short

FRANC2D/L: A Crack PropagationSimulator for Plane Layered Structures

Short User's GuideVersion 1.4, May, 1997

Daniel Swenson and Mark JamesKansas State University • Manhattan, Kansas

Page ii Table of Contents

FRANC2D/L Short User's Guide

Table of Contents

Introduction ............................................................................................1

Basics of Implementation..................................................................2Data Structure.................................................................................2Finite Elements................................................................................5

Continuum Elements ...................................................................5Interface Element ........................................................................5Rivet and Adhesive Elements.......................................................5Plate Bending Elements...............................................................5

Layers ..............................................................................................6Material Properties ..........................................................................6Fracture ...........................................................................................6Remeshing During Crack Growth.....................................................7Solution Procedures..........................................................................7Computer Graphics ..........................................................................7

FRANC2D/L Files ....................................................................................9

CASCA and Input Files......................................................................9CASCA *.csc Files.............................................................................9Input *.inp Files ...............................................................................9

FRANC2D/L Restart Files..................................................................9*.wdb Files .......................................................................................9*.rsp Files.........................................................................................10*.epr Files.........................................................................................10*.mon Files.......................................................................................10

FRANC2D/L Output Files..................................................................10*.grf Files .........................................................................................10gra*.ps Files .....................................................................................10sif Files.............................................................................................11

FRANC2D/L Example..............................................................................12

Plate with Hole..............................................................................................................Error! Bookmark not defined.

Building an Initial Mesh with CASCA ..............................................13Performing a FRANC2D/L Simulation..............................................13

Running the FRANC2D/L Program ............................................13Defining the Problem Type ..........................................................14Boundary Conditions...................................................................14Nodal Constraints .......................................................................16Setting the Material Properties ....................................................16Applied Displacements ................................................................17

Table of Contents Page iii


Load Definition ...........................................................................17Perform Analysis.........................................................................17Post-Processing............................................................................18Crack Initiation...........................................................................19Stress Analysis and Fracture Analysis.........................................20Crack Propagation.......................................................................20Automatic Crack Propagation ......................................................21Stress Intensity History ...............................................................22

A Word About Plots.................................................................................24

Acknowledgments ...................................................................................25

Bibliography............................................................................................26

Index.........................................................................................................27

Introduction Page 1


IntroductionFRANC2D/L is an interactive program for the two-dimensional analysis ofstructures. Its capabilities include elastic and elastic-plastic materialresponse, simulation of linear elastic (LEFM) and elastic-plastic crack growth(using the crack tip opening angle approach), analysis of layered structures(such as lap joints or bonded repairs), and a linear plate bending option.

This manual is intended to be a simple description of the basic features ofFRANC2D/L. A more complete manual can be downloaded athttp://www.engg.ksu.edu/~franc2d.

Within the FRANC2D/L program, all user commands are made by clickingthe mouse on one of the options displayed on the menu which always appearsto the right of the operations window (Figure 1). The commands arearranged in a tree, and the user travels up or down to each branch, selectingthe desired option with the left button of the mouse. A message window isalways present below the operations window to prompt the user on thenext step in the requested procedure. For some operations FRANC2D/Lcreates a separate detached movable window called the auxiliary window.At times it may be necessary to move this window in order to viewinformation in a number of windows simultaneously. Entry intoFRANC2D/L, some data entry, and I/O operations invoked during therunning of FRANC2D/L are made from the program control window. Thisis the window from which the program was started.

program controlwindow

$ franc2dFilename:tutorial

auxiliary window

title window

messagewindow

menuwindow

command options

operationswindow

Figure 1: The FRANC2D/L window system

Introduction


The FRANC2D/L program uses two types of cursors. The normal cursor hasthe shape of an arrow. When you see this cursor it means that the programis waiting for you to select a menu option or some other graphical input. Thesecond cursor is a stylized wristwatch. When you see this cursor it meansthat either the program is processing data (e.g., performing a stressanalysis), or it is waiting for input in the program control window.

The coordinate system used within the program is always fixed so that the xand u coordinates are horizontal, increasing to the right. The y and vcoordinates are vertical, increasing going up.

FRANC2D/L is based on the FRacture ANalysis Code (FRANC2D) originallydeveloped by Paul Wawrzynek at Cornell University (Wawrzynek andIngraffea, 1987). FRANC2D represented a significant step in thedevelopment of discrete fracture analysis programs because of its modularsoftware design and topological data structure. The layer, bending, andmodified nonlinear material capabilities have been implemented at KansasState University.

Basics of Implementation

This section provides very brief descriptions of the implementation of thedata base, data structure, and finite element concepts used in FRANC2D/L.Most engineers write finite element programs in which the nodes andelements are the fundamental objects, used to indirectly describe thegeometry and boundary conditions. Such an approach is not adequate formore advanced applications such as crack growth (where the geometry ischanging) or automatic meshing and mesh refinement (where we want to usedifferent meshes for the same geometry). Such tasks require a higher levelgeometric and problem description as implemented in FRANC2D/L.

Data Structure

The core of the program is the data base, Figure 2. This is the repository ofall the information used by the various parts of the program. The data baseis only accessible through the data base access routines. All higher levelroutines are required to use the two types of access routines (modify andquery routines) to store and retrieve information.

Introduction Page 3


The layer above the data base routines is the collection of routines whichimplement the computational functionality of the program. These are looselygrouped into six categories. Pre-processing routines perform modifications tothe model description and boundary conditions. Remesh routines modify theelement mesh for crack propagation. Fracture mechanics routinesimplement the various crack propagation theories and automatic load factormodification. Post-processing routines display stress and displacementinformation. Finite element routines formulate element stiffness matrices,assemble global stiffness matrices, minimize problem bandwidths, solve fordisplacements, and recover element stresses. The numerical analysisroutines perform functions necessary for the solution of systems of linear ornon-linear equations.

Encircling the functional routines is the user interface, which is a collectionof menu drivers and display routines to allow the analyst to interact with theprogram.

The data structure used in FRANC2D/L is designed around a modifiedwinged-edge data structure (Baumgart, 1975 and Weiler, 1985) which wasoriginally developed to store surface topology of polyhedra. The datastructure consists of three topological entities: vertices, edges, and faces.Vertices correspond to finite element nodes, and faces represent finiteelements, Figure 3.

DataBase

Modify

Query

Fracture

Remesh

Post-Process

NumericalAnalysis

Finite ElementAnalysis

Pre-Process

User Interface

Figure 2: Conceptual organization of FRANC2D/L

Introduction


The main feature of this data structure is that each topological entitycontains adjacency information which greatly reduces the time required toperform adjacency queries. The data structure is designed such that mostadjacency queries are edge based, as the multiplicity of elements adjacent toan edge is known a priori, unlike that of a face or a vertex. An edge has twoadjacent vertices, two adjacent faces, and four adjacent edges. The data baseis accessed for modification or for queries.

The local adjacency information embedded in the winged-edge data structureis 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 astructure being analyzed. This allows one to delete elements for crackpropagation without deleting the edges which define the structural boundary.The adjacency information also allows one to identify all the elementsadjacent to a node so if the node is dragged to a different location elementstiffness matrices can be recomputed.

Right FaceLeft Face

Head Vertex

Tail Vertex

Right CW WingLeft CCW Wing

Left CW Wing Right CCW Wing

Figure 3: Winged-edge datastructure

Introduction Page 5


Finite Elements

Continuum Elements

FRANC2D/L uses standard eight or six noded serendipity elements withquadratic shape functions. These elements perform well for elastic analysisand have the advantage that the stress singularity at the crack tip can beincorporated in the solution by moving the side nodes to the quarter-pointlocations (Henshell and Shaw, 1975).

Interface Element

Interface elements are used to represent contact between surfaces. The usercan specify a relationship between surface tractions and the relativedisplacements of the surfaces. This relationship is used to create an elementstiffness matrix or generate contact loads, depending on the solutionprocedure.

Rivet and Adhesive Elements

Rivets are treated as elastic shear springs, where the rivet stiffness is amaterial constant. Rivets can only be introduced at nodes. When a rivetconnects two layers, it must be defined at a node in the upper layer. Thiseliminates the need to interpolate the displacements at a rivet point in orderto calculate the rivet forces. At the same time it allows for efficient storageof information in the data base.

An adhesive element is similar to a rivet element, except that the shear forceis distributed over an entire element and is not confined to a node. It isassumed that the adhesive layer is homogenous, linear elastic, and isotropic.The adhesive is assumed to deform only in shear and this deformation isuniform throughout the adhesive thickness. The surface shear transmittedthrough the adhesive is assumed to act as a surface traction on theadherends.

Plate Bending Elements

FRANC2D/L has a limited plate bending analysis capability. The apparent 2-D mesh can actually represent a plate, with each element being a plateelement. The mesh can be loaded out of plane or bending induced by in-planeloading of layers that are offset in the Z direction (normal to plane). TheDiscrete Kirchoff Triangle element (Cook, Malkus, and Plesha, 1989) is used.A triangular element was selected so that remeshing could be performed withthe standard scheme already implemented in FRANC2D/L. The user iscautioned that only linear bending is modeled, stress stiffening and large

Introduction


displacement effects are not included. If these effects are important, the userwill need to perform a full 3-D analysis using a different program.

Layers

FRANC2D/L can model layered structures, such as riveted lap-splice or abonded joints. In a FRANC2D/L analysis, simplifying assumptions are made,but for many cases the essential features of the response can still becaptured. The assumptions include:

• Each layer is considered as an individual two-dimensional (or plate)structure.

• 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 entireelement of each layer.

• Only linear out-of-plane displacements and bending effects are included ifa plate bending analysis is performed.

As noted, each layer is represented as a separate two dimensional finiteelement mesh. See the complete user’s manual for further discussion oflayers.

Material Properties

Either elastic or elastic-plastic materials can be used in FRANC2D/L. Elasticmaterials can be isotropic or orthotropic. The elastic-plastic material uses avon Mises yield surface with multi-linear hardening.

Fracture

The fracture calculations incorporated in FRANC2D/L use either two-dimensional linear elastic fracture mechanics (LEFM) concepts or (undercontinuing development) the CTOA criterion for elastic-plastic crack growth.The stress intensity factors which govern the fracture process in the LEFMcontext are calculated using the displacement correlation, modified crackclosure, or J-integral methods.

Using LEFM, FRANC2D/L can model quasi-static crack propagation andcrack propagation due to fatigue loading. While the user can select differenttheories for the propagation direction, the one usually used is the sigma thetamax theory [Erdogan and Sih, 1963]. This approach minimizes the mode IIstress intensity during propagation.

Introduction Page 7


The CTOA approach to elastic-plastic crack growth allows the user to find anultimate strength at any crack length by performing an elastic-plastictearing analysis. At this time, crack growth can occur only along pre-definedcrack paths.

Remeshing During Crack Growth

When performing a discrete crack analysis, not only the geometry of thecrack is represented explicitly at each step, but the mesh must be modified ateach step to reflect the current crack configuration. The remeshing strategyadopted in FRANC2D/L deletes the elements in the vicinity of the crack tip,moves the crack tip, and then inserts a trial mesh to connect the new crackto the existing mesh. The modified Suhara-Fukuda algorithm [Shaw andPitchen, 1978] is used to generate this trial mesh of triangulated elements.The user is allowed to modify the mesh if desired, however, this is rarelynecessary. In fact, most propagation analyses use the automatic option,where the crack is propagated for a specified number of steps automatically.

Solution Procedures

Two solution methods are available to the user. The first is a direct equationsolver for symmetric systems stored in skyline format. For nonlinearproblems, the modified Newton procedure is used. The direct solver isusually the preferred solution method. If nonlinear interface elements arebeing used, the user has the option of a dynamic relaxation solver. Thissolver is usually slower than the direct solver, but will always converge fornonlinear contact problems.

Computer Graphics

The FRANC2D/L program maximizes the graphical interaction between theuser and the model by making graphical interaction an integral part of thealgorithms. The ability to see a display of the model being analyzed and viewthe results in a graphical form is a very valuable functionality. The analystinteracts with the program through a menu driven user interface. This is acollection of routines which create and drive menus and call the appropriateaction routines after an analyst chooses a menu option.

The low level graphics routines in the program have been encapsulated in onecollection of routines called the application independent graphics subsystem(GRA). These routines are written in the C programming language to allowportability on UNIX (and Windows 95/NT) platforms. These routines arewritten in a modular fashion whereby the device dependent graphics code issegregated from rest of the graphics code.

Introduction


The fact that FRANC2D was originally written in 1987 is reflected in themenu structure. The menus were designed for display using low levelXWindows commands. This has allowed us to port the code to Windows95/NT in a simple fashion. The advantage is that the Unix and Windows95/NT versions are identical; the disadvantage is that the program does notuse dialog boxes or pull-down menus. We hope you will find the interfaceadequate, if not ideal.

FRANC2D/L Files Page 9


FRANC2D/L Files

There are a number of different types of files generated or used by theFRANC2D/L program. The contents of these files and their uses arediscussed here. In most cases, the *'s in the figure are replaced by file nameschosen by the analyst.

CASCA and Input Files

CASCA *.csc Files

The CASCA program is a simple mesh generating program. Although strictlyspeaking, 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 tosave their current work and recover it later. This is convenient when a meshdescription cannot be completed at one sitting or to make modifications to anexisting mesh. A *.csc file is created when the WRITE option (not WRITEMESH) is selected in CASCA.

Input *.inp Files

The *.inp files define the mesh for a new FRANC2D/L simulation. These arehuman readable ASCII files that describe an initial mesh in a format similarto those used by most other finite element programs. The *.inp file is writtenby CASCA using the WRITE MESH option.

FRANC2D/L Restart Files

The FRANC2D/L program generates two types of restart files *.wdb and*.rsp. Restart files allow one to save current work and recover it later. Thisis convenient when a simulation cannot be completed at one sitting or toreview the results of previous simulations. The FRANC2D/L restart files aregenerated by the WRITE option within FRANC2D/L.

*.wdb Files

The *.wdb files contain most of the information associated with a simulation.This includes the mesh, boundary conditions, cracks, and stress-intensityfactors. WDB stands for Winged-edge Data Base, the data structure used tostore mesh topology and organize most of the other information stored by theprogram. Unlike the *.rsp files, information in the *.wdb file cannot be

FRANC2D/L Files


recovered if the file is deleted. The *.wdb files are unformatted and are nothuman readable.

*.rsp Files

The *.rsp (ReSPonse) files contain analysis results, specifically, nodaldisplacements. This information is stored in a file so the analysis results canbe viewed without repeating an analysis. The files can be deleted to savespace. The information in these files can be regenerated by performing astress analysis.

*.epr Files

The *.epr (Elastic-Plastic Response) files contain the results of a nonlinearmaterial analysis, including stresses and strains. This information is storedduring a nonlinear analysis, at intervals specified by the user, and can beused to restart a nonlinear analysis or to view results when an analysis iscompleted.

*.mon Files

The *.mon (MONitor) files contain temporal monitor results at nodes andelements during an elastic-plastic analysis. Specify nodes and element pointsto monitor in the Monitor menu of the elastic-plastic analysis menu.

FRANC2D/L Output Files

*.grf Files

The *.grf files are created when the FILE option is selected on the line plotpage menu (See the LINE PLOT option). These ASCII format files containthe 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 bylines containing an X-Y data pair.

gra*.ps Files

The gra*.ps files are postscript hardcopy files. These files are created byselecting 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 aregenerated sequentially and automatically by the program. A typical series isgra0.ps, gra1.ps, gra2.ps ... The file number is incremented each time thedata window is SNAP'd. WARNING: The file name sequence startswith gra0.ps each time the program is run and new files will

FRANC2D/L Files Page 11


overwrite old files. All gra*.ps files need to be renamed if they are tobe saved permanently.

sif Files

Sif files contain Stress-Intensity Factor histories. A file name extension isnot generated automatically for these files. The files contain stress-intensityfactors for all cracks for all crack lengths that have been analyzed, in aformatted human readable form. A postprocessing script is available toextract data for XY plots.

Tutorial Example Problem


FRANC2D/L ExampleIn this portion of the manual, the use of the FRANC2D/L program isillustrated. The steps necessary to perform a crack propagation analysis aredescribed. It is intended that you repeat the steps on your computer as theyare described.

The example consists of a plate with a hole, as shown in Figure 4.

The manual describes the steps necessary for the FRANC2D/L program toassign boundary conditions, perform a stress analysis, introduce cracks, andpropagate cracks. There are a large number of options and features availablein FRANC2D/L. Only a subset of these are described in this example.However, the example illustrates the most basic analysis and can give youthe confidence to try other features, which are described in the completeuser’s manual.

0.5 in R8.0 in

4.0"

σ=10,000 psi

E=10.0E6 psiν=0.25thick=0.04 in

σ=10,000 psi

Figure 4: Schematic of plate with hole

Tutorial Example Problem Page 13


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 atypewriter font, such as tutorial.inp.

Building an Initial Mesh with CASCA

Creating the mesh used in this problem is described in the CASCA user’smanual. Alternately, you can download the input file, named plate.inp, fromthe web at http://www.engg.ksu.edu/~franc2d. To do this, you will need toproceed to the software download section of the web page. Place plate.inp inyour desired working directory.

Performing a FRANC2D/L Simulation

Running the FRANC2D/L Program

We now run FRANC2D/L.

Windows 95/NT: Start an MS-DOS window and go to your workingdirectory. From the working directory, type the path to theFRANC2DL executable followed by the input file name (for example“C:\My Documents\Franc2dl\franc2dl.exe plate.inp”).You will be asked whether you want a big or small window, type sto select small. At this point a new FRANC2D/L window will becreated.

Unix: Select the window in which you will run FRANC2D/L. In thatwindow, go to your working directory and type the path to theFRANC2DL executable followed by the input file name (for example“~/Franc2dl/franc2dl.exe plate.inp”). You will be askedwhether you want a big or small window, type s to select small. Atthis point a new FRANC2D/L window will be created.

Note: the above description is appropriate when no restart file is available. Ifyou have saved a restart file (*.wdb), you should use the plate.wdbfilename when running FRANC2D/L. The restart file remembers all yourproblem definition data in addition to the mesh.

Also, note that the executables can be placed in your search path (or aliasesused) so that you only need to type franc2dl to start the program.



When FRANC2D/L starts, the mesh will bedisplayed with the nodes highlighted. This isuseful for node selection, but you may want to turnit off if you have many nodes. To do this, selectANNOTATE, OFF MARKER, and RETURN.The display should now look like Figure 5.

We will now follow the steps to define an analysis.To do this, select PRE-PROCESS and severaloptions will be available.

Defining the Problem Type

Select PROBLEM TYPE to define plane stress,plane strain, axisymmetric, or bending problems.The default is plane stress, so RETURN to thepre-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. Nodescan be fixed either individually, or along an edge.Each node can be fixed in the X direction, the Y, orboth. The fixities work like pushbutton on/offswitches; if a fixity is attached to a node, it can beturned off by reapplying the same type of fixity.

Symmetry on the plate will be enforced byapplying X constraints along the left edge. Selectthe FIX EDGE option and then X. The procedurefor adding a boundary condition to an edge is athree step process:

1. Specify a starting node.2. Specify the adjacent node in the direction toward the ending point.

Note that if you select a corner node as the starting node, theadjacent node will be a mid-side node that is not graphicallydisplayed unless the VERT MARKER option is active in theANNOTATE page.

3. Specify the ending node.

Before indicating the boundary conditions, let us zoom in on the mesh at thebottom of the hole. There are several ways to zoom. The simplest is to just

Figure 5: Initial Mesh



click on ZOOM. Do this several times until you see the mesh around thehole clearly. (Another way to zoom is to select PAN and then MAGNIFY.This allows you to define a zoom box. After defining the box select QUIT toget out of the pan mode.)

We now specify the boundary conditions. Do this by pointing to the node atthe bottom of the hole and clicking. You will see a square. This is thetolerance box. The program attempts to select a tolerance box appropriatefor the current view. If desired the, the prompt window (- <--- Tolerance --->+) can be used to adjust the size of the tolerance box. If you click in thiswindow toward the right, the tolerance box gets bigger; to the left it getssmaller. The closer you are to the left and right edges, the faster thetolerance box will change size.

You should now select an adjacent node.Remember that these are eight-nodedelements, so the next nearest node is a mid-side node. You will want to click at themiddle of the element edge just below thefirst node you selected. Now select RESETto zoom out, and point and click at the lowerleft node on the plate to indicate where theconstraints should stop. The display willshow a series of X's to indicate that all thenodes along the left edge of the patch arefixed in the X direction, Figure 6. Repeatthis for the left edge above the hole.

In addition, we will constrain the Y rigidbody motion of the plate by fixing the Ydisplacement of the center node on the rightedge of the plate. In the fixity page, selectFIX IND, then Y, and finally the node. SeeFigure 7.

RETURN to the pre-process page.Figure 6: X Fixities



Nodal Constraints

Constraints are used to tie different nodes together. We will not useconstraints in this analysis.

Setting the Material Properties

From the pre-process page, select the MATERIAL option. A new windowwill appear, and it may be necessary to rearrange the window to see themenu. The new window contains the material properties for the currentdisplayed material (1) and also gives the total number of materials (1). Thedefault properties are for steel. We will change this because our plate ismade of a aluminum alloy. Select E, and enter the Young's modulus of10.0E6 psi (the EEX key adds the exponent). Select THICKNESS, and setthe thickness to 0.04. The KIc and density are not necessary for a fatigueanalysis so you can leave the default values. To see which elements havewhich material numbers, select SWITCH ELEM. If desired, selectingelements would change their material numbers to the current materialnumber. RETURN brings you back to the material definition page.Selecting RETURN again brings you to the pre-process page.

Figure 7: Y Fixity



Applied Displacements

The user can specify non-zero displacements in the applied displacementspage. We will not do this in our problem.

Load Definition

Select LOADS to enter the loads page. We will apply a distributed load tothe top and bottom of the plate. Select the DIST. LOAD option. There arefour choices for specifying the direction of the load, select the Y GLOBALoption because we want the boundary traction to be in the Y direction.

You now have three options for the form of the load distribution along theedge: constant, linear, or quadratic. Select the CONSTANT option. Wemust now specify the portion of the boundary to load, just as we did for fixity.Select the top left node, the adjacent node just to the right, and the top rightnode.

You must now specify the magnitude of the load. Loads are given astractions. Input the value directly as a traction and the current materialthickness as well as element edge lengths will be used to create equivalentnodal loads. To specify loads that will give a stress of 10,000 psi in the plate,enter 10,000. It is important that the material thickness be set correctlybefore the loads are defined. If you change the material thickness, it will benecessary to respecify the loads.

Repeat for the bottom edge with a traction of -10,000 psi.

We have now specified the boundary conditions. You can RETURN from theload page and the pre-processing page to get back to the main page. This is agood time to save a restart file by using the WRITE FILE option. Use thename plate.

Perform Analysis

We are now ready to do stress analysis. From the main page, selectANALYSIS, LINEAR, and DIRECT STIFF. The program will now performa linear elastic stress analysis using a direct equation solver. This will take afew seconds and the steps are displayed in the terminal window. The stepare:

• Reduce Bandwidth: automatic nodal renumbering to reduce thebandwidth of the global stiffness matrix.

• Zero Gstf: zero the space used for the global stiffness matrix.



• Assemble: assemble the element stiffness matrices into the globalstiffness matrix.

• Decomposition: perform direct elimination of the global stiffnessmatrix.

• Backsubstitution: perform backsubstitution to recover nodaldisplacements.

When the analysis has been completed the program will print a short reportthat summarizes the size of the model and the timerequired for the analysis.

Post-Processing

You can now RETURN to the main page and selectthe POST-PROCESS option to enter the post-processing page. It might be good to RESET the viewif you have not already done this.

The first thing to look at isthe deformed mesh. This isa quick check to see thatthe boundary conditionshave been applied properly.For the plate with holeproblem, the deformedmesh for the plate shouldlike Figure 8.

You can RETURN fromthis page, and select theCONTOUR option. Thisallows you to display colorstress contours. You canview individual componentsof the stress tensor, as wellas principal stresses. Ofparticular interest are thestresses in the Y direction,Figure 9. Note that the CONTOUR CNTRLSmenu on the contour page allows you to displaythe contours on a deformed mesh and to controlthe contour range. There are a number of otherpost-processing features available. When you aredone post-processing, RETURN to the mainmenu.

Figure 8: Deformedmesh

Figure 9: Stress Contours



Crack Initiation

At this point we will put a crack in the plate. First, however, you shouldmake a restart file. Select WRITE and use the name plate_0. This willsave the analyzed uncracked configuration. You may wish to return to thisconfiguration to investigate different initial crack locations.

To initiate a crack, select the MODIFY option and then the NEW CRACKoption. The only crack face option in FRANC2D/L is NON-COHESIVE, anormal traction free crack surface. Select NON-COHESIVE. Cracks canstart from the edge of a structure (EDGE CRACK), or can be completelyinternal (INT CRACK). For this model, select EDGE CRACK. You mustnow specify the location of crack initiation.

The stress contours showed the highest stresses at the right of the hole. Thisis 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 areother reasons to believe that a crack is likely at another location (themanufacturing 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 locationof crack placement. Select the node on the right edge of the hole to be thecrack mouth. Select DONE after you click on the node, Figure 10.

You must now specify the crack tip. You cando this by specifying the exact crack-tipcoordinates, or by merely pointing andclicking at some location in the plate. In thepresent analysis, since we want the crack tobe normal to the hole and we want to specifyan initial crack length of 0.10, you select KEYPOS (KEY POSition) and enter the crack tipcoordinates at X=0.60, and Y=0.0. Theprogram will now ask for the minimumnumber of elements along the crackextension. It is almost always safe to enter 2for this question. The actual number ofelements placed along the crack extension is afunction of the local mesh density. Finerinitial meshes will cause more elements to beused, and thus give more accurate stress-intensity factors.

Figure 10: Selection of CrackInitiation Point



The program will now delete anumber of elements. Youshould click anywhere in theFRANC2D/L window, and theprogram will insert the crack.When you click again theprogram will insert crack-tipelements. One more click andthe program will display amesh that fills the region nearthe new crack. The ACCEPToption updates the programdata structure to include thesenew elements. The updatedmesh will look as shown inFigure 11.

Stress Analysis and Fracture Analysis

Because you now have a new (cracked) structure, a new stress analysis mustbe performed. To do this, RETURN to the main menu, and select theANALYSIS and DIRECT STIFF options.

You can now post-process the analysis results. If you select theDEFORMED MESH option, you will see the crack faces opening.

More importantly, we can now compute stress-intensity factors. To do thisselect the FRACT MECH option. The stress intensity factors inFRANC2D/L are calculated using several methods. Modified crack closureusually provides the most accurate results (MOD CRK-CLOS.). Thecalculated stress intensity factor is 14,710 psi-in1/2.

Crack Propagation

Before we grow the crack, you may wish to save a restart file, using a namesuch as plate_1. To grow the crack, enter the MODIFY page and select theMOVE CRACK option. There are two crack propagation options. We willfirst use the standard method (STAND METH). We will use theAUTOMATIC method later.

Figure 11: Mesh with Crack



If you select the STAND METH option, you will notice a colored lineextending from the crack tip. This is the direction in which the programpredicts the crack will propagate, using the maximum circumferential stresstheory. For the problem we are working, the crack propagates in a straightline because of symmetry, but general curving crack propagation can bemodeled.

There are three options for specifying the new crack tip location. First, youcan point and click anyplace on the model. The program will grow the crackto that point. Second, you can usethe KEY POS option and enter theX and Y coordinates of the newcrack tip with the keypad. Thethird option is to use the predicteddirection of crack propagation, butenter the crack increment. This isthe KEY INCR option. Select KEYINCR and enter 0.10 for theincrement. You will need tospecify the minimum number ofelements along the increment, 2,and the program will remesh justas it did for crack nucleation.

The trial new mesh is shown inorange. You can ACCEPT thismesh, or use the ADD NODES andKILL ELEM options to modify themesh before it is accepted. The new mesh is shown in Figure 12. Once themesh is accepted, another stress analysis must be performed. Do this now.

Automatic Crack Propagation

Crack propagation can also be performed automatically. Enter the MODIFYpage, select MOVE CRACK and AUTOMATIC. You can use the CRACKINCR option to set the amount of crack growth at each step. For the plateproblem use 0.10. Use the STEPS option to set the number of propagationsteps. Set that to 9, and select PROPAGATE to begin the crackpropagation. This will take a few minutes to finish. The final deformedmesh is shown in Figure 13.

Figure 12: Mesh after Growth



Stress Intensity History

To get a history of the stress intensity as a function of crack length, selectthe POST-PROCESS and FRACT MECH options. We will look at stress-intensity factor histories (SIF HISTORY). This allows you plot the K valuesas a function of the crack length, and to save this information to a file. Theplot of KI as a function of crack length shows that the stress intensityincreases with crack length. The comparison with tabulated values isexcellent. Select MCCI File (Modified Crack Closure) to save the data to afile that you specify in the program control window.

Figure 13: Displaced Mesh



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 0.2 0.4 0.6 0.8 1 1.2

Crack Length (in)

Str

ess

Inte

nsi

ty (

psi

-in

1/2)

FRANC2D/LHandbook

Figure 14: Comparison of FRANC2D/L and Analytic Solutions



A Word About PlotsFRANC2D/L outputs the plots using PostScript. If you have a PostScriptprinter, you can embed these plots directly in your word processor documentand they will be displayed correctly when printed. If you do not have aPostScript printer (and you want a preview of how the plot will look in yourdocument) we have found the freeware GhostScript program very useful. Itcan be downloaded at http://www.cs.umd.edu/~rgc/nt.html. GhostScriptallows you to first convert to an Encapsulated PostScript format and then tocreate a preview image that is associated with the file. The preview image isdisplayed during editing and for printing on non-PostScript printers. Thehigh resolution PostScript figures will be printed when the document isprinted on PostScript printers. This approach was used for this manual.

Acknowledgements Page 25


AcknowledgmentsProf. Anthony Ingraffea (Cornell University) has focused on the goal ofdeveloping the ability to rapidly model discrete crack growth for about fifteenyears. FRANC2D/L represents the work of several generations of students:Prof. Ingraffea modeled discrete crack growth by changing a mesh describedby a deck of computer cards, Victor Sauoma modeled discrete crack growthon a Tektronix terminal, Walter Gerstle modeled crack growth on an Evansand Sutherland display, and finally, Paul Wawrzynek (Wash) used aworkstation, started from scratch, and introduced robust data schemes to theengineers who had come before. Layering has been added by SudhirGondhalekar and Srinivas Krishnan at Kansas State University. MarkJames is the most significant developer of the code at Kansas State. He hasstabilized the code, added new features, maintained the multiple platformversions, and done all the work necessary to make the code a genuinelyuseable tool. In addition, he is extending FRANC2D/L to includeelastic/plastic fracture. The approach is the crack tip opening angle methodof Dr. Jim Newman, NASA. The port of GRA to Windows 95/NT was done byBrian Hardeman.

The addition of layers has been supported by the Mechanics of MaterialsBranch at NASA Langley Research Center under the direction of Dr. JimNewman and Dr. Charlie Harris. We appreciate comments received fromDave Dawicke, an early user of the program.

Acknowledgements


BibliographyBaumgart, B. G., 1975, “A Polyhedron Representation for Computer Vision,”AFIPS Proceedings, Vol. 44, pp. 589-596.

Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and Applications ofFinite Element Analysis, Third Edition, John Wiley & Sons, 1989.

Erdogan, F., and Sih, G. C., 1963, “On Crack Extensions in Plates UnderPlane Loading and Transverse Shear,” A.S.M.E. Journal of BasicEngineering, Vol. 85, pp. 519-527.

Henshell, R. D., Shaw, K. G., (1975), "Crack Tip Finite Elements areUnnecessary," International Journal for Numerical Methods in Engineering,Vol. 9, pp. 495-507.

Shaw, R. D. and Pitchen, R. G., (1978), "Modifications to the Suhara-FukudaMethod of Network Generation," International Journal for NumericalMethods in Engineering, Vol. 12, pp. 93-99.

Wawrzynek, P., Ingraffea, A. R., (1987), "Interactive Finite Element Analysisof Fracture Processes: An Integrated Approach," Theoretical and AppliedFracture Mechanics, v.8, pp. 137 - 150.

Weiler, K., (1985), "Edge-Based Data Structures for Solid Modeling Curved-Surface Environments," IEEE Comp. Graph. & App., Vol. 5, No. 1, pp. 21-40.

IndexACCEPT 20Acknowledgments 24, 25ADD NODES 21ANALYSIS 17Applied Displacements 17AUTOMATIC 20, 21auxiliary window 1Bandwidth 17Boundary Conditions 14CONSTANT 17Constraint 16CONTOUR 18CONTOUR CNTRLS 18coordinate system 2CRACK INCR 21Crack Initiation 19Crack Propagation 20, 21cursor 2Data Structure 2DEFORMED MESH 20DIRECT STIFF 17DIST. LOAD 17DSP CORR SIF 20EDGE CRACK 19Elements

Continuum 5Interface 5Plate Bending 5Rivet and Adhesive 5

File*.grf 10

Files*.csc 9*.epr 10*.inp 9*.mon 10*.rsp 10*.wdb 9gra*.ps 10Output 10Restart 9sif 11

FIX EDGE 14FIX IND 15FIXITY 14FRACT MECH 20, 22Fracture 6Graphics 7INT CRACK 19Introduction 1KEY INCR 21KEY POS 19, 21KILL ELEM 21Layers 6LOADS 17MATERIAL 16Material Properties 6, 16message window 1MODIFY 20mouse 1MOVE CRACK 20, 21NEW CRACK 19NON-COHESIVE 19operations window 1POST-PROCESS 18Postprocessing 17, 18Problem Type 14program control window 1PROPAGATE 21Remeshing 7SIF HISTORY 22Solution Procedures 7STAND METH 20STEPS 21Stress Analysis 17SWITCH ELEM 16THICKNESS 16Tolerance 15Tutorial 12winged-edge data structure 3WRITE FILE 17Y GLOBAL 17Young's modulus 16

short

Documents

input files

restart files

output files

adhesive elements

bending elements

crack propagationsimulator

crack growth

franc2dl simulation