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Problem 17: Analysis of a cracked body with ADINA-M/OC ADINA R & D, Inc. 17-1 Problem description It is desired to analyze the cracked body shown using a 3D finite element mesh: 0.030 0.030 0.03 radius 0.035 radius 0.05 radius Cracked body dimensions Top view 0.1 0.05 0.0275 0.0275 All dimensions in meters Front view 10 N vertical load applied to top holes 6 Bottom holes fixed Material properties: E = 2.07 10 N/m ´ 11 2 n = 0.29 Crack line Crack line

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• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-1

Problem description It is desired to analyze the cracked body shown using a 3D finite element mesh:

0.030

0.030

Cracked body dimensions

Top view

0.1

0.05

0.0275

0.0275

All dimensions in meters

Front view

10 N vertical loadapplied to top holes

6

Bottom holes fixed

Material properties:

E = 2.07 10 N/m 11 2

= 0.29

Crack line

Crack line

• Problem 17: Analysis of a cracked body with ADINA-M/OC

We use the CRACK-M features of the AUI to create a mesh suitable for fracture mechanics analysis. These features require that the model be divided into bodies as follows: 1) Crack front bodies, that surround the crack front line. Crack front bodies are topologically equivalent to half-cylinders. Mapped meshing is used in crack front bodies. 2) Crack sleeve bodies, that surround the crack front bodies. Free-form meshing is used in crack sleeve bodies. 3) Bodies that represent the remaining part of the model. Free-form meshing is used in these bodies. The arrangements of bodies used in this model are shown in the following figure. This figure shows a section through the model. The faces of the cracked area are shown slightly separated, but this is just to visually show the cracked area. In the model, the faces of the cracked area are initially coincident.

B6

B7

B10

B11

0.03

0.035

0.040

B3

B4

B4, B6, B8, B10 are cracked bodies.B5, B7, B9, B11 are crack sleeve bodies.B1, B3 are bodies for the rest of the model.

Not drawn to scale.Holes in rest of model not shown.

B5

B1

B8

B9

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-3

Notice that the cracked area is entirely surrounded by either crack bodies or crack sleeve bodies. The ADINA-M/OC (ADINA-M using the OpenCascade geometry kernel) geometry modeler is used in this analysis. (The ADINA-M/PS geometry modeler can also be used, but only if the input is modified.) In the fracture mechanics analysis, we calculate J-integrals at various stations along the crack front. In this calculation, it is assumed that the crack propagates along the surface of self-similar crack advance. However, actual crack propagation is not considered. For the theory used in fracture mechanics, see Chapter 10 of the ADINA Theory and Modeling Guide. In this problem solution, we will demonstrate the following topics that have not been presented in previous problems: \$ Using sheets to section bodies \$ Creating bodies by revolving sheets \$ Creating bodies by transformations \$ Linking faces of ADINA-M/OC geometry \$ Defining constraint sets \$ Creating CRACK-M definitions \$ Using the Active Zone icon to plot only updated geometry \$ Using cutting planes to examine the mesh and the results \$ Using the fracture mechanics analysis features. Before you begin Please refer to the Icon Locator Tables chapter of the Primer for the locations of all of the AUI icons. Please refer to the Hints chapter of the Primer for useful hints. Note that you must have a version of the AUI that includes the ADINA-M/OC geometry modeler. In addition you need to allocate at least 80 MB of memory to the AUI. This problem cannot be solved with the 900 nodes version of the ADINA System because the model contains more than 900 nodes. Invoking the AUI and choosing the finite element program Invoke the AUI with the ADINA-M/OC modeler (for example, using the command aui9.0 -occ for Linux versions) and choose ADINA Structures from the Program Module drop-down list. Choose EditMemory Usage and make sure that the ADINA/AUI memory is at least 80 MB.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Defining model control data Problem heading: Choose ControlHeading, enter the heading Problem 17: Analysis of a cracked body with ADINA-M/OC and click OK. Master degrees of freedom: Choose ControlDegrees of Freedom, uncheck the X-Rotation, Y-Rotation and Z-Rotation buttons and click OK. Overview of geometry definition Before proceeding with the geometry definition, we outline with sketches the steps used. You may want to refer to these steps when working through this problem. Step 1) Define geometry without crack.

x y

Pipe body created

B1

B = body

B1

B3

Body sectionedinto halves

Top holes created Bottom holes created

z

Step 2) Define sheet for upper right crack body.

Points and linesfor upper rightcrack front body

After creation ofsheet body, sheetbody is face 1 ofbody 4

P101

L1B4F1

L2

L3

P102P103

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-5

Step 3) Define sheet for upper right crack sleeve body.

Points and lines for upper rightcrack sleeve body

Sheet for face of upper right cracksleeve body, after subtraction of body 4

P104

L1

L2

L3

L4

B5

B5

P105P106

F1

F1

P107

After creation of sheet body,sheet body is face 1 of body 5

Step 4) Revolve sheets +180 degrees, then revolve sheets -180 degrees.

Sheet revolved intoupper crack bodies

Sheet revolved into uppercrack sleeve bodies

Section view of cracked bodies and crack sheet bodies

B4

B5

B6

B7

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Step 5) Create reflection of upper crack bodies and upper crack sleeve bodies.

B4

E1 E1

E1E1

F3 F3

F3F3

F6 F6

F6F6

B8

B9

B5

E = edge, F = face

Reflected bodies separatedin this figure for clarity

B6

B10

B11

B7

The right-hand side bodies (6, 7, 10, 11) will be used for the definition of the first CRACK-M, and the left-hand side bodies (4, 5, 8, 9) will be used for the definition of the second CRACK-M. Step 6) Subtract crack bodies and crack sleeve bodies from rest of model.

B4

E1 E1

E1E1

F3 F3

F3F3

F6 F6

F6F6

B8

B9

B1 B3

B5

B6

B10

B11

B7

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-7

Defining geometry, step 1: Model without crack

Pipe: Click the Define Bodies icon , add body 1, set the Type to Pipe, the Radius to 0.05, the Thickness to 0.02, the Length to 0.1, make sure that the Center Position is (0.0, 0.0, 0.0), set the Axis to Z and click Save. (We do not want to close the dialog box yet.) Sectioning of pipe: Add body 2, set the Type to Sheet, set Defined By to Y-Plane and click

OK. Click the Boolean Operator icon , set the Modifier Type to Subtract, set the Target Body to 1, enter 2 in the first row of the table and click OK. When you click the Wire Frame

icon , the graphics window should look something like this:

TIME 1.000

X Y

Z

Creation of holes: To make the first set of holes, we create a cylinder and subtract it from the

pipe bodies. Click the Define Bodies icon , add body 4, set the Type to Cylinder, the Radius to 0.015, the Length to 0.15, the Center Position to (0.0, 0.0, 0.0275), make sure that the Axis is X and click OK.

Now click the Boolean Operator icon , set the Operator Type to Subtract, set the Target Body to 1, check the Keep the Subtracting Bodies button, enter 4 in the first row of the table and click Save. Set the Target Body to 3, enter 4 in the first row of the table and click OK.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Unfortunately the rendering of the geometry bodies is not very good. Click the Modify Mesh

Plot icon , click the Surface Depiction... button, set the Open Cascade Curve Tolerance to 0.01 and click OK twice to close both dialog boxes. The graphics window should look something like this:

TIME 1.000

X Y

Z

We make the second set of holes in a similar way. Click the Define Bodies icon , add body 4, set the Type to Cylinder, the Radius to 0.015, the Length to 0.15, the Center Position to (0.0, 0.0, -0.0275), the Axis to Y and click OK.

Now click the Boolean Operator icon , set the Operator Type to Subtract, set the Target Body to 1, check the Keep the Subtracting Bodies button, enter 4 in the first row of the table and click Save. Set the Target Body to 3, enter 4 in the first row of the table and click OK. The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-9

TIME 1.000

X Y

Z

Defining geometry, step 2: Sheet for upper right crack body Active zone for crack geometry: In steps 2 and 3, we will concentrate on the crack geometry. When we create the crack geometry, we do not want to plot the rest of the model. So we create an initially empty zone, set this zone to be the "active zone", and plot the active zone.

Click the Change Zone icon and click the ... button to the right of the Zone Name field. Add zone CRACK and click OK. The AUI gives a warning "No data input rows entered for zone CRACK". Click OK to close the warning message. In the "Change Zone of Mesh Plot" dialog box, set the Zone Name to CRACK and click OK. The AUI gives an alert message "Nothing to plot in mesh plot. Creating empty mesh plot." Click OK to close the alert

message. Now click the Active Zone icon , set the first row of the table to CRACK and click OK.

Sheet for upper right crack body: Click the Define Points icon and scroll down to the bottom of the table. The highest point number currently defined should be 36 (38 for Windows versions). Add one more row with the following information and click OK.

Point # X1 X2 X3 101 0.035 0.0 0.0

Click the Define Lines icon , add line 1, set the Type to Extruded, set the Initial Point to 101, set the components of the Vector to 0.003, 0, 0 and click Save. Add line 2, set the Type

• Problem 17: Analysis of a cracked body with ADINA-M/OC

to Revolved, set the Initial Point to 102 and the Angle of Rotation to 180. Then, in the Axis of Revolution box, set "Defined by" to Vector, set the components of vector A to (0.035, 0, 0), the components of vector B to (0, -1, 0) and click Save. Add line 3, set the Type to Straight, set Point 1 to 103 and Point 2 to 101, then click Save. Finally add line 4, set the Type to Combined, enter 1, 2, 3 in the first three rows of the table and click OK.

Click the Define Bodies icon , add body 4, set the Type to Sheet, set the External Line Loop # to 4 and click OK.

When you click the XZ View icon , the Point Labels icon , the Line/Edge Labels icon

, the Surface/Face Labels icon and the Volume/Body Labels icon , the graphics window should look something like this:

P101 P102P103 E1

E2

E3

F1B4

TIME 1.000

XY

Z

Defining geometry, step 3: Sheet for upper right crack sleeve body

Sheet for upper right crack sleeve body: Click the Define Points icon and scroll down to the bottom of the table. The highest point number currently defined should be 103. Add one more row with the following information and click OK.

Point # X1 X2 X3 104 0.04 0.0 0.0

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-11

You can't see point 104 because it is outside of the graphics window. Use the Pick icon and the mouse to shrink the mesh plot until point 104 is visible.

Click the Define Lines icon , add line 1, set the Type to Extruded, set the Initial Point to 104, set the components of the Vector to 0, 0, 0.005 and click Save. Add line 2, set the Type to Extruded, set the Initial Point to 105, set the components of the Vector to -0.01, 0, 0 and click Save. Add line 3, set the Type to Extruded, set the Initial Point to 106, set the components of the Vector to 0, 0, -0.005 and click Save. Add line 4, set the Type to Straight, set Point 1 to 107 and Point 2 to 104, then click Save. Finally add line 5, set the Type to Combined, enter 1, 2, 3, 4 in the first four rows of the table and click OK.

Click the Define Bodies icon , add body 5, set the Type to Sheet, set the External Line Loop # to 5 and click OK.

Click the Boolean Operator icon , set the Operator Type to Subtract, set the Target Body to 5, check the Keep the Subtracting Bodies button, enter 4 in the first row of the table and click OK. The graphics window should look something like this:

P101 P102P103 P104

P105P106

P107 E1

E2

E3

E1

E2

E3

E4

E5

E6

F1B4

F1

B5

TIME 1.000

XY

Z

Defining geometry, step 4: Revolving sheets

Click the Body Revolved icon , set the Revolve Face # to 1, the Body # to 4, the Angle of Revolution to 180, the Axis to Z and click Apply. Set the Revolve Face # to 1, the Body # to

• Problem 17: Analysis of a cracked body with ADINA-M/OC

5, the Angle of Revolution to 180, the Axis to Z and click Apply. Set the Revolve Face # to 1, the Body # to 4, the Angle of Revolution to -180, check the "Merge Revolved Body with Original Body" button, set the Axis to Z and click Apply. Set the Revolve Face # to 1, the Body # to 5, the Angle of Revolution to -180, check the " Merge Revolved Body with Original Body " button, set the Axis to Z and click OK.

When you click the Iso View 1 icon , the Point Labels icon , the Line/Edge Labels

icon , the Surface/Face Labels icon and the Volume/Body Labels icon , the graphics window should look something like this:

TIME 1.000

X Y

Z

Defining geometry, step 5: Reflecting bodies

Click the Define Bodies icon , add body 8, and set the Type to Transformed. Click the ... button to the right of the Transformation Label field and add transformation 1. Set the Type to Reflection, make sure that the Plane is XY and click OK. In the Define Body dialog box, make sure that "Define by" is set to Copying, set the Parent Body to 4 and the Transformation Label to 1. Then enter 5, 6, 7 in the table and click OK. The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-13

TIME 1.000

X Y

Z

Defining geometry, step 6: Subtracting crack bodies and crack sleeve bodies from rest of model Since we have finished defining the crack bodies and crack sleeve bodies, we no longer want

to show just these bodies. Click the Change Zone icon , make sure that the Zone Name is

WHOLE_MODEL and click OK. Use the Pick icon and the mouse to resize the mesh plot into the graphics window.

We also want to turn off the Active Zone feature. Click the Active Zone icon , clear the table and click OK.

Click the Boolean Operator icon , set the Operator Type to Subtract, set the Target Body to 1, check the Keep the Subtracting Bodies button, enter 4, 5, 8, 9 in the first four rows of the table and click Save. Now set the Operator Type to Subtract, set the Target Body to 3, check the Keep the Subtracting Bodies button, enter 6, 7, 10, 11 in the first four rows of the table and click OK. The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

TIME 1.000

X Y

Z

Specifying loads and boundary conditions In order to define the loads and boundary conditions, we need to know some of the point and face numbers on bodies 1 and 3. The point and face numbers are slightly different depending upon whether the Linux version or the Windows version of the AUI is used. Therefore we provide separate instructions for the Linux version and the Windows version. Linux version The figure on the next page shows the point and face numbers of bodies 1 and 3.

Fixities: Click the Apply Fixity icon , set the Apply to field to Faces, set the Body # to 1, enter face 11 in the first row of the table and click Save. Now set the Body # to 3, enter face 6 in the first row of the table and click OK.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-15

F11 of B1

F6 of B3

F6 of B1 F7 of B3

F7 of B1

F8 of B3

F12 of B3

Face 6 of body 3, and face 11 of body 1 are fixed.Face 6 of body 1 and faces 12 and 13 of body 3 are constrained to point 15.Face 7 of body 1 and faces 7 and 8 of body 3 are constrained to point 20.

P15

Linux version

P20

Z

XY

F13 of B3

Constraint equations: We constrain the faces upon which we apply the forces to points, then we apply the forces to the points. Choose ModelConstraintsConstraint Equations, define the following constraint sets and click OK.

Constraint Set

Entity Type

Entity #

Body #

Slave DOF

Master Entity Type

Point # Master DOF

1 Face 7 1 Z-Trans Point 20 Z-Trans 2 Face 7 3 Z-Trans Point 20 Z-Trans 3 Face 8 3 Z-Trans Point 20 Z-Trans 4 Face 6 1 Z-Trans Point 15 Z-Trans 5 Face 12 3 Z-Trans Point 15 Z-Trans 6 Face 13 3 Z-Trans Point 15 Z-Trans

(we abbreviate Z-Translation by Z-Trans in this table)

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Loads: Click the Apply Load icon , make sure that the Load Type is Force and click the Define... button to the right of the Load Number field. In the Define Concentrated Force dialog box, add force 1, set the Magnitude to 5E5, the Direction to (0, 0, 1) and click OK. In the Apply Load dialog box, make sure that the Apply to field is set to Point. In the first two rows of the table, set the Point # to 15 and 20 respectively, then click OK to close the dialog box. Windows version The following figure shows the point and face numbers of bodies 1 and 3.

F11 of B1

F6 of B3

F6 of B1 F13 of B3

F7 of B1

F12 of B3

F8 of B3

Face 6 of body 3, and face 11 of body 1 are fixed.Face 6 of body 1 and faces 7 and 8 of body 3 are constrained to point 15.Face 7 of body 1 and faces 12 and 13 of body 3 are constrained to point 21.

P15

Windows version

P21

Z

XY

F7 of B3

Fixities: Click the Apply Fixity icon , set the Apply to field to Faces, set the Body # to 1, enter face 11 in the first row of the table and click Save. Now set the Body # to 3, enter face 6 in the first row of the table and click OK. Constraint equations: We constrain the faces upon which we apply the forces to points, then we apply the forces to the points. Choose ModelConstraintsConstraint Equations, define the following constraint sets and click OK.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-17

Constraint Set

Entity Type

Entity #

Body #

Slave DOF

Master Entity Type

Point # Master DOF

1 Face 7 1 Z-Trans Point 21 Z-Trans 2 Face 12 3 Z-Trans Point 21 Z-Trans 3 Face 13 3 Z-Trans Point 21 Z-Trans 4 Face 6 1 Z-Trans Point 15 Z-Trans 5 Face 7 3 Z-Trans Point 15 Z-Trans 6 Face 8 3 Z-Trans Point 15 Z-Trans

(we abbreviate Z-Translation by Z-Trans in this table)

Loads: Click the Apply Load icon , make sure that the Load Type is Force and click the Define... button to the right of the Load Number field. In the Define Concentrated Force dialog box, add force 1, set the Magnitude to 5E5, the Direction to (0, 0, 1) and click OK. In the Apply Load dialog box, make sure that the Apply to field is set to Point. In the first two rows of the table, set the Point # to 15 and 21 respectively, then click OK to close the dialog box. All versions

When you click the Boundary Plot icon and the Load Plot icon , the graphics window should look something like this:

B

B

U1

U2

U3

B - - -

TIME 1.000

X Y

Z

PRESCRIBEDFORCETIME 1.000

500000.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Linking adjacent body faces Face links: Choose GeometryFacesFace Link, add face link 1, set the Type to Created for All Faces/Surfaces and click OK. The AUI displays a warning message "Face 1 of body 4 and face 2 of body 5 cannot be linked..." This message is OK because the listed faces are not adjacent to each other. Click OK to close the warning message. Also note that the AUI writes the message 32 face-links are created to the bottom of the Message Window. Creating CRACK-M definitions The crack front is a closed line. So we create one CRACK-M definition for each 180 degree segment of the line, then merge the CRACK-M definitions. The CRACK-M definitions for the 180 degree segments are shown in the following sketch.

B4

E1 E1

E1E1

F3 F3

F3F3

F6 F6

F6

CRACK-M 1: Crack front body 1 = 6

Crack front face 1 = 3Crack front edge 1 = 1Crack front body 2 = 10Crack front face 2 = 3Crack front edge 2 = 1Cracked surface body 1 = 7Cracked surface face 1 = 6Cracked surface body 2 = 11Cracked surface face 2 = 6

CRACK-M 2: Crack front body 1 = 4

Crack front face 1 = 3Crack front edge 1 = 1Crack front body 2 = 8Crack front face 2 = 3Crack front edge 2 = 1Cracked surface body 1 = 5Cracked surface face 1 = 6Cracked surface body 2 =9Cracked surface face 2 = 6

F6

B8

B9

B5

B6

B10

B11

B7

Choose ModelFracture3-D Crack Front (ADINA-M) Define, add the following information into the dialog box and click Save (do not close the dialog box yet).

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-19

Crack Front #

Crack Front Body #1

Face Edge Crack Front Body #2

Face Edge Cracked Surface Body #1

Face Cracked Surface Body #2

Face

1 6 3 1 10 3 1 7 6 11 6 2 4 3 1 8 3 1 5 6 9 6 Now add Crack Front # 3, set the Type to Combine, set Crack Front A to 1, Crack Front B to 2 and click OK. Subdividing the CRACK-M Choose ModelFracture3-D Crack Front (ADINA-M) Subdivide, set "Apply to Crack Front" to 3, set "# Subdivisions along Crack Front" to 36, "# Subdivisions in Radial Direction" to 3, set "# Subdivisions in Tangential Direction for" both Body 1 and Body 2 to 6, then click OK. Defining the material

Click the Manage Materials icon and click the Elastic Isotropic button. In the Define Isotropic Linear Elastic Material dialog box, add material 1, set the Young=s Modulus to 2.07E11, the Poisson=s ratio to 0.29 and click OK. Click Close to close the Manage Material Definitions dialog box. Defining the element groups Although one element group could have been used in this model, we use two element groups instead, one element group in the crack bodies and crack sleeve bodies, and another element group for the rest of the model.

Element group definition: Click the Define Element Groups icon , add group number 1, set the Type to 3-D Solid and click Save. Then add group number 2, make sure that the Type is 3-D Solid and click OK. Meshing the CRACK-M Choose ModelFracture3-D Crack Front (ADINA-M) Mesh Crack, set the Crack Front # to 3, set the "3-D Solid Element Group #" to 1, the "Nodes per Element" to 27, and click OK. The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

B

B

U1

U2

U3

B - - -

TIME 1.000

X Y

Z

PRESCRIBEDFORCETIME 1.000

500000.

Note that elements 1 to 1296 in element group 1 are used to mesh the CRACK-M. We want the nodes near the crack front line to be at the quarter-points. Choose ModelFracture3-D Crack Front (ADINA-M) Quarter Point, make sure that "Place Mid-Side Nodes At" is set to "Quarter Position" and click OK. Subdividing the crack sleeve bodies We will specify a uniform element size in the crack sleeve bodies. Click the Subdivide

Bodies icon , set the Body to 5, and set the Element Edge Length to 0.005. Then set the first three rows of the table to 7, 9, 11 and click OK. Meshing the crack sleeve bodies Choose ModelFracture3-D Crack Front (ADINA-M) Mesh Body, mesh the following bodies and click OK. (You can ignore and close the Warning dialog boxes that appear.) Crack Front Body # 3-D Solid Element Group # Nodes per Element 5 1 27 7 1 27 9 1 27 11 1 27 The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-21

B

B

U1

U2

U3

B - - -

TIME 1.000

X Y

Z

PRESCRIBEDFORCETIME 1.000

500000.

Subdividing the rest of the model We will specify a uniform element size in the bodies for the rest of the model. Click the

Subdivide Bodies icon , set the Body to 1, and set the Element Edge Length to 0.007. Then set the first row of the table to 3 and click OK. Meshing the rest of the model

First click the Hidden Surfaces Removed icon so that we don't see the dashed hidden lines in the mesh.

Click the Mesh Bodies icon , make sure that the Element Group is set to 2, set the Nodes per Element to 27, set "Pyramid Elements" to Yes, set "Mid-Side Nodes" to "Place on Straight Line", set the first two rows of the table to 1, 3 and click OK. You can ignore and close the Warning dialog boxes that appear. The graphics window should look something like the figure on the next page. Specifying fracture mechanics calculations Fracture control: Choose ModelFractureFracture Control, check the Fracture Analysis field, set the Dimension to 3-D Crack and click OK.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

C

B

B

B

BBBB

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BBBBB

B

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BB

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BBB

BB

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BB

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BBBB

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BBBBBBB

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BB B BBB

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B

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U1

U2

U3

B CC - - -

TIME 1.000

X Y

Z

PRESCRIBEDFORCETIME 1.000

500000.

Virtual shifts: We will create the virtual shifts automatically from the CRACK-M. Choose ModelFracture3-D Crack Front (ADINA-M) Virtual Shift, make sure that the Crack Front # is 3, then click OK. The AUI writes the message "148 virtual shifts defined for crack front body 3" to the message window. Generating the data file, running ADINA, loading the porthole file

Click the Save icon and save the database to file prob17. Click the Data File/Solution

icon , set the file name to prob17, make sure that the Run Solution button is checked and click Save. When ADINA is finished, close all open dialog boxes, choose Post-Processing from the Program Module drop-down list (you can discard all changes), click the Open icon

and open porthole file prob17. Plotting the deformed mesh

We need to magnify the plotted displacements. Click the Scale Displacements icon . The displacement magnification factor appears to be too large for this model, so we will reduce it.

Click the Modify Mesh Plot icon and click the Model Depiction button. Set the Magnification Factor to 40 and click OK twice to close both dialog boxes.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-23

Now click the Shading icon . The graphics window should look something like this:

TIME 1.000 DISP MAG 40.00

X Y

Z

Determining the maximum displacement Choose ListExtreme ValuesZone, set Variable 1 to (Displacement:Z-DISPLACEMENT) and click Apply. The AUI reports that the maximum Z-displacement is 1.58755E-4 at node 31314 (your node number may be different, but the Z-displacement should be very close to ours). Click Close to close the dialog box. Plotting the element groups in different colors In the remaining mesh plots, we do not want to view the constraint equations. Choose DisplayGeometry/Mesh PlotDefine Style, set the Constraint Depiction to OFF and click OK. Click the Clear icon , then the Mesh Plot icon . Notice that the constraint

equation lines are not displayed. Now click the Cut Surface icon , set the Type to Cutting Plane, the Below the Cutplane field to Display as Usual, the Above the Cutplane field to Do not Display and click OK.

Click the Color Element Groups icon . The graphics window should look something like the figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

TIME 1.000

X Y

Z

Click the Color Element Groups icon to turn off the element group colors. Examining the meshing near the crack line

Click the Clear icon , then the Mesh Plot icon . In the Model Tree, expand the Zone keyword, right click on 2. EG1 and choose Display. Let=s magnify the displacements so that we can see the crack opening under the load. Click

the Scale Displacements icon . The graphics window should look something like the top figure on the next page. Now let's look at just the mapped mesh. Remember that elements 1 to 1296 in element group 1 are used to mesh the crack front bodies in the CRACK-M. Click the Change Zone icon

, click ... to the right of the Zone Name field, add zone CRACK, click the Edit field, enter the text ELEMENTS 1 TO 1296 OF ELEMENT GROUP 1 in the first row of the table, then click OK. In the Change Zone of Mesh Plot dialog box, set the Zone Name to CRACK and click OK. The graphics window should look something like the bottom figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-25

TIME 1.000 DISP MAG 57.41

X Y

Z

TIME 1.000 DISP MAG 57.41

X Y

Z

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Now let's just look at part of the mapped mesh. Click the Change Zone icon , set the zone name to CRACK, click ... to the right of the Zone Name field, click the Edit field, change the text so that it reads ELEMENTS 1 TO 324 OF ELEMENT GROUP 1 in the first row of the table, then click OK. In the Change Zone of Mesh Plot dialog box, set

the Zone Name to CRACK and click OK. Use the Pick icon and the mouse to rotate the plot until the graphics window looks something like this:

TIME 1.000 DISP MAG 57.41 X

YZ

Now click the Node Symbols icon and zoom into the top of the mesh plot. The graphics window should look something like the figure on the next page. You can see that the nodes near the crack front line are located at the quarter-points.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-27

Plotting the virtual shifts The following diagram shows the corner nodes on the crack front line and arrows depicting the first 37 virtual shifts for these nodes.

VS1, VS37

VS2

- Corner node on crack front line

VS36

x

y

Notice that virtual shifts 1 and 37 are at the same node.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

Virtual shifts 1 to 37 shift only the node on the crack front, virtual shifts 38 to 74 shift the elements in ring 1, virtual shifts 75 to 111 shift the elements in rings 1 and 2, and virtual shifts 112 to 148 shift the elements in rings 1, 2 and 3. For example, virtual shift 38 shifts the same node as virtual shift 1, but virtual shift 38 shifts the elements in ring 1 as well. And virtual shift 75 shifts the same node as virtual shift 1, but virtual shift 75 shifts the elements in rings 1 and 2.

Click the Modify Mesh Plot icon and click the Virtual Shift Depiction... button. In the Define Virtual Shift Depiction dialog box, click the Plot field, and click OK twice to close both dialog boxes. The graphics window should look something like this:

Now repeat the above steps, and in the Define Virtual Shift Depiction dialog box, set the Virtual Shift # to 2. The graphics window should look something like the top figure on the next page. Repeat the above steps, and in the Define Virtual Shift Depiction dialog box, set the Virtual Shift # to 39. The graphics window should look something like the bottom figure on the next page.

• Problem 17: Analysis of a cracked body with ADINA-M/OC

ADINA R & D, Inc. 17-29

Virtual shift 39 shifts the same crack front node as virtual shift 2, but virtual shift 39 also shifts the first ring of elements around the crack front. Graphing the J integral for each virtual shift Choose Definitionsodel LineVirtual Shift, add line LINE and click the Auto button. In the From row, set the Virtual Shift # to 1, in the To row, set the Virtual Shift # to 111 and

• Problem 17: Analysis of a cracked body with ADINA-M/OC

click OK. The table in the Define Model Line dialog box is filled in. Click OK to close this dialog box.

Now click the Clear icon , choose GraphResponse Curve (Model Line), set the X Coordinate to (Fracture: VIRTUAL_SHIFT_NUMBER), set the Y Coordinate to (Fracture: J-PARAMETER_3) and click OK. The graphics window should look something like this:

0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120.65.

70.

75.

80.

85.

90.

95.

100.

105.

110.

115.

*10

2

LINE GRAPH

Line LINE

VIRTUAL_SHIFT_NUMBER

J-PA

RAM

ETER

_3

Remember that virtual shifts 1 to 37 correspond to only nodes on the crack front shifted, virtual shifts 38 to 74 correspond to 1 ring of elements shifted and virtual shifts 75 to 111 correspond to 2 rings of elements shifted. There is very little difference between the results for 0, 1 and 2 rings for this problem. Choose GraphList. The value of J-PARAMETER_3 for virtual shift 1 should be around 1.11491E+04 (Pa-m). Exiting the AUI: Choose FileExit (you can discard all changes).