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GEOCRACK User`s Manual - Cornell Fracture Group

1. Active Layer 1 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 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 FRANC2D L User s Guide Tutorial Example Problems Page 44 Active Layer 1 Figure 37 Deformed mesh plot A contour of the SIGI 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 Active Layer 1 Figure 38 Principal stress contours FRANC2D L User s Guide Tut
2. FRANC2D L User s Guide Appendix A Input File Format Page 100 Card Set 5 Nodal Coordinates Number of cards in set Num Nodes Node Number I 4 Node number X Coord R 4 X coordinate of node Y Coord R 4 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 d OX Bax ay 2 Y fixity 3 X Applied displacement 4 Y Applied displacement Value R 4 T 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 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 The node loaded Case I 4 The load case that contains the load 1 6 X load I 4 The X force to apply FRANC2D L User s Guide Appendix A Input File
3. 27 41 49 103 20 35 37 96 97 20 35 37 FRANC2D L User s Guide Index Page 118 SWITCH ALL 91 SWITCH ELEM 24 SWITCH ELEMent 90 SWITCH INTerFaCe 91 TAU MAX 103 TENSION 103 THICKNESS 24 39 47 TOGGLE ALL 41 49 Tolerance 25 Transition 45 Translating 22 37 45 Tutorial 15 UDISP 102 VDISP 102 VON MISES 90 92 WRITE FILE 27 41 49 86 Write Mesh 22 36 37 45 X GLOBAL 94 Y GLOBAL 26 40 48 94 Young s modulus 24 39 47 FRANC2D L User s Guide Index Page 119 FRANC2D L User s Guide
4. IX XIX XI T p 4576 b b Nh X LX DXX x gt x Va ke C V 7 G S o ex Xj T4 74 ed LXX LX x i I pod oe raris ed i Od A XS ERO When you are done postprocessing RETURN to the main menu fey AL X om X SC PLAS 94 XIXI CN Crack Initiation and Growth QO At this point we will put a crack in the plate First IA 900 or ae LX AA Xx NX however you should make a restart file This will i save the analyzed uncracked configuration You may i wish to return to this configuration to investigate different initial crack locations Figure 34 Adhesive Elements 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 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 wil
5. Once you insert the interface it remains Therefore you do not need to replace the interface after changing the applied displacement for subsequent solutions Analysis To begin solving the model select the ANALYSIS button from the main menu From the ANALYSIS menu select the LINEAR button From the linear solution menu select the DYNamic RELA Xation button The program provides the following cues in the terminal window and waits for your responses Once you have input the solver criteria the program begins the solution Once the solution residual becomes less than the tolerance you input or the solver exceeds the maximum number of iterations you specified the program provides a summary of the solution DYNAMIC RELAXATION ANALYSIS Enter the tolerance fraction of appl load le 3 Enter the max number of iterations 5000 Starting iterations Iteration Max Acc Mass Residual Norm Target Max delta u 100 0 1947E 05 0 1924E 05 90 69 0 3754E 04 200 6306 6241 90 69 0 2064E 04 300 2607 2587 90 69 0 1301E 04 400 1352 1344 90 69 0 9112E 05 500 815 1 811 5 90 69 0 6713E 05 600 548 5 546 6 90 69 0 5265E 05 700 402 7 401 6 90 69 0 4399E 05 800 ILIRA 317 0 90 69 0 3882E 05 FRANC2D L User s Guide Tutorial Example Problems Page 68 900 270 4 270 4 90 69 0 3620E 05 1000 277 8 24729 90 69 0 3547E 05 1100 281 8 28159 90 69 0 3618E 05 1200 283 0 283 0 90 69 0 3805E 05 1300 283 7 2903 7 90 69 0 4134E
6. 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 The most recent additions and expansions of the program were conducted at Cornell 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 The data base is only accessible FRANC2D L User s Guide Introduction Page 4 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 Post Process Data Base Pre Process Finite Element Analysi
7. 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 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 subsy
8. 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 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 FRANC2D L User s Guide Tutorial Example Problems Page 30 Mesh Generation for Layer
9. Index 116 FRANC2D L User s Guide Introduction Page 1 FRANC2D L User s Guide Introduction Page 2 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
10. converge the compressive stiffness of the normal stresses law is probably too high Try a lower value You do not need to rebuild the interface just change the material property Post Processing To review the results select the POST PROCESS button on the main menu Select DEFORMED MESH to see the displaced shape Unlike deformed meshes with explicit FRANC2D L User s Guide Tutorial Example Problems Page 69 cracks the opening of the interface elements does not necessarily mean that the interface elements have broken forming a crack nnm m DAC Siti ail it A I un S y A TT ei RC VA ih E DEA i 1 In Carus Er I i H3 p mur Figure 50 Deformed mesh To view the opening and stresses along the interface elements return to the POST PROCESSing Menu and select FRACTure MECHanics For plots along the interface elements select INTERFaCe PLoTS The program will prompt you to Specify the starting nodal point Select the first node of the interface Next you will be prompted to Specify the adjacent corner nodal point This is the next corner node along the interface not the next node that would be a mid side node Finally the program will ask you to Specify the ending corner nodal point This is the last node along the interface that again should be a corner node If you cannot select the entire length of the non linear interface to display crack opening while post
11. element is checked for existing interface elements If existing elements are found then the elements are joined This was implemented for the use in polycrystal models where hundreds of interface elements are present FRANC2D L User s Guide Bibliography Page 114 Acknowledgements 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 115 Bibliography Bittencourt T N 1993 Computer Simulation of Linear and Nonlinear Crack Propagation in Cement
12. 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 2 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 such as layerl and a layerl 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 layerl and a layerl inp file will be created You may need to move the CASCA window to see the prompt in the terminal window Figure 21 Layer 1 Mesh 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 intersections 4 0 units to close the outline To leave this mode of addi
13. 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 t 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 n
14. 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 Introduction Page 3 auxiliary window menu window program control window mU tutorial
15. Interface Elements 60 Single Edge Notch Beam 60 FRANC2D L Menu Reference Guide 73 Main Page 73 PRE PROCESS 74 MODIFY 74 ANALYSIS 74 POST PROCESS 74 ANNOTATE 74 ELement NOde INFOrmation 75 WRITE FILE 75 LAYER 75 RESET 75 ZOOM 75 PAN 75 a SNAP d 76 INTERFC ON OFF 76 END 76 PREPROCESSING Functions 77 PROBLEM TYPE 77 FIXITY 77 GB FIX 78 CONSTRAINTS 78 MATERIAL 79 APPLD DISP 81 LOADS 81 SINGULARITY 83 GB TOUGH 83 MONITOR 83 MODIFICATION Functions 84 ADD ELEM KILL ELEM DRAG NODE 84 NEW CRACK MOVE CRACK SUBDIVIDE SHOW ANGLE 84 DEFINE TEARING 85 ADD NonLinear INTerFaCe 85 ADD ADHESIVE 86 MORE OPTIONS 86 ANALYSIS Functions 87 FRANC2D L User s Guide Table of Contents Page 3 LINEAR 87 MATerial NONLINear 87 POST PROCESSING Functions 89 CASE ALL 89 FRACTure MECHanics 89 LINE PLOT 89 CIRCLE PLOT 89 RADIAL PLOT 90 REACTIONS 90 STRESS BAR 90 CONTOUR 9 DEFORMeD MESH 91 POINT INFO 02 NODE INFO 92 FRACTURE MECHANICS Functions 93 FRANC2D L Software Distribution 95 World Wide Web 95 Anonymous FTP 95 Appendix A Input File Format 97 Appendix B FRANC2D L Solver Routines 102 Linear Equation Solver 102 Dynamic Relaxation Solver 102 Appendix C Version 1 1 Release Notes 104 Appendix D Version 1 2 Release Notes 106 Appendix E Version 1 3 Release Notes 108 Appendix F Version 1 4 Release Notes 110 Appendix G Version 2 0 Release Notes 113 Acknowledgements 114 Bibliography 115
16. MOVE CRACK gt STAND METH menu option Figure 40 Initial 0 46 0 0 using 6 element subdivisions on the crack face Finally mesh CRACKSTAND METH menu and extend the crack a final time Le eese op 2 element subdivisions on the crack face Figure 41 below shows the mesh in the region of the initial half inch crack FRANC2D L User s Guide ve Layer 1 p LER NIY SAM NaN AN AINAN RISA V P A VY AIC ANA NAA Y D V KN INN NS RO DIA XN SINAI SV SV N roblems Page 56 There are a couple of important aspects to introducing the crack in this manner First the mesh is graded from the edge of the model reducing the mesh size and number of degrees of freedom and in this case without compromising the solution since there s no significant action behind the crack tip Second the material properties specify that we measure the CTOD fracture criterion at 0 04 behind the crack tip The final crack extension step grew the crack 0 04 with two elements The default minimum number of crack extension elements in FRANC2D L is two elements so the fracture criterion will always be measured with no fewer than two elements behind the crack tip It certainly would have been possible to use more elements along the crack face for that last 0 04 of extensign Experience has shown that for many applications with 2024 T3 aluminum as we are using here a 0 02 element size i adequate O
17. 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 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 FRACTURE MECHANICS Functions Page 93 FRACTURE MECHANICS Functions POST PROCESS gt CASE ALL FRACT MECH gt CASE ALL DISP CORR SIF This button allows the user to select a load case to be used INTERACTION by the other available features in this page SIF HISTORY FATIGUE PLOTS i 1 ENTEGRAL DiSPlacement CORRelation SIF MD CRK CLOS DUMP SIFs Stress intensity factors for a selected crack are obtained INTREG ELTS 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 Min
18. 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 constant unit shear load on all four faces of the element The sign convention for a positive shear load is shown above FRANC2D L User s Guide Tutorial Example Problems Page 52 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 fac
19. and T6 6 noded triangles and I6 6 noded interface elements so the adjacent node will be a midside node GB FIX PRE PROCESS gt This command enables the user to FIX or FREE known zero GB FIX gt displacement degrees of freedom DOF along grain boundaries FIX IND X These processes can be made node by node or along edges of FIX IND Y E IND XY the boundary It is possible to fix free independently selected FIX EDGE X nodes or fix free edges FIX INDependent allows the user to FIXEDGEY independently fix selected DOF s FIX EDGE allows the user FIX EDGE XY o fix DOF s along an edge CONSTRAINTS PRE PROCESS gt CONSTRAINTS allows the user to specify that groups of nodes CONSTRAINTS or edges are constrained to have the same displacements The CONS IND user can either specify constraints on individual nodes CONS GONSEDSE 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 FRANC2D L User s Guide PREPROCESS Functions Page 79 MATERIAL PRE PROCESS gt This option enables the user to s
20. for which the material number assigned to the adjacent elements does not match This is useful for placing many interface elements The optional models for normal stres COD are LINEAR LINear SOFTENing TENSion CUT OFF EXPonential SOFTENing USeR DEFINED and UNZIPPING 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 TK RK KK KK RK ckck ckck ck KR RK KR KK KK ROKK KK KK KK gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt NORMAL Input for linear elastic behavior in a non linear interface KKK ck KKK KKK KKK KKK KKK KK KKK KKK KEK KKK KKK KKK ck ck ok ok ko ck ck ko ck ko Sk ck KKK KK KKK KK and the question Is this a symmetry interfac 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 th
21. interface models are defined the opening values are normalized such that 0 25 indicates the opening at which the peak stress has been reached and decohesion has begun The value of 1 indicates full decohesion Hit RETURN to go back to the postprocessor page By selecting ELAST PLASTIC contour plots for elastic plastic materials are shown Currently the contours are calculated for isotropic VON MISES only The contours can be toggled between ALL YIELDING YIELDED The components that can be displayed include the principle plastic strains EPS XX PL EPS YY PL EPS XY PL and EPS ZZ PL ISO STRAIN EFFective Plastic STRAIN ISO STRESS EFFective STRESS 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 FRANC2D L User s Guide POST PROCESSING functions Page 92 POINT INFO
22. 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 Figure 16 Mesh after Growth 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 L set the number of propagation steps QoK Set that to 12 and select PPROPAGATE to begin the crack 5 propagation This will take a few minutes to finish The final deformed mesh is shown in Figure 17 ON NEN ox M EK Km X e V 4 S K KN x A F iw CR kr E H Ed a Er LT UA NI 79 aA NP NR PK es LAS IRB N LN Fatigue Crack Growth Analysis o perform a fatigue crack growth analysis of the plate select the Figure 17 Displaced Mesh FRANC2D L User s Guide Tutorial Example Problems Page 27 POST PROCESS and FRACT MECH options We will first look at stress intensity 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
23. of the local mesh density Finer initial meshes SS will cause more elements to be used NS and thus give more accurate stress E intensity factors NOS pre The program will now delete a number t V of elements You should click Figure 14 Selection of Crack Initiation Point 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 FRANC2D L User s Guide Tutorial Example Problems Page 25 VA my X X C Ky VAS A X N A Stress Analysis and Fracture Analysis Figure 15 Mesh with Crack 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
24. of this strategy is that the crack path must be defined before the simulation begins For computational efficiency the program uses a dynamic relaxation solution scheme that is explained in detail in the thesis The cohesive capabilities in FRANC2D L are applicable to any material exhibiting cohesive crack behavior In this example cohesive crack behavior means that once the stress ahead of the crack tip reaches a limiting tensile value stress is transferred across the crack according to a function of the crack opening This generic model can be considered a general Dugdale Barenblatt model To illustrate the steps required to implement the defined crack path strategy in FRANC2DI L this tutorial focuses on a concrete single edge notched beam in three point bending Figure 43 FRANC2D L User s Guide Tutorial Example Problems Page 61 a d x i al D Figure 43 Single edge notched beam At this time the cohesive cracking aspects of FRANC2D L are not very user friendly Until this is updated follow the steps outlined in this tutorial closely The NOTE comments relate to especially important information to avoid problems Save the model often and use different checkpoint names so that you can go back to a particular step if there is an irrecoverable mistake Modeling the Beam Use the CASCA program to generate the geometry and mesh information for the model Ensure that the crack path consists of element boundaries If
25. one layer so no translation is necessary Simply read the plate inp file directly into FRANC2D L FRANC2D L User s Guide Tutorial Example Problems Page 19 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 KlIc is used for quasi static analysis and need not be set otherwise Density is only used
26. parameters for nonlinear analyses Proceed into the CONTROL PARAM menu to set the appropriate control values For this 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 FRANC2D L User s Guide Tutorial Example Problems Page 48 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 Repo
27. 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 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 FRANC2D L User s Guide Tutorial Example Problems Page 13 oo rograms franc2dl p programs casca oe 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 14 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
28. processing you may have a discontinuous interface Once you have selected the interface the side menu will change giving a list of plots that can be made along the interface To view the crack development along the interface select OPENING The Opening vs Position plot will appear in the auxiliary window For this example the opening displacement exceeds the critical opening displacement specified of 5 58e 3 specified in the interface material model This indicates that the interface has been broken forming a crack FRANC2D L User s Guide Tutorial Example Problems Page 70 Opening vs Position 0 0070 0 0050 0 0030 Opening 0 00100 0 00100 0 500 0 500 1 500 2 500 3 500 Postion on line Figure 51 Opening vs Position along centerline interface elements The portion of the interface that has opened can also be determined by selecting NORMAL STRESS to view the stress being carried across the interface If the interface has opened it will no longer transfer stress across it The Normal Stress vs Position plot also illustrates the softening occurring along the interface FRANC2D L User s Guide Tutorial Example Problems Page 71 Mormal Stress vs Position 200 000 200 000 Normal 600 000 1000 000 0 500 0 500 1 500 2 500 3 500 Postion on line Figure 52 Normal Stress vs Position along interface elements To observe the stress distributions in the rest of the body return to the POST PROCESS menu and sele
29. reached The equations that are solved are a M f Ku c FRANC2D L User s Guide Appendix B FRANC2D L Solver Routine Page 103 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 104 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 f
30. request to swenson ksu ksu edu FRANC2D L User s Guide Appendix A Input File Format Page 97 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 Ck ck ck ck ck kk ck Ck Sk KKK ck kk KK KKK KKK ck kk ck kk ck kk kk ck Ck ck ck kk ck kk ck kk Ck kk kk ck kk ck kk kk KKK KK KKK KK ck kk k MULTI LAYER PROBLEM FILE FORMAT KOK ckckckckckck ck ck ck ck ck ck KK KK KCKCkCkckck ck ckck ck ck ck Ck ck ck kk kk kk kk kk kk Ck Kk kk Ck Ck kk Sk kk Kk Sk Sk kk Se kk kk Sk kk KKK ko ko KKK KK 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
31. values is excellent 45000 a 40000 seanG FRANC2D L a Handbook E 30000 25000 20000 15000 Stress Intensity psi in1 2 10000 5000 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 an 7 C AK 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 The Paris model is very simple and may not be appropriate for some materials non zero load ratios and very high or very low AK ranges In many cases it is more appropriate to FRANC2D L User s Guide Tutorial Example Problems Page 28 extract a AK vs a history computed within FRANC2D L and use this information with a more sophisticated growth model FRANC2D L User s Guide Tutorial Example Problems Page 29 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
32. 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 elements will change their material numbers to the current value RETURN to the pre process page Figure 9 FRANC2D L Mesh 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 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 FRANC2D L User s Guide Tutorial Example Problems Page 20 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 mo
33. 05 1400 283 0 283 0 90 69 0 4495E 05 1500 279 8 2 T9 90 69 0 4843E 05 1600 274 6 274 5 90 69 0 5189E 05 1700 267 8 267 7 90 69 0 5534E 05 1800 259 6 259 5 90 69 0 5843E 05 1900 250 4 250 3 90 69 0 6114E 05 2000 240 3 240 2 90 69 0 6343E 05 2100 229 5 229 4 90 69 0 6527E 05 2200 218 3 218 2 90 69 0 6662E 05 2300 206 8 206 6 90 69 0 6748E 05 2400 TOS 194 9 90 69 0 6782E 05 2500 83 53 93 2 90 69 0 6767E 05 2600 171 6 171 4 90 69 0 6708E 05 2700 160 2 160 1 90 69 0 6599E 05 2800 149 0 148 9 90 69 0 6445E 05 2900 138 2 138 1 90 69 0 6257E 05 3000 27 8 127 7 90 69 0 6034E 05 3100 117 8 T2 90 69 0 5786E 05 3200 108 4 108 3 90 69 0 5518E 05 3300 99 42 99 34 90 69 0 5234E 05 3400 91 04 90 96 90 69 0 4942E 05 Converged in 3406 iterations Load Residual Norm 90 96 KKK KK KKK ck Ck KKK KKK KKK KKK KK KKK KKK KKK KKK KK KKK KKK KKK KKK KKK KKK KKK KKK KK KKK KKK FRANC Analysis Report 2538 Equations 0 Nonlin Interface Eq Total Time inc overhead 763 seconds Ck Ck ck ck ck ck KKK KKK KK KKK KK KKK KKK KKK KKK KK KKK KKK KKK KKK KK KKK KKK KKK KKK KKK KKK KK KKK Analysis done If the dynamic relaxation analysis crashes with a floating error or the residual error keeps growing while the solver is working the shear stiffness is probably too high Try a lower value You do not need to rebuild the interface just change the material property If the dynamic relaxation analysis oscillates and does not converge or is slow to
34. 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 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 FRANC2D L User s Guide Appendix A Input File Format Page 98 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 aterial I 4 Elem Nodes 1 I 4 Element number aterial number for element First node number Elem Nodes 8 I 4 Eighth node number ote Nod
35. ANC2D 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 1 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 1 j a coeff LowEq eqn and Prof eqn is illustrated below a 1 PE aQ aG Agr 9 a 4 12 3 8 a 5 a 6 aT a 8 a coeff 8 3 6 9 1 2 3 8 LowEq eqn 1 1 3 1 Prof eqn 1 2 5 To find any element of A A 1 j a Prof i LowEq 1 jJ Dynamic Relaxation Solver The dynamic relaxation solver follows the description given by Underwood This essentially performs a dynamic solution with damping until all motion stops When that occurs the desired static equilibrium solution has been
36. ANC2D L User s Guide Tutorial Example Problems Page 18 The two regions adjacent to the hole have five sides However if we think of the arc on i CN i AS TIT JT i Y EN see N LETTES PITTE fof K AN ae ag a ea i f ay Z 777 zz A ANT ae ee a a S m A a TA OO Figure 8 Final Mesh 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 Translating the Mesh For problems with multiple layers the layers must be superimposed using a translator program This example has only
37. 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 1015 Elem Num I 4 Element number aterial I 4 Material number for element Elem Nodes 1 I 4 First node number Elem Nodes 8 I 4 Eighth node number ote 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
38. FRANC2D L A Crack Propagation Simulator for Plane Layered Structures Version 1 5 User s Guide Erin Iesulauro Cornell University e Ithaca New York FRANC2D L User s Guide Table of Contents Page 1 Table of Contents Introduction 2 Basics of Implementation 3 Data Structure 3 Finite Elements 5 Layers 6 Fracture 7 Remeshing During Crack Growth 8 Solution Procedures 8 Computer Graphics 8 FRANC2D L Files 9 CASCA and Input Files 9 CASCA csc Files 9 Input inp Files 9 FRANC2D L Restart Files 9 wdb Files 9 rsp Files 10 FRANC2D L Output Files 10 orf Files 10 gra ps Files 10 sif Files 10 FRANC2D L Tutorial Examples 11 Example 1 Plate with Hole 14 Building an Initial Mesh with CASCA 14 Performing a FRANC2D L Simulation 19 Example 2 Adhesively Bonded Lap Joint 29 Building an Initial Mesh with CASCA 29 Performing a FRANC2D L Simulation 32 Example 3 Plate with Hole and Patch 36 Building the Mesh with CASCA 36 Performing a FRANC2D L Simulation 38 Example 4 Additional Example 42 Crack Growth with Interference Between Plug and Hole 42 Example 5 Incremental Elastic Plastic Analysis 46 FRANC2D L User s Guide Table of Contents Page 2 Notch Root Displacement 46 Example 6 Incremental Elastic Plastic Analysis 50 Non Proportional Loading 50 Example 7 Elastic Plastic Tearing with Remeshing and Mapping 54 Middle Crack Tension with Remeshing 54 Example 8
39. Format Page 101 An Two Y load I 4 The 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 example file for a two element problem is given below Element Mesh al jJ 1 1 1 E 07 3 E 01 1 E 00 1 E 00 000000000 0 13 2 di 1 8 10 Al 13 6 7 9 2 1 11 12 L 3 2 5 13 is 0 000000E 00 1 0000 OO 2 0 000000E 00 0 0000 00 3 0 000000E 00 5 0000 01 4 2 000000E 00 0 0000 OO 5 5 000000 01 0 0000 OO 6 1 000000E 00 0 0000 OO 7 1 500000E 00 0 0000 OO 8 2 000000E 00 1 0000 OO 9 2 000000E 00 5 0000 01 10 1 500000E 00 1 0000 OO 11 1 000000E 00 1 0000 00 12 5 000000E 01 1 0000 OO 13 1 000000E 00 5 0000 01 FRANC2D L User s Guide Appendix B FRANC2D L Solver Routine Page 102 Appendix B FR
40. GUE PLTS 34 CIRCLE PLOT 102 Fective Plastic STRAIN 104 COMPONENT 104 FILE 102 COMPRESSION 103 Files CONSTANT 26 40 48 94 CSC 12 CONSTRAINTS 89 orf 13 CONTOUR 103 inp 12 CONTOUR ConTroLS 103 rsp 12 coordinate system 5 wdb 12 CRACK INCR 33 gra ps 13 Crack Location 29 49 Output 13 Crack Propagation 31 50 Restart 12 cursor 4 sif 14 Data Size 18 Finite Elements 8 DEFINE TEARING 98 FIX EDGE 25 40 48 deformed contour 103 FIX IND 26 48 deformed mesh 103 FIXITY 25 40 48 88 DEFoRMeD MESH 104 FRACT MECH 31 50 DEFORMED MESH 31 50 FRACTure MECHanics 101 DELETE CASE 93 FRACTURE MECHANICS Functions 106 DIRECT STIFF 27 41 49 85 99 ftp 108 DiSPlacement CORRelation SIF 106 GB FIX 89 DISPlacementS 101 GB TOUGH 95 DIST LOAD 93 GENERATE INT PT 45 DIST LOAD 26 40 48 Geometry 18 DISTributed LOAD 94 Get Circle 19 DOF 48 93 Get Line 20 35 37 FRANC2D L User s Guide Index Page 117 Grid HILL Input File Format INT CRACK INT SEPAR INTEGRATE INTERACTION INTERFaCe ON OFF Interface Elements Inserting INTERface METHod INTERFaCe PLoTS INTERnal CRACK Introduction ISO STRAIN ISO STRESS KEY INCR KEY POS KILL ELEM KILL ELEMents KILL INTerFace LAYER Layers LINE PLOT LINEAR Lines Connect LOADS Main Page MATERIAL MATerial NONLINear Menu Reference Guide Mesh message window MODIFICATION Functions MODIFY MONITOR MORE OPTIONS mouse MOVE CRACK NEW CRACK NEW LINE NEW
41. MAT NL INTERFACE COUPLED EXPonential SOFTENing LINEAR LINear SOFTening NORMAL SHEAR TENsion CUT OFF UNZIPPING User DEFINED No of Segments 18 90 92 110 30 104 102 106 87 70 75 97 107 101 94 19 35 36 93 84 24 39 47 90 85 99 84 21 36 37 4 96 31 41 49 85 95 98 4 31 33 96 97 30 96 101 102 39 48 90 91 91 91 91 91 91 91 91 91 91 21 36 37 NODE INFO Non Linear INTERFACE NON COHESIVE NORMAL operations window PAN PLACE ALL INTerface POINT INFO POINT LOAD POINT LOADS POST PROCESS Postprocessing POST PROCESSING Functions PRE PROCESS PRE PROCESSING Functions PROBLEM TYPE program control window PROPAGATE QUADRATIC RADIAL PLOT Ratio REACTION REFINE INTERFace RESET Restart Files Revert Ratio RIVET Set Scale SHEAR SHOW ANGLE SIF HISTORY SIG1 SIG 2 SIGRR SIGRT SIGTT SIGXX SIGXY SIGYY SINGULARITY Software Distribution Spacing XY STAND METH STANDard METHod STEPS STN E DENS STRAIN STRAIN STRESS Stress Analysis STRESS BAR Subdivide SUBDIVIDE Subregions 105 90 30 96 94 101 4 87 91 104 93 94 27 42 49 85 27 41 49 101 24 39 47 85 88 88 4 33 94 102 21 103 97 27 86 12 21 90 18 94 101 96 97 33 50 106 103 103 102 102 102 101 102 103 101 102 103 101 102 103 95 108 18 32 97 33 103 103 101 103
42. ODIFY menu again FRANC2D L User s Guide Tutorial Example Problems Page 66 Figure 47 Sequence of node selection for the first and continuing NL interface elements Figure 48 Sequence of node selection for the last NL interface element FRANC2D L User s Guide Tutorial Example Problems Page 67 Interfaces can be placed all the way to the edge of body When the interfaces elements are fully opened this will break the body When using the Dynamic Relaxation solver this is unacceptable The line of interface elements must terminate within the body If using the Non Linear solver the line of interface elements must continue completely through the body The last interface element of a line that terminates within the body is a 5 noded element rather than 6 noded The Non Linear solver can not handle 5 noded elements To check that the interface has been inserted return to the main menu and select the BOUNDARY button This button toggles off the mesh The nonlinear interface should be shown as a thin line inside the geometry borders Fig 49 You may select the MESH button to toggle the mesh back on The interface can also be check from the menu by selecting INTeRFaCe ON This changes the color of the mesh to orange and the boundaries and interfaces to white If interface elements are present the corresponding material number is displayed next to the elements Selecting INTeRFaCe OFF returns the entire model to being displayed in white
43. POST PROCESSing 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 FRANC2D L User s Guide Menu Reference Guide Page 75 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 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 conve
44. Page 107 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 ill shaped 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 nothin
45. 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 You are now presented with a number of options that you can use to specify the outline of
46. added Under strain contours in the Post Processing menu a contour was added for the coupled opening parameter A of the coupled cohesive zone models The feature color codes the interface elements according to the values of l All interface models are normalized such that 0 25 corresponds to the critical value of X at which softening or decohesion begin The value of 1 indications full decohesion of the interface element The maximum value of reached by each interface element is now carried with the element This allows for determining when an element is unloading and when it has reloaded to the defined curve The INTERFaCe ON OFF button was added in several locations to easy in viewing the interface elements A few changes were made to the memory storage for faces The position of the material number was moved to allow for a larger number of materials to be defined Also for the interface elements the Tedge and Bedge identifiers were combined into 1 node so that a node could be dedicated to store Lambda Max Lambda Max is used for the coupled cohesive zone model to identify when an element is being unloaded On the MATERIAL page for defining interface element models the option PLACE ALL INTS was added to the bottom menu This option searches through all edges in the model If an edge is found for which the left material and right material do not match an interface element is added Initially a four noded element is added Then each end of the
47. ate 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 minimum number of divisions when specifying the boundary In this case it is necessary to specify the patch as a boundary Figure 4 Inner Plate because we will use the same boundary as a starting point Border for the patch mesh in the final example FRANC2D L User s Guide Tutorial Example Problems Page 16 Figure 5 Completed Border 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 Select the Get Line opt
48. 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 Appendix F Version 1 4 Release Notes Page 110 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 update
49. blems Page 53 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 Eps Franc2D L Eps Exact Error Gamma Franc2D L Gamma Exact Error 1 0 00111 0 00111 0 02 0 0001 1 0 0001 1 2 45 2 0 00171 0 00171 0 03 0 00031 0 00031 3 57 3 0 00271 0 00271 0 07 0 00071 0 00071 3 56 4 0 00401 0 00411 0 13 0 00141 0 00131 3 19 5 0 00571 0 00571 0 16 0 00231 0 00231 2 79 10 0 01771 0 01771 0 26 0 01341 0 01321 1 52 20 0 04761 0 04771 0 35 0 06611 0 06571 0 64 30 0 07461 0 07491 0 36 0 14421 0 14371 0 37 40 0 09691 0 09721 0 35 0 23431 0 23371 0 25 50 0 11541 0 11581 0 33 0 33041 0 32981 0 18 FRANC2D L User s Guide Tutorial Example Problems Page 54 Example 7 Elastic Plastic Tearing with Remeshing and Mapping Middle Crack Tension with Remeshing This example describes some of the new elastic plastic tearing capabilities implemented in FRANC2D L These new capabilities are located within the MODIFY DEFINE TEARING and MODIFYMOVE CRACK The new functionality is not fully implemented and only works for a single edge crack It is strongly urge for you to work the example problem since the order of the steps and part of the explanation is embodied there This example problem describes some of the basic features of FRANC2D L for elastic plastic tearing with remeshing and state variable mapping The problem d
50. cept 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 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 FRANC2D L User s Guide Appendix C Version 1 1 Release Notes Page 105 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 No
51. ct CONTOUR Also from available from the POST PROCESS menu is the LINE PLOT This plots the stress for line you specify This option is usefully for plotting stresses either side of the interface Interface Elements and Analyses for Material Non Linear Newton Raphson Solver in FRANC2D L There are a few things to consider when conduction a simulation using interface elements One is which solver is to be used If linear elastic materials are being used then either Dynamic Relaxation solver demonstrated above or the Material Non Linear FRANC2D L User s Guide Tutorial Example Problems Page 72 solver may be appropriate However is elastic plastic materials are being used then the Dynamic Relaxation solver will not be appropriate due to the history dependence of the material In this case the Newton Raphson solver should be used Once the solver has been chosen this will determine how the interface elements may be placed with in the model As seen in the beam tutorial the interface elements were placed along the crack path However the interface elements were not placed all the way to the boundary edge of the model Since Dynamic Relaxation had been chosen the line of interface elements could only touch the boundary at one end The Dynamic Relaxation solver applies a wave to the model with damping and solved for the steady state solution If the interface elements had been carried all the way to the top edge of the beam it would have split into
52. current load norm and total displacement norm for convergence Both load and displacement criteria must be met for convergence Max Iterations is the maximum number of iterations allowed during an analysis load sub step Load Factor n ia a scale factor for each load case to define the recombination of loads for the current analysis step Appl Disp Factor is a scale factor for the applied displacements for the current analysis step Accelerate Iter is a switch for possible acceleration algorithms Currently only the Secant or NONE options are recommended and the Secant method sometimes causes the plasticity algorithm to fail For most problems NONE is recommended New Analysis forces a new analysis Current Step indicates the current load step in the loading sequence Note that for an Incremental analysis the current step increments with each load sub step For an Incremental Unzipping analysis the current step increments each time a crack tip is propagated Final Step indicates the final load step in an analysis sequence for an Incremental analysis and indicates the final propagation step for an Incremental Unzipping analysis Save Frequency indicates the save frequency to automatically save an elastic plastic response to the Autosave File during an analysis sequence The frequency is keyed off of the Current Step number A file is saved when the Current Step number modulo the Save Frequency is zero Print Fr
53. d INTERFC ON OFF Turns on and off the interfaces present in a model This includes boundaries and interfaces between areas of different material definitions If an interface element is present the corresponding material number is displayed next to the element 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 FRANC2D L User s Guide PREPROCESS Functions Page 77 PREPROCESSING Functions It should be understood that FRANC2D L does not create the PRE PROCESS gt i PROBLEM TYPE Original mesh The user must create the model without any FIXITY cracks by means of an external mesh generator Translators are GB FIX available for CASCA PATRAN and ANSYS mesh generators CONSTRAINTS s MA MATERIAL All other preprocessing functions can be performed within APPLD DISP FRANC2D L LOADS SINGULARITY GB TOUGH In the preprocessing stage the user is able to create modify the MONITOR 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 t
54. d 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 closed form 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 op
55. d 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 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 that 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 a
56. d through the J 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 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 Software Distribution Page 95 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 ed
57. e 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 probably a problem somewhere else in the analysis e g load step is too large or other parameters have inappropriate values FRANC2D L User s Guide PREPROCESS Functions Page 81 The HILL material model has also been added to the NEW MAT page This material is
58. e 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 FRANC2D L User s Guide Tutorial Example Problems Page 49 Notch Root Displacement Example O Test Data FRANC2D L Analysis 0 02 0 03 0 04 Notch Root Displacment in FRANC2D L User s Guide Tutorial Example Problems Page 50 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 Y 26 25 E 28 300 v 0 3 For linear isotropic hardening the Hill 1950 plasticity book gives the exact solution for the axial and shear strains as Y 3c Y E in l 2H Y E 7 3 n 55 Nd y g 8 E G where Y is the yield stress in tension E is Young s Modulus H is the plastic modulus and G is the elastic shear modulus
59. e 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 Ck Ck ck ck ck ck kk ck kk ck kk ck kk KK KKK KKK KKK ck kk ck kk Ck ck ck kk ck kk ck kk ko kk Ck kk kk ck kk ck kk kk Sk Sk kc ko KKK KKK KR KKK KK KAA SINGLE LAYER PROBLEM FILE FORMAT X X RRR KKK KK KK KKK K A A K K AE K K K AE K K K AE K ee E A K k E K ee k K K ckckck ck k k K ckckck ck ck ck ck ck ck k ck ck kockckok 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 Connectivity Card Set 1 Title card Number of cards in set 1 FRANC2D L User s Guide Appendix A Input File Format Page 99 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 Number of materials Prob Type I 4 Analysis type 0
60. e of the upper layer Figure 24 RETURN from the fixity page and enter the loads page We will apply a distributed el a a A FCR Ui i DEG ER ER ES DE t PERI TEES ce Et FREE RES TUR RE Figure 24 X Fixity in Top Layer 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 FRANC2D L User s Guide Tutorial Example Problems Page 34 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
61. e upper left node in the model this will monitor this particular node as the solution progresses for each load step Next set the FILE NAME to something like mt1 mon This is the output file that will contain the monitor data Running the Analysis Return to the AUTO TEARING menu and hit the PROPAGATE menu to start the analysis The analysis routines will increment the far field displacement while monitoring the crack tip fracture parameters When the critical value is reached the remeshing routines will be invoked to extend the crack by the specified amount Then the analysis will resume and the process will repeat for the specified number of steps in this case five steps Figure 42 below shows the load crack extension data extracted from the mt1 mon output file This data was extracted using two scripts designed for post processing the mon file FRANC2D L User s Guide Tutorial Example Problems Page 59 3 M T Crack Growth Load kip 3 7 T T T 0 0 05 0 1 0 15 0 2 0 25 Crack Extension in Figure 42 Load crack extension data from mtl mon Some Hints It s obvious or should be that the density of the mesh where you initiate a crack needs to be about the same size as the elements that you introduce In the example above we grade the element size along the crack face so that this will be true The elements near the free edge but along the crack face are larger but sti
62. elect FIX IND then Y and finally the node See Figure 11 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 Figure 11 Y Fixity 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
63. 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 FRANC2D L User s Guide Tutorial Example Problems Page 22 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 e Reduce Bandwidth automatic nodal renumbering to reduce the bandwidth of the global stiffness matrix e Zero Gstf zero the space used for the global stiffness matrix e Assemble assemble the element stiffness matrices into the global stiffness matrix e Decomposition perform direct elimination of the global stiffness matrix e Backsubstitution perform backsubstitution to recover nodal displacements When the analysis has been completed the program will print a short report that summa
64. ements 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 Elastic plastic Unzipping along a row of interface elements Orthotropic materials elastic only are now supported during a nonlinear analysis FRANC2D L User s Guide Appendix F Version 1 4 Release Notes Page 111 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 extendi
65. ents 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 LOADS FRANC2D L User s Guide PREPROCESS Functions Page 82 PRE PROCESS gt This command allows the user to input various types of LOADS loads into load cases Up to six load cases may be input CASE and any number of load types may be present in a load case DELETE CASE The options are CASE DELETE CASE POINT POINT LOAD DIST LOAD LOAD DIST LOAD THERMAL LOAD RESID THERMAL LOAD LOAD and RES CRK STR The option DOF can be RESID LOAD RES CRK STR used to view the various loading degree of freedom directions Following is a description of each of these commands 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 an
66. equency indicates the print frequency as the nonlinear iterations progress for any analysis step This is printed to the command window Increment Method this option is currently inactive so use Fixed Analysis Mode is set to Incremental as the default and is appropriate for elastic plastic analysis with no fracture processes Use Incremental Relax to relax to the residual stresses for the problem relaxes loads to zero load and applied FRANC2D L User s Guide ANALYSIS functions Page 88 displacements to zero displacement Use Incremental Unzipping to simulate unzipping fracture analyses Autosave File automatically save an elastic plastic response file here during an auto analysis sequence The program tries to determine this file name automatically from the current input file name or response file name but it can be set to any name The file name displayed will be appended with an underscore and the current step number to create the file name used for saving the current response ANALYZE ONE analyses one analysis step This means to superimpose the current load cases using the current load factors into a single force and displacement vector break the loads and displacements into the correct number of load sub steps and produce a series of equilibrium steps RELAX TO RESID relaxes the problem to the residual state zero loads for loaded equations and zero displacement for applied displacement equations WRITE RESULTS wr
67. erated Repeat for the other region of the hole a Return to the main menu The mesh Figure 30 Patch with should now look Subdivisions like Figure 31 Select Write Mesh and specify the file name call it layer1 without the inp extension on the XTerm terminal window Select END and CONFIRM EXIT to leave Figure 31 Patch mesh 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 Scastofranc 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 layerl 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 FRANC2D L User s Guide Tutorial Example Problems Page 38 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 Figure 33 Plate Layer Conceptually the layers should be viewed as laye
68. ered for the Normal Model will avoid numerical instability problems It is desired to have a high compressive stiffness to model the linear response of the interface element However if the peak of the curve becomes to narrow convergences problems may be encountered Divergence during the solution procedure may indicate that the peak of the interface material model is too narrow Figure 46 Linear softening models with wide and narrow peaks The last pre processing task is to apply the LOADS From the pre processing menu select the LOADS button If we actually apply loads to the model we can only capture behavior up to the peak load In order to track post peak behavior we apply displacements to the model Therefore select the APPLieD DISPLacement For this example we apply a point displacement Selecting the PoinT DISPLacement button NOTE The applied displacement must be the Ist load case FRANC2D L User s Guide Tutorial Example Problems Page 65 NOTE If you need to change the location of an applied displacement or otherwise need to remove an applied displacement you must also go back to the FIXITY menu remove the fixities and reapply them NOTE The program converts the applied displacement to nodal equivalent loads Therefore the material properties must be specified before applying the displacement The solution scheme used in FRANC2D L does not propagate the crack The dynamic solver finds the equilibrium configuration
69. escribed here is for an analysis of a 3 M T middle crack tension specimen This is a good introductory example because the problem size is relatively small and because there are other numerical as well as experimental results readily available for comparison Figure 1 below shows the mesh for the example We assume symmetry along the vertical center line of the specimen but model both the top and bottom halves The problem will be run in displacement control The crack will be introduced on the left edge as an edge crack midway between the top and bottom and symmetry boundary conditions on the left edge of the model will enforce the middle crack behavior Problem Set up Start the FRANC2D L program and read in the mtl inp mesh file Go to the PRE PROCESS menu and verify that the problem type is plane stress Next set the bottom edge to have Y fixity and the left edge to have X fixity Go to the MATERIAL option and change material one to VON MISES Some of the material properties are already set correctly Set the HARDENING E property to the file option and read in the data from the mat2024 txt file Set the YIELD STRESS to 50 ksi and set the PROB TYPE to Plane Stress Set the critical crack tip opening displacement CTODc to 0 0035 The CTODc INIT value should be the same as CTODc Next we will describe the applied displacement boundary condition on the top edge of the model Go to the APPLD DISP menu option in the PRE PROCESS menu Selec
70. esired to FREE a previously fixed node or edge segment one only needs to reselect that node or FRANC2D L User s Guide PREPROCESS Functions Page 78 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
71. ess 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 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 e Each layer is considered as an individual two dimensional structure under a state of plane stress or plane strain e Only linear out of plane displacements and bending effects are included FRANC2D L User s Guide Introduction Page 7 e Individual layers can be connected with rivets or adhesive bonds e 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 t
72. etect whether the same mesh is required to preserve adhesive bonding and will automaticlly enforce the same mesh requirement when necessary 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 FRANC2D L User s Guide Introduction Page 8 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
73. for the model for the applied displacement To propagate the crack apply a larger displacement and rerun the analysis This method can be used to generate points on the load versus displacement or load versus CMOD graph The solution to each applied displacement is one data point Add the NL Interfaces Once the pre processing is complete we are ready to add the non linear interface From the main menu select the MODIFY button From the modify menu select the ADD NL INTerFaCe button After selecting the ADD NL INTerFaCe button the program window will give you the command to select the first node of the first int elem Select the first node of the interface starting from the boundary It must be the node at the outer face where the crack begins node A in Fig 47 Hit the DONE button The program window will give you the command to specify end node of elem amp hit DON Select the node at the other end of the first element node B in Fig 47 Hit the DONE button The program window will give you the command to end interface specify previous node At this point if you wish the interface to continue select the corner node of the next element node D in Fig 47 and then hit DONE Continue selecting adjacent corner nodes until you have selected all of the desired elements To end the interface reselect the last node you selected node C in Fig 48 and hit DONE If everything worked correctly you will be automatically taken to the M
74. for v 0 3 The figure below shows the exact strain path and FRANC2D L results for selected applied loads FRANC2D L User s Guide Tutorial Example Problems Page 51 Since a single material point is sufficient to model the problem only one Q8 Plane Stress Tube in Tension Torsion element in a single layer is necessary for a FRANC2D L model Create a mesh with a single square Q8 element aligned with the coordinate axes After starting the FRANC2D L program select the PRE PROCESS menu option Set the Analytical Solution problem type to plane e Franc2D L Result stress 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 o lt 0 04 Shear Strain 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 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
75. ft 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 incorporated in the
76. g 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 It is worth noting here that the fracture mechanics functions are not designed to be used with elastic plastic material models Previously when elastic plastic materials where present this option would not be activated However it is now activated in order to allow access to the INTERFaCe PLoTS option 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 t
77. g to attach to FRANC2D L User s Guide Appendix E Version 1 3 Release Notes Page 108 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
78. he 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 sub groups 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 d
79. he 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 POST PROCESSING functions Page 90 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 generate 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 arbi
80. he 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 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 FRANC2D L User s Guide Appendix D Version 1 2 Release Notes
81. he 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 compariso of the calculated shear stresses in the adhesive and an analytic solution Normalized Shear Stress a ANALYTIC FRANC2D L 0 0 5 1 Normalized Position Figure 28 Comparison of Analytic and FRANC2D L Adhesive Stresses for the adhesive When you are done postprocessing RETURN to the main menu FRANC2D L User s Guide Tutorial Example Problems Page 36 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
82. imum 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 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 FRANC2D L User s Guide FRACTURE MECHANICS Functions Page 94 Stress intensity factors for a selected crack are obtaine
83. ion 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 should look like Figure 6 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 FRANC2D L User s Guide Tutorial Example Problems Page 17 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 fi
84. ites an elastic plastic response set without writing the wdb database file READ RESULTS reads a specific elastic plastic response set Though some internal checks are made the user is ultimately responsible for making sure that the response set matches the current wdb model MONITOR is a simple method of monitoring the temporal nature of the elastic plastic state evolution at points in elements and at nodes without manually recording data as the problem progresses and without saving full elastic plastic response data files If a data file name is defined the monitoring is activated and if no data file is defined the monitoring is deactivated The monitor points and nodes can be retained with the monitoring deactivated Point to nodes and or faces to indicate monitor locations Activate the DELETE option then point to existing monitor locations to remove the monitor location The output will be a file with a mon extension This file can be post processed external from FRANC2D L to create X Y columns of the data monitored FRANC2D L User s Guide POST PROCESSING functions Page 89 POST PROCESSING Functions POST PROCESS gt CASE ALL CASE ALL FRACT MECH LINE PLOT This button allows the user to select a load case The CIRCLE PLOT remaining functions of this page will be performed for the RADIAL PLOT REACTIONS selected load case STRESS BAR CONTOUR i DEFORMD MESH FRACTure MECHanics POINT INFO NODE INFO By hittin
85. itious Materials Ph D Dissertation Department of Civil and Environmental Engineering Cornell University Ithaca NY 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 Iesulauro E 2002 Decohesion of Grain Boundaries in Statistical Representations of Aluminum Polycrystals MS Thesis Department of Civil and Environmental Engineering Cornell University Ithaca NY James M A 1998 A Plane Stress Finite Element Model for Elastic Plastic Mode I II Crack Growth Ph D Dissertation Department of Mechanical and Nuclear Engineering Kansas State University Manhattan Kansas Newman J C Jr Dawicke D S and Bigelow C A 1992 Finite Element 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 Jour
86. k ck ck Ck ck Ck ck ck Ck ck Ck ck ck Ck ck ck ck ck ck ck ck ck ck kk ck ck ck ko ck ck kk kk ck Sk Sk kx kx ko ko ko ko gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt SHEAR Display of parameters for linear elastic behavior in a non linear Interface ck ck ck ck Ck KKK KKK KKK KKK KKK KKK KK KKK ck ck ck ck ko ck ko ko ck KKK KKK KKK Stiffness 7 0000000E 07 To input the cohesive relationship for normal stresses select the NORMAL button in the non linear material menu For this example use a LINear SOFTENing relationship After selecting the model type the program prompts you for input in the terminal window The first question is SIs this a symmetry interfac Yes 1 No 0 We have modeled the entire beam instead of taking advantage of the symmetry plane To answer no type zero 0 in the terminal window The program goes on to prompt you for the tensile strength critical crack opening when no more stress is transferred and compressive stiffness of the relationship SWhat is the Tensile strength of the material 350 SWhat is the Critical Opening displacement 5 58e 3 SWhat is the Compressive stiffness Te The program then provides a summary of the interface properties in the terminal window ck ck ck ck Ck ck Ck ck ck Ck ck Ck ck ck Ck ck Ck ck ck Ck ck ck ck ck Ck ck ck ck ck ck ck ko ck ko ko ck Sk Sk kx kx ko ko ko ko gt gt gt gt gt gt gt g
87. l see the crack faces opening FRANC2D L User s Guide Tutorial Example Problems Page 41 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 in 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 45000 40000 FRANC2D L No Patch a ANALYTIC No Patch 4 FRANC2D L With Patch 35000 30000 25000 20000 15000 Stress Intensity psi in1 2 10000 5000 0 0 2 04 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 42 Example 4 Additional Example Crack Gr
88. ll well formed while the elements at the tip transition nicely What s sometimes not so obvious is that the mesh that you re propagating into must also be about the same size or slightly larger if you want than the step size that you re taking with the program This is crucial to obtain the most accurate results especially with elastic plastic analysis where there are no special crack tip elements to capture crack tip behavior FRANC2D L User s Guide Tutorial Example Problems Page 60 Example 8 Interface Elements Single Edge Notch Beam Introduction This example provides step by step instructions to begin cohesive crack modeling using FRANC2D L and the defined crack path strategy A familiarity with CASCA and FRANC2DYL is assumed in the presentation of information Tulio Bittencourt performed much of the work to allow cohesive crack modeling in FRANC2D as part of his Ph D research For more technical information and background on the cohesive crack modeling capabilities in FRANC2D please refer to his thesis Additional work implementing interface elements in FRANC2D L and using them along with elastic plastic materials was done by Mark James at Kansas State University as part of his Ph D research and by Erin Iesulauro as part of her MS research Although Bittencourt describes a few strategies for solving cohesive crack problems with FRANC2D this tutorial only focuses on the Defined Crack Path Strategy The limitation
89. n 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 wdb Files FRANC2D L User s Guide FRANC2D L Files Page 10 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 ca
90. n 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 gral 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 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
91. nal 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 Curved Surface Environments IEEE Comp Graph amp App Vol 5 No 1 pp 21 40 FRANC2D L User s Guide Index Page 116 Index CASE 93 DRAG NODE 96 LAYER 47 86 DSP CORR SIF 31 50 MAT 39 48 90 DUMP SIFs 107 ZOOM 86 DYN RELAX 85 99 a SNAP d 87 EDGE CRACK 30 97 ACCEPT 30 EFF STRESS 103 ADD ADHESIVE 49 98 EFFective STRESS 104 ADD ELEM 96 ELASTic ISOTROPIC 90 ADD NODES 32 97 ELASTic ORTHotropic 90 ADD NonLinear INTerFaCe 98 ELASTic ORTHOTROPIC 91 ADH_TAU ZX 103 ELAST PLASTIC 104 ADH_TAU ZY 103 ELement NOde INFOrmation 86 ADHESIVE 39 48 90 EPS 1 103 ANALYSIS 27 41 49 85 EPS 2 103 ANALYSIS Functions 99 EPS MAX 104 ANNOTATE 86 EPS XX PL 104 APPLD DISP 93 EPS XY PL 104 EDGE DISP 93 EPS YY PL 104 PT DISP 93 EPS ZZ PL 104 AUTOMATIC 32 33 97 EPSXX 103 auxiliary window 4 EPSXY 103 Bandwidth 27 EPSYY 103 Bilinear 4side 22 EQuatioN NUMber 85 99 BOUNDARY 103 Fatigue Crack Growth 33 Boundary Conditions 25 40 41 48 FATIGUE PLoTS 106 CHandGe BOUNDS 103 FATI
92. ne point to consider the element size needs to be fixed during crack growth so that the fracture criterion can be sampled at a fixed distance behind the crack tip as the crack propagates FRANC2D L User s Guide Tutorial Example Problems Page 57 Figure 41 Initial mesh with the intitial crack Automatic Tearing This section describes the control parameters that are necessary for the Newton s method solver and for the propagation algorithm First we need to initialize the tearing data structures for the crack Enter the MODIFYDEFINE TEARING TIP menu The crack tip will automatically be initialized for tearing and highlighted boxes will be drawn at each node on the crack face Highlighted boxes indicate that the nodes are tied for unzipping For this internal crack no unzipping will be used Use INIT SAWCUT to untie the crack face nodes by setting the initial sawcut length to 22 nodes only the crack tip node will be highlighted Now go to the MODIFY gt MOVE CRACK AUTO TEARING menu In the CONTROL PARAM menu change the following analysis control parameters Load Sub Steps 100 Max Iterations 300 Appl Disp Factor 35 Return to the AUTO TEARING menu and confirm the following tearing control parameters FRANC2D L User s Guide Tutorial Example Problems Page 58 EL SIZE 0 02 CRK INC 2 EL BACK 2 STEPS 5 UNZIP NO CRIT COD Enter the MONITOR menu and use the ADD NODE option to define monitor data for th
93. ner 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 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 Figure 7 After Line Subdivision 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 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 FR
94. ng 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 FRANC2D L User s Guide Tutorial Example Problems Page 31 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 Write option Give a name such as Figure 22 Layer 2 Mesh 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 inp
95. ng 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 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 extrapolati
96. ngle edge notched beam mesh FRANC2DI L Pre Processing The first two pre processing tasks are set the boundary conditions and input the material properties It does not matter which task comes first The boundary conditions are set through the FIXITY menu This is described in the FRANC2D L primer The material properties are set through the MATERIAL menu After selecting the MATERIAL button an auxiliary window will activate By default the model has the properties of Material 1 By selecting the E NU and THICKNESS buttons you can change the properties of Material 1 For this example I set the properties to E 4e6 Nu 0 18 and Thickness 3 125 Once I set the properties the text in the auxiliary window read as follows Total number of materials 1 Material number 1 Material type Isotropic Young s Modulus 0 400E 07 Poisson ratio 0 180 Thickness 3 13 KIc 1 00 Density 0 868E 1 Alpha 0 000E 00 FRANC2D L User s Guide Tutorial Example Problems Page 63 For the cohesive interface we generate a new material by selecting the NEW MAT button Select the NL INTERFACE button Initially the cohesive laws for shear and normal stresses are not defined To set the shear select the SHEAR button For this example use a LINEAR law with a stiffness of 7e7 Input the stiffness in the terminal window After inputting the stiffness the program provides the following information in the terminal window c
97. nient 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 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 FRANC2D L User s Guide Menu Reference Guide Page 76 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 selecte
98. nts 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 AUTOMATIC and INTERface METHod 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 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 FRANC2D L User s Guide MODIFICATION Functions Page 85 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 forme
99. nts 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 GB TOUGH This command always toughness to be assigned to interfaces This is used in conjuctions with the MODIFY gt MOVE CRACK gt INTerface METHod without interface elements MONITOR This is a simple method of monitoring the temporal nature of the elastic plastic state evolution at points in elements and at nodes without manually recording data as the problem progresses and without saving full elastic plastic response data files If a data file name is defined the monitoring is activated and if no data file is defined the monitoring is deactivated The monitor points and nodes can be retained with the monitoring deactivated Point to nodes and or faces to indicate monitor locations Activate the DELETE option then point to existing monitor locations to remove the monitor location The output will be a file with a mon extension This file can be post processed external from FRANC2D L to create X Y columns of the data monitored FRANC2D L User s Guide MODIFICATION Functions Page 84 MODIFICATION Functions MODIFY gt The modify page allows the user to modify both the geometry ADD ELEM of the struc
100. o bottom PROBLEM TYPE FIXITY GB FIX CONSTRAINTS MATERIAL APPLD DISP LOADS SINGULARITY GB TOUGH AND MONITOR The following is a description of each of these commands PROBLEM TYPE PRE PROCESS gt This command allows the user to change the current problem PROBLEM TYPE gt type using plane stress plane strain or linear bending PLANE STRESS assumptions For layered structures axisymmetry is not valid PLANE STRAIN AXISYMMETRIC and so is not an option for problems with more than one layer BENDING Bending analyses are not allowed for models that contain Q8 Q8 TO T6 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 FIXITY PRE PROCESS gt This command enables the user to FIX or FREE known zero FIXITY displacement degrees of freedom DOF These processes can FIX IND be made node by node or along edges of the boundary It is PELEREATE 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 along an edge 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 nodes If it is d
101. on 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 Eff Stress ksi 0 0 2000 ek 0 00483 0 015 56 9 0 040 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
102. on on the last segment rather than just printing an error message FRANC2D L User s Guide Appendix F Version 1 4 Release Notes Page 112 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 Appendix G Version 1 5 Release Notes Page 113 Appendix G Version 1 5 Release Notes Release notes for Franc2D L v2 0 1 02 Beta Summary of Changes Number of possible material definitions was increased to 500 Cohesive zone models were expanded The Normal options now include linear softening The Coupled model was also
103. or 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 siz 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 ex
104. orial Example Problems Page 45 SigXX vs Position 0 000 a_r 200 000 400 000 L SigXX 600 000 800 000 1000 000 Lr rr l 0 500 ritis bin a aa Lora 0 500 1 500 2 500 3 500 Postion on line 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 X21 Y 0 on the interface on the X axis You may need to zoom in to select the node When finished select DONE Select KEY POS and give a value of X22 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 46 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
105. ow 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 an adhesive Optionally the user can specify individual elements The display will mark each element that has an adhesive with an X Figure 34 FRANC2D L User s Guide Tutorial Example Problems Page 40 This is a good time to save a restart file by using the WRITE FILE option Stress Analysis and Postprocessing IR 5 EAE Kb QV AV GP 4 CN We are now ready to do stress analysis From the main page select the ANALYSIS option and the DIRECT STIFF option C XNA X MS 49 4 LA VIC i 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 o Cs EV A 4y a0 XD X CX ix ar LX X KOLO DDS A J 48 Xx
106. owth 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 AII 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 key
107. pad 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 6 0E 4 500 000 LSE4 OO O ajl ol 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 FRANC2D L User s Guide Tutorial Example Problems Page 43 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
108. pecify material type and MATERIAL properties A separate window is created to echo the MAT material properties selected Default isotropic elastic hd MAT properties are initially displayed in this window Besides the Nu most common ELASTic ISOTROPIC and ELASTic THICKNESS ORTHotropic types the user can define a VON MISES BONS isotropic elastic plastic HILL orthotropic elastic CHANGE TYPE plastic or Non Linear INTERFACE material The user can also specify the RIVET stiffness and the ADHESIVE properties The first button in the command menu MATerial scrolls through all existing material sets To create a new material set hit NEW MA Terial 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 KlIc 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 proper
109. plots FRANC2D L User s Guide Tutorial Example Problems Page 11 FRANC2D L Tutorial Examples In this portion of the manual the use of the FRANC2D L program is illustrated by three tutorial examples Crack growth from a hole in a panel 2 Alap 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 B E 10 0E6 psi MESS 0 25 EE v U thick 0 04 in Adh Gz10 0E3 psi Adh thick 0 005 in Figure 1 Schematic of Plate with Hole FRANC2D L User s Guide Tutorial Example Problems Page 12 The second example is a lap joint with the two layers bonded by adhesive as shown in Figure 2 Adh G 10 0E3 psi Adh Thick 0 005 in 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
110. r 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 to rearrange the window to see the menu The new window contains the material properties We will change the properties Select Figure 32 Patch Layer 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 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 39 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
111. r s Guide Menu Reference Guide Page 74 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 two options LINEAR and MATerial NONLINear There are three options under LINEAR 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 The MATerial NON LINear button activates the non linear Newton Raphson solver POST PROCESS This button activates the post processing page whose functions are described in detail in the
112. re 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 gt 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 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 Figure 10 X Constraints FRANC2D L User s Guide Tutorial Example Problems Page 21 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 s
113. rizes 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 FRANC2D L User s Guide Tutorial Example Problems Page 23 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 Crack Initiation Figure 12 Deformed Mesh At this point we will put Figure 13 Stress Contours 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 traction free crack surface Select NON COHESIVE Cracks can start f
114. rom 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 FRANC2D L User s Guide Tutorial Example Problems Page 24 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 1 pointing and clicking at some location Ex in the plate In the present analysis m since we want the crack to be normal to Ee the hole and we want to choose Ce arbitrarily an initial crack length of Le 0 10 you select KEY POS and enter cs 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 A the crack extension is a function
115. rrows 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 FRANC2D L User s Guide PREPROCESS Functions Page 83 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 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 eleme
116. rt 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 gt 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 Th
117. ry 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 FRANC2D L User s Guide Tutorial Example Problems Page 33 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 edg
118. s 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 Vertices correspond to finite element nodes and faces represent finite elements shown below FRANC2D L User s Guide Introduction Page 5 Le
119. s at each gauss point The user has the option of turning the mesh off by selecting FRANC2D L User s Guide POST PROCESSING functions Page 91 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 By selecting STRAIN contour plots of strain components EPSXX EPSYY EPSXY principal strains EPS 1 EPS 2 and maximum strain EPS MAX Again the user can plot displacements DISP U DISP V An additional feature has been added to aid in determining the failure of interface elements defined as COUPLED INT SEPAR color codes the interface elements to indicate the amount of decohesion that has occurred A color contour is displaced in the auxiliary window In case multiple
120. s 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 database rather than limit each layer to only it s fraction of the database For instance previously a single layer problem could only occupy 1 5 of the database size for a version of the program compiled for 5 layers Now the full database is available for all layers 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 pre cracked 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 displac
121. sed versions To retrieve a program use commands similar to those from the following transcript tp cd Sun 50 CWD command successful tp get franc2d1 Z get the FRANC2D L executable 00 Port command successful 150 Opening data connection for franc2d1 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 f 2 f 2 oe uncompress franc Z uncompress the files uncompress casca Z chmod a x franc2dl make the files executable by all chmod a x casca oo oe oo 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
122. 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 FRANC2D L User s Guide Introduction Page 6 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 1s 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 rz Qu u where T Shear str
123. stem 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 ca
124. stress intensity factor is 14 710 psi in 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 FRANC2D L User s Guide Tutorial Example Problems Page 26 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 orange You can ACCEPT this
125. t EDGE DISP then Y DISP Give a value of 0 001 for the displacement value then apply the displacement on the top edge of the model Return to the main menu and save a restart file using the WRITE FILE option FRANC2D L User s Guide Tutorial Example Problems Page 55 Verify the boundary conditions by running a linear elastic analysis Use the ANALYSISLINEAR DIRECT STIFF option The number of equations should be 1567 and the solution time is almost negligible on most of today s faster machines Return to the main menu and proceed to POST PROCESS and view the DEFORMED MESH Next use NODE INFO and verify that the Y displacement on the top edge is 0 001 Confirm that the stress in the problem is uniform in the CONTOUR option by viewing the SIG Y component The Y stress should be about 1 73 ksi Introducing the Crack The crack we want is an edge crack Go to the MODIFY gt NEW CRACK gt NON COHESIVE EDGE CRACK option Introduce the crack at the node on the left edge of the model that is mid way between the top and bottom of the model The initial 2a W for the experiment we want to model is 1 3 This means that the crack tip will ultimately be at coordinates 0 5 0 0 however it is beneficial to grade the mesh density along the crack face from the edge of the model to the crack tip With this in mind set the initial crack tip at 0 25 0 0 and use 3 element subdivisions on the crack face Accept the default mesh then return and enter the
126. t gt gt gt gt gt gt gt gt gt gt SHEAR Display of parameters for linear elastic behavior in a non linear Interface ck ck ck ck Ck KKK KKK KKK KKK KK KK KKK Ck ck ck ck ck ko ck ck ko ck ko Sk ck Mk Sk KKK KK KK Stiffness 7 0000000E 07 FRANC2D L User s Guide Tutorial Example Problems Page 64 E RLLLL IE ck ck ck ck ck ck Ck ck ck Ck ck 0k Ck ck Ck ck ck ck ck Ck ck ck ck ck ck ck ck ck ck ck ck ck Ck ck ck ko ck ko ck ck Sk Sk ko kx kv A ko gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt gt NORMAL Display of parameters for linear softening behavior in a non linear Interface with Linear elastic compressive behavior ck ck ck ck ck ck Ck ck ck ck ck Ck ck ck Ck ck Ck ck ck ck ck ck ck ck Ck ck ck ck ck ck ck ck ko ck kk ck ko ck ko Sk Sk M Sk ko ok Symmetry flag 0 0000000E 00 Tensile strength 350 0000 Critical opening 5 5800001E 03 Compressive stiffness 7 0000000E 07 The last step in this process is to set the THICKNESS of the interface Use the same thickness as the global thickness 3 125 for our example Once this is complete the text in the auxiliary window reads as follows Total number of materials 2 Material number 2 Material type Nonlinear Interface Shear Model Linear Normal Model Linear Softening Thickness 3 13 NOTE Careful selection of the compressive stiffness value kc ent
127. te 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 FRANC2D L User s Guide ANALYSIS functions Page 87 ANALYSIS Functions ANALYSIS LINEAR LINEAR MAT NONLIN As discussed earlier the linear solver options are DIRECT STIFF DYN RELAX and EQuatioN NUMber MATerial NONLINear The approach of the MATerial NONLINear is to treat the load cases defined during preprocessing as increments in load from the current equilibrium state Each analysis step takes the current load cases either loads or displacements superimposes the cases and breaks them into the number of specified load sub steps Equilibrium is established at each of these load sub steps before continuing on to the next The Load Factors and Appl Disp Factor in the control page describe how the load cases will be superimposed for the current analysis step Menu options include CONTROL PARAM ANALYZE ONE RELAX TO RESID WRITE RESULTS READ RESULTS and MONITOR CONTROL PARAM produces a list of parameters in the auxiliary window The Load Sub Steps is the number of sub steps for the current analysis step This number may be altered during analysis if the load increment changes as an analysis progresses Global Tolerance is the fraction of the
128. tes Page 106 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 T
129. 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 1ayer2 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 lt x 2 ex 1 E 225 z zee C Ra 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 ZOOM to see the lines more clearly The display should look like Figure 30 Return to the main menu Figure 29 After Deleting Regions FRANC2D L User s Guide Tutorial Example Problems Page 37 Finally select Mesh We could use Bilinear 3side but in this case we will obtain a better mesh of the circular region if we use Transition Select 1 Transition point to the top right quarter subregion of the hole select GENERATE INT PT and a mesh will be gen
130. the path is a straight line a subregion line will ensure that the path is a boundary between finite elements For the beam in this example the dimensions are as follows L 27 5 d 6 0 S 24 0 ao 2 0 b 3 125 t 0 125 FRANC2D L uses the zoom level in the main program window to determine the tolerance distance for nearest nodes and edges Because of this you may have difficulty generating two different points to be the tip of the notch By zooming in you will be able to create the two points by typing in coordinates To control how the mesh is created it is helpful to divided the model into subregions before subdividing the edges Figure 44 shows subregions that were used to create the mesh shown in Figure 45 Since the position of the supports has been determined creating subregions at the ends of the beam of a width of 1 75 ensures the placement of nodes at the support locations An additional subregion line can be placed from the center of the notch to the top edge of the beam After creating the subregions each boundary line was then subdivided to determine the number of elements along the edge The mesh was created using the Automatic option Once the model is meshed you can generate the file to be read into FRANC2D L User s Guide Tutorial Example Problems Page 62 FRANC2D L Once the model is meshed you can generate the file to be read into FRANC2D L E 9 1 75 10 2 1 75 WP FE EEEHE Figure 45 Si
131. 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 LCXXDXXOXOXXDOXX i be connected by adhesive DXPXPXPSDRPXPXPXPXUX Optionally the user can specify eS a aaa individual elements The display TX XIXby ips cuter ta LO pOXDXXDXOXOXDXUXUX in Figure 25 Lo PPIX LO AXX E OX IX DX PNCPAS XDD DAI TES 16 good iue ee JXDXPSPXDXDSPXUXDXIX EE opion Figure 25 Adhesive 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 FRANC2D L User s Guide Tutorial Example Problems Page 35 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 t
132. ties 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 l 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 shear and coupled 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 The COUPLED button is used to specify a linear softening coupled cohesive zone model Finally THICKNESS is used to input FRANC2D L User s Guide PREPROCESS Functions Page 80 thickness The SWITCH INTerFaCe button is used to change all interface elements models to the current one The PLACE ALL INTerface button searches the entire model and places interface elements along edges
133. tion of propagating the crack by an incremental distance along that line DEFINE TEARING The DEFINE TEARING options allows crack propagation to be defined under a CTOA crtiteria The crack tip will automatically be initialized for tearing and highlighted boxes will be drawn at each node on the crack face Highlighted boxes indicate that the nodes are tied for unzipping For this internal crack no unzipping will be used 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 that 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 FRANC2D L User s Guide MODIFICATION Functions Page 86 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 that 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 dele
134. 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 SEHE a a TS ae GIG S N N N N LL AV AAAS EBENEN EBENEN KREET AAAY Active Layer 1 10400 ksi o 09 S v Curve described below 50 ksi FRANC2D L User s Guide Tutorial Example Problems Page 47 1 0 not used Max Iter 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 d
135. tors 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 LoadFactor2 00 Save Frequency 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 POST PROCESS 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 Load Factor 1 0 0 Load Factor 2 Final Step 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 FRANC2D L User s Guide Tutorial Example Pro
136. trary 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 STRESS BAR The stress bar option displays the tensile TENSION and or compressive COMPRESSION stress flow in the structure by displaying vectors of principal stresse
137. ture and the mesh Modifications may involve KILL ELEM addition deletion of individual elements dragging of nodes nlp ds initiation and propagation of cracks and creation of material NEW CRACK propag gt DEFINE TEARING interfaces or boundary contacts MOVE CRACK SUBDIVIDE SHOW ANGLE ADD ELEM KILL ELEM DRAG NODE ADD NL INTERFC ADD ADHESIVE MORE OPTIONS 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 that can be seen by clicking on the BOUNDARY button during element deletion Note that mid side 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 segme
138. two pieces when the solver applied the wave By stopping the interface elements within the model this leaves a five noded interface element as the terminal element Currently the Newton Raphson solver is unable to handle the five noded interface elements Therefore when using this solver all interface elements must connect to either a boundary or another interface element at each end FRANC2D L User s Guide Menu Reference Guide Page 73 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 pre processing functions modification functions post processing 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 Cornel PRE PROCESS FRacture ANalysis Code Version L1 4 MODIFY ANALYSIS POST PROCESS ELNOINFO WRITE LAYER RESET ZOOM PAN Active Layer 1 a SNAP d INTERFC ON lt tolerance gt END FRANC2D L Use
139. u 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 swenson ksu ksu edu 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 Within the Sun directory there are at least three files FRANC2D L User s Guide Software Distribution Page 96 casca Z franc2dlZ 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 uncompres
140. ut to FRANC2D L and in the process merge the twolayers Type Scastofranc 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 layerl 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 FRANC2D L User s Guide Tutorial Example Problems Page 32 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 franc2d1 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 The material properties are common between layers Figure 23 Mesh Display in FRANC2D L 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 necessa
141. valid only for plane stress Things to note when inputting material properties are that the YIELD STRESS button has several inputs required The first is yield stress in primary direction Next is the yield ratio in secondary direction The secondary yield stress is the yield stress at 90 degrees counter clockwise from the primary direction The ratio entered is displayed in the auxiliary window as Alpha This corresponds to Al in most Hill derivations Alpha is calculated according to Eq Next is the yield ratio in shear direction This is displayed as Beta and corresponds to A2 in most derivations Beta is determined by Eq 4 Finally the material angle from Cartesian is requested This is the angle measured counter clockwise from the global X axis to the primary direction This is displayed in the auxiliary window as Material Angle w Cartesian 2 O5 Alpha Eq 1 0 5 gu Beta Eq 2 O y APPLD DISP PRE PROCESE S This option allow the user to input applied displacements along APPLD DISP boundaries and at interior nodes Applied displacements PT DISP automatically add loads to load case one and are incompatible EDGE DISP with other load types therefore load case one must be empty to cup eem lied displ ts Apply other load types in oth DONE 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 displacem
142. 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 the loads the material thickness must be set before the loads are applied to get the expected results New Menu Structure in Preprocessing FRANC2D L User s Guide Appendix E Version 1 3 Release Notes Page 109 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
143. 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 you select QUIT the circle will be ignored Repeat this to generate the lower part of the circle The display should be as Figure 3 Circle shown in Figure 3 Border FRANC2D L User s Guide Tutorial Example Problems Page 15 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 pl

GEOCRACK User`s Manual - Cornell Fracture Group

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