Cracked Hole Finite Element Modeling

Transcription

1 Craked Hole Finite Element Modeling (E-20-F72) Researh Report Submitted to: Lokheed Martin, Program Manager: Dr. Stephen P. Engelstad Prinipal Investigator: Dr. Rami M. Haj-Ali Shool of Civil and Environmental Engineering Georgia Institute of tehnology Atlanta, GA September 2001

2 V- Craked Hole Finite Element Modeling Table of Contents Projet Summary 1. General Overview and Objetives 1 2. The CHM Program Program Arrays and Parameters Output Files Program Input File 4 3. Template Input File 8 4. The VCCT Program 8

3 Projet Summary The overall goal of this projet is to develop a parametri finite element (FE) mesh generating software for reating models with raks emanating from the edge of a irular hole in a nothed plate. The term raked hole mesh (CHM) will be used in this report to refer to the generated FE model. Also, the term parametri mesh generator (PMG) is used in this report. These terms are both used to desribe the developed program, i.e CHM program or PMG program. The software input will be relatively small and inlude the geometry of the plate, the nothed irular hole, and information about the rak systems that emanate for the irular edge. The geometry input is followed by mesh input in the form of number of elements at different major diretions and areas of the model. The output of the program inludes different files that define the geometry and FE mesh of the model. These files an be used as part of the input to a FE software, suh as ABAQUS. Furthermore, the output CHM files inlude PATRAN neutral files that are generated to allow inorporating the CHM as part of a general global model, suh as a global mesh for a lap splie joint struture. Several examples were generated using the proposed raked hole mesh program. These demonstrate the general apability of the CHM automated modeling approah. A seond post proessing program that is apable of using the ABAQUS output files and alulates the rak's strain energy release rate (ERR), using the virtual rak losure tehnique (VCCT), is also desribed. The program is alled "aba_vt". Different examples are generated and ompared with ERR solution ases that are found in the literature. Finally, a ase where the loal CHM model is integrated in a global model is demonstrated.

4 1. General Overview and Objetives Multi-site fatigue raks typially initiate at the loaded fastener holes in skin splies. These multiple site damage (MSD) raks an signifiantly redue the residual strength of the struture. Current modeling approahes may not be suffiiently aurate to allow apturing the loal deformation and damage evolution. This requires a detailed modeling approah that inludes the loal geometry, interating damage systems, and aount for the ontat behavior of the fastener and the splie. Detailed finite element (FE) modeling of metalli fastened joints is ruial to aurately model existing andor potential damage development. Refined shell element models an be used for this purpose. In addition, it is important to develop automated omputer programs that are apable of generating a parametri and refined FE mesh. A new "raked hole" finite element modeling approah is developed in this study. The main goal of this projet is to develop a omputer program that an at as a parametri mesh generator (PMG) for raked (or nothed but unraked) plate. Figure 1 shows different possible rak onfigurations that an be generated by the PMG. The program generates the meshes rapidly and effiiently. These an be used repetitively at numerous loations (e.g., in a skin splie), reduing the labor of re-reating this "mesh" numerous times. The mesh an be used as a substruture or an be ondensed to a superelement by only retaining stiffness at the nodes on the interfae boundaries of the substruture. The PMG output inludes files that an be used in the input stage of the finite element software ABAQUS. A post proessing program is also developed in this projet. The purpose of this program is to read the ABAQUS binary result file "fil files" and apply the virtual rak losure tehnique (VCCT) to obtain the energy release rate (ERR) at the rak tip. In this ase, the PMG program has a parameter (IVCCT) that indiates the need to reate a VCCT-raktip mesh area. Soft and stiff springs are loated behind and in front of the rak tip, respetively. The PMG program reates an additional output file in ase the VCCT mesh is needed. This file inludes the tip nodal information and the spring elements. It is needed as an input for the "aba_vt" post-proessing program. The apability of the PMG program to effetively generate ompliated mesh models is demonstrated. Also, the VCCT modeling feature is applied on symmetrially emanating raks and ompared with an analytial solution available in the literature. l

5 2. The CHM Program This setion desribes the CHM or PMG program and the way it is applied. As previously mentioned, the possible general rak onfigurations that the program an generate FE models are shown in Fig. 1. The mesh is onsidered as a plane type mesh where plane stress or plate type elements are used. The main features of the CHM ode and the way it is ativated are now desribed. 2.1 Program Arrays and Parameters The file "Param_ommon" inludes many parameters and array definitions. These parameters and the array sizes an be hanged based on future hanges that a user deems neessary. Also, the default array sizes an be inreased to allow produing very detailed meshes. The following are major parameters and arrays: max_num_raks: max_num_theta: max_num_intrv_r: max_el_blk: max_nel_r: max_nset: max_elset: max_tip_nodes: max_tip_els: max_rows: max nd row: Maximum number of raks allowed Maximum number of angular intervals allowed Maximum number of intervals in the radial diretion Maximum number of elements in eah blok Maximum number of radial elements in a blok Maximum number of nodes in a given nodal set Maximum number of elements in a given element set Maximum number of nodes in a detailed rak tip area Maximum number of elements in a detailed rak tip area Maximum number of rows within the transition zone Maximum number of nodes in a row within the transition zone Toljheta: Tol_r_d: Tol_eq: Tol max r: idofs: Tolerane in the angular diretion in terms of angles (degrees) Tolerane in the radial diretion Tolerane used for nodal equivalene Toleranefration of the radial distane that defines the last irular perimeter that is onneted to the outer retangular perimeter. number of nodal degrees of freedom (2=plane stress, 6 for plate or shell type elements) 2

6 The urrent default parameters allow the PMG to generate a wide range of appliable FE models with reasonable size of nodes and elements on the order of hundreds of elements. Having said that, the program is also apable of reating large sale meshes by inreasing the "max_el_blk" and the "max_num_blks" parameters. Other parameters may also need to be hanged depending on the desired proedures that are needed with the large sale mesh. 2.2 Output Files The output of the PMG program is in the form of several files that define the different part of the FE model and the way it is interfaed with the global model. Some of these files are not omplete andor part of them need to be redefined. For example, the boundary onditions may need to be redefined depending on the physial problem and loading onditions at hand. The name of an output file starts with a prefix string that is supplied by the user and followed by an attahed suffix desribing the type of the file. The following are the names of the output files: "prefix"_abaqus.inp This is the abaqus input file that inludes the nodal and element definitions. In addition, the file may inlude nodes and elements in a transition area that onnets with the global mesh. the interfae with the global mesh an also be in the form of nodal onstraints between the fine loal mesh and the oarse global mesh. The transition area and globalloal interfae is an optional feature of the ode. Alternatively, one an use the PMG program to define a loal mesh, i.e. a retangular plate with a nothed irular hole with a number of raks emanating from the noth. A fititious stati problem with elasti material definition, axial loading, and boundary onditions are added to the file in order to omplete its definition. The user should be aware to modify andor add the desired properties and proedural definitions that are appropriate to their model. "prefix "jibaqusjsup.inp This file is similar to the first abaqus file exept it defines the CHM definition as a superelement. This is by using the "*SUPER,ID=Z1001, FILE=sup_libl, RECOVERY=YES" option in Abaqus. This ommand line maybe modified in the file by the PMG users to reflet a proper element number andor library filename et. The retained DOF of the superelement are urrently defined by the outer nodal perimeters that an interfaed with the global mesh. The proedure for defining the superelement ends with the Abaqus ommand line: "*END SUPER" followed by an inomplete global model. This model needs to be ompleted by the user in order to properly define the superelement within the global model. Furthermore, the material definitions in the superelemnt may need to be modified. 3

7 "prefix"_patran_pl.out "prefix"_patranjr.out "prefix"_patran_all.out These three files are PATRAN neutral files that inlude the definitions of the nodes and elements of the model. The first file will always be generated. The seond and third files will be generated in ase a triangular transition zone is requested from the PMG program, in this ase, the seond file ontains the nodes and elements of the transition zone alone while the third file ontains all nodal and element definitions. "prefix"_yt. inp This file is generated in the ase where the VCCT method is needed for evaluating the ERR at the different rak tips. The information about the rak tip nodes, and the soft and hard spring elements added in the model, is written in this file. This file is needed later as an input to the VCCT program in order to post proess the ERR from the analysis results. "prefix"_ses This file is generated to report the elements that are deleted in the mesh and replaed with a detailed rak-tip rings for J-integral alulations. It also may inlude warning or error messages. nodal onstraints This file is generated when the method for interfaing with the global mesh is nodal onstraints. The nodal onstraints are generated using quadrati shape funtions between the global oarse nodal edges and the loal fine mesh. The orner nodes are diretly linked with eah other. The file should be used with the "*EQUATION" option in Abaqus. 2.3 Program Input File One input file is needed to generate a FE mesh. Eah line of input that begins with the harater "C" or "" is ignored. Therefore, one an use this to write omment lines. The input parameters are desribed using shemati mesh illustrations. 1) Input Stage #1: Geometry parameters The plate width, height, and diameter of the nothed hole (a,b,d) need to be given in the first line of input. Figure 2 identifies these input parameters and desribes the initial stage of the mesh and how it is partitioned to a default 8 bloks. The dotted square inludes part of an input file illustrating the urrent line of input. Note that lines that begin with "C" or "" are used as omment line. Also, the atual lines of input that are needed are marked with horizontal left arrow. Other lines are omment lines,, Finally, the loal hole-enter oordinate is set to (0,0,0). This an be hanged later allowing the nodes to be translated one the mesh is ompleted prior to reating the transition zone. 4

8 2) Input Stage #2: Optional Non default Partition Lines This option is in addition to the default lines that are shown as dashed lines in Fig. 3. These additional lines may be needed to define refined mesh areas espeially near rak systems. The example in Figure 3 illustrates the addition of 6 lines at different angles around a raked lines that will be later defined. 3) Input Stage #3: Crak Systems The data for the rak systems (rak tip oordinates) is given in this step. Figure 4 illustrates an example where two rak systems are defined by their tip oordinates. This example desribes horizontal system of unsymmetrial raks, however, other rak systems an be easily defined, as shown in Fig. 1. Figure 5 shows the urrent status of the model after the first three stages of input. It is interesting to note that eah rak tip has defined a irular line of nodes. An end irular perimeter of nodes is also defined with a radius being the minimum of half of the width or the length times a given ratio (0.85). This ratio is defined in the ommon parameters file. Finally, the IWCT parameter near the number of raks indiates whether to apply the VCCT approah for these rak tips (non zero value) or that the VCCT method will not be used (zero IVCCT value). The setion on the VCCT program explains how the CHM program effets the model in the ase where the VCCT option is requested. 4) Input Stage #4: Added Cirular Lines Cirular lines are by default reated in the mesh beause of rak tips, at the (0.85) ratio of minimum radius, or as the nothed irular hole itself, see Fig. 5. This optional input stage allows adding more irular lines to the model in order to ontrol the refinement of the mesh at different areas. Figure 6 shows an example of adding two additional irular lines to the urrent model. 5) Input Stage #5: Mesh seeds in the Cirumferential Diretion The line segments in the irumferential diretion are reated as a result of the intersetion of the radial lines and the irular lines. These segments are seeded for meshing at this stage. The only input that is required is the number of elements that eah line segment will have. Later, speifi line segments an be modified to have different number of elements. Figure 7 shows an example of the seeds as a result of the given input. 6) Input Stage #6: Mesh seeds in the Radial Diretion A similar input is needed to mesh seed the radial line segments with equal number of elements. Figure 8 shows an example using three elements in the radial diretion. 7) Input Stage #7: Modify Mesh seeds in the Radial Diretion 5

9 The previously defined number of elements is for all segments in the radial diretion. In the urrent stage of input, ertain line segments ranges an be seleted or defined with different number of elements than that in the previous stage. Figure 9 illustrates the use of the urrent input option to override the number of elements from 3 elements to 2 and from 3 elements to 4 in other segments. Note that the last range overrides the previously defined ranges as shown in the example. 8) Input Stage #8: Mesh seeds for the last radial segment The last radial segment onnets the plates' outer perimeter of nodes to the last irular line of nodes. The number of element in this zone is defined separately in this stage. Figure 10 shows the number of radial elements that divides this last radial segment. 9) Input Stage #9: Refined Meshes Around Crak- Tips The next input in this stage is to define whether there is a need for refined rak tip meshes. If so, a non zero number is needed to indiate the number of rak tips that need mesh refinement around their tips. Figure 11 shows an example where it is indiated that no mesh refinement is needed around any rak tip. This is useful when working to prepare the mesh for the VCCT alulations of the ERR. In this ase, a later stage will be added to invoke the VCCT option. It should be noted that it is highly reommended that the length of elements in the radial diretions are set to be equal behind and in front of the rak tip. This an be ahieved in the input stage #4 where added irular lines an bound the rak tip to insure equal length of elements. Figure 12 illustrates the seond option where a refined mesh around one of the rak tips is needed, the first input is the number of these tips. The seond line of input identifies the following three parameters: 1) theta Crak angle whih needs detailed tip meshing 2) frat_rmaxl-[ 0+, 1.0]-Fration whih determines the radius for the first ring or irle as Rmin=frat_rmaxl*Min(Lr,Lt) 3) frat_rmax2 [0+, 1.0]-Fration whih determines the radius for the last irular tip ring Rmax=frat_rmax2*Min(Lr,Lt) Note: ( frat_rmax2 > frat_rmaxl) The above frations and distanes are applied to the area that is free of elements around the rak tip. In order to reate this area, elements need to be deleted in the radial diretion behind the rak (rl diretion), in the radial diretion in front of the rak tip (r2 diretion), in the angular diretion below the rak fae (tl diretion), and in the irumferential dire- 6

10 tion on top of the rak fae (t2 diretion). Figure 13 illustrates the ase where the number of these elements are defined in one line of input. In addition this line of input requires two additional numbers that define the number of irular rings to define around the rak tip and the number of transition rings of elements that needed to onnet with the rest of the mesh. Finally, Fig. 14 shows the outome of the refined mesh around the rak tip. 10) Input Stage #10: Nodes and Elements Renumbering Two numbers are needed in the next line of input. The first number is added to the node numbers that are generated thus far. This is useful in ase the urrent mesh needs to be part of another global model and to avoid node number dupliations. The seond number is used in a similar fashion with the element numbers. 11) Input Stage #11: Translation of the Nodes Thus far, the model was reated in a loal oordinate system where its enter (the hole or the plate enter) has a (0,0,0) oordinate. In this step, a line of input that ontain the x,y, and z position of the enter is needed. 12) Input Stage #12: Transition Mesh Zone and Interfaing with a Global Model This stage inludes input for interfaing with a global model by reating transition mesh or applying nodal onstraints between the oarse global mesh and the loal CHM. The first input line requires an integer input for a flag (ionnet). If the input is zero, no interfaing or mesh transition is ourred. In the ase it is not zero, the global nodes that the loal model will interfae with need to be given. The list of nodes must be onseutive and starts from the lower left orner and ounter lokwise. Two types of files for these nodes an be read by the CHM program. The first is a free formatted ASCII file that eah line has node number and the (x,y,z) oordinate. The seond file is a patran neutral file that has only the nodes that the loal model will be onneted to. The parameter (Inp_type) is used for this purpose in the next line of input. If the parameter is set to 1, that the input file is an ASCII type, else, it is a Patran neutral file. The next line of input is the file name. This input must begin from the first olumn, i.e. no spae before the first harater, othenvise, the Unix system will not be able to open the orret file. The following input line must onsist of 4 node numbers that exist within the external nodal file. These are the four verties of the global nodal perimeter starting from the lower left orner and progressing in a ounter lokwise diretion. The next input line is a number that indiates if the loal-global interfae is through layers of triangular elements (IOPT=l) or through nodal onstrains (other value). No additional input is required in the later ase. Figure 15 shematially shows the nodal onstrains approah. If the triangular elements are need- 7

11 ed for transition, an additional line with two parameters is required. These are the number of layers (rows) of elements to be used (at least 2) and the nodal redution fration between the layers of nodes as we transition between refine to oarse lines of nodes. Figure 16 shows examples of the triangular transition zone. 3. Template Input File A template file was reated as an example to help in reating input files to the CHM program. Figures 17 and 18 show this file. The needed input lines are not ommented with a "" or "C" haraters at the beginning. The needed numerial input in these lines is marked using the symbols $1 and $FM for integer and free format floating numbers, respetively. The range of some of the input variables is fixed and given to aid in reating input files. 4. The VCCT Program A seond program that is able to read and post proess the ABAQUS binary results file was written during this projet. The aim is to use the rak information data and read the displaements and fore values in the springs to alulate the ERR. The input to this program inludes a file with the information about the number of raks, the tip nodal numbers, spring elements, and other needed information. The CHM program automatially generates this information one the IVCCT parameter is used. This feature is previously explained. Therefore, the user must prepare the mesh around the rak to have the same element size before and after the rak tip. One this feature is requested, the nodes near the rak tip are onneted with soft and hard spring elements, as shown in Fig. 19. The fores from the hard springs and the displaements from the soft springs are used in the post proessing program to alulate the EER. Next, the program was used to verify the VCCT modeling of the CHM and the postproessing programs. To this end, the known solution of a nothed plate with two symmetrially edge raks, Fig. 20, is used for this purpose. The FE mesh reated by the CHM program is also shown in Fig 20. The CHM program also reated the input information for the postproessing program (aba_vt.f). Figure 21 illustrates the auray of the proposed models along with the post proessing verifiation of the developed ode for seven ases of geometry. 8

12 p- Figure 1. Different possible rak onfigurations that an be meshed with the urrent mesh generator 9

13 Input Stage #1 1) Geometry of the plate and hole a = width b = hight D = Diameter of the hole o NOTE: At this stage, there are 8 initial bloks \ N \ '! ' \ i \ i ' \ \ blok-3 I blok-2 V \ \ e4= % e^an-d) N l 7 \ I e = 180 v D.! J_=_0 O blok-4 \! - blok-1 blok-5 T^ \ \ \ 8 J= 270 \ \ 8 = 360' \ blok-8 \ \ \ blok-6 blok-7 \ \ Loal Coordinates at O Figure 2. Input stage #1: initial geometry with default partition of 8-bloks. 10

14 Input Stage #2 2) Input Additional Radial Lines (degrees) that will be added to the default radial lines Note: These lines may or may NOT have radial raks emanating from the edge of the hole. Angle (degrees) assoiated with eah line -* ** Default radial line Non-default (added) radial line NOTE: At this stage, there are 14 total bloks _v^_ Figure 3. Input stage#2: adding more partition radial lines. 11

15 Input Stage #3: Crak Tips Crak Systems: 3) How many rak systems in this meshmodel? Num_raks 2 IVCCT 0 For eah rak system, enter the angle and the radius of the rak tip (poolar oordinates) Max Value of R_tip for eah rak: Max(R) < 0.85*Min(a2,b2) (0.85 predefined fator) Theta R Figure 4. Input stage #3: Crak systems. 12

16 Current status: Default lines Non-default (added) lines Last irular bound withj 1 \ \ I \ Cirular bounds due to I \ rak tips \ V- J *l Figure 5. Current status of the model after the first three stages of input. 13

17 Input Stage #4: Added Cirular Lines 4) Number of additional irular lines (not due to rak tips) these will add additional "radial intervals" Total Radial Intervals= Number of DIFFERENT rak tips + num_add_r_int + 1 Num_add_r_intrv 2 -^ Rl R2 R3... R(Num_add_r_intrv) *m Default lines Non-default (added) lines \ Last irular bound with:! \ \ R = 0.85Jvtin(a,b)2 j A \ \, \ \ ' ^E^N \-\ ~-'\~.i(ir>^\'- Added \ )K \ Intervals '\ _ I Cirular bounds due to I VN^^^'-^. 7 \ ' \ v \ \ \ \ rak tips \ ' I Figure 6. Input stage #4: added irular lines. 14

18 Input Stage #5: Mesh Seeds in the Angular Diretion \ \ Last irular bound with \ R = 0.85 Min(a,b)2 \ 5) Mesh seeds in the angular diretion. All line segments in the irumferential diretion will have the same following number of elements (> 2). num_el_theta ( > 2 ) -^ 2 X y \ \ \ "s >r^<y'7}' 2-elements will be meshed between ALL line segments in the angular diretion - Mesh Seed, \ Added A Intervals Cirular bounds due to rak tips \ Figure 7. Input stage #5: Mesh seeds in the irumferential diretion. 15

19 Input Stage #6: Mesh Seeds in the Radial Diretion 6) Mesh seeds in the radial diretion. num_el_r 3 *+ - Mesh Seed in Theta diretion - Mesh Seed in the r-diretion NOTE: 2-elements will be meshed between ALL line segments in the irumferential diretion 3-elements will be meshed between ALL line segments in the radial diretion ALL lines in the r-diretion will share the same mesh seed segments Added Intervals 7 Cirular bounds due to rak tips Figure 8. Input stage #6: mesh seeds in the radial diretion. 16

20 Input Stage #7: Mesh Seeds for Speifi Radial Segments 7) Overwrite speif number of seeds in the radial segments within given ranges: R(i) < r > R(i+1) num_el_rp rl r2 num_el_r_mod Mesh Seed in Theta diretion - Mesh Seed in the r-diretion, \ Added A Intervals \ i 7 Cirular bounds due to rak tips Figure 9. Input stage #7: mesh seeds for speifi radial segments 17

21 Input Stage #8: Mesh Seeds for the Last Radial Segment 8) Number of element to add in the last radial segment between the last irular line and the plate perimeter num_el_add_r 4 ^ \ \ Last irular bound with: \ R = 0.85 Min(a,b)2 \ \ \ \ V \ \ x. V \ x - Mesh seeds in the angular diretion - Mesh seeds in the r-diretion - Mesh seeds for the last radial segment Figure 10. Input stage #8: mesh seeds in the last radial segement. 18

22 Input Stage #9: (Option-1: Prepare for VCCT Mesh) No Refined Meshes Around Crak-Tips 9) Detailed Crak Tip Meshes (YN) (YN) = (*0) num_det_tips 0 «^ Figure 11. Input stage #9:

23 Input Stage #9: Refined Meshes Around Crak-Tips (Option-2: Plastiity or J Calulation) Define a refined mesh only around the right rak. 9) Refined Meshes Around Tips num_det_tips Identify whih rak: theta frat_rmaxl frat_rmax ~+ num_el_tip_rl num_el_ti_r2 num_el_tip_tl num_el_tip_t2 num_rings num_add_rings Note: next figure explains the above input variables Figure 12. Input stage

24 theta frat_rmaxl frat_rmax "* num_el_tip_rl num_el_ti_r2 num_el_tip_tl num_el_tip_t2 num_rings num_add_rings * A irle is reated around the tip deleted area of elements suh that its radius is 0.85 of the minimum lenght in the 4-diretions (tl,t2,rl,r2) to ensure that the irle is bounded is a fration of the distane for the first ring of elements. These are ollapsed for 1r or lsqrt(r) singularity. 5 is the number of rings between the 0.05 and 0.85 of the irle's raduis Input Stage #9: Refined Meshes Around Crak-Tips (Option-2: Plastiity or J Calulation) (ont.) 2 are additional two rings of elements for transition between the irle and the original mesh Figure 13. Input stage #9: refined meshes around rak tips (ont). 21

25 Input Stage #9: Refined Meshes Around Crak-Tips (Option-2: Plastiity or J Calulation) (ont.) Figure 14. Input stage #9: refined meshes around rak tips (ont). 22

26 X - Edge node from the global oarse mesh - Edge node in CHM model Edge-3 X K X X X X ^ ^ ^ B m ^~~^w~~^^ ^ ^^^^"^w' 1 Edge-4 X X Edge-2 <«- \ y^ LI Edge-1 nodal onstraints between any given edges Figure 15. Loal-global mesh onnetion through nodal onstraints 23

27 X - Edge node from the global oarse mesh Figure 16. Loal-global transition examples using layers of triangular elements. 24

28 *0I2#l f J&1&07 j input_template "]' $FM1 $FM1 $FM2 $FM2 Input to Craked_hole Mesh Generator $FM3 $FM3 $... $... Note: 1) Any line that starts with the letters "" or "C" is onsidered a omment line 2) "$" Charater in this template means input 4) Number of additional irular lines 3) $FM - Free format real input variable (not due to rak tips) 4) $1 - Free format integer input variable these will add additional "radial intervals" Coordinate System: X-Y (in-plane) oordinates. Total Radial Intervals= Number of DIFFERENT rak tips + num_add_r_int + 1 The oordinate system is INITIALLY loated at the enter of the hole. Num_add_r_intrv 1) Geometry of the plate and hole a = width b = hight D = Diameter of the hole $11 IF $11=0 omment the next input line Rl R2 R3 R(Num_add_r_intrv) $FM $FM $FM i $I1*($FH) 2) Input Additional Radial Lines (degrees) that will be added to the default radial lines 5) Mesh seeds in the angular diretion. All line segments in the irumferential Note: These lines may or may NOT have diretion will have the same following radial raks emanating from the number of elements (> 2). edge of the hole. num_el_theta ( > 2 ) Number of added radial lines $11 $1 Angle (degrees) assoiated with eah radial line 6) Mesh seeds in the radial diretion. IF $11=0 omment the next input line num_el_r $I1*($I) $1 Crak Systems: 7) Overwrite speif number of seeds in the 3) How many rak systems in this meshmodel? radial segments within given ranges: R(i) < r > R(i+1) Num_raks IVCCT num_el_rp $11 (0,$I) $11 For eah rak system, enter the angle and the radius of the rak tip (poolar oordinates) IF $11=0 omment the next input lines in this step Max Value of R tip for eah rak: rl r2 num el_r_mod Max(R) < 0.85*Min(a2,b2) (0.85 predifined fator) $11 input lines $FM $FM $1 IF $11=0 omment the next input lines $FM $FM $1 $FM $FM $1 Theta R Figure 17. Input template for the CHM program (12). 25

29 :16:07 input_template 8) Number of element to add in the last radial segment between the last irular line and the plate perimeter num_el_add_r $1 9) Detailed Crak Tip Meshes (YN) (YN) = (*0) num_det_tips $11 theta - Crak Angle whih needs detailed tip meshing the positive theta-diretion. ring or irle as Rmax=frat_rmax*Min(Lr,Lt) fra_rmax2 - [0+,1.0] Fration whih determines the Radius for the last irular ring ( frat_rmax2 > frat_rmaxl ) num_el_tip_rl - Number of elements to delete from the rak tip in the negative r-diretion. num_el_tip_r2 - Number of elements to delete from the rak tip in the positive r-diretion. num_ei_tip_ti - Number o elements to delete from the rak tip in the negative theta-diretion. num_el_tip_t2 - Number of elements to delete from the rak tip in the positive theta-diretion. num_rings - Number of irular rings around the rak-tip IF $11=0 omment the next input line FOR EACH rak_tip input: theta frat_rmaxl frat_rmax2 $FM 0.001<$FM< K $FM <1.0 num_el_tip_rl num_el_ti_r2 num_el_tip_tl num_el_tip_t2 numrings num_add_rings $1 $1 $1 $1 $1 $1 Repeat the above two lines of input $11 times Suggestion (may not always work) ) Input a number to add to the new nodes and elements C nd_shift iel_shift $1 $1 Input the global x-y-z oordinate of the hole (all nodes oordinates will be transformed from loal to global oordinates using this enter point) xg_enter,yg_enter,zg_enter $FM $FM $FM 11) Transition Zone and onnetion to the global model Ionnet =.eq. 0 - No onnetion to the global mesh is needed.else. - Perform onnetion with a given nodes set generated previously in a different FE model Ionnet (0,$I1) If above input is zero omment all lines in this input step ASCIIpatran filename for the nodes in the outside perimeter (note: filename annot start with the letter "" or "C") Inp_type =.eq.l - asii nodal file (node#,x,y,z) Inp_type =. eq.2 - patran nodal setgroup (patran file ontains ONLY the edge nodes) Note: Both above files MUST have sequential node numbers Inp_type $(1.2) $file_name Input the nodes for the 4-orners (vertex) $11 $11 $11 $11 IOPT=.eq. 1 - Triangular transition mesh.else. Rigid link onstraints $(1,11) IF( IOPT.ne.l) Then omment the next input line Triangular transition zone num_erow num_erow = Number of element rings between the two edges of node sets a and b. (>1) red_fat = Redution fator for the elementsnodes as going from inside to outside rings 0. < red_fat <= 1. red_fat $1 O.OOK $FM < 1.0 Figure 18. Input template for the CHM program (22). 26

30 A i Free surfaes ~ * "> rak tip T i Spring-1 and Spring-2 are soft springs Spring-3 and Spring-4 are hard springs t i i = 2BA (F 3 8 i + F 4 6 2> F and 6 are the fore and displaement in a spring B- Thikness Figure 19. Shematis showing the appliation of the VCCT to determine the ERR 27

31 2b 2s &\ \ fll^ 2b _^d Figure 20. Verifiation problem for the VCCT and CHM modeling 28

32 3.0 i i r o 1.2 O Newman Current FE CHM models 0.6 = 0.5 b K 0 = ajta 0.0 J I ab J L J L Figure 21. Variation of stress intensity fator for symmetri rak emanating from a nothed hole. 29