Using XFEM in Abaqus to Model Fracture and Crack Propagation

3/11/2014

Live eSeminar

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Using XFEM in Abaqus to Model Fracture and Crack Propagation 1/23/2014

Arun Krishnan, PhD Simulia Central

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3/11/2014

Training Spotlight on Modeling Fracture and Failure with Abaqus

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Agenda: Introduction to Fracture and Failure What is XFEM? Basic XFEM Concepts Damage Modeling Creating an XFEM Fracture Model Examples of XFEM models Limitations Demo: Crack Growth in a Three-point Bend Specimen using XFEM

45 minutes

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Modeling Fracture & Failure with Abaqus Training Course Schedule

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North America Schedule Location February 11-13, 2014

Houston, TX

March 25-27, 2014

Online / West Lafayette, IN Followed by Hands-on Workshop on Mar. 28, 2014

July 15-17, 2014

Online / Minneapolis (Eagan), MN Followed by Hands-on Workshop on July 18, 2014

October 7-9, 2014

Houston, TX

October 28-30, 2014

Online / Cincinnati (Mason), OH Followed by Hands-on Workshop on Oct 31, 2014

November 18-20, 2014

Cleveland, OH Followed by Hands-on Workshop on Nov. 11, 2014

http://www.3ds.com/simulia-training International Schedule

Location

February 25-27, 2014

Vélizy-Villacoublay, France

*Download the French PDF course overview here. March 25-27, 2014

Stockholm, Sweden

April 7-9, 2014

Munich, Germany

April 28-30, 2014

Warrington, United Kingdom

May 7-9, 2014

Vienna, Austria

September 15-17, 2014

Beijing, China

October 22-24, 2014 Munich, Germany October 27-29, 2014 Vienna, Austria November 3-5, 2014 Hammersmith, United Kingdom December 17-19, 2014

Maarssen, Netherlands

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Introduction (1/3) – What is Fracture Mechanics? Fracture mechanics is the field of solid mechanics that deals with the behavior of cracked bodies subjected to stresses and strains.

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These can arise from primary applied loads or secondary self-equilibrating stress fields (e.g., residual stresses).

The objective of fracture mechanics is to characterize the local deformation around a crack tip in terms of the asymptotic field around the crack tip scaled by parameters that are a function of the loading and global geometry. Different theories have been proposed to describe the fracture process in order to develop predictive capabilities (LEFM, Cohesive zone models, EPFM etc.)

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Introduction (2/3) – Basic concepts (LEFM) Fracture modes

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Linear Elastic Fracture Mechanics (LEFM) considers three distinct fracture modes: Modes I, II, and III These encompass all possible ways a crack tip can deform. The objective of LEFM is to predict the critical loads that will cause a crack to grow in a brittle material. Stress intensity factor For isotropic, linear elastic materials, LEFM characterizes the local crack-tip stress field in the linear elastic (i.e., brittle) material using a single parameter called the stress intensity factor K.

K depends upon the applied stress, the size and placement of the crack, as well as the geometry of the specimen. Critical value of K is denoted as Kc and known as fracture toughness.

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Introduction (3/3) – Fracture Modeling Methods Two major objectives in fracture mechanics simulations: Stationary crack To determine J-integral, stress intensity factors, crack propagation direction etc.

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Propagating crack (for crack propagation and delamination) Cohesive elements/surface Virtual Crack Closure Technique (VCCT) Material damage and failure Low-cycle fatigue XFEM Shortcomings of traditional methods in FEM for fracture mechanics simulations Time consuming to prepare mesh for crack (focused mesh, crack-tip singularity, degenerate elements) Need advance knowledge of potential crack path (Cohesive elements, VCCT)

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What is XFEM (1/3) – eXtended Finite Element Method The classical fracture modeling techniques only permit crack propagation along predefined element boundaries. (not through elements) XFEM is a technique to model bulk fracture which permits a crack to be located in the element interior

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Mesh-independent crack modeling. Can be used in conjunction with the cohesive zone model or VCCT Modeling delamination in conjunction with bulk crack propagation Can be used for stationary crack and propagating crack simulations Can be used in general static and implicit dynamics procedures (Standard) Easy to use and very powerful technique. (available in Abaqus since 2009) Applications of this technique include Modeling of bulk fracture (Eg. Cracks in pressure vessels) Failure in composites (Eg. Fiber and matrix cracking in laminated composites

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What is XFEM (2/3) – Advantages of XFEM Ease of initial crack definition Mesh is generated independent of the crack Partitioning of geometry not needed at the crack location as in the case of conventional FEM

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Nonlinear material and nonlinear geometric analysis Solution-dependent crack initiation and propagation path Crack path and the crack location do not have to be specified a priori Mesh refinement studies are much simpler Reduced remeshing effort Improved convergence rates in case of stationary cracks Due to the use of singular crack tip enrichment

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What is XFEM (3/3) – Basic ingredients of XFEM Mesh-independent crack modeling – basic ingredients 1.

Need a way to incorporate discontinuous geometry – the crack – and the discontinuous solution field into the finite element basis functions

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eXtended Finite Element Method (XFEM) 2.

Need to quantify the magnitude of the discontinuity – the displacement jump across the crack faces Heavyside function Phantom nodes

3.

Need a method to locate the discontinuity Level set method (LSM)

4.

Crack initiation and propagation criteria At what level of stress or strain does the crack initiate? What is the direction of propagation? Cohesive elements Virtual Crack Closure Technique

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Basic XFEM Concepts (1/3) – Displacement interpolation XFEM displacement interpolation

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Heaviside enrichment term H(x)

Heaviside distribution

aI

Nodal enriched DOF (jump discontinuity)

N

Nodes belonging to elements cut by crack

  4   h  u (x)   N I (x)  u I  H (x )a I   F (x)b I      1 I N    I N    I N  uI

Nodal DOF for conventional shape functions NI

Crack tip enrichment term F(x) 

bI

NΛ

Crack tip asymptotic functions Nodal DOF (crack tip enrichment) Nodes belonging to elements containing crack tip

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Basic XFEM Concepts (2/3) – Level set method Level set method for locating a crack A level set (also called level surface or isosurface) of a real-valued function is the set of all points at which the function attains a specified value

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Example: the zero-valued level set of f (x, y)  x2  y2  r2 is a circle of radius r centered at the origin Popular technique for representing surfaces in interface tracking problems Two functions  and  are used to completely describe the crack The level set  = 0 represents the crack face The intersection of level sets  = 0 and  = 0 denotes the crack front Functions are defined by nodal values whose spatial variation is determined by the usual finite element shape functions (example follows) Function values need to be specified only at nodes belonging to elements cut by the crack

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Basic XFEM Concepts (3/3) – Level set method Calculating  and  The nodal value of the function  is the signed distance of the node from the crack face Positive value on one side of the crack face, negative on the other

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The nodal value of the function is the signed distance of the node from an almost-orthogonal surface passing through the crack front The function  has zero value on this surface and is negative on the side towards the crack

=0

= 0 Node





1

0.25

1.5

2

0.25

1.0

3

0.25

1.5

4

0.25

1.0

1

2

3

4

0.5

1.5

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Damage Modeling (1/3) Two distinct types of damage modeling within an XFEM framework Cohesive damage Linear elastic fracture mechanics (LEFM)

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Cohesive damage Uses traction-separation laws Follows the general framework introduced earlier for element-based cohesive behavior Damage properties are specified as part of the bulk material definition LEFM-based damage Uses the virtual crack closure technique (VCCT) VCCT for XFEM uses the same principles as those presented earlier Damage properties are specified via an interaction property assigned to the XFEM crack Enables modeling low-cycle fatigue

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Damage Modeling (2/3) – Cohesive Damage Modeling T

Delamination applications

N

Traction separation law

GT C

Linear elasticity with damage Available in both Abaqus/Standard and Abaqus/Explicit Modeling of damage Damage initiation I. Traction or separation-based criterion Damage evolution Removal of elements

 Typical traction-separation response 7

Shear mode

6 5

GTC

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Typically characterized by peak strength (N) and fracture energy (GTC) Mode dependent

Normal mode

4 3 2 1 0 0

0.2

0.4

0.6

0.8

1

Mode Mix

Dependence of fracture energy on mode mix

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Damage Modeling (3/3) – LEFM-based Damage Modeling VCCT uses LEFM concepts

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Based on computing the energy release rates for normal and shear crack-tip deformation modes.

Pure Mode I Modified VCCT

Compare energy release rates to interlaminar fracture toughness.

See Rybicki, E. F., and Kanninen, M. F., "A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral," Engineering Fracture Mechanics, Vol. 9, pp. 931-938, 1977.

Node numbers are shown

Nodes 2 and 5 will start to release when: 1 v1,6 Fv ,2,5  GI  GIC Mode II treated 2 bd similarly where GI  mode I energy release rate GIC  critical mode I energy release rate b  width

*An “enhanced” version of VCCT is available to model ductile fracture.

Fv,2,5  vertical force between nodes 2 and 5 v1,6  vertical displacement between nodes 1 and 6

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Creating an XFEM Fracture Model (1/4) Steps 1.

Define damage criteria a.

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b.

2.

If cohesive damage is being used, define damage criteria in the material model If LEFM is being used, then specify damage criteria in the interaction property definition

Define an enrichment region Crack type – stationary (3D only) or propagating (2D or 3D)

3.

Define an initial crack, if present, and assign the appropriate interaction property

4.

If needed, set analysis controls to aid convergence

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Creating an XFEM Fracture Model (2/4) Step-dependent enrichment activation

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Crack growth can be activated or deactivated in analysis steps

*STEP . . . *ENRICHMENT, NAME=Crack-1, ACTIVATE=[ON|OFF]

1

2

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Creating an XFEM Fracture Model (3/4) Output quantities Two output variables are especially useful

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PHILSM I. The scaled signed distance function  used to represent the crack surface II. The scale factor is chosen on a per element basis. III. Needed for visualizing the crack STATUSXFEM I. Indicates the status of the element with a value between 0.0 and 1.0 II. A value of 1.0 indicates that the element is completely cracked, with no traction across the crack faces Any other output variable available in the static stress analysis procedure

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Creating an XFEM Fracture Model (4/4) Postprocessing The crack location is specified by the zero-valued level set of the signed distance function 

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Abaqus/CAE automatically creates an isosurface view cut named Crack_PHILSM if an enrichment is used in the analysis The crack isosurface is displayed by default Contour plots of field quantities should be done with the crack isosurface displayed Ensures that the solution is plotted from the active parts of the overlaid elements according to the phantom nodes approach If the crack isosurface is turned off, only values from the “lower” element are plotted (corresponding to negative values of ) Probing field quantities on an element currently returns values only from the “lower” element (on the side with negative values of )

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (1/11) Model crack initiation and propagation in a plate with a hole Crack initiates at the location of maximum stress concentration Half model is used to take advantage of symmetry

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Modeled using traction-separation based cohesive damage Reference: Abaqus Benchmark Problem 1.19.2

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (2/11) 1 Define the damage criteria

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Damage initiation *MATERIAL . . . *DAMAGE INITIATION, CRITERION=MAXPS, TOL=0.01 22e6 Damage initiation tolerance (default 0.05)

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (3/11) 1 Define the damage criteria (cont’d)

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Damage evolution

*DAMAGE INITIATION, CRITERION=MAXPS, TOL=0.01 22e6 *DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=1.0 2870.0, 2870.0, 2870.0

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (4/11) 1 Define the damage criteria (cont’d)

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Damage stabilization

*DAMAGE 22e6 *DAMAGE 2870.0, *DAMAGE 1.e-5

INITIATION, CRITERION=MAXPS, TOL=0.01 EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=1.0 2870.0, 2870.0 STABILIZATION Coefficient of viscosity 

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (5/11)

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2 Define the enriched region

Pick enriched region Propagating crack

Specify contact interaction (frictionless small-sliding contact only)

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (6/11) 2 Define the enriched region (cont’d) Keyword interface *ENRICHMENT, TYPE=PROPAGATION CRACK, NAME=CRACK-1, ELSET=SELECTED_ELEMENTS, INTERACTION=CONTACT-1

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Frictionless small-sliding contact interaction 3 No initial crack definition is needed Crack will initiate based on specified damage criteria

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (7/11) 4 Set analysis controls to improve convergence behavior

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Set reasonable minimum and maximum increment sizes for step Increase the number of increments for step from the default value of 100

*STEP, NLGEOM=YES *STATIC, inc=1000 0.01, 1.0, 1.0e-09, 0.01 . . .

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (8/11) 4 Set analysis controls to improve convergence behavior (cont’d)

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Use numerical scheme applicable to discontinuous analysis

*STEP, NLGEOM=YES *STATIC, inc=10000 0.01, 1.0, 1.0e-09, 0.01 . . . *CONTROLS, ANALYSIS=DISCONTINUOUS

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (9/11) 4 Set analysis controls to improve convergence behavior (cont’d)

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Increase value of maximum number of attempts before abandoning increment (increased to 20 from the default value of 5)

*STEP, NLGEOM=YES *STATIC, inc=10000 0.01, 1.0, 1.0e-09, 0.01 . . . *CONTROLS, ANALYSIS=DISCONTINUOUS *CONTROLS, PARAMETER=TIME INCREMENTATION , , , , , , , 20 8th field

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (10/11) Output requests Request PHILSM and STATUSXFEM in addition to the usual output for static analysis

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PHILSM is needed for visualizing the crack

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Example 1 – Crack Initiation and Propagation using Cohesive Damage (11/11) Postprocessing Crack isosurface (Crack_PHILSM) created and displayed automatically

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Field and history quantities of interest can be plotted and animated as usual

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Example 2 – Low Cycle Fatigue Same problem as in Examples 1 but subjected to cyclic distributed loading.

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VCCT is used for fracture criterion

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Example 3 – Propagation of an Existing Crack Model with crack subjected to mixed mode loading Initial crack needs to be defined

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Crack propagates at an angle dictated by mode mix ratio at crack tip

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Example 4 – Delamination and Through-thickness Crack Model through-thickness crack propagation using XFEM and delamination using surface-based cohesive behavior in a double cantilever beam specimen Interlaminar crack grows initially

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Through-thickness crack forms once interlaminar crack becomes long enough and the longitudinal stress value builds up due to bending The point at which the through-thickness crack forms depends upon the relative failure stress values of the bulk material and the interface

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Example 4 – Delamination and Through-thickness Crack This model is the same as the double cantilever beam model presented in the surface-based cohesive behavior lecture except:

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Enrichment has been added to the top and bottom beams to allow XFEM crack initiation and propagation

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Limitations of XFEM modeling Can only use linear brick and linear/quadratic tet continuum elements. Crack branching, interacting cracks not possible. Intended for single/few non-interacting cracks. An element cannot be cut by more than one crack.

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Frictional small-sliding contact is considered The small-sliding assumption will result in nonphysical contact behavior if the relative sliding between the contacting surfaces is indeed large Only enriched regions can have a material model with damage If only a portion of the model needs to be enriched define an extra material model with no damage for the regions not enriched Probing field quantities on an element currently returns values only from the “lower” element (corresponding to negative values of )

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Demo: Crack Growth in a Three-point Bend Specimen using XFEM

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1. In this demo, we will see XFEM modeling of a three-point bend specimen a. Create and instance a part to represent the crack geometry b. Use the crack editor to create an enriched region and specify an initial crack. c. Request XFEM-related output d. Specify analysis controls to aid convergence

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3/11/2014

Modeling Fracture & Failure with Abaqus Training Course Schedule

www.3ds.com | © Dassault Systèmes

North America Schedule Location

http://www.3ds.com/simulia-training International Schedule

Location

Online / West Lafayette, IN Followed by Hands-on Workshop on Mar. 28, 2014

February 25-27, 2014

Vélizy-Villacoublay, France

March 25-27, 2014

Stockholm, Sweden

Online / Minneapolis (Eagan), MN Followed by Hands-on Workshop on July 18, 2014

April 7-9, 2014

Munich, Germany

April 28-30, 2014

Warrington, United Kingdom

May 7-9, 2014

Vienna, Austria

October 7-9, 2014

Houston, TX

Beijing, China

October 28-30, 2014

Online / Cincinnati (Mason), OH Followed by Hands-on Workshop on Oct 31, 2014

September 15-17, 2014

February 11-13, 2014

Houston, TX

March 25-27, 2014

July 15-17, 2014

November 18-20, 2014

Cleveland, OH Followed by Hands-on Workshop on Nov. 11, 2014

*Download the French PDF course overview here.

October 22-24, 2014 Munich, Germany October 27-29, 2014 Vienna, Austria November 3-5, 2014 Hammersmith, United Kingdom December 17-19, 2014

Maarssen, Netherlands

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3/11/2014

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