Using/Obtaining Material Properties for Advanced FE analysis · PDF file• ABAQUS courses...

Copyright 2004 ABAQUS, Inc.

Using/Obtaining Material Properties for Advanced FE analysis

Frans PeetersGeneral Manager European OperationsABAQUS, Inc.Lisbon, December 4, 2004


4th FENET Annual Industry Meeting

Presentation Overview

• Introduction• Constitutive modeling• Rubber elasticity• Progressive damage and failure• Summary



Introduction

• Advanced material behaviour– Large variety of physical phenomena

– Choice of constitutive model requires knowledge about behaviour and limitations of models

– Availability of accurate material data for complete range of applied stress states, temperatures and other state conditions is crucial for obtaining correct prediction of behaviour

– Need for properties which describe behaviour. Existing data is often unsuitable as it characterizes certain indirect aspects, e.g. hardness



Constitutive modeling

• ABAQUS courses address model details, material testing and usage aspects for a large variety of material models.

Metal inelasticity course covers topics like ;– Ductile Metal Response– Classical Metal Plasticity – Cyclic Loading of a Flange– Johnson-Cook Plasticity– Metal Failure Models– Creep and Swelling– Viscoplasticity– Gray Cast Iron Plasticity– Porous Metal Plasticity

Geotechnical course covers topics like;– Modified Drucker-Prager/Cap Model – Critical State (Clay) Plasticity Model – Jointed Material Model



Constitutive modeling – cont.

Rubber-viscoelasticity course covers;– Rubber Elasticity Models– Physical Testing– Curve Fitting – Time Domain Viscoelasticity– Frequency Domain Viscoelasticity– Time-Temperature Correspondence– Hysteresis in Elastomers

Composite course covers topics like;– Microscopic Modeling– Reinforcement Modeling– Macroscopic Modeling– Mixed Modeling– Submodeling and Composites




• Modeling issues for metallic behaviour

– Is material virgin in initial situation? Preceding processes/treatments may result in anisotropy, residual stresses, inhomogeneous properties

– In case of time dependent behaviour, often insufficient data to describe sophisticated models

– Combination/interaction of phenomena may cause extra challenges

– No material data for extreme situations (long creep times, high strain rates, etc.)

– Lack of accurate properties when dealing with elevated temperatures T>0.4Tm



Enforcing numerically “loss of memory” in case of annealing or melting to avoid unrealistic results

plate region

weld region

symmetry axis

Residual stresses without annealing Residual stresses with annealing




• Modeling issues for non-metallic behaviour

– Large number of plastic materials but only basic parameters available. Time and rate effects often treated as confidential information by raw material supplier.

– Reinforcements cause extra complexity

– Certain rubber materials show strong dependency on filler materials which results in broad range of properties

– Hysteric effects necessitate extra calibration to describe “saturated”behaviour

– Cell-type material may violate continuous mechanics assumptions

– Data for in vivo behaviour of biological material not obtainable.




• Hysteresis in Elastomers– Many rubbers are known to be

rate-dependent and to exhibit hysteresis upon cyclic loading.

– The figure at right shows a typical hysteresis response (uniaxial compression at constant strain rate) for a filled rubber subjected to different final strains (from Bergstrom and Boyce1).

1. Bergstrom, J.S., and M.C. Boyce, “Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers,” Journal of the Mechanics and Physics of Solids, vol. 46, pp. 931-954, 1998.




• Recommendations for successful advanced material modeling – Obtain good understanding of constitutive models

– Obtain complete set of properties necessary to describe chosen model

– Obtain good insight in specific behaviour by performing a variety of numerical tests on small sized model covering complete load spectrum


Rubber Elasticity



Rubber Elasticity

• Rubber materials are widely used in many engineering applications, as indicated in the figures below:

TireDeck lid Gasket

Mount Boot Bushing



Rubber Elasticity

– The mechanical behavior of rubber (hyperelastic or hyperfoam) materials is expressed in terms of a strain energy potential

where S is a stress measure and F is a measure of deformation.

– Because the material is initially isotropic, we write the strain energy potential in terms of the strain invariants and Jel :

and are measures of deviatoric strain.

Jel is the volume ratio, a measure of volumetric strain.

( )( ) U FU U F SF

∂= =

∂, such that ,

1 2( , , )elU U I I J= .

1 2, ,I I

1I 2I



Rubber Elasticity

Physically motivated models

Arruda-BoyceVan der Waals

Phenomenological modelsPolynomial (order N)

Mooney-Rivlin (1st order)Reduced polynomial (independent of )

Neo-Hookean (1st order)Yeoh (3rd order)

Ogden (order N)Marlow (independent of )

2I

Material parameters(deviatoric behavior)

24

≥ 2N2N132N

N/A2I



Rubber Elasticity

• Comparison of the solid rubber models

– Gum stock uniaxial data (Gerke):

• Crude data but captures essential characteristics.



Rubber Elasticity

– Unit-element uniaxial tension tests are performed with ABAQUS.

• All material parameters are evaluated automatically by ABAQUS.Video Clip

Van der Waals model response

Gum stock dataGum stock data

Arruda-Boyce model responseOgden (N=2) model response

Gum stock data

Yeoh model response

Gum stock data

Mooney-Rivlin model response

Gum stock data

Neo-Hookean model response

Marlow model response

Gum stock data



Rubber Elasticity

– Choosing a strain energy function in a particular problem depends on the availability of sufficient and “accurate” experimental data.

• Use data from experiments involving simple deformations:

– Uniaxial tension and compression

– Biaxial tension and compression

– Planar tension and compression

• If compressibility is important, volumetric test data must also be used.

– E.g., highly confined materials (such as an O-ring).



Rubber Elasticity

Schematic illustrations of deformation modes



Rubber Elasticity

• Comparison of Simple Tension and Equibiaxial behaviour prediction using uniaxial test data



Rubber Elasticity

• Defining rubber elasticity in ABAQUS/CAE: hyperelasticity



Rubber Elasticity

• Entering test data

Nominal stress and strain

Click MB3



Rubber Elasticity

• Automatic evaluation of the models using ABAQUS/CAE

– Verify correlation between predicted behavior and experimental data.

– Use ABAQUS/CAE to perform standard unit-element tests.

• Supply experimental test data.

• Specify material models and deformation modes.

– X–Y plots appear for each test.

• Predicted nominal stress-strain curves plotted against experimental test data.



Rubber Elasticity

– The hyperelastic material curve fitting capability allows to compare different hyperelastic models with the test data.


Progressive Damage and Failure



General Framework for Damage and Failure Modeling

• Components of failure modeling– Undamaged constitutive behavior

(e.g., elastic-plastic with hardening)

– Damage initiation (point A)

– Damage evolution (path A–B)

– Choice of element removal (point B)

• Damage evolution models minimize mesh dependency

ε

σA

B

Undamaged response

Damaged response

Typical material response showing progressive damage




• Damage initiation– Defines the point of initiation of

degradation of stiffness

– Determined by a user-specified criterion

– Does not actually lead to damage unless damage evolution is also specified

• Output variables associated with each criterion

• Useful for evaluating the severity of current deformation state Ductile ShearForming limit

Different damage initiation criteria on an aluminum double-chamber profile




• Damage initiation criteria– Ductile criterion

• Fracture due to nucleation, growth, and coalescence of voids

– Shear criterion• Fracture due to shear band localization

– Localized necking criterion• Fracture due to through-thickness localized necking

of aluminum sheet• Forming Limit Diagram (FLD)• Marciniak-Kuczynski (M-K) analysis

• Damage evolution criteria– Effective plastic displacement– Fracture energy



Video Clip


• Element removal– ABAQUS offers the choice to remove the

element from the mesh once the material stiffness is fully degraded

– Used in combination with the general contact functionality in ABAQUS/Explicit provides for an EROSION capability

– In ABAQUS/Viewer, failed elements can be removed based on their STATUS.



Example: Fastener damage and failure

Rigid spot welds Compliant spot welds with damage and failure



Cohesive Elements

• Model progressive failure at interfaces– Adhesive joints with finite thickness

• Constitutive modeling based on any ABAQUS material

• Enables failure modeling in ABAQUS/Explicit consistent with general framework

– Delamination (adhesive layer of zero thickness)

• Based on a traction separation description for delamination

• Enables failure modeling consistent with general framework

– Damage initiation criteria

– Damage evolution criteria

ABAQUS/Standard analysis of a T-peel specimen with two discretized adhesive

patches



Cohesive Elements: Example

Cohesive elements (adhesive)

Failed regions

Video Clip



Cohesive Elements: Example 2



Virtual Crack Closure Technique (VCCT)• Analyze damage tolerance of

composite structures– Characterize onset and growth of

delamination– Mixed-mode propagation– Uses LEFM concepts

• Boeing has selected ABAQUS to commercialize their proprietary implementation of the Virtual Crack Closure Technique

Modeling of debonding along skin-stringer interface



Summary

• Modeling of advanced material behaviour requires good understanding of models, good insight in behaviour and requires accurate and sufficient material data

• Chosen models should be verified in complete loading range• In coming years direct modeling of progressive damage and failure

will become feasible


Using/Obtaining Material Properties for Advanced FE analysis

Frans PeetersGeneral Manager European OperationsABAQUS, Inc.Lisbon, December 4, 2004

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