1 Problem DescriptionConsider a finite plate in tension with a central crack as shown in Fig 1 The plate is made of Steel with Youngs modulus E = 200 GPa and Poissons ratio _ = 03 Let b = 02 m a = 002 m_ = 100 MPa Determine the stress intensity factors (SIFs)

Figure 1 Through-thickness crack

Note that for this problem tabulated solutions for the mode-I SIF KI are available in theliterature For example an analytical solution given by WD Pilkey (Formulas for Stress Strainand Structural Matrices) isKI = C whereC = (1 1048576 01 _2 + 096 _4)q1= cos(__) _ =abUse of this solution yields KI = 25680 MPa_pm

2 Assumptions and Approach21 Assumptions

_ Linear elastic fracture mechanics (LEFM)_ Plane strain problem122 Approach_ Since the LEFM assumption is used the SIFs at a crack tip may be computed using theANSYSs KCALC command The analysis used a _t of the nodal displacements in thevicinity of the crack tip (see the ANSYS Inc Theory Reference)_ Due to the symmetry of the problem only a quarter model is analyzed_ The crack-tip region is meshed using quarter-point (singular) 8-node quadrilateral elements(PLANE82)

3 Preprocessing1 Give the Job a NameUtility MenugtFilegtChange Jobname The following window comes up Enter a name for example `CentralCrack and click onOK

2 Define Element TypeMain MenugtPreprocessorgtElement TypegtAddEditDelete

_ This brings up the Element Types window Click on the Add button_ The Library of Element Types window appears Highlight `Solid and `8node 82 asshown Click on OK

_ You should see `Type 1 PLANE82 in the `Element Types window as follows

_ Click on the Options button in the above window The below window comes upSelect `Plane strain for `Element behavior K3 and click OK

_ Click on the Close button in the `Element Types window

3 Define Material PropertiesMain MenugtPreprocessorgtMaterial PropsgtMaterial Models3_ In the right side of the `Define Material Model Behavior window that opens doubleclick on `Structural then `Linear then `Elastic then finally `Isotropic

The following window comes up Enter in values for the Youngs modulus (EX = 2E5)and Poissons ratio (PRXY = 03) of the plate material

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Linear elastic fracture mechanics (LEFM)_ Plane strain problem122 Approach_ Since the LEFM assumption is used the SIFs at a crack tip may be computed using theANSYSs KCALC command The analysis used a _t of the nodal displacements in thevicinity of the crack tip (see the ANSYS Inc Theory Reference)_ Due to the symmetry of the problem only a quarter model is analyzed_ The crack-tip region is meshed using quarter-point (singular) 8-node quadrilateral elements(PLANE82)

3 Preprocessing1 Give the Job a NameUtility MenugtFilegtChange Jobname The following window comes up Enter a name for example `CentralCrack and click onOK

2 Define Element TypeMain MenugtPreprocessorgtElement TypegtAddEditDelete

_ This brings up the Element Types window Click on the Add button_ The Library of Element Types window appears Highlight `Solid and `8node 82 asshown Click on OK

_ You should see `Type 1 PLANE82 in the `Element Types window as follows

_ Click on the Options button in the above window The below window comes upSelect `Plane strain for `Element behavior K3 and click OK

_ Click on the Close button in the `Element Types window

3 Define Material PropertiesMain MenugtPreprocessorgtMaterial PropsgtMaterial Models3_ In the right side of the `Define Material Model Behavior window that opens doubleclick on `Structural then `Linear then `Elastic then finally `Isotropic

The following window comes up Enter in values for the Youngs modulus (EX = 2E5)and Poissons ratio (PRXY = 03) of the plate material

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ This brings up the Element Types window Click on the Add button_ The Library of Element Types window appears Highlight `Solid and `8node 82 asshown Click on OK

_ You should see `Type 1 PLANE82 in the `Element Types window as follows

_ Click on the Options button in the above window The below window comes upSelect `Plane strain for `Element behavior K3 and click OK

_ Click on the Close button in the `Element Types window

3 Define Material PropertiesMain MenugtPreprocessorgtMaterial PropsgtMaterial Models3_ In the right side of the `Define Material Model Behavior window that opens doubleclick on `Structural then `Linear then `Elastic then finally `Isotropic

The following window comes up Enter in values for the Youngs modulus (EX = 2E5)and Poissons ratio (PRXY = 03) of the plate material

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Click on the Close button in the `Element Types window

3 Define Material PropertiesMain MenugtPreprocessorgtMaterial PropsgtMaterial Models3_ In the right side of the `Define Material Model Behavior window that opens doubleclick on `Structural then `Linear then `Elastic then finally `Isotropic

The following window comes up Enter in values for the Youngs modulus (EX = 2E5)and Poissons ratio (PRXY = 03) of the plate material

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

The following window comes up Enter in values for the Youngs modulus (EX = 2E5)and Poissons ratio (PRXY = 03) of the plate material

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Click OK then close the `De_ne Material Model Behavior window

4 De_ne KeypointsMain MenugtPreprocessorgtModelinggtCreategtKeypointsgtIn Active CSWe are going to create 5 keypoints given in the following tableKeypoint X Y1 0 02 002 03 01 04 01 015 0 014_ To create keypoint 1 enter `1 as keypoint number and `0 and `0 as the X and Ycoordinates in the following window Click on Apply

_ Repeat the above step for keypoints 2 through 5 Note that you must click on OKinstead of Apply after entering data of the _nal keypoint

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

5 De_ne Line SegmentsMain MenugtPreprocessorgtModelinggtCreategtLinesgtLinesgtIn Active Coord_ Pick keypoint 1 then keypoint 2 to create a line connecting them (line 1)_ Repeat the previous step to create lines connecting keypoints 2 and 3 (line 2)keypoints 3 and 4 (line 3) keypoints 4 and 5 (line 4) and keypoints 5 and1 (line 5)

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Click on OK to close the `Lines in Active Coord window (picking window)

_ Turn on the numbering by selecting Utility MenugtPlotCtrlsgtNumbering Thebelow window appears Check the boxes for `Keypoint numbers and `Line numbersas shown then click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Select Utility MenugtPlotgtLines Your graphics window should look like this

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

6 Discretize Lines L3 L4 and L5Main MenugtPreprocessorgtMeshinggtSize CntrlsgtManualSizegtLinesgtPickedLines_ Pick lines 3 and 4 Click on the OK button in the picking window_ The window opens Enter `4 for No of element divisions then click Apply

_ Pick line 5 then click OK in the picking window_ In the below window that comes up again enter `6 for No of element divisionsand `02 for `Spacing ratio then click OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

7 Create the Concentration Keypoint (Crack Tip)Main MenugtPreprocessorgtMeshinggtSize CntrlsgtConcentrat KPsgtCreate_ Pick keypoint 2 then click OK in the picking window_ In the below window that appears you should see `2 as `Keypoint for concentrationEnter `00025 (= a=4) for `Radius of 1st row of elems input `8 for `No of elemsaround circumf and select `Skewed 14pt for `midside node position Click OK

8 Create the AreaMain MenugtPreprocessorgtModelinggtCreategtAreasgtArbitrarygtBy Lines_ Pick all _ve lines (L1 through L5) Click OK in the picking window

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

9 Apply Boundary ConditionsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtDisplacementgtSymmetry BCgtwith Area_ Pick line 2 Click Apply (in the picking window) Pick the area Click Apply_ Pick line 5 Click Apply Pick the area Click OK10 Apply LoadsMain MenugtPreprocessorgtLoadsgtDe_ne LoadsgtApplygtStructuralgtPressuregtOn Lines_ Pick line 4 Click OK in the picking window_ In the below window that comes up select `Constant value for `Apply PRES on lines as aenter `-100 for `Load PRES value then click OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

11 Mesh the ModelMain MenugtPreprocessorgtMeshinggtMeshgtAreasgtFree_ Pick the area Click OK in the picking window_ Close the `Warning window In your ANSYS window a mesh as shown at the top ofnext page should appear

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

4 Processing (Solving)Main MenugtSolutiongtAnalysis TypegtNew Analysis_ Make sure that `Static is selected Click OKMain MenugtSolutiongtSolvegtCurrent LS_ Check your solution options listed in the `STATUS Command window_ Click the OK button in the `Solve Current Load Step window_ Click the Yes button in the `Verify window_ You should see the message `Solution is done in the `Note window that comes up Closethe `Note and `STATUS Command windows

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

5 Postprocessing1 Zoom the Crack-Tip RegionUtility MenugtPlotCtrlsgtPan Zoom Rotate This brings up the following window

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ In the above window click on the Win Zoom button and zoom the crack-tip regionthen click on the Close button to close the window_ Plot the nodes by selecting Utility MenugtPlotgtNodes_ Turn on the node numbering by selecting Utility MenugtPlotCtrlsgtNumbering then check the box for `Node numbers then _nally click on OK Your ANSYSGraphics windows should be similar to the following

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

2 De_ne Crack-Face PathMain MenugtGeneral PostprocgtPath OperationsgtDe_ne PathgtBy Nodes_ Pick the crack-tip node (node 14) then the quarter-point node (node 27) and _nallythe third node (node 26) on the crack face Click OK_ In the below window that appears enter `K1 for `Define Path Name then click OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

3 De_ne Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtLocal Coordinate SystemsgtCreate Local CSgtBy 3Nodes11_ Pick node 14 (the crack-tip node) then node 29 and _nally node 140 This bringsup the following window

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_ Note from the above window that the reference number of the crack-tip coordinatesystem is 11 Click on the OK button4 Activate the Local Crack-Tip Coordinate SystemUtility MenugtWorkPlanegtChange Active CS togtSpeci_ed Coord Sys _ In the below window that comes up enter `11 for `Coordinate system number thenclick OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

_

_ To activate the crack-tip coordinate system as results coordinate system select MainMenugtGeneral PostprocgtOptions for Outp In the window that appears (asshown at the top of next page) select `Local system for `Results coord system andenter `11 for `Local system reference no Click OK in this window

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

5 Determine the Mode-I Stress Intensity Factor using KCALCMain MenugtGeneral PostprocgtNodal CalcsgtStress Int Factr_ In the below window that opens select `Plain strain for `Disp extrapolat based onand `Half-symm bc for `Model Type

_ Click on OK The window shown at the top of next page appears and it shows that theSIFs at the crack tip (node 4) areKI = 26567 KII = 0 KIII = 0Note that the results KII = 0 and KIII = 0 are obvious for this problem The ANSYSsolution for KI (25567 MPa_pm) is in very good agreement with that obtained fromWD Pilkey (25680 MPa_pm) The discrepancy is_ =KPilkeyI 1048576 KANSYSI

KPilkeyI

=

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK

25680 1048576 2556725680= 044

_ Close the `KCALC Command window_ You may want to recover the whole meshed model by selecting Utility MenugtPlotCtrlsgtPan Zoom Rotate then click on theFit button and close the `Pan-Zoom-Rotate window selecting Utility MenugtPlotgtElements6 Exit ANSYS Saving All DataUtility MenugtFilegtExit In the window that opens select `Save Everything and click on OK