................................................................10
gra*.ps Files .....................................................................................10
sif Files.............................................................................................10
FRANC2D/L Tutorial Examples.............................................................12
Example 1: Plate with Hole ...............................................................15
Building an Initial Mesh with CASCA ..............................................15
Performing a FRANC2D/L Simulation..............................................20
Example 2: Adhesively Bonded Lap Joint .......................................30
Building an Initial Mesh with CASCA ..............................................30
Performing a FRANC2D/L Simulation..............................................34
Example 3: Plate with Hole and Patch ............................................38
Building the Mesh with CASCA........................................................38
Performing a FRANC2D/L Simulation..............................................40
Example 4: Additional Example........................................................45
Crack Growth with Interference Between Plug and Hole .................45
Example 5: Incremental Elastic-Plastic Analysis ...........................50
Notch Root Displacement .................................................................50
Example 6: Incremental Elastic-Plastic Analysis ...........................54
Non-Proportional Loading.................................................................54
FRANC2D/L Menu Reference Guide .....................................................58
FRANC2D/L User's Guide
Table of Contents
iii
Main Page ...........................................................................................58
PRE-PROCESS ................................................................................59
MODIFY ..........................................................................................59
ANALYSIS .......................................................................................59
POST-PROCESS ..............................................................................59
ANNOTATE .....................................................................................59
ELement/NOde INFOrmation .........................................................60
READ FILE......................................................................................60
WRITE FILE ....................................................................................60
- LAYER +........................................................................................60
RESET .............................................................................................60
- ZOOM +.........................................................................................60
PAN .................................................................................................61
a SNAP d..........................................................................................61
END .................................................................................................61
PREPROCESSING Functions...........................................................62
PROBLEM TYPE .............................................................................62
FIXITY.............................................................................................62
CONSTRAINTS................................................................................63
MATERIAL ......................................................................................63
APPLD DISP....................................................................................66
LOADS.............................................................................................66
SINGULARITY ................................................................................68
MODIFICATION Functions ..............................................................69
ADD ELEM, KILL ELEM, DRAG NODE .........................................69
NEW CRACK, MOVE CRACK, SUBDIVIDE, SHOW ANGLE..........69
INTERFaCe : ON/OFF .....................................................................70
ADD NonLinear INTerFaCe .............................................................71
ADD ADHESIVE..............................................................................71
MORE OPTIONS .............................................................................71
POSTPROCESSING Functions.........................................................72
-CASE:ALL+.....................................................................................72
FRACTure MECHanics.....................................................................72
LINE PLOT......................................................................................72
CIRCLE PLOT..................................................................................72
RADIAL PLOT .................................................................................73
REACTIONS ....................................................................................73
STRESS BAR ...................................................................................74
CONTOUR .......................................................................................74
DEFORMeD MESH .........................................................................74
POINT INFO....................................................................................74
NODE INFO ....................................................................................75
FRACTURE MECHANICS Functions...............................................76
FRANC2D/L Software Distribution.......................................................78
World Wide Web...............................................................................78
FRANC2D/L User's Guide
Table of Contents
iv
Anonymous FTP ...............................................................................78
Appendix A: Input File Format..............................................................80
Appendix B: FRANC2D/L Solver Routines ...........................................86
Linear Equation Solver .....................................................................86
Dynamic Relaxation Solver...............................................................86
Appendix C: Version 1.1 Release Notes.................................................88
Appendix D: Version 1.2 Release Notes.................................................90
Appendix E: Version 1.3 Release Notes .................................................92
Appendix F: Version 1.4 Release Notes .................................................94
Acknowledgments ...................................................................................97
Bibliography............................................................................................98
Index.........................................................................................................99
FRANC2D/L User's Guide
Introduction
Page 1
Introduction
FRANC2D/L is a highly interactive program for the simulation of crack
growth in layered structures. The program is an extension of FRANC2D to
make possible the representation of layered structures such as lap joints or
bonded repairs. In addition, a linear bending option is available to account
for the eccentricities of the layers when appropriate.
Each layer is
represented by a separate mesh that can overlap with other meshes and be
connected with rivet or adhesive elements. Each layer is assumed to be flat,
but either two-dimensional (in-plane) or three-dimensional (plate with
bending) calculations can be performed.
This manual is a reference for the use of the program. The first section
describes the files and file naming conventions used by the program. The
second section is a tutorial illustrative example. (Most of the commonly used
features of the program are introduced in the tutorial.) The third section is a
menu reference, which describes each option on all of the FRANC2D/L
menus.
In this manual, words with all letters upper-case and bold, such as FIXITY,
refer to options on a FRANC2D/L or a CASCA (mesh generator) menu.
Words with all letters in lower-case, italics, and bold, such as message
window, refer to a screen window or other specific screen area in which the
function being discussed is controlled.
Within the FRANC2D/L program, all user commands are made by clicking
the mouse on one of the options displayed on the menu which always appears
to the right of the operations window, see figure below. The commands are
arranged in a tree, and the user travels up or down to each branch
recursively by selecting the desired option with the left button of the mouse.
A message window is always present below the operations window to
prompt the user on the next step in the requested procedure. For some
operations FRANC2D/L creates a separate detached movable window called
the auxiliary window. At times it may be necessary to move this window
in order to view information in a number of windows simultaneously. Entry
into FRANC2D/L, some data entry, and I/O operations invoked during the
running of FRANC2D/L are made from the program control window. This
is the window (usually an XTerm) from which the program was started.
The FRANC2D/L program uses two types of cursors. The normal cursor has
the shape of an arrow. When you see this cursor it means that the program
is waiting for you to select a menu option or some other graphical input. The
second cursor is a stylized wristwatch. When you see this cursor it means
that either the program is processing data (e.g., performing a stress
analysis), or it is waiting for input in the program control window.
FRANC2D/L User's Guide
Page 2
Introduction
auxiliary window
title window
command options
menu
window
program control
window
$ franc2d
Filename:
tutorial
message window
The FRANC2D/L window system
The coordinate system used within the program is always fixed so that the x
and u coordinates are horizontal, increasing to the right. The y and v
coordinates are vertical, increasing going up.
The FRacture ANalysis Code (FRANC2D) was originally developed by Paul
Wawrzynek at Cornell University. FRANC2D represented a significant step
in the development of discrete fracture analysis programs because of its
modular software design and topological data structure. This manual follows
the format of the original FRANC2D manual. The layered and bending
capabilities described in this manual have been implemented at Kansas State
University.
Basics of Implementation
This section provides very brief descriptions of the implementation of the
data base, data structure, and finite element concepts used in FRANC2D/L.
Data Structure
The core of the program is the data base (shown below). This is the
repository of all the information used by the various parts of the program.
FRANC2D/L User's Guide
Page 3
Introduction
The data base is only accessible through the data base access routines. All
higher level routines are required to use the two types of access routines
(modify and query routines) to store and retrieve information.
User Interface
Remesh
Modify
Fracture
PostProcess
Data
Base
Numerical
Analysis
Query
PreProcess
Finite Element
Analysis
Conceptual Organization of FRANC2D/L
The layer above the data base routines is the collection of routines which
implement the computational functionality of the program. These are loosely
grouped into six categories. Preprocessing routines perform modifications to
the model description and boundary conditions. Remesh routines modify the
element mesh for crack propagation.
Fracture mechanics routines
implement the various crack propagation theories and automatic load factor
modification.
Postprocessing routines display stress and displacement
information. Finite element routines formulate element stiffness matrices,
assemble global stiffness matrices, minimize problem bandwidths, solve for
displacements, and recover element stresses.
The numerical analysis
routines perform functions necessary for the solution of systems of non-linear
equations.
Encircling the functional routines is the user interface, which is a collection
of menu drivers and display routines to allow the analyst to interact with the
program.
The data structure used in FRANC2D/L is designed around a modified
winged-edge data structure (Baumgart, 1975; Weiler, 1985; and Woo, 1985)
which was originally developed to store surface topology of polyhedra. The
data structure consists of three topological entities: vertices, edges, and faces.
FRANC2D/L User's Guide
Page 4
Introduction
Vertices correspond to finite element nodes, and faces represent finite
elements (shown below).
Left CCW Wing
Right CW Wing
Head Vertex
Left Face
Right Face
Tail Vertex
Left CW Wing
Right CCW Wing
Winged-Edge Data Structure
The main feature of this data structure is that each topological entity
contains adjacency information which greatly reduces the time required to
perform adjacency queries. The data structure is designed such that most
adjacency queries are edge based, as the multiplicity of elements adjacent to
an edge is known a priori, unlike that of a face or a vertex. An edge has two
adjacent vertices, two adjacent faces, and four adjacent edges. The data base
is accessed for modification or for queries.
The local adjacency information embedded in the winged-edge data structure
is very useful for performing tasks associated with finite element analysis.
For example, it is a simple matter to identify the edges on the boundary of a
structure being analyzed. This allows one to delete elements for crack
propagation without deleting the edges which define the structural boundary.
The adjacency information also allows one to identify all the elements
adjacent to a node so if the node is dragged to a different location element
stiffness matrices can be recomputed.
Finite Elements
Continuum Elements
FRANC2D/L uses standard eight or six noded serendipity elements with
quadratic shape functions. These elements perform well for elastic analysis
and have the advantage that the stress singularity at the crack tip can be
FRANC2D/L User's Guide
Introduction
Page 5
incorporated in the solution by moving the side nodes to the quarter-point
locations (Henshell and Shaw, 1975).
Interface Elements
Interface elements are used to represent contact between surfaces. The user
can specify a relationship between surface tractions and the relative
displacements of the surfaces. The surface tractions are then integrated to
give equivalent nodal loads. These loads are then included during the
dynamic relaxation solution.
Rivet and Adhesive Elements
Rivets are treated as elastic shear springs, where the rivet stiffness is a
material constant. Rivets can only be introduced at nodes. When a rivet
connects two layers, it must be defined at a node in the upper layer. This
eliminates the need to interpolate the displacements at a rivet point in order
to calculate the rivet forces. At the same time it allows for efficient storage
of information in the data base.
An adhesive element is similar to a rivet element, except that the shear force
is distributed over an entire element and is not confined to a node. It is
assumed that the adhesive layer is homogenous, linear elastic and isotropic.
The adhesive is assumed to deform only in shear and this deformation is
uniform throughout the adhesive thickness. The surface shear transmitted
through the adhesive is assumed to act as a surface traction on the
adherends. The shear stresses in the adhesive are given by:
τ=
G
( u − u2 )
h 1
where:
τ = Shear stress
G = Shear modulus
h = Thickness of adhesive
u = Displacements in layers 1 and 2
The adhesive forces are obtained by using the adhesive shear stresses as
surface tractions on the layers and integrating. Since the surface tractions
are proportional to the relative displacement of the two layers, the adhesive
force can be expressed in terms of nodal displacements of the top and bottom
layers. This gives a stiffness matrix for the adhesive elements.
FRANC2D/L User's Guide
Introduction
Page 6
Layers
A layered structure, such as a riveted lap-splice joint or a bonded lap joint, is
actually a three dimensional structure. A three dimensional finite element or
mathematical modeling of such a structure will involve several degrees of
complexity. In FRANC2D/L simplifying assumptions are made which still
allow us to capture the essential features of the response. The assumptions
include:
•
•
•
•
Each layer is considered as an individual two-dimensional structure under
a state of plane-stress or plane-strain.
Only linear out-of-plane displacements and bending effects are included.
Individual layers can be connected with rivets or adhesive bonds.
A rivet is treated as an elastic shear spring between two nodes of each
layer. An adhesive is assumed to distribute shear forces across an entire
element of each layer.
As noted, each layer is represented as a separate two dimensional finite
element mesh. In the single layered version of FRANC2D/L the finite
element information is stored in a central data base using a modified winged
edge data structure. This data base is accessed by all the program subgroups. The strategy adopted to incorporate multiple layers in FRANC2D/L
was to store the finite element mesh in a separate data-base for each layer.
At any particular instant, only one layer is made available in the central data
base. This is achieved by making use of two utility functions which load or
unload a layer from the central data base. The analyst can choose to work on
any particular layer by clicking on a menu button in the user interface. This
strategy retains the modularity of the original program.
The data structure for the face has been modified to incorporate two
additional pieces of information. These are face numbers corresponding to a
face in the layers above and below it. This eases the navigation from one
layer to another. To implement this all the layers must have exactly the
same mesh in the regions in which they overlap where adhesives are used to
attach the layers. This is required in the initial mesh and is automatically
managed during remeshing. Although identical meshes simplify data
management in the layers, identical meshes are also necessary to ensure
correct integration of adhesive shear stresses on each side of a crack face.
For regions where no adhesives will be used to attach layers the mesh is not
required to be the same. The remeshing routines will automatically detect
whether the same mesh is required to preserve adhesive bonding and will
automaticlly enforce the “same mesh” requirement when necessary.
FRANC2D/L User's Guide
Introduction
Page 7
Fracture
The fracture calculations incorporated in FRANC2D/L use two-dimensional
linear elastic fracture mechanics (LEFM) concepts. The stress intensity
factors which govern the fracture process in the LEFM context are calculated
using the displacement correlation or modified crack closure techniques.
FRANC2D/L can model quasi-static crack propagation and crack propagation
due to fatigue loading. The crack will propagate in the direction predicted
using any of the three propagation theories implemented in FRANC2D/L.
They are the sigma theta max theory [Erdogan and Sih, 1963], the G theta
max theory [Hussain et al., 1974], and the S theta min theory [Sih, 1974].
Effectively, all approaches give the same crack trajectories and minimize the
mode II stress intensity.
Remeshing During Crack Growth
When performing a discrete crack analysis, not only the geometry of the
crack is represented explicitly at each step, but the mesh must be modified at
each step to reflect the current crack configuration.
The automatic
remeshing strategy adopted in FRANC2D/L is to delete the elements in the
vicinity of the crack tip, move the crack tip, and then insert a trial mesh to
connect the new crack to the existing mesh. The modified Suhara-Fukuda
algorithm [Shaw and Pitchen, 1978] is used to generate this trial mesh of
triangulated elements. The user is allowed to modify the mesh if it is not
satisfactory. This technique exploits the interactive nature of the software
and ensures that the decision about the suitability of a mesh lies with the
analyst.
Solution Procedures
Two solution methods are available to the user. The first is a direct linear
equation solver for symmetric systems stored in skyline format. The linear
solver is preferred and may be used for all cases except when nonlinear
interface elements are being used. For this case it is necessary to use the
dynamic relaxation solver. This solver is usually slower than the direct
solver, but will always converge for nonlinear contact problems. Appendix B
provides more information on the solvers.
Computer Graphics
The FRANC2D/L program maximizes the graphical interaction between the
user and the model by making graphical interaction an integral part of the
algorithms. The ability to see a display of the model being analyzed and view
FRANC2D/L User's Guide
Introduction
Page 8
the results in a graphical form is a very valuable functionality. The analyst
interacts with the program through a menu driven user interface. This is a
collection of routines which create and drive menus and call the appropriate
action routines after an analyst chooses a menu option.
The low level graphics routines in the program have been encapsulated in one
collection of routines called the application independent graphics subsystem
(GRA). These routines are written in the C programming language to allow
portability on UNIX platforms. These routines are written in a modular
fashion whereby the device dependent graphics code is segregated from rest
of the graphics code.
FRANC2D/L User's Guide
FRANC2D/L Files
Page 9
FRANC2D/L Files
There are a number of different types of files generated or used by the
FRANC2D/L program. The contents of these files and their uses are
discussed here. In most cases, the *'s in the figure are replaced by file names
chosen by the analyst.
CASCA and Input Files
CASCA *.csc Files
The CASCA program is a simple mesh generating program. Although strictly
speaking, it is not part of FRANC2D/L, it is distributed with FRANC2D/L,
and can be used to generate initial meshes for FRANC2D/L simulations. The
*.csc files are restart files generated by CASCA. A restart file allows one to
save their current work and recover it later. This is convenient when a mesh
description cannot be completed at one sitting or to make modifications to an
existing mesh. A *.csc file is created when the WRITE option (not WRITE
MESH) is selected in CASCA.
Input *.inp Files
The *.inp files are the means by which new problems are specified for a
FRANC2D/L simulation. These are human readable ASCII files that describe
an initial mesh in a format similar to those used by most other FEM
programs. The format of these files is specified in Appendix A. The *.inp
files can be generated by translating (merging) CASCA files that describe
each layer. The CASCA files are written using the WRITE MESH option.
Similar translation is required if another mesh generation program is used.
Translators are available for ANSYS element and node files and PATRAN
neutral files.
FRANC2D/L Restart Files
The FRANC2D/L program generates two types of restart files *.wdb and
*.rsp. Restart files allow one to save their current work and recover it later.
This is convenient when a simulation cannot be completed at one sitting or to
review the results of previous simulations.
It is recommended that
FRANC2D/L analysts get in the habit of making restart files frequently. The
FRANC2D/L restart files are generated by the WRITE option within
FRANC2D/L.
FRANC2D/L User's Guide
FRANC2D/L Files
Page 10
*.wdb Files
The *.wdb files contain most of the information associated with a simulation.
This includes the mesh, boundary conditions, cracks, and stress-intensity
factors. WDB stands for Winged-edge Data Base, the data structure used to
store mesh topology and organize most of the other information stored by the
program. Unlike the *.rsp files, information in the *.wdb file cannot be
recovered if the file is deleted. The *.wdb files are unformatted and are not
human readable.
*.rsp Files
The *.rsp (ReSPonse) files contain analysis results, specifically, nodal
displacements. This information is stored in a file so the analysis results can
be viewed without reperforming an analysis. The information in these files
can be regenerated by performing a stress analysis. The files can be deleted
to save space.
FRANC2D/L Output Files
*.grf Files
The *.grf files are created when the FILE option is selected on the line plot
page menu (See the LINE PLOT option). These ASCII format files contain
the data points used to create the plot displayed in the auxiliary window.
The first line in the file gives the number of X-Y pairs, and is followed by
lines containing an X-Y data pair.
gra*.ps Files
The gra*.ps files are postscript hardcopy files. These files are created by
selecting the SNAP option on any menu. The files contain a hardcopy image,
in postscript format, of the contents of the data window. The file names are
generated sequentially and automatically by the program. A typical series is
gra0.ps, gra1.ps, gra2.ps ... The file number is incremented each time the
data window is SNAP'd. WARNING: The file name sequence starts
with gra0.ps each time the program is run and new files will
overwrite old files. A hardcopy needs to be renamed if it is to be
saved.
sif Files
Sif files contain Stress-Intensity Factor histories. A file name extension is
not generated automatically for these files. The files contain stress-intensity
FRANC2D/L User's Guide
FRANC2D/L Files
Page 11
factors for all cracks for all crack lengths that have been analyzed, in a
formatted human readable form. A postprocessing script is available to
extract data for XY plots.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 12
FRANC2D/L Tutorial Examples
In this portion of the manual, the use of the FRANC2D/L program is
illustrated by three tutorial examples:
1. Crack growth from a hole in a panel
2. A lap joint analysis using an adhesive
3. Crack growth from a hole in a panel with a patch.
The steps necessary to build a model and perform a crack propagation
analysis are described. It is intended that you repeat the steps on a
workstation as they are described.
Examples 1 and 3 are similar, consisting of the cracked panel and, in example
3, a covering patch, as shown in
Figure 1.
σ
Patch over
plate with hole
0.5" R
E=10.0E6 psi
ν=0.25
thick=0.04 in
Adh. G=10.0E3 psi
Adh. thick=0.005 in
8.0"
4.0"
σ
Figure 1: Schematic of Plate with Hole
FRANC2D/L User's Guide
Tutorial Example Problems
Page 13
The second example is a lap joint, with the two layers bonded by adhesive, as
shown in Figure 2.
E=10.0E6 psi
ν=0.0
Thick = 0.04 in
Adh. G=10.0E3 psi
Adh. Thick=0.005 in
σ
σ
Top Layer
4"
Adhesive
Bottom
Layer
6"
Figure 2: Lap Joint
In all examples, the analysis is described in two sections. The first section
describes the procedures used to build an initial mesh using the CASCA
program, which is distributed with FRANC2D/L. Models can be created with
any other mesh generating program, provided a translator is available to
convert the mesh description to the FRANC2D/L *.inp format.
The second section describes the steps necessary for the FRANC2D/L
program to assign boundary conditions, perform a stress analysis, to
introduce cracks, and to propagate cracks. There are a large number of
options and features available in FRANC2D/L. Only a subset of these are
described in these examples. However, the examples have been chosen to
illustrate the most frequently used options, and to give you the confidence to
try the other features, which are described in the menu reference section.
In the tutorial, menu options are indicated by bold text, such as Data Size.
Text that you enter in the program control window are indicated with a
typewriter font, such as tutorial.inp. On UNIX systems, the programs
FRANC2D/L User's Guide
Tutorial Example Problems
Page 14
are run by typing the program name with the appropriate path. The location
of the program will vary from site to site, but the commands to run the
programs will look something like:
% programs/franc2dl
% programs/casca
As mentioned above, the coordinate system used within the programs are
always fixed so that the x and u coordinates are horizontal, increasing to the
right. The y and u coordinates are vertical, increasing going up.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 15
Example 1: Plate with Hole
Building an Initial Mesh with CASCA
Setting an Appropriate Data Space
Begin by running the CASCA program. Initially you will have three types of
options: setting the data space (Set Scale), reading a restart file (Read), and
adjusting your view (RESET, MAGNIFY, ZOOM, PAN, and SNAP).
Because we are starting a new problem from scratch, we will select Set
Scale.
At this point we want to adjust the data space and the grid to conform to our
current problem. By default, the data window is 12 units wide by 12 units
high with a grid spacing of one unit. For the patched plate problem, if we
choose the center of the hole to be the origin of our data space, the plate
extends 4.0 inches below this point. A nice round number would be to set the
data space to 10 units (±5 units). To do this select the Data Size option, and
enter 10 on the keypad (ENT stands for enter).
One can use the grid to speed the entry of geometrical data. When the grid
is turned on, the intersection points on the grid have "gravity", and mouse
clicks near these points will "snap" to the grid intersection. In the lug
problem, it is convenient to set the grid spacing to 0.5. This is done by
selecting the Spacing XY option and entering 0.5.
If you select RETURN, the grid disappears, and new options are available in
the main menu. One is Grid, which redisplays the grid, and turns on the
snap-to gravity. You should go ahead and select Grid. You should also
notice a Geometry option. This allows you to specify the outline of your
problem, which is the geometry used when generating a mesh. Go ahead and
select Geometry.
Creating the Problem Outline
FRANC2D/L User's Guide
Tutorial Example Problems
Page 16
You are now presented with a number of options that you can use to specify
the outline of your object. For the patched plate with hole
problem, we will begin with the hole. To take advantage of
symmetry, we will mesh only the right half of the problem.
First select Get Circle.
Because we will specify
subregions from the circle, we will define the circle as two
arcs. An arc is specified by three points: the beginning and
ending points and the center. Because of the grid gravity,
we can specify the three points by pointing to the screen.
First point to the grid intersection just above the center,
then to the grid point just to the right of the center, and
finally to the center. You should see a 90 degree arc. To
accept this arc, you must select DONE from the menu. If
Figure 3: Circle you select QUIT, the circle will be ignored. Repeat this to
Border
generate the lower part of the circle. The display should be
as shown in Figure 3.
The plate outline can be specified with the Lines Connect option. Select
this option. To start the connected lines, click on the top point of the circle
arc. Then move up 3 grid intersections (1.5 units), click, to the right 4 grid
intersections (2.0 units), click, down 8 grid
intersections (4.0 units), click, to the left 4 grid
intersections (2.0 units), click, and, finally, to the
lower point of the circle arc and click. To leave this
mode of adding line segments, select QUIT. The
display should be like Figure 4.
To define the rest of the plate outline, select Lines
Connect and click on the top left point of the
patch. Then move up 4 grid intersections (2.0
units), click, to the right 4 grid intersections (2.0
units), click, and down 4 grid intersections (2.0
units) to the top right of the patch and click.
Select QUIT. Repeat for the plate region below
the patch, see Figure 5.
This completes the border definition. RETURN to
the main page. In general, it is best to use the
Figure 4: Inner Plate
minimum number of divisions when specifying the
Border
boundary. In this case, it is necessary to specify
the patch as a boundary because we will use the same boundary as a starting
point for the patch mesh in the final example.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 17
Adding Subregions and Subdivisions
You should now notice that a number of
additional options are available on the main page.
The next one we will use is Subregions. This
allows you to break your object up into a number
of simpler regions that are more convenient for
meshing. It will also allow us to define the patch
geometry. When you select this option you will
see a number of options that are similar to those
available on the geometry page.
In the patched plate
problem, we want to
divide the plate with a
hole into four separate
regions for meshing.
Most of the lines have
already been defined,
we will add one more
to the plate model.
Figure 5: Completed
Border
should look like Figure 6.
Select the Get Line
option, and specify a
line from the right of
the hole to the border
on the right of the
plate. Select DONE
(not QUIT) to accept
this line.
You now
have
divided
the
patched plate into four
regions. The problem
This is all the division that is necessary, you
should now RETURN to the main menu and
select Subdivide.
In the subdivision page, one specifies nodal
densities along the boundaries for all the regions
in the structure. The arrows along all the edges
indicate their orientation, and are used when
grading the nodal spacing along the edges.
Figure 6: Subregion
Added
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We will start with the two arcs defining the hole. We will define 10
subdivisions on the quarter circle. To do this, select No. of Segments and
enter 10. Now select the Subdivide option and click on both arcs defining
the circle. You should see triangles to indicate the
nodal densities. Continue to subdivide the radial
lines extending from the circle by selecting them.
The QUIT option allows you to leave the selection
mode. Now select No. of Segments and enter 4.
Define this nodal density for the two horizontal
segments on the top and the two segments on the
bottom of the plate (remember that you must
select Subdivide to enter the selection mode and
QUIT to return). To define the two segments on
the right edge away from the circle, select No. of
Segments and enter 6. We also want a finer mesh
near the X axis, so select Ratio and enter 1 and 2
to define a 1:2 ratio. Now select Subdivide and
the lower right line segments. Next, since the
arrow of the upper right line segment is towards
the X axis, select Revert Ratio and that line
segment. Finally, specify 5 divisions on the top and
bottom left and right lines defining the plate edge.
Also, return the ratio to 1:1. After subdividing all
line segments, the plate should now look like
Figure 7.
Figure 7: After Line
Subdivision
As illustrated above, the Ratio option can be used
to specify a mesh with a density that varies along a
line. For instance, selecting Ratio and entering 1
and 2 means the mesh size will vary a factor of two
in the direction of the arrow defining the line
segment. The Revert Ratio option can be used to
change the arrow direction.
Mesh Generation for Plate
Return to the main page. The next step is to generate meshes for the four
regions. Select the Mesh option to move to the mesh page. The first two
options on this page allow you to select element types. The defaults are Q8
quadrilateral elements, and T6 triangular elements. You must use these
second order elements with FRANC2D/L. For a plate bending analysis, only
the T6 elements may be used.
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All four regions of the patched plate can be meshed with the bilinear four
sided meshing algorithm (Bilinear 4side). This algorithm requires a
rectangular region with equal numbers of nodes on opposing sides.
The two regions adjacent to the hole have five sides. However, if we think of
the arc on the circle as one side, the radial lines as
each a side and the opposing top and right box edges
as one logical side, we have a four sided region with
equal nodes on opposing sides. We mesh this by
selecting the Bilinear 4side option and clicking in
the region. A mesh is generated. If the program is
not able to determine the four corners of the region,
it prompts you to specify these points. Repeat
selecting the Bilinear 4side option and clicking on
the rest of the regions. The mesh is shown on the
left.
Meshing of the plate is now complete, you should
RETURN to the main page. Create a CASCA
restart file by means of the Write option. Give a
name such as plate, and a plate.csc file will be
written.
A *.inp file can also be created for
FRANC2D/L by selecting the Write Mesh option.
Again specify the name plate, and a plate.inp file
will be created. You may need to move the CASCA
window to see the prompt in the terminal window.
Select END and CONFIRM EXIT to leave CASCA.
Figure 8: Final Mesh
Translating the Mesh
For problems with multiple layers, the layers must be superimposed using a
translator program. This example has only one layer, so no translation is
necessary. Simply read the plate.inp file directly into FRANC2D/L.
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Performing a FRANC2D/L Simulation
Setting the Analysis Type and Material Properties
You should now run the FRANC2D/L program. The program will ask for a
filename. Enter plate, with no extension. The
program will then ask for a file type. Enter 1,
which indicates that we want to read the plate.inp
file created in CASCA. Because we have used a
mixture of Q8 and T6 elements, the program will
start in 2-D mode (no bending). Only T6 elements
can be used for bending analyses; however,
FRANC2D/L can convert Q8 elements into T6
elements from the PROB TYPE menu. The display
should now be as shown in Figure 9.
First we will set the appropriate material properties.
Select PRE-PROCESS.
Now select the
MATERIAL option. A new window will appear, and
it may be necessary to rearrange the window to see
the menu. The new window contains the material
properties. The default properties are for steel. We
must change this because our plate is made of a
aluminum alloy. Select E, and enter the Young's
modulus of 10.0E6 psi (the EEX key adds the
exponent).
Select THICKNESS, and set the
thickness to 0.04. The KIc and density are not
necessary for a fatigue analysis so you can leave the
default values. Within FRANC2D/L, KIc is used for
quasi-static analysis, and need not be set otherwise.
Density is only used when there is loading due to
accelerations (radial accelerations or self weight).
Neither of those are present in this analysis, so
density can be left at 1.0 also. To see the material
numbers displayed, select SWITCH ELEM. QUIT
will return you to the material menu, or selecting Figure 9: FRANC2D/L
elements will change their material numbers to the
Mesh
current value. RETURN to the pre-process page.
Boundary Conditions
The next step is to specify boundary conditions. First we will add kinematic
constraints or fixities. Select FIXITY to move to the fixity page. Nodes can
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be fixed either individually, or along an edge. Each node can be fixed in the
X direction, the Y, or both. The fixities work like pushbutton on/off switches;
if a fixity is attached to a node, it can be turned off by reapplying the same
type of fixity.
Symmetry on both the plate and the patch will be enforced by applying X
constraints along the left edge. Select the FIX EDGE option and then X.
The procedure for adding a boundary condition to an edge is a three step
process: you 1) specify a starting node, 2) specify the adjacent node in the
direction toward the ending point, and 3) specify the ending node. Do this by
pointing to the lower left corner of the plate and click. You will see a square.
This is the tolerance box. The program
assumes that you are trying to select the
node within this box. If there is more
than one node within the box, the
program will pick one, which may or may
not be the one you had in mind.
Therefore, you should try to ensure that
there is only ever one node within the
box. This can be done by changing the
size of the box. The prompt window
(below the data window) can be used to
adjust the size of the tolerance box. If
you click in this window toward the
right, the tolerance box gets bigger; to
the left it gets smaller. The closer you
are to the left and right edges, the faster
the tolerance box will change size.
WARNING: The whole box is active,
even if the - <--- Tolerance ---> + message
is only in the left portion of the box.
You should now select an adjacent node.
Remember that these are eight-noded
elements, so the next nearest node is a
mid-side node. You will want to click at
the middle of the element edge just above
the left corner. Finally, you should point
Figure 10: X Constraints
and click at the left node on the lower edge of the hole to indicate where the
constraints should stop. The display will show a series of X's to indicate that
all the nodes along the left edge of the patch are fixed in the X direction,
Figure 10. Now repeat this for the left edge above the hole.
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In
addition,
we
will
constrain the Y rigid body
motion of the plate by fixing
the Y displacement of the
center node on the right
edge of the plate. In the
fixity page, select FIX IND,
then Y, and finally the
node. See Figure 11.
Figure 11: Y Fixity
RETURN from the fixity page, and enter the loads page. We will apply a
distributed load to the top and bottom of the plate. Select the DIST. LOAD
option. There are four choices for specifying the direction of the load: 1)
normal to the surface, 2) tangent to the surface, 3) in the global X direction,
and 4) in the global Y direction. Select the Y GLOBAL option because we
want the boundary stress to be in the Y direction.
You now have three options for the form of the load distribution: constant,
linear, or quadratic. Select the CONSTANT option. We must now specify
the portion of the boundary to load just as with the fixity. Load specification
uses a tolerance box, just as with the fixity. Again, you will want to try to
make sure that there is only one node in the tolerance box. A little trick to
see the size of the current tolerance box is to click someplace where you know
there is no node. This may show you that the tolerance box is much too
large. You can adjust it by clicking on the left side of the adjustment
window, and then clicking in the middle of the hole again. Once you have the
tolerance box the right size, select the top left node, the adjacent node just to
the right, and the top right node.
You must now specify the magnitude of the load. Loads are given as
tractions. Input the value directly as a traction and the current material
thickness as well as element edge lengths will be used to create equivalent
nodal loads. To specify loads that will give a stress of 10,000 psi in the plate,
enter 10,000. (Previously, loads were input as force/unit depth). It is
important that the material thickness be set correctly before the loads are
defined to obtain the expected results
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We have now specified the boundary conditions. You can RETURN from the
load page and the pre-processing page to get back to the main page. This is a
good time to save a restart file by using the WRITE FILE option.
Stress Analysis and Postprocessing
We are now ready to do stress analysis. From the main page, select the
ANALYSIS option and the DIRECT STIFF option. The program will now
perform a linear elastic stress analysis using a direct elimination (Gauss
elimination) solver. This will take a few seconds and the steps are displayed
in the terminal window. The step are:
•
Reduce Bandwidth: automatic nodal renumbering to reduce the
bandwidth of the global stiffness matrix.
•
Zero Gstf: zero the space used for the global stiffness matrix.
•
Assemble: assemble the element stiffness matrices into the global
stiffness matrix.
•
Decomposition: perform direct elimination of the global stiffness
matrix.
•
Backsubstitution:
displacements.
perform
backsubstitution
to
recover
nodal
When the analysis has been completed the program will print a short report
that summarizes the size of the model and the time required for the analysis.
You can now RETURN to the main page and select the POST-PROCESS
option to enter the postprocessing page. It might be good to select the
RESET option if you have not already done this.
The first thing to look at is the deformed mesh. This is a quick check to see
that the boundary conditions have been applied properly. For the plate with
hole problem, the deformed mesh for the plate should like like Figure 12.
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You can RETURN from this page, and select the
CONTOUR option. This allows you to display
color stress contours. You can view individual
components of the stress tensor, as well as
principal stresses. Of particular interest are the
stresses in the Y direction, Figure 13.
There are a number of other postprocessing
features
available.
When you are done
postprocessing,
RETURN
to
the
main menu.
Figure 13: Stress Contours
Figure 12: Deformed
Mesh
Crack Initiation
At this point we will put a crack in the plate. First, however, you should
make a restart file. This will save the analyzed uncracked configuration.
You may wish to return to this configuration to investigate different initial
crack locations.
To initiate a crack, select the MODIFY option and then the NEW CRACK
option. The crack face option in FRANC2D/L is NON-COHESIVE, a normal
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traction free crack surface. Select NON-COHESIVE. Cracks can start from
the edge of a structure (EDGE CRACK), or can be completely internal (INT
CRACK). For this model, select EDGE CRACK. You must now specify the
location of crack initiation.
The stress contours showed the highest stresses at the right of the hole. This
is the likely location for crack initiation, and we will start the crack there.
However, if cracking had been observed at another location, or if there are
other reasons to believe that a crack is likely at another location (the
manufacturing procedure, for example), the crack could be initiated there.
To start a crack, it will be easier if you ZOOM and PAN to see the location
of crack placement. Select the node on the right edge of the hole to be the
crack mouth. Select DONE after you click on the node, Figure 14. You
must now specify the crack tip.
You can do this by specifying the
exact crack-tip coordinates, or by
merely pointing and clicking at
some location in the plate. In the
present analysis, since we want
the crack to be normal to the hole,
and we want to choose, arbitrarily,
an initial crack length of 0.10, you
select KEY POS and enter the
crack tip coordinates at 0.60, 0.0.
The program will now ask for the
minimum number of elements
along the crack extension. It is
almost always safe to enter 2 for
this question. The actual number
of elements placed along the crack
extension is a function of the local Figure 14: Selection of Crack Initiation
Point
mesh density. Finer initial meshes
will cause more elements to be used, and thus give more accurate stressintensity factors.
The program will now delete a number of elements. You should click
anywhere in the FRANC2D/L window, and the program will insert the crack.
When you click again the program will insert crack-tip elements. One more
click and the program will display a mesh that fills the region near the new
crack. The ACCEPT option updates the program data structure to include
these new elements. The updated mesh will look as shown in Figure 15.
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Figure 15: Mesh with Crack
Stress Analysis and Fracture Analysis
Because you now have a new (cracked) structure, a new stress analysis must
be performed. To do this, RETURN to the main menu, and select the
ANALYSIS and DIRECT STIFF options.
You can now postprocess the analysis results. If you select the DEFORMED
MESH option, you will see the crack faces opening.
More importantly, we can now compute stress-intensity factors. To do this
select the FRACT MECH option.
The stress intensity factors in
FRANC2D/L are calculated using several methods. Modified crack closure
usually provides the most accurate results (MOD CRK-CLOS.).
The
calculated stress intensity factor is 14,710 psi-in1/2.
Crack Propagation
Before we grow the crack, you may wish to save a restart file. To grow the
crack, enter the MODIFY page and select the MOVE CRACK option. There
are two crack propagation options. We will use the standard method
(STAND METH). We will use the AUTOMATIC method later.
If you select the STAND METH option, you will notice a line extending from
the crack tip. This is the direction in which the program predicts the crack
will propagate. This direction is the direction of maximum hoop stress
around the crack tip. For the problem we are working, the crack propagates
in a straight line, but this is not required. The crack can curve as it
propagates.
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There are three options for specifying the new crack tip location. First, you
can point and click anyplace on the model that you would like. The program
will grow the crack to that point.
Second, you can use the KEY POS
option and enter the X and Y
coordinates of the new crack tip
with the keypad. The third option
is to use the predicted direction of
crack propagation, but enter the
crack increment. This is the KEY
INCR option. Select KEY INCR
and enter 0.10 for the increment.
You will need to specify the
minimum number of elements
along the increment, 2, and the
program will remesh just as it did
for crack nucleation.
The trial new mesh is shown in
Figure 16: Mesh after Growth
orange. You can ACCEPT this
mesh, or use the ADD NODES and
KILL ELEM options to modify the mesh before it is accepted. The new mesh
is shown in Figure 16. Once the mesh is accepted, another stress analysis
must be performed.
Crack propagation can also be
performed
automatically.
Enter the MODIFY page,
select MOVE CRACK and
AUTOMATIC. You can use
the CRACK INCR option to
set the amount of crack growth
at each step. For the plate
problem use 0.10. Use the
STEPS option to set the
number of propagation steps.
Set that to 12, and select
PROPAGATE to begin the
crack propagation. This will
take a few minutes to finish.
The final deformed mesh is
shown in Figure 17.
Figure 17: Displaced Mesh
Fatigue
Crack
Growth
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Analysis
To perform a fatigue crack growth analysis of the plate, select the POSTPROCESS and FRACT MECH options. We will first look at stressintensity factor histories (SIF HISTORY). This allows you plot the K values
as a function of the crack length, and to save this information to a file. The
plot of KI as a function of crack length shows that the stress intensity
increases with crack length. The comparison with tabulated values is
excellent.
45000
Stress Intensity (psi-in1/2)
40000
FRANC2D/L
Handbook
35000
30000
25000
20000
15000
10000
5000
0
0
0.2
0.4
0.6
0.8
1
1.2
Crack Length (in)
Figure 18: Comparison of FRANC2D/L and Analytic Solutions
Selecting the FATIGUE PLTS option allows you to perform a simple fatigue
life analysis based on the Paris model. This model states that the crack
growth rate is an exponential function of the stress-intensity factor range:
da
m
= C(∆K ) .
dN
C and m are material specific input parameters. Within FRANC2D/L, only
mode I values of the stress-intensity ranges are used. The crack length is the
distance along the arc length of the crack.
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The Paris model is very simple and may not be appropriate for some
materials, non-zero load ratios, and very high or very low ∆K ranges. In
many cases it is more appropriate to extract a ∆K vs a history computed
within FRANC2D/L, and use this information with a more sophisticated
growth model.
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Example 2: Adhesively Bonded Lap Joint
This example uses two layers and illustrates the use of adhesive bonding.
Building an Initial Mesh with CASCA
Setting an Appropriate Data Space
Again, run the CASCA program. Select Set Scale and RETURN, to the
main menu. Select Grid to display the grid. Select Geometry.
Creating the Mesh Outline for Layer 1
We want to create a simple lap joint, with each layer four inches long and
two inches wide. The overlapped region will be two inches.
The top layer outline can be specified with the Lines Connect option. Select
this option. Click on the center, then move up 2 grid intersections (2.0 units),
click, to the left 4 grid intersections (4.0 units), click, down 2 grid
intersections (2.0 units), click, to the right 4 grid intersections (4.0 units) to
close the outline. To leave this mode of adding line segments, select QUIT.
RETURN to the main page.
Adding Subregions and Subdivisions
Select Subregions. Select the Get Line
option, and specify a line from two grid
points to the left of the center, then two
grid points up to the edge. Select DONE
(not QUIT) to accept this line.
The
problem should look like Figure 19.
This is all the division that is necessary,
you should now RETURN to the main
menu and select Subdivide.
Figure 19: Layer 1 Border
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Select No. of Segments and enter 10.
Now select the Subdivide option and
click on all four sides defining the right
square. Also select the left line. Again,
select No. of Segments and enter 5.
Define this nodal density for the two
remaining horizontal segments. After
subdividing all line segments, the plate
should now look like Figure 20.
Figure 20: Layer 1 Subdivide
Mesh Generation for Layer 1
Return to the main page. Select the Mesh option to move to the mesh page.
We mesh the layer by selecting
the Bilinear 4side option and
clicking in each region. A mesh is
generated, Figure 21. Meshing of
the plate is now complete, you
should RETURN to the main
page.
Create a CASCA restart file using
the Write option. Give a name
Figure 21: Layer 1 Mesh
such as layer1, and a layer1.csc
file will be written. A *.inp file can also be created for FRANC2D/L by
selecting the Write Mesh option. Again specify the name layer1, and a
layer1.inp file will be created. You may need to move the CASCA window to
see the prompt in the terminal window.
Select END and CONFIRM EXIT to leave CASCA.
Creating the Mesh Outline for Layer 2
At this point, we will essentially repeat the above steps for layer 2. The only
difference is that the layer 2 mesh will be refined on the left where the
adhesive will join the two layers.
For layered problems, there is an important rule that must be followed. This
is, in the overlapped regions, the meshes in all layers must be identical.
The second layer outline can be specified with the Lines Connect option.
Select this option. Click 2 grid intersections to the left of center, then move
up 2 grid intersections (2.0 units), click, to the right 4 grid intersections (4.0
units), click, down 2 grid intersections (2.0 units), click, to the left 4 grid
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intersections (4.0 units) to close the outline. To leave this mode of adding
line segments, select QUIT. RETURN to the main page.
Adding Subregions and Subdivisions
Select Subregions. Select the Get Line option, and specify a line from the
enter, then two grid points up to the edge. Select DONE (not QUIT) to
accept this line.
This is all the division that is necessary, you should now RETURN to the
main menu and select Subdivide.
Select No. of Segments and enter 10. Now select the Subdivide option and
click on all four sides defining the left square. Also select the right line.
Again, select No. of Segments and enter 5. Define this nodal density for the
two remaining horizontal segments.
Mesh Generation for Layer 2
Return to the main page. Select the
Mesh option to move to the mesh
page. We mesh the layer by selecting
the Bilinear 4side option and
clicking in the region. A mesh is
generated. Meshing of layer 2 is now
complete, you should RETURN to
the main page.
Create a CASCA restart file using the
Figure 22: Layer 2 Mesh
Write option. Give a name such as
layer2, and a layer2.csc file will be written. A *.inp file can also be created
for FRANC2D/L by selecting the Write Mesh option. Again specify the
name layer2, and a layer2.inp file will be created. You may need to move
the CASCA window to see the prompt in the terminal window.
Select END and CONFIRM EXIT to leave CASCA.
Translating the Mesh
We now must translate the mesh for input to FRANC2D/L and in the
process, merge the two layers. Type:
%castofranc
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You will be asked for the number of layers, type 2. You will then be asked
for the casca file corresponding to the first layer, type layer1.inp. You will
then be asked for the casca file corresponding to the second layer, type
layer2.inp. Type layers.inp when asked for the output file. Finally
type adhesive example when asked for the problem title. Translation will
then be performed.
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Performing a FRANC2D/L Simulation
Setting the Analysis Type and Material Properties
You should now run the FRANC2D/L program. We can speed starting
FRANC2D/L by typing the filename at the same time, this would typically be
something like franc2dl layers.inp. The display should now be as
shown in Figure 23. This shows layer 1. To view other layers, select
- LAYER +.
Conceptually,
the
layers
should
be
viewed as layer 1
being on top, with
each additional layer
stacked below in the
order of their number.
Boundary conditions
for each layer are
specified independently.
layers.
Figure 23: Mesh Display in FRANC2D/L
The material properties are common between
First we will set the appropriate material properties. By default, each layer
has a material number equal to the layer, so there are two materials in this
problem. Select PRE-PROCESS. Now select the MATERIAL option. A
new window will appear, and it may be necessary to rearrange the window to
see the menu. The new window contains the material properties. We will
change these. Select E, and enter the Young's modulus of 10.0E6 psi (the
EEX key adds the exponent). Select Nu, and enter a value of 0.0 (this will
help comparison with a simplified analytic solution). Select THICKNESS,
and set the thickness to 0.04. The KIc and density are not necessary for a
fatigue analysis so you can leave the default values.
In the materials menu, select - MAT + (on the + side) to go to material 2. In
the same manner as for material 1, change Young's modulus, Poisson's ratio,
and the thickness.
Since we will use an adhesive between layers, we need to define the adhesive
material properties. Select NEW MAT and ADHESIVE. Define the
thickness as 0.005 inch and the shear modulus as 10,000 psi. RETURN to
the pre-process page.
Boundary Conditions
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The next step is to specify boundary conditions. Select FIXITY to move to
the fixity page. We will use symmetry on both layers along the bottom edge.
For each layer fix the lower edge in the Y direction. Select the FIX EDGE
option and then Y. Select the starting node, adjacent node in the direction
toward the ending point, and ending node. Next, select - LAYER + to go to
layer 2, and repeat. We will also constrain the upper layer in the X direction
on the left side. Go back to the first layer and using FIX EDGE, fix the left
edge of the upper layer, Figure 24.
Figure 24: X Fixity in Top Layer
RETURN from the fixity page, and enter the loads page. We will apply a
distributed load to the right side of the bottom layer. Make sure layer 2 is
being displayed, then select LOADS and the DIST. LOAD option. Select the
X GLOBAL option because we want the boundary stress to be in the X
direction. Select the CONSTANT option. Select the top right node, the
adjacent node just below, and the bottom right node.
You must now specify the magnitude of the load. Loads are given as
tractions. Input the value directly as a traction and the current material
thickness as well as element edge lengths will be used to create equivalent
nodal loads. To specify loads that will give a stress of 10,000 psi in the plate,
enter 10,000. (Previously, loads were input as force/unit depth). It is
important that the material thickness be set correctly before the loads are
defined to obtain the expected results.
We have now specified the boundary conditions. You can RETURN from the
load page and the pre-processing page to get back to the main page.
Adhesive Between Layers
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Our final task in defining the problem is to specify the type of connection
between layers. We will use the adhesive for which we previously defined
the material properties. Adhesives are defined on the upper layer of the two
layers that are to be joined. Make sure layer 1 is in the display, then select
MODIFY from the main
page. Select TOGGLE ALL
to specify that all elements
of layer 1 that overlap layer
2 will be connected by
adhesive.
Optionally, the
user can specify individual
elements. The display will
mark each element that has
an adhesive with an X, as
shown in Figure 25.
Figure 25: Adhesive
restart file by using the WRITE FILE option.
This is a good time to save a
Stress Analysis and Postprocessing
We are now ready to do stress analysis. From the main page, select the
ANALYSIS option and the DIRECT STIFF option. The program will now
perform a linear elastic stress analysis. When the analysis has been
completed the program will print a short report that summarizes the size of
the model and the time required for the analysis.
You can now RETURN to the main page and select the POST-PROCESS
option to enter the
postprocessing page.
The first thing to look at
is the deformed mesh.
This is a quick check to
see that the boundary
conditions have been
applied properly. For the
second
layer,
the
deformed mesh should
like like Figure 26.
Figure 26: Layer 2 Deformed Mesh
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You can RETURN from this
page,
and
select
the
CONTOUR option.
This
allows you to display color
stress contours. You can view
individual components of the
stress tensor, as well as
principal
stresses.
Of
particular interest are the
shear stresses in the adhesive
in the XZ direction (ADH_TAU
ZX), .
Finally, RETURN and select
LINE PLOT. This allows you
to specify the end points of a
line and then plot stress values
along the line.
shows a
Figure 27: Shear Contours in Adhesive
comparison of the calculated
shear stresses in the adhesive and an analytic solution for the adhesive.
700
Normalized Shear Stress
600
500
ANALYTIC
FRANC2D/L
400
300
200
100
0
-1.5
-1
-0.5
0
0.5
1
1.5
Normalized Position
Figure 28: Comparison of Analytic and FRANC2D/L Adhesive
Stresses
When you are done postprocessing, RETURN to the main menu.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 38
Example 3: Plate with Hole and Patch
Building the Mesh with CASCA
Restarting CASCA Using a Previous File
This example is an extension of the example 1. We do not need to start from
the beginning, but can just use the existing CASCA file to make this mesh.
Copy the example 1 *.csc file to the directory in which you want to work,
then run the CASCA program. Select Read and enter the name of the
CASCA file without extensions (for instance, plate). Turn off the Grid and
view the mesh by entering Mesh. At this point, you will see the previous
mesh.
Saving Mesh for Plate Layer
Our goal is to make a patch that fits over the plate with a hole. In addition,
in the overlapped region, the mesh in both layers must
be identical. Clearly, we already have the mesh for the
plate with hole, so no further work is necessary.
Return to the main page. Select Write Mesh and give
the file name (layer2).
Mesh Generation for Patch
To create the mesh for the patch we will modify the
work we have already performed. This is a good way
of ensuring that in the overlapped region, the meshes
are identical.
To begin to modify the mesh, select Mesh. Next select
Delete, pick the region above the patch, and select
DONE. Repeat for the region below the patch. The
mesh should now look as shown in Figure 29. Return
to the main menu.
Select Geometry and delete the line segments on the
plate above and below the patch. Add three radial
lines from the problem center to the hole diameter,
since we will now mesh the region of the patch that
covers the hole. Return to the main menu.
Select Subdivide. Set No. of Segments to 3, and
Subdivide each of the radial lines. You may want to
Figure 29: After
Deleting Regions
FRANC2D/L User's Guide
Tutorial Example Problems
Page 39
ZOOM to see the lines more clearly. The display
should look like Figure 30. Return to the main
menu.
Finally, select Mesh.
3side, but in this
case, we will
obtain a better
mesh
of
the
circular region if
we
use
Transition.
Select
Transition,
point to the top
right
quarter
subregion of the
hole,
select
Figure 30: Patch with
GENERATE
Subdivisions
INT PT, and a
mesh will be generated. Repeat for the other
region of the hole. Return to the main menu.
The mesh should now look like Figure 31.
We could use Bilinear
Select Write Mesh and specify the file name
(call it layer1) without the .inp extension on
the XTerm terminal window.
Figure 31: Patch mesh
Select END and CONFIRM EXIT to leave CASCA.
Merging/Translating the Two Layer Meshes
We now must merge the two layers into a single problem for input to
FRANC2D/L. We do this using the castofranc translator supplied with
FRANC2D/L. Type:
%castofranc
You will be asked for the number of layers, type 2. You will then be asked
for the casca file corresponding to the first layer, type layer1.inp. Type
layer2.inp when asked for the second file. Type example3.inp when
asked for the output file. Finally type Tutorial when asked for the problem
title. Translation will then be performed.
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Tutorial Example Problems
Page 40
Performing a FRANC2D/L Simulation
Setting the Analysis Type and Material Properties
You should now run the FRANC2D/L program. The program will ask for a
filename. Enter example3.inp.
The display should now be as shown in Figure 32.
We are looking at the first layer (patch), with only
the outline of the second layer shown. To see the
second layer, select - LAYER +. The display will
change to that in Figure 33.
Conceptually, the layers
should be viewed as layer
1 being on top, with each
additional layer stacked
below in the order of their
number.
Boundary
conditions for each layer
are
specified
independently.
The
material properties are
common between layers.
First we will set the
appropriate
material
properties.
By default,
each layer has a material
number equal to the
layer, so there are two
materials in this problem.
Select PRE-PROCESS.
Now
select
the
MATERIAL option.
A
new window will appear,
and it may be necessary
Figure 32: Patch Layer
to rearrange the window
to see the menu. The new window contains the
material properties. We will change the properties.
Select E, and enter the Young's modulus of 10.0E6
psi (the EEX key adds the exponent). Select
THICKNESS, and set the thickness to 0.04.
Figure 33: Plate Layer Select - MAT + (on the + side) to go to material 2.
In the same manner as for material 1, change Young's modulus and the
thickness.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 41
Since we will use an adhesive between layers, we need to define the adhesive
material properties. Select NEW MAT and ADHESIVE. Define the
thickness as 0.005 inch and the shear modulus as 10,000 psi. RETURN to
the pre-process page.
Boundary Conditions
The next step is to specify boundary conditions. First we will add kinematic
constraints or fixities. Select FIXITY to move to the fixity page. Symmetry
on both the plate and the patch will be enforced by applying X constraints
along the left edge. Do this by selecting the FIX EDGE option and then X.
Apply X fixity on the left edge of the patch. The display will show a series of
X's to indicate that all the nodes along the left edge of the patch are fixed in
the X direction. Repeat for the plate by selecting -LAYER+ to display the
plate and fixing the left edge of the plate in the X direction. In addition, we
will constrain the Y rigid body motion of the plate by fixing the Y
displacement of the center node on the right edge of the plate. In the fixity
page, select FIX IND, then Y, and finally the node.
You can RETURN from this page, and enter the loads page. We will apply a
distributed load to the top and bottom of the plate. Select the DIST. LOAD
option. Select the Y GLOBAL option because we want the boundary stress
to be in the Y direction. Select the CONSTANT option. We must now
specify the portion of the boundary to load just as with the fixity.
You must now specify the magnitude of the load. Loads are given as
tractions. Input the value directly as a traction and the current material
thickness as well as element edge lengths will be used to create equivalent
nodal loads. To specify loads that will give a stress of 10,000 psi in the plate,
enter 10,000. (Previously, loads were input as force/unit depth). It is
important that the material thickness be set correctly before the loads are
defined to obtain the expected results. The -DOF+ allows you to look at loads
in any direction.
We have now specified the boundary conditions. You can RETURN from the
load page and the pre-processing page to get back to the main page.
Our final task in defining the problem is to specify the type of connection
between layers. We will use the adhesive for which we previously defined
the material properties. Adhesives are defined on the upper layer of the two
layers that are to be joined. Make sure layer 1 is in the display, then select
MODIFY from the main page. Select ADD ADHESIVE. Select TOGGLE
ALL to specify that all elements of the patch will be connected to the plate by
FRANC2D/L User's Guide
Tutorial Example Problems
Page 42
an adhesive. Optionally, the user can specify individual elements. The
display will mark each element that has an adhesive with an X, Figure 34.
This is a good time to save a restart file by
using the WRITE FILE option.
Stress Analysis and Postprocessing
We are now ready to do stress analysis. From
the main page, select the ANALYSIS option
and the DIRECT STIFF option.
You can now RETURN to the main page and
select the POST-PROCESS option to enter
the postprocessing page. By now, you should
be familiar with some of the options for
viewing the results. Note in particular, using
both contour plots and line plots how the
patch carries load from the plate.
When you are done postprocessing, RETURN
to the main menu.
Figure 34: Adhesive
Elements
Crack Initiation and Growth
At this point we will put a crack in the plate. First, however, you should
make a restart file. This will save the analyzed uncracked configuration.
You may wish to return to this configuration to investigate different initial
crack locations.
Make sure that the plate (layer 2) is being displayed. Next, repeat the exact
steps that were used in example 1 to introduce a crack to the plate.
Everything is exactly the same. The crack will be introduced to the mesh.
If you look at the patch (layer 1), you will see that its mesh has also changed
to match the cracked layer. This is necessary for the adhesive elements to
transmit load correctly between layers. However, there is no crack in the
patch; all the elements are continuously connected.
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Tutorial Example Problems
Page 43
Stress Analysis and Fracture Analysis
Because you now have a new (cracked) structure, a new stress analysis must
be performed. To do this, RETURN to the main menu, and select the
ANALYSIS and DIRECT STIFF options.
You can now postprocess the analysis results. If you select the DEFORMED
MESH option, you will see the crack faces opening.
More importantly, we can now compute stress-intensity factors. To do this
select the FRACT MECH option.
The stress intensity factors in
FRANC2D/L are calculated using a displacement correlation technique (MD.
CRK-CLOS.). The calculated stress intensity factor is 4,381 psi-in1/2.
Crack Propagation
You can now use the same approach to grow the crack as used in Example 2.
After the analysis is complete, select the POST-PROCESS and FRACT
MECH options to examine the stress-intensity factor histories (SIF
HISTORY). This allows you to plot the K values as a function of the crack
length, and to save this information to a file. The plot of KI as a function of
crack length shows that the stress intensity is approximately constant with
the addition of the patch, Figure 35. This is because the patch carries the
load as the crack grows. It also correlates with the crack face opening plot,
which shows approximately a constant crack face opening.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 44
45000
40000
FRANC2D/L: No Patch
ANALYTIC: No Patch
FRANC2D/L: With Patch
Stress Intensity (psi-in1/2)
35000
30000
25000
20000
15000
10000
5000
0
0
0.2
0.4
0.6
0.8
1
1.2
Crack Length (in)
Figure 35: Effect of Patch on Reducing Stress Intensity
FRANC2D/L User's Guide
Tutorial Example Problems
Page 45
Example 4: Additional Example
Crack Growth with Interference Between Plug and Hole
This analysis will demonstrate the ability to model a hole with interference
fit between a plug and the hole. A crack will then be grown from the edge of
a hole. This problem illustrates the use of interface elements and the
dynamic relaxation solver. The radius of the plug (hole) is 1 inch, and the
outer radius is 3 inches. For this example retrieve the plug.inp example file.
Start FRANC2D/L using the plug.inp file.
We want to make the plug rigid. To do this, go the the pre-processing menu
and add a new material that is 10 inches thick. Then specify this material
for the plug elements.
Next, fix the left edge in the X direction. NOTE: All fixities on edges must be
specified before introducing interface elements at the edge. If the fixity is
specified before the interface, the fixity will be correctly transferred to both
sides of the new interface.
We will now define the material properties for the nonlinear material
interface. The user can specify an opening/stress relationship in both the
normal and shear directions.
PREPROCESS→ MATERIAL→ NEW MAT→
Select NL INTERFACE followed by SHEAR. Select LINEAR. In the
auxiliary window, give the stiffness as 0.0. Thus, this interface will have no
resistance to sliding displacements.
From the material menu select
NORMAL and USeR-DEFINED followed by DEFINE FUNCtion. Respond
to the questions as follows:
$Is this a symmetry interface [Yes-1, No-0]: 0
On the keypad enter the number of points as 3. We now enter the
multilinear curve describing the opening/stress relationship for the interface.
We want an interface that will have an interference of 1.5x10-4 in (radial).
To do this we will pick a stiffness that is large enough to give a negligible
deformation under the expected normal loads. For this problem we will
accept an error in displacement of 1/100 of the interference at a load of 1,000
psi. This gives a stiffness of 6.66x108 psi/in. Then input the three points as:
FRANC2D/L User's Guide
Tutorial Example Problems
Displacement
-6.0E-4
1.5E-4
6E-4
Page 46
Stress
-500,000
0
0
This will create a subwindow showing the properties for that interface.
Select THICKNESS and specify a value of 1.0. Return to the pre-processing
menu.
Because FRANC2D/L expects loads to be applied, apply a zero value point
load to any node in the mesh. RETURN to the main menu.
MODIFY→ ADD NL_INTFC→
Select the first node of the interface. This will be at a radius of 1 inch and is
the clean circle in the mesh. Select DONE. Next, select the ending node of
the element edge in which an interface will be added and select DONE. You
will now see a box around the selected edge. Now, select each new node
indicating an edge for which the interface will be extended and repeat the
final selection to complete the process. Return to the modify menu and select
the INTERFC:ON button to see a the new boundaries as shown in Figure
36.
Figure 36: Interface around hole
We are now ready for the solution. From the main page, select ANALYSIS,
LINEAR, DYN RELAX. At this time you will be asked for the maximum
number of iterations and the convergence tolerance. The number of
iterations is problem dependent, but 1000 may be an initial starting point.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 47
The convergence tolerance is a measure of the unbalanced loads in the
structure. A value of 0.01 is usually a good initial value, but a tighter
tolerance may be required.
The solution should now proceed.
When it converges (in about 475
iterations), proceed to the post-processing menu. Select DEFORMD MESH
to see the deformed mesh. Notice that the interface elements have opened an
amount approximately equal to the initial interference (Figure 37).
Figure 37: Deformed mesh plot
A contour of the SIG1 stress is shown in Figure 38. The central plug is
compressed, while there are tensile stresses in the cylinder.
Finally, a line plot from the center to the edge gives the radial stresses
(Figure 39). The peak stress is about 900 psi, which compares to the ideal
value of 1,000 psi corresponding to a rigid plug and interface.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 48
Figure 38: Principal stress contours
Figure 39: Line plot of radial stresses
We will now introduce a crack at the interface and calculate the stress
intensity.
MODIFY→ NEW CRACK→ NON-COHESIVE→ EDGE CRACK→
For simplicity, select as the crack starting node, the node located at X=1, Y=0
(on the interface on the X axis). You may need to zoom in to select the node.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 49
When finished, select DONE. Select KEY POS and give a value of X=2, Y=0
and 6 elements along the crack extension. After 2 clicks, ACCEPT the new
mesh in the cylinder. Then ACCEPT the new mesh in the plug. Rerun the
analysis and note the results again using the deformed mesh and the stress
contours.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 50
Example 5: Incremental Elastic-Plastic Analysis
Notch Root Displacement
This analysis will demonstrate the ability to model elastic plastic
deformations at a stress concentration. The numerical results will be
compared to experimental results. The geometry and numerical results come
from a NASA publication (Newman, Dawicke and Bigelow, 1992). The first
step is to retrieve the example problem bluntnotch.inp and the mat2024.txt
file that contains a material hardening definition. Also retrieve the mon.awk
script file to post-process part of the monitor output data. Start FRANC2D/L
using the bluntnotch.inp file. The figure below shows the bluntnotch.inp
mesh.
Begin by going into the
PRE-PROCESS menu.
Make sure that the
problem type is plane
stress. Next apply X
fixity to the left edge of
the model and Y fixity
to the bottom of the
model to the right of the
“hole”. This simulates
symmetry
on
the
horizontal and vertical
centerlines of the test
specimen.
Next,
set
up
the
material definition for
the problem. It’s best to
do this before applying
loads, since the load
definition may depend
on the material definition. For instance, distributed loads need the correct
material thickness to be correctly converted into work equivalent loads. Use
the CHANGE TYPE option to change the current material to a VON MISES
material. The material properties are are for 2024-T3 aluminum:
E
nu
thickness
Hardening
Yield Stress
10400 ksi
0.3
0.09”
Curve(described below)
50 ksi
FRANC2D/L User's Guide
Tutorial Example Problems
Prob Type
CTODc
CTODc Init
Density
Max Iter
Page 51
Plane Stress
1.0 (not used)
1.0 (not used)
1.0 (not used)
50 (default value)
The Hardening Modulus needs some explanation. The Curve designation
indicates that a multi-linear curve representation is used for the hardening
modulus. Under the HARDENING E option choose the READ CURVE and
read the mat2024.txt file. If you don’t have the file you can use the DEFINE
CURVE option and type in the following values or you can create your own
input file with the following data. Note that the first line of the input file
should contain the number of points to follow (e.g. 7 in this case). After you
read in the hardening curve, the program will display the curve in the
auxiliary window.
Eff Strain
0.0
0.00483
0.015
0.040
0.1
0.16
0.2
Eff Stress (ksi)
0.0
50.0
56.5
62.5
68.5
71.0
71.0
Finally, use the APPLD DISP option and the EDGE DISP option to set the Y
value of applied displacement along the top edge of the model to 0.001”.
Applied displacements always go into Load Case 1, so if there happens to
already be another type of loads in Load Case 1, they must be deleted before
the applied displacement boundary conditions can be applied.
Linear Elastic Analysis
The preprocessing for the blunt notch problem is now complete. Save a
restart file (for instance: bluntnotch.wdb) and proceed to the ANALYSIS
menu. Run a linear elastic analysis and check that the response of the model
is correct. Return to the POST-PROCESS menu and check the results. The
maximum value of EFF STRESS (from the CONTOUR menu) should be
about 14.5 ksi, and the notch root displacement (the top node inside the hole)
should be about (X:-2.191E-04, Y:2.403E-04) (from the NODE INFO menu)
Elastic-Plastic Analysis
Return to the ANALYSIS / MAT NONLIN menu. The auxiliary window will
now display the control parameters for nonlinear analyses. Proceed into the
CONTROL PARAM menu to set the appropriate control values. For this
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Tutorial Example Problems
Page 52
analysis we will only change the Load Sub-Steps to 45, the Appl Disp Factor
to 45, and the Final Step to 45. Return from this menu and proceed to the
MONITOR menu. The monitor feature allow us to easily collect history data
as the solution progresses. Select the ADD NODE option and point to the top
node inside the hole (the one where we checked the displacement during the
linear elastic analysis). The node should be highlighted if you correctly
selected the node. Next set the file name to the checkpoint file name (in this
example: bluntnotch.mon) or to some file name meaningful for the
analysis. Data will be monitored for this node as the solution progresses for
each converged solution state and written to this file. Return to the main
menu and save a restart file. This will save a full restart file, including all of
the current analysis control parameters.
Finally, we get to run the analysis: proceed back into the ANALYSIS / MAT
NONLIN menu and select the ANALYZE ONE option. This will use the
current control data to apply the current loads to the model. In this case, the
applied displacements will be scaled by 45 and applied to the model over a
series of 45 Load Sub-Steps. In effect we’re applying 45 separate 0.001” load
increments to the model. In the FRANC Analysis Report in the program
control window, the Applied Disp Y Force should be about 15.7 kips. The
final notch root displacement from the NODE INFO menu is about:
(X:-6.23E-03, Y:2.91E-02) inches. The final load is about 15.7 kips /
(0.09”*5”) = 34.9 ksi, where the thickness is 0.09” and the width of the
specimen is 5”.
We will now compare the response results save from the monitor into the
bluntnotch.mon file. Run the mon.awk script as described below to process
the monitor
data. Awk is a simple programming language typically available

on UNIX systems (named for the authors: Aho, Weinberger and Kernighan).
A version is available for Win32 from the Free Software Foundation (GNU)
as gawk. On some systems it is better to use nawk (new awk). So, after all
of that, run the script as:
nawk -f mon.awk bluntnotch.mon > bluntnotch.out
The result is a file that can be read into your favorite spread sheet and
processed for an X-Y plot. Two sets of data are available: first come the
global forces as a function of the step number, then come the nodal data for
the monitor node as a function of step number. The data for the node are
UX: x nodal displacement, UY: y nodal displacement, RX: x reaction force at
the node, and RY: y reaction at the node.
Note: The experimental data are recorded for the full notch root displacement
using a clip gauge. The analysis only computes half of the displacement
value, so double the values of the results to compare with the graph.
FRANC2D/L User's Guide
Tutorial Example Problems
Page 53
The figure below compares the analysis data to the test data. Using the
multi-linear hardening rule gives a good approximation to the experimental
data.
Try running the analysis with an elastic-perfectly plastic model, or with a
bilinear approximation to the given stress strain curve and compare the
results with the results below.
Notch Root Displacement Example
40
35
30
25
20
15
10
Test Data
5
FRANC2D/L Analysis
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Notch-Root Displacment (in)
FRANC2D/L User's Guide
Page 54
Menu Reference Guide
Example 6: Incremental Elastic-Plastic Analysis
Non-Proportional Loading
This example demonstrates a number of FRANC2D/L features for a
materially-nonlinear analysis, including the von Mises material model with
linear isotropic hardening and nonproportional loading. A thin tube is first
stressed in tension to the point of yielding and is then twisted under constant
axial stress. A single material point is sufficient to model the problem. The
figure below shows the loading path and material properties.
τ
σ
B
Et = 280
Yo = 26.25
A
O
σ
Point
O
A
B
σ
0.0
26.25
26.25
τ
0.0
0.0
24.0
E= 28,300
ν = 0.3
ε
For linear isotropic hardening the Hill (1950) plasticity book gives the exact
solution for the axial and shear strains as:
Yo  3τ 2  Yo
ε=
ln 1 + 2  +
2H' 
Yo  E
γ =
τ 3 τ
Yo
3 
 +
tan −1 
τ −
H ' 
 Yo   G
3
where Yo is the yield stress in tension, E is Young’s Modulus, H’ is the plastic
modulus, and G is the elastic shear modulus for ν = 0.3. The figure below
shows the exact strain path and FRANC2D/L results for selected applied
loads.
FRANC2D/L User's Guide
Menu Reference Guide
Page 55
Since a single material
point is sufficient to
model the problem, only
Plane Stress Tube in Tension/Torsion
one Q8 element in a
0.05
single
layer
is
0.05
τ=2
necessary
for
a
0.04
FRANC2D/L
model.
0.04
Create a mesh with a
0.03
single
square
Q8
element aligned with
0.03
the coordinate axes.
0.02
τ=1
After
starting
the
0.02
FRANC2D/L program,
Analytical Solution
0.01
select
the
PREFranc2D/L Result
τ=4
0.01
PROCESS
menu
0.00
option. Set the problem
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
type to plane stress.
Shear Strain
Create a new von Mises
material and set the
material properties as
described above. Since the problem will use applied traction loading, the
thickness can be any reasonable finite value. For the results presented in
this tutorial a value of t = 1.0 was used. Use the SWITCH ALL option of the
von Mises material page to switch the element material properties to the new
von Mises material.
Apply fixity boundary conditions as shown in the figure below. The bottom
side of the model should be fixed in the Y direction, and one point on the
bottom edge should also be fixed in the X direction. This allows both pure
shear and axial loading.
X,Y
Y
Y
Next apply the traction loading for the problem. We will take advantage of
multiple load cases in FRANC2D /L to apply the nonproportional loading
necessary for this problem. First apply an axial load of 26.25 ksi in the X
direction. Use the X-GLOBAL option in the LOADS menu and apply a
traction of magnitude 26.25 first in the +X direction on the right side of the
model, then apply a traction of magnitude -26.25 in the -X direction. Apply
these axial loads in Load Case 1. Next we will apply the shear loads, but will
place them in Load Case 2. Select the SHEAR menu option. Apply a
FRANC2D/L User's Guide
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Menu Reference Guide
constant unit shear load on all four faces of the element. The sign convention
for a positive shear load is shown above.
The loading applied in each load case is interpreted as a load increment from
the previous converged state. When a new analysis is initiated the element
state information such as stresses and material hardening parameters as
well as the nodal displacments are zeroed, and the loads take the solution
from the unstressed state to the prescribed loaded state. Since superposition
in the linear sense is not valid for a nonlinear analysis, the separate load
cases are used to advantage as separate load increments that can be
activated and deactivated through a set of load factors. The load factors
provide a scale factor through which the separate load cases are added
together for the total load increment. So at any time any scaled combination
of the separate load cases can be active by setting to zero the load factor for
load cases to be inactive, and setting to nonzero values the load factors of the
active load cases. This provides a convenient mechanism for nonproportional
loading, where (as in this problem) the load progresses in one direction to
some prescribed magnitude, then progresses in another direction.
For this problem the first load increment takes an elastic step from the initial
state to the point of yielding in tension by setting Load Factor (1) to a value
of 1.0 and all others to 0.0. Then successive small steps will be taken in
shear, maintaining the axial loads at a constant value by setting Load Factor
(1) to a value of 0.0 and Load Factor (2) to a value of 1.0. This represents the
nonproportional aspect of the loading.
Set the following analysis control parameters in the CONTROL PARAM
menu:
Load Sub-Steps
Global Tolerance
Max Iterations
Load Factor 1
Load Factor 2
Accelerate Iter
New Analysis
Save Frequency
1
0.0001
500
1.0
0.0
Secant
YES
0
These are the control parameters for the first step in tension to the yield
point. Use ANALYZE ONE to take this first load step. Return to the POSTPROCESS menu to verify that the current stress state is uniaxial tension
with an X stress of 26.25 ksi, then return to the CONTROL PARAM menu to
change the control for the shearing load steps. Change the following
parameters’ values:
Load Sub-Steps
2
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Menu Reference Guide
Load Factor 1
Load Factor 2
Final Step
0.0
1.0
100
This will provide an analysis step of 0.5 ksi in the shear stress, while holding
the axial stress constant. Use the strain option of the POINT INFO menu
during post-processing to check the strain results after applying four steps
with the 1 ksi shear stress load. The results will be comparable with the
results in the table below for Tau = 4.0.
Tau
1
2
3
4
5
10
20
30
40
50
Eps (Franc2D/L)
0.00111
0.00171
0.00271
0.00401
0.00571
0.01771
0.04761
0.07461
0.09691
0.11541
Eps (Exact)
0.00111
0.00171
0.00271
0.00411
0.00571
0.01771
0.04771
0.07491
0.09721
0.11581
% Error
-0.02
-0.03
-0.07
-0.13
-0.16
-0.26
-0.35
-0.36
-0.35
-0.33
Gamma (Franc2D/L)
0.00011
0.00031
0.00071
0.00141
0.00231
0.01341
0.06611
0.14421
0.23431
0.33041
Gamma (Exact)
0.00011
0.00031
0.00071
0.00131
0.00231
0.01321
0.06571
0.14371
0.23371
0.32981
% Error
2.45
3.57
3.56
3.19
2.79
1.52
0.64
0.37
0.25
0.18
FRANC2D/L User's Guide
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Menu Reference Guide
FRANC2D/L Menu Reference Guide
This section of the manual describes the menu options available in the
FRANC2D/L program. These are grouped as: the main page, preprocessing
functions, modification functions, postprocessing functions, and fracture
mechanics functions. This follows the organization of these options in menu
pages in the program. If the plate bending option is used, the menu options
will include Z loads, displacements, rotations as appropriate.
Main Page
One begins and ends a work session in FRANC2D/L on the main page as
shown below. The menu on this page contains all the principal control
functions for navigating through FRANC2D/L. Each of these will now be
described.
FRANC2D/L
KSU-Cornell
PRE-PROCESS
FRacture ANalysis Code
Version L1.4
MODIFY
ANALYSIS
POST-PROCESS
ANNOTATE
EL/NO INFO
READ FILE
WRITE FILE
- LAYER +
RESET
- ZOOM +
Active Layer : 1
PAN
a SNAP d
- <-- tolerance --> +
END
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Menu Reference Guide
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PRE-PROCESS
This button activates the pre-processing page whose functions are described
in detail in the PREPROCESSING Functions section, below. Some of the
typical functions used here are specifying the problem type (plane stress,
plane strain, axisymmetric, or plate bending), material properties, and
boundary conditions.
MODIFY
This button activates the modify page whose functions are described in detail
in the MODIFICATIONS Functions section, below. Some of the typical
functions used here are adding and deleting elements, initiating and
propagating cracks, adding non-linear interfaces, and adding adhesives and
rivets for load transfer between layers.
ANALYSIS
This button activates the analysis page which contains three options:
DIRECT STIFF, DYN RELAX, and EQuatioN NUMber. The user should
hit this button when the preprocessing stage is complete and a solution is
sought.
DIRECT STIFF invokes a standard Gauss elimination type solver for linear
problems. DYN RELAX invokes a dynamic relaxation solver used for
problems containing non-linear interface elements. EQuatioN NUMber
displays the equations associated with each degree of freedom.
POST-PROCESS
This button activates the post-processing page whose functions are described
in detail in the POSTPROCESSING Functions section, below. Functions
used from this menu include review of fracture mechanics information such
as stress intensity factors and stability diagrams, as well as various methods
of extracting response data, such as line plots, stress bars, contour plots, and
point and node data.
ANNOTATE
This button activates the annotate page which allows the user to see element
(face, in topological jargon), node, and edge numbers, fixity conditions, and
the location of crack tips. Each of the buttons on this page toggles the item
displayed on-and-off.
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ELement/NOde INFOrmation
This button allows the user to see information about an individual node or
element. When a node is selected, its number, coordinates, equation
numbers, and displacements for each load case are displayed in the program
control window. When an element is selected, similar information is
given.
READ FILE
This button allows the user to input another problem, or restart the current
one, without terminating a FRANC2D/L session. When the button is hit, the
request for this function must first be CONFIRMed or REJECTed. If
confirmed, the name of the desired file is input into the program control
window via the keyboard.
WRITE FILE
This button allows the user to save the current problem for later reuse. The
problem is given a file name in the program control window via the
keyboard.
- LAYER +
This button allows the user to change the active layer. All operations, such
as setting boundary conditions, are applied to the active layer. Selecting the
layer allows the analyst to move through the layers.
RESET
This button allows the user to RESET the original image of the entire
structure in the operations window. It is convenient to use after the PAN,
ZOOM, or MAGNIFY functions described below.
- ZOOM +
This button allows the user to enlarge (+) or shrink (-) the size of the image
of the structure in the operations window. The button itself is a rheostat:
hitting at the extremes of the button causes rapid enlargement (or
shrinking). Hitting near the center of the button causes slow enlargement
(shrinking). An incremental change in the size of the image occurs with each
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click of the mouse button. The ZOOM function is one method of enlarging
the size of the image. Another is described next within the PAN function.
PAN
This button allows the user to translate the image of the structure within the
operations window. The image will translate towards the point in the
operations window at which the cursor is placed when the mouse button is
clicked.
When this button is hit, a new menu appears with two buttons: QUIT and
MAGNIFY. QUIT returns one to the Main Page. The MAGNIFY function
is the second, more rapid, way to enlarge a portion of the image of the
structure in the operations window. Two points defining the opposite
corners of a box around the area to be enlarged are requested. The smaller
the distance between these points, the greater will be the magnification.
a SNAP d
Creates a PostScript ® file containing the contents of the operations window if
d is selected, or the auxiliary window if a is selected.
END
Hitting this button is the first step in terminating a session with
FRANC2D/L. The next step is to hit the CONFIRM button which then
appears. If the END button is hit mistakenly, hitting the REJECT button
which follows will return the user to the Main Page.
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PREPROCESS Functions
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PREPROCESSING Functions
PRE-PROCESS →
PROBLEM TYPE
FIXITY
CONSTRAINTS
MATERIAL
APPLD DISP
LOADS
SINGULARITY
It should be understood that FRANC2D/L does not
create the original mesh. The user must create the
model, without any cracks, by means of an external
mesh generator. Translators are available for CASCA
PATRAN and ANSYS mesh generators. All other
preprocessing functions can be performed within
FRANC2D/L.
In the preprocessing stage the user is able to create/modify the boundary
conditions (known displacements, loads, stresses or strains), define/undefine
materials (one model can consist of several different materials) or
define/undefine crack tips. The pre-process command is the upper most one
on this menu. By hitting this button, one moves onto the preprocessing
menu page. The options here are, from top to bottom: PROBLEM TYPE,
FIXITY, CONSTRAINTS, MATERIAL, APPLD DISP, LOADS, and
SINGULARITY. The following is a description of each of these commands.
PROBLEM TYPE
This command allows the user to change the current
problem type using plane stress, plane strain or linear
bending assumptions.
For layered structures,
axisymmetry is not valid and so is not an option for
problems with more than one layer.
Bending
analyses are not allowed for models that contain Q8
elements. Only six noded triangles are allowed for
bending analyses. The Q8 TO T6 option splits all Q8 elements in the model
into two T6 elements so that bending can proceed on the current model.
PRE-PROCESS →
PROBLEM TYPE →
PLANE STRESS
PLANE STRAIN
AXISYMMETRIC
BENDING
Q8 TO T6
FIXITY
This command enables the user to FIX (or FREE)
known zero displacement degrees-of-freedom (DOF).
These processes can be made node-by-node, or along
edges of the boundary.
It is possible to fix/free
independently selected nodes or fix/free edges. FIX
INDependent allows the user to independently fix selected DOF's. FIX
EDGE allows the user to fix DOF's along an edge.
PRE-PROCESS →
FIXITY→
FIX IND
FIX EDGE
DELETE ALL
The first time this command is selected, the fixities produced by the external
mesh generator or by a previous run of FRANC2D/L are shown. This is done
graphically by means of the letters X, Y, or XY displayed on the restrained
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nodes. If it is desired to FREE a previously fixed node or edge segment, one
only needs to reselect that node or edge to toggle the fixity off. Alternatively,
the DELETE ALL option removes all fixity in the current layer.
The procedure for picking a node consists of positioning the cursor on the
desired node and clicking the button once. The first time this is done, a
square will appear at the cursor's location, and a search will be made for the
node inside that box. In order to select only the desired node, it may be
necessary to reduce or enlarge the size of the box.
A prompt will now appear in the message window: "tolerance" with minus
and plus signs. By clicking the cursor on the proper side, plus or minus, the
box will be enlarged or reduced to surround only the desired node. In the case
of individual fixities, once a node, or series of nodes, is selected, it is
necessary to point to the DONE command in the bottom section of the menu
to return to the new fixity option. Once the DONE option is selected the
fixities are drawn graphically, so the user can accept or reject those shown.
An edge specification consists of selecting the initial, adjacent and final nodes
along the segment for which fixity is desired. The specification of the
adjacent node informs FRANC2D/L of the direction one wants to follow along
the edge. It should be noted that FRANC2D/L uses only quadratic order
elements (Q8, 8-noded quads, and T6, 6-noded triangles, and I6, 6-noded
interface elements), so the "adjacent" node will be a midside node.
CONSTRAINTS
CONSTRAINTS allows the user to specify that groups
of nodes or edges are constrained to have the same
displacements. The user can either specify constraints
on individual nodes (CONS IND) or constrain edges
(CONS EDGE). Specification is similar to the fixities
described above. Each constraint is given a group identification that is
displayed when the constraint is active. The user can scroll through the
constraint groups using the - GROUP + button. Constraints can be applied
across different layers. DELete GROUP allows the user to remove a
constraint group in the current layer.
Change the layer to remove
constraints from the same group in different layers.
PRE-PROCESS →
CONSTRAINTS→
CONS IND
CONS EDGE
MATERIAL
FRANC2D/L User's Guide
PREPROCESS Functions
PRE-PROCESS →
MATERIAL→
- MAT +
NEW MAT
E
Nu
THICKNESS
KIc
DENSITY
properties.
Page 64
This option enables the user to specify material type
and properties. A separate window is created to echo
the material properties selected. Default, isotropic,
elastic properties are initially displayed in this window.
Besides the most common ELASTic ISOTROPIC and
ELASTic ORTHotropic types, the user can define a
Non Linear INTERFACE material. The user can
also specify the RIVET stiffness and the ADHESIVE
The first button in the command menu, - MATerial +, scrolls through all
existing material sets.
To create a new material set, hit NEW MATerial. You will then be prompted
for the material type desired. Whenever a material property set is displayed
in its own window, the abbreviation for each of the corresponding material
properties appears as a button on the control menu. For example, for an
ELASTic ISOTROPIC type the command zone has the E (Young’s
modulus), Nu (Poisson's ratio), THICKNESS, KIc (plane strain fracture
toughness) and DENSITY. If the user wishes to modify a value, hitting that
button will cause the keypad to appear for entering the new value.
The SWITCH ELEMent button allows the user to change the initial
specification of an element's material. The first time that this is selected, the
mesh is shown with the material type number enclosed in each element.
Clicking into an element will change the original properties to the current
property set number shown in the auxiliary material information window.
The button SWITCH ALL allows the user to change the material
specification for all elements to the current one.
For an ELASTic ORTHOTROPIC material the requested (and displayed)
properties are: E1, E2, E3, (Young’s moduli in the principal material
directions 1,2,3 respectively), G12, (Shear modulus in 12), Nu12, Nu13,
Nu23, (Poisson's ratios in their respective directions), the angle BETA (the
angle in degrees between the global X-axis and the 1-principal material
direction, measured positive CCW), THICKNESS, KIc1 and KIC2 (the
principal material toughnesses against propagation in the 1- and 2-directions,
respectively. The toughness is assumed to vary elliptically between these
two directions), and DENSITY.
The Non-Linear INTERFACE button defines a combination of nonlinear
models for normal and shear stiffnesses. The NORMAL button is used to
define the normal stress/COD model attached to this material type. The
SHEAR button is used to specify the shear stress/CSD model,
and
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PREPROCESS Functions
THICKNESS to input thickness. The SWITCH INTerFaCe button is used
to change all interface elements models to the current one.
The optional models for normal stress/COD are LINEAR and USeRDEFINED. The input data for these models is made in the program
control window via the keyboard. For example, if the user selects LINEAR
then in the program control window will appear the message:
************************************************************
>>>>>>>>>>>>>>>>>>>>>>>>>> NORMAL<<<<<<<<<<<<<<<<<<<<<<<<<<<
Input for linear elastic behavior in a non-linear interface
************************************************************
and the question:
$ Is this a symmetry interface [Yes-1, No-0]
After the appropriate number is entered, the program requests:
$ What is the stiffness of the interface?
and the appropriate values may be entered.
USeR-DEFINED allows the user to specify a multi-linear stress/COD
relationship. The data is input as pairs of opening/stress data.
As for the normal stress, the optional models for shear stress/COD are
LINEAR, and USeR-DEFINED.
The VON MISES material model has been added to the NEW MAT
materials page. This material is valid for plane stress and plane strain
problem types (as indicated in the material attribute: Problem Type). Note
that the global problem type as specified in the pre-processing page is still
valid and is used as the problem type for all elastic materials. The material
type attribute in the von Mises page is necessary in particular for plane
strain core analyses, which requires two different von Mises materials: one
for plane stress and one for plane strain. The hardening modulus can either
be a constant value (zero or greater than zero representing the slope of the
total uniaxial stress, total uniaxial strain curve), or a multi-linear curve,
starting at (0,0). The multi-linear curve can reside in a file, where the first
line of the file is the number of points in the file, followed by the data points,
one x-y point per line. The first column of data is the total uniaxial strain
and the second column is the total uniaxial stress in units consistent with the
elastic modulus. The yield stress should be specified consistent with the
second uniaxial stress point of the multi-linear curve. The Max Internal Iter
is the number of iterations internal to the plasticity algorithm. The default is
usually appropriate for most problems. If this maximum is exceeded, there is
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probably a problem somewhere else in the analysis (e.g. load step is too large,
or other parameters have inappropriate values).
APPLD DISP
This option allow the user to input applied
displacements along boundaries and at interior nodes.
Applied displacements automatically add loads to load
case one and are incompatible with other load types,
therefore, load case one must be empty to use applied
displacements. Apply other load types in other load
cases. The PT DISP option is used to apply point
displacements, and the EDGE DISP option is used to apply edge
displacements. DELETE ALL deletes all applied displacements for the
entire model. While displacements are being added the displacement values
are displayed on the screen. Selecting DONE transfers the displacements
into the database and returns to the pre-process menu. Note that all applied
displacements must be set during one session. The user may reenter the
APPLD DISP menu to view applied displacements, but all applied
displacements will be removed with any attempt to add new displacements to
the current set, thus forcing the user to start over.
PRE-PROCESS →
APPLD DISP→
PT DISP
EDGE DISP
DELETE ALL
DONE
LOADS
This command allows the user to input various types
of loads into load cases. Up to six load cases may be
input, and any number of load types may be present
in a load case. The options are: -CASE+, DELETE
CASE, POINT LOAD, DIST LOAD, THERMAL
LOAD, RESID LOAD, and RES CRK STR. The
option -DOF+ can be used to view the various
loading degree-of-freedom directions. Following is a
description of each of these commands.
PRE-PROCESS →
LOADS→
- CASE +
DELETE CASE
POINT LOAD
DIST LOAD
THERMAL LOAD
RESID LOAD
RES CRK STR
The - CASE + command toggles between different load cases. The loading
conditions for each case are displayed in the message window.
DELETE CASE deletes the current load case in only the current layer. Use
this option in each layer to fully delete a load case.
POINT LOADS allows the user to specify the location and magnitude of
point loads. After selecting this menu button, the user is prompted for the
magnitudes in the X and Y directions. These are input via the keypad which
appears at the bottom of the menu window. To select a numerical value, the
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cursor is positioned on the desired number and clicked. This will display the
number in the keypad display window. If the number is correct, the keypad
ENT key is then clicked. If the number is incorrect, it is possible to correct it
with the keypad ARROW key. Sign change and exponentiation may also be
performed in the usual way with the keypad.
After the magnitudes are entered, the cursor is clicked on all the nodes
which are to receive them. Any number of nodes may receive point loads. To
finish this option DONE is then clicked.
With the DISTributed LOAD option the user can enter different boundary
pressure types. According to their effect on the sides of the loaded elements,
these types are classified as NORMAL, SHEAR, X GLOBAL and Y
GLOBAL. The distribution of the loading can be CONSTANT, LINEAR or
QUADRATIC, for all the four types.
The elements to be loaded are indicated by the specification of initial,
adjacent and ending nodes, as in specifying fixities. In the input of initial or
adjacent nodes, if the cursor box is too large, it is possible that more than one
node may be selected. In this case you will be asked which node is desired
through the TOGGLE NODE menu button. When the correct one is
indicated by arrows, it is selected by the ACCEPT menu button.
The magnitudes of the distributed load are input via the keypad. LINEAR
asks for the values of the pressure at the initial and the ending point of the
distribution. QUADRATIC asks for the magnitude at the initial and ending
points and requests the location, as a fraction between 0.0 and 1.0, of the
third pressure point, as well as its magnitude. The calculated values of the
equivalent nodal loads are then displayed adjacent to all loaded nodes.
The THERMAL LOAD option is used to apply two different simple types of
element based thermal loads.
The first is based on a MATERIAL
DISTribution. A temperature and coefficient of thermal expansion are
specified for each material in the model. These are then used to create a load
case during the analysis.
The ELEM DIST option is more general, but still implemented on an
element basis. Up to ten regions can be defined by defining a region from a
box (as in the magnify option to the pan button), or by pointing to elements
and adding them to a region. Each region will have a temperature and a
coefficient of thermal expansion defined that will be used to create a load
case during the analysis.
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SINGULARITY
This command allows the user to specify nodes to define/undefine as crack
tips. It is useful for situations in which the mesh around a crack is rebuilt
manually, and it is desired that all the elements with a node at the crack tip
be made singular through the quarter-point procedure. FRANC2D/L cannot
automatically propagate a crack along a line of symmetry, and this is a
situation in which this function may be useful. It may also be used to create
a point of r1/2 singularity under a point load, at a re-entrant corner, etc.
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MODIFICATION Functions
MODIFICATION Functions
MODIFY →
ADD ELEM
KILL ELEM
DRAG NODE
NEW CRACK
MOVE CRACK
SUBDIVIDE
SHOW ANGLE
INTERFC:ON/OFF
ADD NL INTERFC
ADD ADHESIVE
MORE OPTIONS
The modify page allows the user to modify both the
geometry of the structure and the mesh. Modifications
may involve addition/deletion of individual elements,
dragging of nodes, initiation and propagation of cracks,
and creation of material interfaces or boundary
contacts.
ADD ELEM, KILL ELEM, DRAG NODE
These buttons allow the user to alter the mesh by
adding and deleting individual elements and dragging nodes. These buttons
are intended for minor mesh modification when the user does not wish to exit
the FRANC2D/L code and re-run the mesh generator. When adding
elements, be sure to first kill any elements lying in the region where the new
elements are to be placed. The act of killing elements results in the creation
of new boundary segments which can be seen by clicking on the
BOUNDARY button during element deletion. Note that midside nodes,
although not displayed, can also be dragged. Rivets are added and killed in
this menu.
NEW CRACK, MOVE CRACK, SUBDIVIDE, SHOW ANGLE
These buttons relate specifically to fracture mechanics operations. They
allow the user to initiate and to propagate edge or internal cracks, perform
convergence studies by refining the mesh adjacent to a crack tip, and display
suggested propagation directions.
Before describing the steps necessary to initiate and propagate cracks, a note
on semantics is necessary. As a crack grows, it creates new boundary
segments, either by moving into the structure from the external boundary, or
by initiating fully internal to the body and starting a new internal boundary.
The NEW CRACK button allows the user to initiate a new crack from a
corner node of an element on the boundary of the structure. This crack is
NON-COHESIVE, that is, there are no stresses on the crack face.
The MOVE CRACK button allows the user to propagate an existing crack by
locating a crack tip node at a new location. Two options are available for
propagation: STANDard METHod, and AUTOMATIC.
With the NEW CRACK button, after specifying if the crack is cohesive or
not, the user may initiate a crack from a boundary using EDGE CRACK, or
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MODIFICATION Functions
Page 70
completely internally using the INTERnal CRACK button. When initiating
a crack with the EDGE CRACK button, the crack must start at an existing
element corner node (not midside node) on the boundary of the body. The
new crack tip can lie anywhere within the structure. When initiating a crack
with the INTERnal CRACK button, both crack tips must lie somewhere
within the structure.
Once a crack is specified, the program will delete elements near the projected
crack path (maintaining both material and structural boundary information),
insert a rosette of eight, quarter-point, T6 elements about the crack tip, and
then mesh the deleted region using a quad-tree algorithm which produces
well-formed T6 elements. The automatically generated mesh is shown to the
user for approval.
The user may ACCEPT the mesh as proposed, or re-run the remeshing
algorithm with altered initial conditions. The user may ADD NODES to the
deleted region. (The algorithm will use these nodes along with additional
nodes which it will generate automatically.) The user may also KILL
ELEMents, thereby enlarging the deletion region and giving the remesh
algorithm more space in which to operate. Finally, the user may REFINE
INTERFace which will add more nodes to all the material interfaces in the
deletion region. One rule of thumb to keep in mind is that the remeshing
algorithm works best when the characteristic lengths of the elements in the
region into which the crack is propagating are about the same as the length of
the crack increment.
The SUBDIVIDE button allows the user to perform convergence studies by
refining the mesh adjacent to a crack tip. The original T6's are shrunk and
additional Q8's are added.
The SHOW ANGLE button displays the computed direction of propagation
for a crack tip. The analysis results of the cracked configuration are used to
compute the mode I and II stress intensity factors which are used in a closedform expression which determines this direction from the maximum
circumferential stress around the crack tip. During crack propagation, if the
analysis results are available, this suggested propagation angle is also
displayed giving the user the option of propagating the crack by an
incremental distance along that line.
INTERFaCe : ON/OFF
The INTERFaCe : ON/OFF button allows the user to turn on and off the
display of the structure interfaces. All edges between two different material
types are displayed.
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ADD NonLinear INTerFaCe
The ADD NonLinear INTerFaCe button allows the user to modify the
structure by the addition of an interface using interface elements. The
interface must start and terminate on the boundary of the structure. It is
inserted element-by-element following the instructions which appear in the
prompt window. Note that a material property set for the interface must
first be created via the preprocessor's MATERIAL button before this function
can be activated. If the interface to be created has non-linear behavior, the
ADD Non-Linear INTerFaCe button must be selected.
ADD ADHESIVE
ADD ADHESIVE allows the user to specify adhesives between layers. Note
that the adhesive is defined in the top layer of the layers joined by the
adhesive. The adhesive is associated with elements which can be selected
individually or for an entire layer.
MORE OPTIONS
MORE OPTIONS brings the KILL INTerFace button and the BI-MAT
NL-INTF button. These allow the user to delete an interface from the mesh
and to add non-linear interface elements along an existing bi-material
interface. The T6 TO CQ8 and CQ8 TO T6 options convert a crack tip from
quarter point elements into the collapsed Q8 elements sometimes used during
elastic-plastic analyses.
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POSTPROCESSING functions
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POSTPROCESSING Functions
POST-PROCESS →
- CASE: ALL
FRACT MECH
LINE PLOT
CIRCLE PLOT
RADIAL PLOT
REACTIONS
STRESS BAR
CONTOUR
DEFORMD MESH
POINT INFO
NODE INFO
-CASE:ALL+
This button allows the user to select a load case. The
remaining functions of this page will be performed for
the selected load case.
FRACTure MECHanics
By hitting this button, the post processor tools related
to fracture mechanics analysis are made available to the user. A new page
with a menu of options is displayed. See the FRACTURE MECHANICS
FUNCTIONS described below.
LINE PLOT
To invoke the line-plot option, the user is first required to input the starting
and ending points of an arbitrary line. The coordinates of these points may
be provided by clicking at the desired positions with the mouse or by entering
the numerical values of the coordinates via the keypad. After the line is
specified, the DONE button must be hit. If the user decides to quit this
function, they should select the QUIT option. The user may then specify
NEW LINE and repeat the previous step to get a new line of reference.
Plots that may be displayed along the specified line include SIGXX, SIGYY,
SIGXY, NORMAL, SHEAR, DISPlacementS, STRAIN, and, in the case of
adhesives between layers, shear stresses in the adhesive. Since the analysis
is elastic, only total response is available for plotting. The user selects one of
the options and the selected distribution of stress is automatically displayed
in an auxiliary window. There are also the options INTEGRATE to
compute the equivalent load along the line, and FILE to store the plot in a
file. For the latter, the user is requested to enter the name of the file in the
program control window and then return. It is possible not only to obtain
distributions of the same stress component along different lines, but also to
display different stress components plots for the same line. The option QUIT
returns control to the postprocessor page.
CIRCLE PLOT
FRANC2D/L User's Guide
Page 73
POSTPROCESSING functions
The user is first required to specify the center of the circle along which the
plot will be provided. This may be done by simply hitting at the desired
position with the mouse, by entering the point coordinates through the
keypad, or by selecting an existing NODE. Then the radius of the circle is
requested. A new menu with the options to be plotted is then generated.
NEW CIRCLE is available to change the plotting path (in this case center
and radius should be provided again).
The options available are SIGXX, SIGYY, SIGXY, SIGRR, SIGTT, SIGRT,
UDISP, VDISP. X and Y refer to the global axes of reference, while R and T
to the local polar coordinate axes. The INTEGRATE and FILE options are
also available. Press the RETURN button to go back to the postprocessor
page.
RADIAL PLOT
An existing node around which the radial plot will be displayed is first
selected. Then the ending point is input. The ending point may be placed in
an arbitrary position. The position of this point is specified with the mouse or
through the keypad option. Then a new menu page is displayed with the
options for the radial plots. The function NEW LINE is available for
changing the radial line.
The user has the options: SIGXX, SIGYY, SIGXY (with respect to the global
axis) and SIGRR, SIGTT, SIGRT (with respect to the local polar system of
reference), as well as UDISP and VDISP. The option FILE may be selected
to store the displayed plot information in a file. By hitting QUIT, the user
returns to the postprocessor page.
REACTIONS
These functions allow the user to specify edges or faces and calculate their
respective total reaction force. This is useful in checking convergence of the
dynamic relaxation solution, reactions for surface areas with adhesives and
reactions due to rivets (rivet reactions are also available using NODE-INFO
on the rivet node. Watch out for unexpected results. Remember that any
node touching an edge or face specification will be included in the reaction
total. If you accidentally include a node that has an applied force, that force
will be included in the total. The algorithm has been modified to give the
correct results for either linear or non-linear problems.
Hit RETURN to go back to the postprocessor page.
FRANC2D/L User's Guide
POSTPROCESSING functions
Page 74
STRESS BAR
The stress bar option displays the tensile (TENSION) and/or compressive
(COMPRESSION) stress flow in the structure, by displaying vectors of
principal stresses at each gauss point. The user has the option of turning the
mesh off by selecting the BOUNDARY button. CHanGe BOUNDS allows
the user to specify the upper and lower bounds of the plots. Hit RETURN to
return to the postprocessor page.
CONTOUR
By selecting STRESS, contour plots of stress components (SIGXX, SIGYY,
SIGXY), principal stresses (SIG 1, SIG 2), maximum shear stresses (TAU
MAX), effective stresses (EFF STRESS) and strain energy density (STN E
DENS) may be displayed. If an adhesive is being used, the user can also plot
shear strains (ADH_TAU ZX, ADH_TAU ZY). Finally, the user can plot
displacements (DISP U, DISP V). The user is expected to make a selection
and the plot contour of the selected item is provided. A color scale is
presented in the auxiliary window. The CONTOUR ConTroLS option
controls plot color, mesh display, and the deformed contour/mesh. Hit
RETURN to go back to the postprocessor page.
DEFORMeD MESH
This option provides the deformed shape of the structure for the existing load
cases. The -CASE+ button allows the user to select the load case for which
the deformed shape is sought. The DEFAULTS option recovers the default
values used to build the deformed shapes. The VALUE option allows the
user to change the magnification factor used. DEF-DASHED displays the
deformed shape in dashed lines. DEF-BOUND displays only the boundaries
of the deformed shape. ORG-OFF turns off the original structure drawing.
ORG-SOLID displays the original structure in solid lines. ORG-FULL
turns on the original mesh. The user must hit RETURN to return to the
postprocessor page.
POINT INFO
This option allows the user to obtain point information at any point in the
structure.
The user selects the COMPONENT (STRESS, STRAIN,
DISPLACEMENT) and then can select a point for the information using
either the mouse of the keypad. The information is displayed in the
program control window. Select DONE when finished.
FRANC2D/L User's Guide
POSTPROCESSING functions
Page 75
NODE INFO
This option allows the user to obtain nodal information for all nodes lying in
the same tolerance box. This is a useful option in case of zero thickness
interfaces. In this case two nodes occupy exactly the same position in space.
Node info output includes the reaction forces for rivet nodes.
FRANC2D/L User's Guide
Page 76
FRACTURE MECHANICS Functions
FRACTURE MECHANICS Functions
POST-PROCESS →
FRACT MECH→
- CASE : ALL
DISP CORR SIF
INTERACTION
SIF HISTORY
FATIGUE PLOTS
J-INTEGRAL
MD CRK-CLOS
DUMP SIFs
INTRFC PLTS
-CASE:ALL+
This button allows the user to select a load case to
be used by the other available features in this page.
DiSPlacement CORRelation SIF
Stress intensity factors for a selected crack are
obtained through the Displacement Correlation
Technique and displayed in an auxiliary window. Values for all the
existing load cases are calculated. If there is more than one crack tip, the
user must first select one of them.
INTERACTION
When the interaction option is selected, a new menu is built. Sigma Theta
Maximum (SIG-THETA, the default), G Theta Maximum (G-MAX) and S
Minimum (S-MIN) interaction theories are available. The position in the
interaction diagram of each of the crack tips stress intensity factor pairs is
displayed in the auxiliary window. With the options KEY LOAD FAC and
ADJ LOAD FAC, the user can modify the load factors, or have the program
automatically adjust them to bring the crack with the highest effective
stress intensity to instability, respectively. If RETURN is pressed the
process returns to fracture mechanics page.
SIF HISTORY
The history of the stress intensity factors over the previous steps of
propagation is displayed in an auxiliary window. KI or KII may be
selected. The information can be stored in a file with the option FILE. The
data in the SIF file is formatted, and a post-processing awk script is available
to generate output for external X-Y plots. The RETURN button takes the
user back to the fracture mechanics page.
FATIGUE PLoTS
The Paris crack growth rate model is provided with the history of stress
intensity factors. The model parameters may be adjusted. A plot of crack
length versus number of cycles is then generated in an auxiliary window.
The program may then be queried for the number of cycles for a given
FRANC2D/L User's Guide
Page 77
FRACTURE MECHANICS Functions
increment of cracking, or the crack increment for a given number of cycles.
Press RETURN to go back to the fracture mechanics page.
J-INTEGRAL
Stress intensity factors for a selected crack are obtained through the JIntegral Technique and displayed in an auxiliary window. Values for all
the existing load cases are calculated. If there is more than one crack tip, the
user must first select one of them.
MD CRK-CLOS
Stress intensity factors for a selected crack are obtained through the
Modified Crack Closure Integral Technique and displayed in an auxiliary
window. Values for all the existing load cases are calculated. If there is
more than one crack tip, the user must first select one of them.
DUMP SIFs
Writes the current stress intensities to the operations window.
INTERFaCe PLoTS
Makes a plot of stresses and displacements along an interface.
FRANC2D/L User's Guide
Page 78
FRANC2D/L Software Distribution
FRANC2D/L Software Distribution
The principle means of distributing the FRANC2D/L program is electronically
using anonymous ftp on the internet. This is by far the easiest way to get
the most up to date version of the program for a specific workstation type.
Currently supported workstations are UNIX* on Sun SPARCstation, Silicon
Graphics, DEC Alpha, IBM RS6000, Hewlett Packard, and Microsoft
Windows 95/NT on the INTEL processor.
World Wide Web
Both Kansas State University and Cornell University have web pages to
describe their software development efforts for two and three-dimensional
crack growth modeling.
The home page for FRANC2D/L is at
http://www.engg.ksu.edu/~franc2d/ and the home page for FRANC3D is at
http://pilsner.cfg.cornell.edu. Access through the web is provided to download
executables, documentation, and examples. Use the ftp protocol to peruse
the local directories directly (ftp://ra.me.ksu.edu/pub/franc2dl/).
Anonymous FTP
An anonymous ftp server has been set up at Kansas State University to help
distribute the software. An example session is shown below.
% ftp ra.me.ksu.edu
Connected to ftp.engg.ksu.edu
220 kali FTP server (Version wu-2.4 Wed Apr 20 12:52:09 CDT
1991) ready.
Name (ftp.engg.ksu.edu:swenson): anonymous
331 Guest login ok, send ident as password.
Password: [email protected] (use your user name and host
here)
230 Guest login ok, access restrictions apply.
ftp> cd franc2dl
250 CWD command successful.
ftp> binary
200 type set to I.
You are now in the distribution directory, and should choose the appropriate
subdirectory for your machine. Currently these are:
sun, sgi, alpha, hp, ibm
Doc (contains the user's guide in postscript format and release notes)
Examples (contains example *.inp files for FRANC2D/L)
FRANC2D/L User's Guide
Page 79
FRANC2D/L Software Distribution
Within the Sun directory there are at least three files:
casca.Z
franc2dl.Z
castofranc.Z
These are executable versions of the programs in compressed format (the
compressed versions, "*.Z", are much smaller, and can be restored with the
Unix uncompress command). There may be additional files in the directory
that are vendor specific and/or uncompressed versions. To retrieve a
program use commands similar to those from the following transcript:
ftp> cd Sun
250 CWD command successful.
ftp> get franc2dl.Z (get the FRANC2D/L executable)
200 Port command successful.
150 Opening data connection for franc2dl.Z (1103567 bytes)
226 Transfer complete.
1103567 bytes received in 43.48 seconds (24.79 Kbytes/s)
ftp> get casca.Z (get the casca executable)
local: casca.Z remote: casca.Z
200 Port command successful.
150 Opening data connection for casca.Z (645613 bytes)
226 Transfer complete.
645613 bytes received in 43.73 seconds (14.42 Kbytes/s)
ftp> quit
221 Goodbye.
%
%
%
%
uncompress franc.Z (uncompress the files)
uncompress casca.Z
chmod a+x franc2dl (make the files executable by all)
chmod a+x casca
The FRANC2D/L program is still actively under development, and versions
on the server are updated from time to time. At any given time, the server
may contain different versions for different workstation types.
Source code for FRANC2D/L can be made available by special arrangement.
However, due to the dynamic nature of the code, no attempt is made to keep
updated versions of the source available on the ftp server. In addition, one
should be aware that there is about 6Mbytes of source code. Such a large
program does not lend itself to casual perusal and modification. To arrange
to have a snapshot of the source code made available, send a request to
[email protected]
FRANC2D/L User's Guide
Page 80
Appendix A: Input File Format
Appendix A: Input File Format
If another mesh generation scheme is to be used, the data should be written
in a file in the following format for reading into the software. FRANC2D/L
reads two input file formats: the original single layer FRANC2D format, and
the new multi-layer FRANC2D/L format. Both are described below. One
subtle difference between the two is that for the multi-layer format the
connectivity records are format free, while for the single layer format the
connectivity records are read using a FORMAT statement. The contents of
the control records are also different for the two, and the multi-layer format
contains an extra control record for each layer.
***********************************************************************
**************** MULTI-LAYER PROBLEM FILE FORMAT ********************
***********************************************************************
For multi-layer problems only the material properties are read using
a FORMAT statement; all other records are format free. Note that this
is not the case for the Single-Layer file format below.
=======================================================================
Card Set 1: Title card
Number of cards in set: 1
Problem_title(Char*40) - Title of problem, 40 chars
=======================================================================
Card Set 2: Control card
Number of cards in set: 1
Num_Layers (I*4) - Number of layers in problem
Num_Mat (I*4)
- Number of materials
Prob_Type (I*4) - Analysis type
0 Axisymmetric
1 Plane Stres
2 Plane Strain
3 Linear Bending
=======================================================================
Card Set 3: Material Properties
Number of cards in set: Num_Mat (See Card Set 2)
FORMAT(I5, 14F10.2)
Mat_Type(I*4)
- The material type
1 Linear elastic isotropic
2 Linear elastic orthotropic
If Mat_Type = 1
Young's modulus (R*8)
Poisson's Ratio (R*8)
Thickness (R*8)
Fracture Toughness KIc (R*8)
Density (R*8)
If Mat_Type = 2
Young's modulus in the 1 direction (R*8)
FRANC2D/L User's Guide
Page 81
Appendix A: Input File Format
Young's modulus in the 2 direction (R*8)
Young's modulus in the 3 direction (R*8)
Modulus of rigidity in the 12 direction (R*8)
Poisson's ratio in the 12 direction (R*8)
Poisson's ratio in the 13 direction (R*8)
Poisson's ratio in the 23 direction (R*8)
Rotation angle beta (R*8)
Thickness (R*8)
Fracture Toughness KIc in the 1 direction (R*8)
Fracture Toughness KIc in the 1 direction (R*8)
Density (R*8)
=======================================================================
Card Set 4: Mesh data
Number of cards in set: 1 for each layer
Num_Nodes (I*4)
Num_Elem (I*4)
=======================================================================
Card Set 5: Connectivity
Number of cards in set: Num_Elem for each layer
Elem_Num(I*4)
Material(I*4)
Elem_Nodes(1)(I*4)
.
.
Elem_Nodes(8)(I*4)
- Element number
- Material number for element
- First node number
- Eighth node number
Note: Node numbers should be specified in a counter clockwise
direction, starting at any corner node. If Elem_Nodes has eight
non-zero elements a Q8 is assumed, if 6 non-zero elements a T6 is
assumed. The side nodes are ignored when input to the winged-edge
data base, but are retained for compatibility with existing
software.
=======================================================================
Card Set 6: Nodal Coordinates
Number of cards in set: Num_Nodes for each layer
Node_Number(I*4)
- Node number
X_Coord(R*4)
- X coordinate of node
Y_Coord(R*4)
- Y coordinate of node
Note: Card sets 4, 5, and 6 are repeated sequentially for each
layer in the problem.
=======================================================================
***********************************************************************
**************** SINGLE-LAYER PROBLEM FILE FORMAT *******************
***********************************************************************
The single layer file format differs from the multi-layer file format
in Card 2, the control card, and in the format of Card Set 4, the
FRANC2D/L User's Guide
Page 82
Appendix A: Input File Format
Connectivity.
=======================================================================
Card Set 1: Title card
Number of cards in set: 1
Problem_title(Char*40) - Title of problem, 40 chars
=======================================================================
Card Set 2: Control card
Number of cards in set: 1
Num_Nodes (I*4)
Num_Elem (I*4)
Num_Mat (I*4)
Prob_Type (I*4)
- Number of materials
- Analysis type
0 Axisymmetric
1 Plane Stres
2 Plane Strain
3 Linear Bending
=======================================================================
Card Set 3: Material Properties
Number of cards in set: Num_Mat (See Card Set 2)
FORMAT(I5, 14F10.2)
Mat_Type(I*4)
- The material type
1 Linear elastic isotropic
2 Linear elastic orthotropic
If Mat_Type = 1
Young's modulus (R*8)
Poisson's Ratio (R*8)
Thickness (R*8)
Fracture Toughness KIc (R*8)
Density (R*8)
If Mat_Type = 2
Young's modulus in the 1 direction (R*8)
Young's modulus in the 2 direction (R*8)
Young's modulus in the 3 direction (R*8)
Modulus of rigidity in the 12 direction (R*8)
Poisson's ratio in the 12 direction (R*8)
Poisson's ratio in the 13 direction (R*8)
Poisson's ratio in the 23 direction (R*8)
Rotation angle beta (R*8)
Thickness (R*8)
Fracture Toughness KIc in the 1 direction (R*8)
Fracture Toughness KIc in the 1 direction (R*8)
Density (R*8)
=======================================================================
Card Set 4: Connectivity
Number of cards in set: Num_Elem for each layer
FORMAT(10I5)
Elem_Num(I*4)
Material(I*4)
- Element number
- Material number for element
FRANC2D/L User's Guide
Page 83
Appendix A: Input File Format
Elem_Nodes(1)(I*4)
.
.
Elem_Nodes(8)(I*4)
- First node number
- Eighth node number
Note: Node numbers should be specified in a counter clockwise
direction, starting at any corner node. If Elem_Nodes has eight
non-zero elements a Q8 is assumed, if 6 non-zero elements a T6 is
assumed. The side nodes are ignored when input to the winged-edge
data base, but are retained for compatibility with existing
software.
=======================================================================
Card Set 5: Nodal Coordinates
Number of cards in set: Num_Nodes
Node_Number(I*4)
X_Coord(R*4)
Y_Coord(R*4)
- Node number
- X coordinate of node
- Y coordinate of node
=======================================================================
Card Set 6: Optional Data (Single layer only)
Number of cards in set: Variable
Flag (Character*40)
~~~~~~~~~~
Flag = 'AFIXITY'
Card Set 6a: Number fixed
Number_Fixed (I*4) - Number of nodes with fixity to follow
Card Set 6b: Fixity Values (repeat Number_Fixed times)
Node (I*4)
- The node fixed
Fix_type (I*4) - The Fixity type:
1 - X fixity
2 - Y fixity
3 - X Applied displacement
4 - Y Applied displacement
Value (R*4)
- Applied Displacement Value
~~~~~~~~~~
Flag = 'LOADTYP'
Card Set 6c: Load types
Elem_Nodes(1)(I*4)
- First Load Case load type
.
.
Elem_Nodes(6)(I*4)
- Sixth Load Case load type
1 - No load case applied
2 - Nodal Forces load type
8 - Applied displacements
There are always 6 values in this record.
Note: Load type data should always appear immediately after
FRANC2D/L User's Guide
Page 84
Appendix A: Input File Format
AFIXITY data and before any loads data.
~~~~~~~~~~
Flag = 'ALOADS'
Card Set 6d: Number of loaded nodes
Number_Loaded (I*4) - Number of nodes with Loads to follow
Card Set 6e: Nodal Load Values (repeat Num_Loaded times)
Node (I*4)
Case (I*4)
X_load (I*4)
Y_load (I*4)
-
The
The
The
The
node loaded
load case that contains the load (1...6)
X force to apply
Y force to apply
~~~~~~~~~~
Flag = 'ACRACKS'
Card Set 6f: Number of crack tips
Number_Tips (I*4) - Number of nodes that are crack tips
Card Set 6g: Tip numbers (repeat Number_Tips times)
Tip_node (I*4) - The node number of the tip
Card Set 6h: Number of crack Mouth Nodes (Typically 2*Number_Tips)
Number_Mouths (I*4) - Number of nodes that are crack mouths
Card Set 6i: M numbers (repeat Number_Mouths times)
M_node (I*4) - The node number of the crack mouth node
Card Set 6j: Number of crack Edge Nodes
(Typically 2*Number_Tips)
Number_Edge (I*4) - Number of nodes that are crack edge nodes
Card Set 6k: E numbers (repeat Number_Mouths times)
E_node (I*4) - The node number of the crack edge node
An example file for a two element problem is given below.
Two Element Mesh
1
1
1
1 1.E+07 3.E-01 1.E+00 1.E+00 0 0 0 0 0 0 0 0 0 0
13
2
1
1
8
10
11
13
6
7
4
9
2
1
11
12
1
3
2
5
6
13
1
0.000000E+00
1.000000E+00
2
0.000000E+00
0.000000E+00
3
0.000000E+00
5.000000E-01
4
2.000000E+00
0.000000E+00
5
5.000000E-01
0.000000E+00
FRANC2D/L User's Guide
Page 85
Appendix A: Input File Format
6
7
8
9
10
11
12
13
1.000000E+00
1.500000E+00
2.000000E+00
2.000000E+00
1.500000E+00
1.000000E+00
5.000000E-01
1.000000E+00
0.000000E+00
0.000000E+00
1.000000E+00
5.000000E-01
1.000000E+00
1.000000E+00
1.000000E+00
5.000000E-01
FRANC2D/L User's Guide
Page 86
Appendix B: FRANC2D/L Solver Routines
Appendix B: FRANC2D/L Solver Routines
Linear Equation Solver
The linear equation solver in FRANC2D/L is a virtual memory solver for
symmetric systems stored in skyline format. The first pass of the solver
performs a LDL transpose decompostion on the coefficient array. The second
pass reduces the known vector and backsubstitutes for the unknown.
The coefficient array is stored in profile (skyline) format. In this format, only
the elements of a row between the first non-zero column and the diagonal are
stored. The map between teh logical A(i,j) storage and the profile storage is
contained in two vectors, LowEq and Prof. Each element of the LowEq
vector contains the number of the lowest numbered coupled equation for teh
corresponding equation in the system. That is, the column number of the
first non-zero element of the row. Each element of the Prof vector contains
the offset into the A vector where the corresponding row begins.
The relationship between A(i,j), a(coeff), LowEq(eqn), and Prof(eqn) is
illustrated below:

  a(1)
8

 a(2) a(3)
3 6




=
A(i, j) =


9  
a(4)

 

1 2 3 8 a(5) a(6) a(7) a(8)
a(coeff ) = 8 3 6 9 1 2 3 8
LowEq(eqn) = 1 1 3 1
Prof (eqn) = 1 2 4 5
To find any element of A:
A(i, j) = a(Prof (i) - LowEq (i) + j)
Dynamic Relaxation Solver
The dynamic relaxation solver follows the description given by Underwood.
This essentially performs a dynamic solution, with damping, until all motion
FRANC2D/L User's Guide
Page 87
Appendix B: FRANC2D/L Solver Routines
stops. When that occurs, the desired static equilibrium solution has been
reached. The equations that are solved are:
a = M -1 f - Ku − cu&
where:
a = Acceleration vector
M = Mass matrix (diagonalized in this implementation)
f = External load vector
K = Stiffness matrix
u = Displacement vector
c = Damping coefficient
u& = Velocity vector
In the solution, all elastic terms are gathered into a compact K matrix
storage scheme. Then for each iteration the external load vector is calculated
(including the terms from the interface element tractions) and the matrix
multiplication is performed and subtracted along with the damping terms.
As can be seen, when the acceleration and velocity terms approach zero,
static equilibrium between external loads adn the internal forces has been
achieved.
As programmed, this solution scheme is stable and will converge, however,
convergence may take many iterations. Convergence is fastest for equation
systems where the ratio between the highest and lowest eigenvalues is small
("solid" problems). For systems with a large difference between the highest
and lowest eigenvalues ("bending" problems), convergence is slow for the low
eigenvalue portion of the solution.
FRANC2D/L User's Guide
Appendix C: Version 1.1 Release Notes
Page 88
Appendix C: Version 1.1 Release Notes
Release notes for Franc2D/L v1.1 8/95 - Beta
Summary of Changes
There were numerous changes, enhancements, fixes, etc. to the program for
the August release. Some of the major changes are listed below.
For most systems (the IBM version is unfortunately excluded here) the
program now uses better dynamic memory allocation at startup time. It is
now possible to expand the global memory block (the 'A' array) at startup
time. When the program starts it prints a message:
Memory allocated: 5000000
indicating the size of the memory block allocated. If you get a message like
UTL_GET: No free blocks of the requested size
from the memory manager, you can quit the program and restart with a
larger memory block by using the "-mem blk_size" option on the command
line.
Memory management during an analysis is more robust; now if there is not
enough memory during a linear direct stiffness solution, the program
indicates that there was not enough memory and will not continue. See
above for expanding the memory block size.
There is now a check on the maximum number of equations in the model.
The maximum is currently 32767 dof. This is a hard limit that cannot be
changed easily in the code.
Three algorithms are now implemented for stress intensity factors: the
modified crack closure integral, the J-integral, and the displacement
correlation method.
There is now an expanded stress intensity factor history mechanism that
saves a sif history for multiple cracks. The mechanism is not fully
compatible with old .wdb files that have multiple cracks, since these files do
not have a history, except for the first crack.
Automatic propagation has been enhanced to work with multiple cracks in
multiple layers. Previously, it only worked for cracks in a single layer.
FRANC2D/L User's Guide
Appendix C: Version 1.1 Release Notes
Page 89
Worked out some problems related to increasing the number of layers in the
program. Currently, the maximum number of layers is fixed for the program
(default is 5 layers). But we can now recompile for more or fewer layers on
request.
Load types are now saved in the .wdb file, so after a restart, the load type
labels will display correctly in the loads menu.
Internal cracks have been revisited to work with multiple layers, adhesives,
and rivets.
Added applied displacements to the preprocessing menu. A restriction on
applied displacements is that they must be the first load case, and must be
the only loads in that load case. Other load types can be applied in other load
cases.
The terminology and implementation for rivets and adhesives has changed
slightly. For a plane analysis, the rivet only requires a stiffness, which
represents the shear stiffness between the layers. The adhesive requires a
shear stiffness 'G' and the thickness of the adhesive. For a bending analysis,
the rivet now requires an excentricity in addition to the shear and bending
stiffnesses. The adhesive requires an eccentricity, shear stiffness, and
uniaxial stiffness.
FRANC2D/L User's Guide
Appendix D: Version 1.2 Release Notes
Page 90
Appendix D: Version 1.2 Release Notes
Release notes for Franc2D/L v1.2 10/95 - Beta
Summary of Changes
There were several bug fixes and enhancements since the last release, the
most notable of which is the relaxing of the "same mesh" restriction. In all
previous version of the program, for multiple layer meshes, the program
forced the mesh to be the same in all layers. This restriction still holds for
layers that are attached by adhesives. The current version automatically
enforces the mesh to be the same for layers that are attached by adhesives,
and allows the mesh to be different when layers are not attached by
adhesives. An additional condition that must be met is that when rivets are
used to transfer the load between layers, the rivet attachments must be
maintained. The current algorithm looks at all layers above the current
cracked layer for rivets that can attach in the cracked layer. The algorithm
then makes sure that nodes in the new mesh exist to which these rivets can
attach.
Caveats
There are several cases where this algorithm does not work well. One is
when a crack tip passes through a crack tip passes though a rivet in the
current cracked layer. When this happens, the rivet would interfere with the
crack tip geometry, so it is removed from the mesh. A message is printed
that tells the rivet location and material number of the rivet deleted from the
mesh. The message is printed at the completion of the remeshing.
The second case where the algorithm does not work well is somewhat more
forgiving. If a crack tip passes under a rivet that would connect from an
upper layer to the current cracked layer, that rivet is ignored for the current
analysis. The rivet still exists in the upper layer, so the remeshing
algorithm will attempt to reattach the rivet during the remeshing phase of
the next propagation crack step. A warning message is printed at analysis
time for this case that indicates that the rivet did not have an attachment
point in both layers.
Since rivets are restored after remeshing using only geometric information, it
is possible that after a crack tip passes through a rivet location, that the rivet
will be added back in (by chance) on a node on the crack face, or on a node on
the crack tip. It may be a good idea to look at the locations of the rivets
using the Annotate menu after propagation steps to verify rivet locations in
the event that a crack is passing exactly along a rivet row. In the event that
FRANC2D/L User's Guide
Appendix D: Version 1.2 Release Notes
Page 91
a rivet is attached to a node on the crack face, the rivet must be on the
correct side of the face for correct load transfer.
Another possible problem when propagating cracks along a rivet row occurs
when the rivets are close to, but not on the crack face. Here, close is defined
as a distance that is a small fraction (say, less than a quarter) of the
characteristic element size in the region. The result is that elements may be
poorly shaped along the crack face. While this can affect the solution to the
problem, currently there is no option for applying loads to the crack face, so
the crack face is traction free. But the rivets are transferring load to the illshaped elements. So the effect of these ill-shaped elements is not clear.
Some Other Updates and Fixes
Adhesives are now displayed using the adhesive material number, rather
than an X
Now works on systems with multiple screens. This allows the use of screen 1
for instance, on X systems with multiple monitors attached to the same
system.
Fixed several problems related to editing the mesh (deleting elements, adding
nodes) during the remeshing phase of crack initiation and propagation.
When adding adhesive materials, the toggle all now correctly recognizes if
there are elements available for attachment in the next layer.
The color contour color values have switched. The highest stress is now RED
and the lowest is BLUE, so watch out!
Changed the add/kill rivet interface to automatically add/kill if there are no
other nodes in the tolerance. If there are others, a tolerance box is presented
centered at the selected node. Accept will still select that node. The keypad
option takes the more conservative approach of always requiring the Accept.
In addition, the routine also now checks if there is a node under the selected
node, and will not add a rivet if there is nothing to attach to.
FRANC2D/L User's Guide
Appendix E: Version 1.3 Release Notes
Page 92
Appendix E: Version 1.3 Release Notes
Release notes for Franc2D/L v1.3 03/96 - Beta
The primary change for this v1.3 release of Franc2D/L is the addition of
rudimentary elastic plastic analysis capablities. Anyone interested in the
elastic-plastic capabilities should contact us at KSU for more information on
material and analysis control parameters for an elastic-plastic analysis.
While these capabilities have been tested, they will be documented fully at a
later date.
Release notes for Franc2D/L v1.3 04/96 - Beta
The primary changes for the 04/96 update are maintenance updates to fix
some problems with remeshing around interface elements and to fix problems
with adhesive stresses for bending problems. In previous versions the
adhesive shear stresses were only calculated for the membrane component of
the deformation for bending problems. In this version for bending problems
the shape functions of the adhesive element are used to extract the stresses
at the gauss points, then these stresses are extrapolated to the nodes and
used for results post processing. An addition for bending problems is the
ability to plot contours of the peel stress (Sig ZZ) for adhesive problems.
Release notes for Franc2D/L v1.3 06/96 - Beta
The big news here is that there is now a Windows 95/NT version of
Franc2D/L. Don't get too excited; the windows version still looks and works
exactly like the Unix version, it just runs on the Intel architecture.
New Adhesive Formulation in Bending
Also included in this version is a new adhesive element formulation for
bending. The previous bending adhesive element was not giving satisfatory
results for stresses. The solution ultimately was to reformulate the element.
The current version produces much better results for the shear and peel
stresses in bending. The membrane version of the adhesive element has not
changed.
Distributed Loads are Now Tractions
Distributed loads are now applied as traction values, rather than as "load
per unit length," as before. The implication is that values are easier to input,
since you don't need to make adjustments for thickness in plane stress
problems, but since the material thickness is used during the application of
FRANC2D/L User's Guide
Page 93
Appendix E: Version 1.3 Release Notes
the loads, the material thickness must be set before the loads are applied to
get the expected results.
New Menu Structure in Preprocessing
The menu structure of the preprocess menu has changed to better reflect the
order that operations are performed. This was prompted by the change to
the Distributed Loads option described above. The problem type is the most
fundamental setting, and loads are the most dependent on other input data.
Thermal Load
Two new options have been added for basic thermal load. The first is based
on loading on a material basis. A temperature and coefficient of thermal
expansion can be defined for each material. Loads are computed at analysis
time. The second option is slightly more general in that values are assigned
to individual elements.
Other Changes
Node Info now contains all displaceements if the problem is bending.
Delete All option in the Fixity menu to remove all fixity in the current layer.
Individual fixities are applied when the node is hit, rather than in batch
at the end.
During automatic propagation there will always be at least one subdivide tip
performed for each auto step, but the program will resubdivide more than
one if several subdivide tip operations are in place when the auto prop starts.
Manual propagation still performs no subdivide tip automatically.
Fixed several remeshing bugs related to tolerancing when adding elements
and related to problems with remeshing for internal cracks.
The layer version of FRANC2D/L can now directly read *.inp files created
from casca without translation. This is useful for single layer problems,
where no translation is necessary, since multiple layers will not be
superimposed. For multiple layer problems translation is still necessary to
combine the meshes for the separate layers into one file.
FRANC2D/L User's Guide
Page 94
Appendix E: Version 1.3 Release Notes
Appendix F: Version 1.4 Release Notes
Release notes for Franc2D/L v1.4 3/97 - Beta
Summary of Changes
This list of changes and updates is also available from our web site.
Tip numbers in the display now match the tip number in the sif history file
for multiple cracks.
Single layers can now take up the entire
layer to only it's fraction of the database.
layer problem could only occupy 1/5 of the
program compiled for 5 layers. Now the
layers.
database, rather than limit each
For instance, previously a single
database size for a version of the
full database is available for all
A new option in the Annotate menu allow output of an ASCII version of the
current problem (including fixity, loads, and crack definitions) for single layer
membrane only problems. This may be useful for exporting geometry to
other programs for analysis.
For distributed loads, the prompt now refers to tractions, rather than the old
force/length.
The linear direct analysis routines were updated to better utilize memory to
prevent fragmentation. The result is that larger problems may fit without
allocating a bigger memory chunk at startup.
For elastic plastic tearing, there is now an initial critical tearing value that
can be used for sawcut simulations if the specimen was not fatigue precracked.
All of the existing nonlinear interface elements are displayed when interface
elements are added to the mesh.
For edge reactions for results of elastic-plastic analysis, the reactions are
calculated from the integrated gauss point stresses, rather from the linear
elastic f=Kx based on the stiffness and displacements.
For unzipping along a row of interface elements, a change in the interface
material type indicates a boundary in the "crack".
Can now switch material numbers for individual interface elements.
FRANC2D/L User's Guide
Page 95
Appendix E: Version 1.3 Release Notes
Elastic-plastic Unzipping along a row of interface elements.
Orthotropic materials (elastic only) are now supported during a nonlinear
analysis.
Z stress (or hoop stress) is now calculated for all results, so calculated
stresses such as the von Mises stress (Effective stress) are correct for both
elastic and elastic plastic analyses for plane stress, plane strain, and
axisymmetry.
Elastic plastic Multi-site damage modeling. Basically tied nodes can be
defined as "initially released" to simulate discrete fractures along a crack
face, typically called multi-site damage.
Critical crack tip opening angle is now implemented as a material property in
the material page. This is helpful for crack propagation where the crack tip
encounters more than one material along it's path.
Added a non-linear elastic rivet force-displacement relation for the rivet
element type for membrane analyses. The rivet stiffness can now be either a
single stiffness value, or a multi-linear table.
Removed the restriction on the max number of equations at 32767.
Previously INTEGER*2 variables were used to perform equation numbering.
Now, equation numbering is performed on 32 bit quantities, extending the
total number of equations to about 2 million (enough for a while, anyway!).
Along the way the database format was restructured to accommodate a
larger number of "database blocks". Previously, the database was limited to
a total number of nodes, elements and edges below 64000. Now this limit is
also about 2 million. Old database formats are automatically converted.
Reworked some remeshing code that worked for adhesives attached "down"
to the next layer, but didn't work for a crack in a layer with an adhesive "up"
above the cracked layer. Note that there is still a limitation on what the
algorithm can and cannot do, but there are work-arounds to the limitations.
See the update entitled "Some Propagation and Modeling Restrictions"
Adhesives can now be added by toggling all within a bounding box. This
makes it much easier to add or delete adhesives in a large area.
The tolerance box now "almost" always stays the same size after
zoom/pan/magnify operations.
Bending problems require T6 elements, since FRANC2D/L doesn't have a Q8
bending element. The PROB TYPE menu now has an option to automatically
split all Q8 elements into T6 elements "on the fly" to allow a membrane mesh
FRANC2D/L User's Guide
Page 96
Appendix E: Version 1.3 Release Notes
with Q8 elements to be used for bending. Input files (.inp) with the bending
flag set and Q8 elements are automatically split when the input file is read
into the database.
Interface elements that go out of bounds of the traction - displacement curve
now use linear extrapolation on the last segment, rather than just printing
an error message.
The low level X-Windows initialization code was rewritten to better work
with HP workstations. Previously FRANC2D/L wouldn't run on some HP's
with non-standard visuals.
Reaction forces are now available for faces that have adhesives attached.
This is useful to determine the load transfer characteristics in lap-splice
regions.
A limited "batch" option is available for users that want to compile the
program themselves and link in custom initialization routines.
A limited crack tip blunting with collapsed Q8 elements is in place. This
paves the way for possible future elastic-plastic fracture computations.
Crack node "picking" now works on a closest node basis.
Remeshing and propagation across material boundaries now works more
reliably.
Midside nodes are now displayed along with the corner nodes as "dots". The
dots can be turned off from the ATTRIBUTES menu, and are always off in
the POST PROCESS menu.
von Mises for Axisymmetry is now working.
FRANC2D/L User's Guide
Acknowledgements
Page 97
Acknowledgments
Prof. Anthony Ingraffea (Cornell University) has focused on the goal of
developing the ability to rapidly model discrete crack growth for about fifteen
years. FRANC2D/L represents the work of several generations of students:
Prof. Ingraffea modeled discrete crack growth by changing a mesh described
by a deck of computer cards, Victor Sauoma modeled discrete crack growth
on a Tektronix terminal, Walter Gerstle modeled crack growth on an Evans
and Sutherland display, and finally, Paul Wawrzynek (Wash) used a
workstation, started from scratch, and introduced robust data schemes to the
engineers who had come before. Layering has been added by Sudhir
Gondhalekar and Srinivas Krishnan at Kansas State University. Mark
James is continuing to work with FRANC2D/L.
The addition of layers has been supported by the Mechanics of Materials
Branch at NASA Langley Research Center under the direction of Jim
Newman and Charlie Harris. We appreciate comments received from Dave
Dawicke, an early user of the program.
FRANC2D/L User's Guide
Bibliography
Page 98
Bibliography
Broek, D., (1986), Elementary Engineering Fracture Mechanics, 4th edition,
Martinus Nijhoff Publishers.
Henshell, R. D., Shaw, K. G., (1975), “Crack Tip Finite Elements are
Unnecessary,” International Journal for Numerical Methods in Engineering,
Vol. 9, pp. 495-507.
Hill, R., (1950), The Mathematical Theory of Plasticity, Oxford University
Press, London.
Newman, J. C., Jr., Dawicke, D. S., and Bigelow, C. A., (1992) “FiniteElement Analyses and Fracture Simulation in Thin-sheep Aluminum Alloy,”
NASA TM 107662, August 1992, NASA Langley Research Center, Hampton,
VA.
Shaw, R. D. and Pitchen, R. G., (1978), “Modifications to the Suhara-Fukuda
Method of Network Generation,“ International Journal for Numerical
Methods in Engineering, Vol. 12, pp. 93-99.
Shih, C. F., Delorenzi, H. G., and German, M. D., (1976), “Crack Extension
Modelling with Singular Quadratic Isoparametric Elements,” International
Journal of Fracture, Vol. 12, pp. 647- 651.
Underwood, P., (1983), “Dynamic Relaxation,” Computational Methods for
Transient Analysis, Vol. 1, Ed. Belytchko T., and Hughes, J. R, North
Holland, Amsterdam.
Wawrzynek, P., Ingraffea, A. R., (1987), “Interactive Finite Element Analysis
of Fracture Processes: An Integrated Approach,” Theoretical and Applied
Fracture Mechanics, v.8, pp. 137 - 150.
Weiler, K., (1985), “Edge-Based Data Structures for Solid Modeling CurvedSurface Environments,” IEEE Comp. Graph. & App., Vol. 5, No. 1, pp. 21-40.
FRANC2D/L User's Guide
Page 99
Index
Index
- CASE +
- LAYER +
- MAT +
- ZOOM +
a SNAP d
ACCEPT
Acknowledgments
ADD ADHESIVE
ADD ELEM
ADD NODES
ADD NonLinear INTerFaCe
ADH_TAU ZX
ADH_TAU ZY
ADHESIVE
ANALYSIS
ANNOTATE
APPLD DISP
AUTOMATIC
auxiliary window
Bandwidth
Bilinear 4side
BOUNDARY
Boundary Conditions
CHandGe BOUNDS
CIRCLE PLOT
COMPONENT
COMPRESSION
CONSTANT
CONSTRAINTS
CONTOUR
CONTOUR ConTroLS
coordinate system
CRACK INCR
Crack Location
Crack Propagation
cursor
Data Size
deformed contour
DEFORMED MESH
DELETE CASE
DIRECT STIFF
DiSPlacement CORRelation SIF
DISPlacementS
DIST LOAD
DIST. LOAD
DISTributed LOAD
-DOF+
DRAG NODE
DSP CORR SIF
DUMP SIFs
67
41, 61
34, 41
61
62
25
97
43, 72
70
27, 71
72
75
75
34, 42, 65
23, 36, 43, 60
60
67
26, 27, 70
1
23
19
75
20, 34, 35, 42
75
73
75
75
22, 35, 42, 68
64
75
75
2
27
24, 43
26, 44
1
15
75
26, 44, 75
67
23, 36, 43, 60
77
73
67
22, 35, 42
68
42, 67
70
26, 44
78
DYN RELAX
60
EDGE CRACK
25, 71
EFF STRESS
75
ELASTic ISOTROPIC
65
ELASTic ORTHotropic
65
ELement/NOde INFOrmation
61
EQuatioN NUMber
60
Fatigue Crack Growth
28
FATIGUE PLoTS
77
FATIGUE PLTS
28
FILE
74
Files
*.csc
9
*.grf
10
*.inp
9
*.rsp
9
*.wdb
9
gra*.ps
10
Output
10
Restart
9
sif 11
FIX EDGE
21, 35, 42
FIX IND
22, 42
FIXITY
21, 35, 42, 63
FRACT MECH
26, 44
FRACTure MECHanics
73
FRACTURE MECHANICS Functions
77
ftp
79
GENERATE INT PT
40
Geometry
15
Get Circle
16
Get Line
17, 30, 32
Grid
15
Input File Format
81
INT CRACK
25
INTEGRATE
73, 74
INTERACTION
77
INTERFaCe : ON/OFF
71
INTERFaCe PLoTS
78
INTERnal CRACK
71
Introduction
1
KEY INCR
27
KEY POS
25, 27
KILL ELEM
27, 70
KILL ELEMents
71
KILL INTerFace
72
-LAYER+
42
LINE PLOT
73
LINEAR
66, 68
Lines Connect
16, 30, 31
FRANC2D/L User's Guide
Page 100
Index
LOADS
Main Page
MATERIAL
Menu Reference Guide
Mesh
message window
MODIFICATION Functions
MODIFY
MORE OPTIONS
mouse
MOVE CRACK
NEW CRACK
NEW LINE
NEW MAT
No. of Segments
NODE INFO
Non Linear INTERFACE
NON-COHESIVE
Non-Linear INTERFACE
NORMAL
operations window
PAN
POINT INFO
POINT LOAD
POINT LOADS
POST-PROCESS
Postprocessing
POSTPROCESSING Functions
PRE-PROCESS
PREPROCESSING Functions
PROBLEM TYPE
program control window
PROPAGATE
QUADRATIC
RADIAL PLOT
Ratio
REACTION
READ FILE
REFINE INTERFace
RESET
Restart Files
Revert Ratio
RIVET
Set Scale
SHEAR
67
59
20, 34, 41, 64
59
18, 31, 32
1
70
26, 36, 43, 60
72
1
26, 27, 70
25, 70
73, 74
34, 42
18, 31, 32
76
65
25, 70
65
68, 73
1
62
75
67
67
23, 36, 43, 60
23, 36, 43
73
20, 34, 41, 60
63
63
1
27
68
74
18
74
61
71
23, 61
9
18
65
15
68, 73
SHOW ANGLE
SIF HISTORY
SIG 1
SIG 2
SIGRR
SIGRT
SIGTT
SIGXX
SIGXY
SIGYY
SINGULARITY
Software Distribution
Spacing XY
STAND METH
STANDard METHod
STEPS
STN E DENS
STRAIN
STRESS
Stress Analysis
STRESS BAR
Subdivide
Subregions
SWITCH ALL
SWITCH ELEM
SWITCH ELEMent
SWITCH INTerFaCe
TAU MAX
TENSION
THICKNESS
TOGGLE ALL
Tolerance
Transition
Translating
Tutorial
UDISP
USeR-DEFINED
VDISP
VON MISES
WRITE FILE
Write Mesh
X GLOBAL
Y GLOBAL
Young's modulus
70, 71
28, 44, 77
75
75
74
74
74
73, 74, 75
73, 74, 75
73, 74, 75
69
79
15
26
70
27
75
73
75
23, 36, 43
75
17, 30, 32, 70, 71
17, 30, 32
65
20
65
66
75
75
20, 34, 41
36, 43
21
40
19, 32, 40
12
74
66
74
66
23, 36, 43, 61
19, 31, 32, 40
68
22, 35, 42, 68
20, 34, 41
FRANC2D/L User's Guide
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