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Ozen Engineering Inc.

1210 E. Arques Ave, Suite 207

Sunnyvale, CA 94085

info@ozeninc.com

Fracture Mechanics in Ansys R16

Session-03

XFEM Method – Meshless

Fracture Mechanics

ie no specific crack tip mesh

XFEM Method

• The extended finite element method (XFEM) is a numerical technique for solution of problems which involve singularities and high gradient changes

• In fracture mechanics context, it can be used to model cracks by enriching the DOF in the model

• XFEM eliminates the necessity of remeshingcrack tip regions

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XFEM Method - Features

• Offers a way to model the cracks without explicitly meshing the crack surfaces

• Allows for arbitrary crack growth within the existing mesh. No morphing or remeshing is needed

• Initial cracks must be present in the model and can be modeled as traction free or with cohesive zone behavior

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XFEM Method - Details

• Supported on Ansys Mechanical APDL

• PLANE182 and SOLID185 elements (w/o midside nodes) are supported

• CINT command is used to calculated maximum circumferential stress criterion as crack propagation criterion

• CGROW command is used to define the crack-growth-set, fracture criterion and solution control parameters

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XFEM Method - History

• XFEM was developed in 1999, by Ted Belytschkoof North Western University USA

• XFEM is a numerical method built on the generalized finite element method (GFEM) and the partition of unity method (PUM)

• There are academic and commercial implementations

• Ansys R16 is the first release of XFEM, there were user defined programming implementation with Ansys

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XFEM Method - Overview

• The techniques used in XFEM can be listed as:– Singularity-Based Approach

• Accounts for crack tip singularities as well as the jumps in displacements across the crack surfaces. Cracks may terminate inside a finite element

– Phantom Node Method• Accounts only for jumps in displacements across the crack surfaces. Crack tip singularity

is not taken into account. Cracks terminate at the edge/face of a finite element.

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XFEM Method – Crack-Growth Simulation Process

• An XFEM crack-growth simulation is assumed to be quasi-static (i.e. inertial effects are negligible)

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1. Create a Finite Element Model with an Initial Crack

2. Define the Crack-Growth Criterion3. Define the Decay of Stresses on the Newly

Created Crack Segments4. Specify Cohesive Zone Behavior on Initial Crack5. Perform the Crack-Growth Criterion Evaluation6. Perform the Crack-Growth Calculation

XFEM Step-01: FE model with initial crack

• Define an enrichment region in the model with possible crack propagation

• Multiple initial cracks can be defined in the region• Enrichment region should be limited, as addition of extra internal

nodes in the model requires extra computational time

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XFENRICH, EncrihmentID, CompName, MAT_ID

Command to define enrichment region

Named assigned to identify enrichment region

Component name which includes the elements for enrichment region

Used to define cohesive zone behavior for crack faces

XFEM Step-01: FE model with initial crack

• Crack geometry in an element is defined by specifying two signed distance functions at the nodes of the element

• The two signed distance functions at the nodes represent the position of the nodes from the crack surface and from the crack front

• PHI cannot be zero!• The initial crack cannot cut the element at the nodes of the element

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XFDATA, LSM, ELEMNUM, NODENUM, PHI

Command to define initial crack

Element number

Node number

Signed normal distance of the node from crack

XFEM Step-02: Define crack-growth criterion

• Crack-growth criterion must be specified for newly cracked segments• The crack segments are such that they fully cut the elements ahead of the

crack• The crack propagates at the rate of only one element at a time

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TB, CGCR,,,STTMAX (or PSMAX)• STTMAX (maximum circumferential stress σθθ

criterion)

• PSMAX (circumferential stress criterion based on σrθ=0

• Ideally both criteria gives same or very similar results

XFEM Step-3&4: Define condition for new crack faces

• When cohesive segments are initiated, the cohesive stresses in the crack segments gradually decrease to zero as the deformation progresses

• This behavior can be defined for initial cracks and existing cracks via TB command

• Contact between crack faces are resolved using frictionless contact. This is default behavior and cannot be changed

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TB, CGCR,,,,RLIN

For Newly Created Crack Segments;Rigid Linear Law is available

TB, CZM,,,,BILI

For Initial Crack Segments;Bilinear Cohesive Law is available

XFEM Step-05: Crack-Growth criterion evaluation

1. Define the elements that form the crack front as a crack front element set

CINT, CXFE, CompName

2. Define the distance ahead of the crack tip at which stress is evaluated

CINT, RADIUS, VALUE

3. Define the number of intervals, min and max for sweep angle

CINT, RSWEEP, NUM_INTERVALS, MIN_ANGLE, MAX_ANGLE

4. Calculate circumferential stressCINT, TYPE, STTMAX (or PSMAX)

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XFEM Step-06: Crack-Growth calculation

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1. Initiate the crack-growth set

CGROW, NEW, SET_NUM

2. Specify the crack calculation ID:

CGROW, CID, ID_NUM

3. Specify XFEM crack-growth method

CGROW, METHOD, XFEM

4. Specify the fracture criterion

CGROW, FCOPTION, MTAB, MAT_ID

Verification Problem from Ansys Help

• VM287Initial Crack Growth Angle in a Pure Shear Problem with the XFEM Method

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Verification Problem from Ansys Help

• VM287Initial Crack Growth Angle in a Pure Shear Problem with the XFEM Method

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Example Problem from Ansys Help

• help/ans_frac/Hlp_G_FRACXFEM.html#d0e5542

Crack Growth in a Three-Point Bending Specimen

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Example Problem from Ansys Help

• help/ans_frac/Hlp_G_FRACXFEM.html#d0e5542

Crack Growth in a Three-Point Bending Specimen

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Example Problem from Ansys Help

• /device,vector,1

• /pnum,node,1

• /pnum,elem,1

• /number

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XFEM Method – Limitations & Assumptions

• Only linear elastic materials can be used in conjunction with the available fracture criteria

• Multiple initial crack can be defined in the region• The XFEM analysis is assumed to be quasi-static, only!• Crack tip singularity effects are not incorporated into the

analysis (ie. Phantom Node Method is the only supported method)

• In 3D XFEM, hexahedral SOLID185 elements are required where crack is initiated and expected to propagate

• Time stepping needs to be small enough to capture crack propagation

• Element birth/death is not supported• Distributed Ansys is not supported

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Following Week Schedule

• April 9th: 10AM-10:45AM PT Fracture Mechanics with Cohesive Zone and Delamination

• April 16th: 10AM-10:45AM PT Fatigue Crack Propagation

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END

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(408) 732-4665

info@ozeninc.com

www.ozeninc.com