Tutorial 15b CT XFEM

Tutorial 15b: X-FEM, Modelling crack propagation Stephanie Miot

St ategic Simulation & Analysis Ltd Sou outh thiill Ba Barn rn,, Sou South thil illl Bu Busi sin n ss Pa Park rk,, Co Corn rnbu bury ry Par ark, k, Ch Char arlb lbur ury, y, Ox Oxfo ford rds s ire, OX7 3EW T. 01608 811777 F. 01608 11770 [email protected] [email protected] W. W . www.ss nalysis.co.uk

1.

Introduction

In this tutorial, you will modify a model of a compact tension (CT) test to define the material properties, include a pre-existing crack and create X- EM domains. You will then perform a st tic analysis and visualize the simulation of the crack propagation with Abaqus/Viewer.

When you complete this tu orial, you will be able to: -

Define the material roperties including the failure criterion

-

Create an initial cra k

-

Define the crack sur ace properties

-

Create X-FEM enric ed domains

Preliminaries The geometry of the com act tension specimen is presented in Figure 1. The material is a carbon/epoxy unidirectional ply. The lay-up is (08,908)S.

Figure 1: Compact tension specimen

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The part is divided in 3 partitions which represent the 3 groups of plies: 08, 9016 and 08. The failure of the interface between the plies is not modelle .

About X-FEM X-FEM can be used in conjunction with two approaches: -

The cohesive zone

odel (X-FEM-based cohesive behaviou )

-

The virtual crack closure technique (X-FEM-based LEFM ap roach)

In this tutorial, both approaches will be used. X-FEM-based cohesive behaviour is best suited for modelling f ilure of ductile material (matrix failure in the 90° ply) while X-FEM-based LEFM approach is appropriate for modelling f ilure of brittle material (fibre failure in the 0° ply).

2.

Setting up the model

Open the model Tutorial1 b.cae.

This file contains the geo etry and the mesh of the CT specimen, the boundary conditions and the loading. In this tutorial, you will create an initial crack, define the material properties a d the crack surface properties and

reate X-FEM

domains to allow cracks to propagate in the structure. You will finally run a static analysis and use the vis alization module to post-process the results of the simulation.


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3.

Initial crack

1. Create a surface to be sed to locale the initial crack in the structure. a. Go into the Part Mod le and create a new part named Crack. Select: 3D, Deformable, Shell Extrusion. b. Draw a horizontal line of 11 mm. Click OK. c. Set the depth of the ex rusion at 6 mm. d. Go into the Assembly

odule and instance the part: Crack.

e. Use the Translate Inst nce tool to position the surface as sho n in Figure 2. The surface is wider th n the part (4 mm) and longer than the i itial crack (10 mm). It should be positioned so that the edges are at 1mm of t e faces of the CT specimen.

Figure 2: C mpact tension specimen with initial crack


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4.

XFEM-based ohesive behaviour

1. Define the orthotropic elastic behaviour of the 90° ply with the following material properties: Elasticity coefficients: -

E1 = 156 GPa

-

ν12 = ν13 =

-

E2 = 8.6 GPa

-

ν23 =

-

E3 = 8.0 GPa

-

G12 = G13 = G23 = 4.5 GPa

-

SL = ST =200 MPa

Coefficients for matrix failu e criterion: - YT = 60 MPa -

Energy release rate in mode I: GIc = 0.3 kJ/m²

-

Energy release rate in mode II: GIIc = 0.8 kJ/m²

-

Energy release rate in mode III: GIIIc = 0.8 kJ/m²

0.34

0.4

a. Go into the Property Module and click the Create Material icon b. In the Edit Material dialog box, name the material T300/920_90. c. From the material edi or’s menu bar, select Mechanical

→

Elasticity

→

Elastic d. Select Type: Engineering constants and enter the material d ta as defined above. e. From the material edi or’s menu bar, select Mechanical

→

Damage for

Traction Separation L ws → Maxs Damage f. Select Direction relati e to local 1-direction: Parallel and accept the default value of the Tolerance: 0.05. g. Specify the maximum tress in the normal and the two shear directions.


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h. Click Suboptions and select Damage Evolution. In the Sub ption Editor dialog box, select Type: Energy and Mixed Mode behaviour:

K. Toggle on

Power and specify η = 2.2. Specify the Fracture Energy for th three failure modes. i.

Click Suboptions an select Damage Stabilization Coh sive. In the Suboption Editor dial g box, specify the Viscosity coefficie t: 1e-5. Then click OK to exit the Suboption editor and OK to exit the Material editor.


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2. Create a new section and assign section properties to the 90° plies. a. In the model tree, expa d Parts and right click Part-1. Click Ma e Current. b. Click the Create Section icon

.

Name

the

section:

ly90.

Select

Category: Solid and T pe: Homogeneous. Click Continue... c. In the Edit Section di log box, select Material: T300/920_90. Click OK to complete the creation o the new section. d. Click the Assign Secti n icon

. Select the 3 middle cells (see Figure 3)

then click Done. e. In the Edit Section Assignment dialog box, select Section: Ply90 and click OK.


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Figure 3: In green, cells to be assigned section: Ply90

3. Define the material ori ntation for the 90° plies. a. Click the Assign Material Orientation icon

then select the 3 middle cells

as shown in Figure 3. b. Click Use Default Orie tation or Other Method.

c. In the Edit Material Orientation dialog box, select Definitio : Coordinate system and click the Edit icon right corner and select

. Click Datum CSYS List... in the bottom

atum csys-1.

d. Specify the Additional Rotation Direction: 3 and the Additio al Rotation / Angle: 90. Accept the default selection of the direction 3 fo the stacking direction. Click OK.


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4. Create an X-FEM domain (or enriched zone). a. Go into the Interaction Module. In the menu bar, click Sp cial / Crack/ Manager... b. In the Crack Manage dialog box, click Create... Name the new domain Crack-90-1 and select ype: XFEM. Click Continue... c. Specify the selection of the crack domain: geometric cells.


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d. Select the 3 middle cell as shown in Figure 3. e. In the Edit Crack dialog box, check that the option: Allow cr ck growth is selected then toggle on Crack location. Click the Edit icon

then select

the surface highlighted ink in Figure 4. Click OK.

Figure 4: XF M domain + crack location for the 90° plies


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5.

XFEM-based EFM approach

1. Define the orthotropi

elastic behaviour of the 0° ply with the following

material properties: Elasticity coefficients: -

E1 = 156 GPa

-

ν12 = ν13 =

-

E2 = 8.6 GPa

-

ν23 =

-

E3 = 8.0 GPa

-

G12 = G13 = G23 = 4.5 GPa

0.34

0.4

a. Go into the Property Module and click the Create Material icon b. In the Edit Material dialog box, name the material T300/920_0. c. From the material edi or’s menu bar, select Mechanical

→

Elasticity

→

Elastic d. Select Type: Engineering constants and enter the material d ta as defined above.

2. Create a new section and assign section properties to the 0° plies. a. Click the Create Section icon

.

Name

the

section:

Ply0.

Select

Category: Solid and T pe: Homogeneous. Click Continue... b. In the Edit Section dialog box, select Material: T300/920_0. Cli k OK. c. Click the Assign Section icon undefined (grey cells i

and select the regions which remain

Figure 3). In the Edit Section Assignment dialog

box, select Section: Pl 0 and click OK.


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3. Define the material ori ntation for the 0° plies. a. Click the Assign Material Orientation icon

then select the 0° plies.

b. Click Use Default Orie tation or Other Method.

c. In the Edit Material Orientation dialog box, select Definitio : Coordinate system and click the Edit icon right corner and select

. Click Datum CSYS List... in the bottom

atum csys-1.

d. Accept the default sel ections for the additional rotation and the stacking directions. Click OK.

4. Define a fracture-ba ed surface behaviour and specify the fracture criterion in enriched ele ents. a. Go into the Interactio

Module and click the Create Interac ion Property

icon b. Name the new intera tion property FibreFailure and acce t the default selection Type: Contact. c. From the Contact Prop rty editor’s menu bar, select Mechanic l

→

Fracture

Criterion. d. Select Direction of cr ck growth: Normal. Modify the Toler nce value to 0.1.


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e. Specify the critical energy release rates for the three failure exponent for the BK la

odes and the

as:

-

GIc = GIIc = GIIIc = 5 mJ/mm²

-

η =

2.


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5. Create an X-FEM domain for each group of 0° plies. a. In the menu bar, click Special / Crack/ Manager... b. In the Crack Manage dialog box, click Create... Name the new domain Crack-0-1 and select T pe: XFEM. Click Continue... c. Specify the selection of the crack domain: geometric cells. d. Select the 3 cells highli hted red in Figure 5. e. In the Edit Crack dialog box, check that the option: Allow cr ck growth is selected then toggle on Crack location. Click the Edit icon

then select

the surface highlighted ink in Figure 5.

Figure 5: XFEM domain + crack location for one group of 0° plies


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f. Toggle on Specify con act property and select FibreFailure.

lick OK.

g. Follow the instructions a to f to create the last X-FEM domain. Select the second group of 0° plie . Name the domain crack-0-2.

Figure 6: XFEM domain + crack location for the second group of ° plies


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6.

Static analysi and post-processing

1. Create new output req ests. The preselected default output does not include the X-FEM variables. To visualize the crack propagation in the Visualization module, you will write additional field output to the output database ile. a. Go into the Step Module. Click the Field Output Manager icon. b. In the Field Output Requests Manager dialog box, click Edit.. to modify the request F-Output-1. c. In the Edit Field Output Request dialog box, in the Output expand the Failure/Fracture list and toggle on the variables expand

the

State/Fi ld/User/Time list

and

toggle

on

ariables list, HILSM. Then the

variable

STATUSXFEM.


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2. Modify the general sol tion controls to improve convergenc behaviour. a. In the menu bar, click

ther

→

General Solution Controls

→

dit → Step-1.

Accept the warning me sage and click Continue... b. In the General Soluti n Controls Editor, click Specify. In he tab: Time Incrementation, toggle on Discontinuous analysis. Then cli k the first tab labelled More and specify IA = 10.

3. Run the job. Note that t e job has been created. a. Go into the Job Modul . Click the Job Manager icon. b. Optional, if possible to un the analysis on multiple cpus: In the Job Manager dialog box, click Edit... In the Parallelization tab, toggle on Use multiple processors and select the number of processors you want to u e. c. In the Job Manager di log box, click Submit to run the Job: CT01.


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4. Analyse the results of he simulation.

a. When the job submission has been completed, in the Job M nager dialog box, click Results or open

CT01.odb in

the Visualization Module.

b. Click the Plot Contour on Deformed Shape icon c. Click the Field Output d. In the Field Output

ialog icon

or click Result → Field Output.

ialog box, in the Primary Variable t b, select the

Output Variable: STA USXFEM. Then click Apply.

e. Click the Create Display Group icon

or click Tools

→

Dis lay Group

→

Create... f. In the Create Display

roup dialog box, select Items: Eleme ts / Method:

Section assignment

nd PART-1-1._PICKEDSET66... Click the Replace

icon

then click Dismiss. You can now visualise the crack in the 90°

plies.


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g. In the Field Output di log box, select the Output Variable: S Component: S22. Then click Apply. h. Click the Contour Options icon

. In the tab: Limits, specify Max = 100.

Click OK. Use the fr me selector or the animation tool to visualise the evolution of the stress field when the crack propagates. i. Click the Replace all icon

. Select the Output Variable: S Component:

S11. Click Apply. j.

Click the Contour Opt ons icon and modify the limits. Specify Max = 1000. Click Apply. Use the rame selector or the animation tool to visualise the evolution of the stress field when the crack propagates.

k. In the Contour Plot O tions dialog box, click Max: Auto-compute. Then in the Field Output dialo box, select PHILSM. You can visualise the values of the level sets used to locate the crack in the mesh.


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Tutorial 15b CT XFEM

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