Failurepredictionforadvancedcrashworthinessof ... · PDF...

International Journal of Impact Engineering 30 (2004) 853–872

Failure prediction for advanced crashworthiness oftransportation vehicles

Anthony K. Picketta,*, Thomas Pyttelb, Fabrice Payenb, Franck Lauroc,Nikica Petrinicd, Heinz Wernere, Jens Christleinf

aCranfield University, SIMS, Bedfordshire MK43 OAL, UKbESI GmbH, Eschborn, Germany

cUniversity of Valenciennes, FrancedUniversity of Oxford, UK

eBMW AG, M .unchen, GermanyfAUDI AG, Neckarsulm, Germany

Accepted 5 April 2004

Abstract

During the past two decades explicit finite element crashworthiness codes have become an indispensabletool for the design of crash and passenger safety systems. These codes have proven remarkably reliable forthe prediction of ductile metal structures that deform plastically; however, they are not reliable for joiningsystems and materials such as high strength steels, plastics and low ductility lightweight materials all ofwhich are liable to fracture during the crash event.In order to improve crash failure prediction of materials and joining systems the CEC has recently

funded a 3 year European research project dedicated to this topic. Specifically the project concernedaluminium, magnesium, high strength steels, plastics and two primary joining techniques; namely spotweldsand weldlines. Numerous new developments were undertaken including improved failure laws, adaptivemeshing and element splitting to treat crack propagation. In the case of sheet stamping, investigations havealso tried to account for process history effects and the metallurgical changes that occur duringmanufacture. This project has recently finished and this paper presents some of the key research results ofthe work concerning materials failure modelling.r 2004 Elsevier Ltd. All rights reserved.

Keywords: Crashworthiness; Material modelling; Failure modelling; Simulation

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*Corresponding author.

E-mail address: [email protected] (A.K. Pickett).

0734-743X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijimpeng.2004.04.004

1. Introduction

Traditionally automotive ‘body in white’ structures are manufactured using individual stampedparts that are spotwelded together. The predominant material used is low cost ductile sheet metalwhich can be readily stamped to shape and joined. During the past 20 years crashworthinesssimulation of these structures has proven remarkably good, largely because crashworthinessexplicit finite element (FE) codes, such as [1,2] can accurately predict the simple plastic bendingand stretching deformation mechanisms that occur. It is not usually necessary to predict materialfailure.In recent years automotive manufacturers are increasingly using new lightweight materials to

reduce weight; these include plastics, composites, aluminium, magnesium and new types of highstrength steels. Many of these materials have limited strength or ductility, or may be used inhighly loaded applications; in each case rupture is a serious possibility during the crash event.Furthermore, the joining of these materials presents another source of potential failure. Bothmaterial and joining failure will have serious consequences on vehicle crashworthiness and mustbe predictable if the numerical model is to be reliably used in the design process.A large amount of research work concerning numerical modelling of material failure can be

found in the literature [3]. However, unfortunately, this work is usually not appropriate forpractical crashworthiness analysis using an explicit FE code which is the established numericaltechnique for crash simulation. Consequently, it has been necessary to undertake a dedicatedEuropean (Framework V) research project, IMPACT [4], to develop models and methodologiesfor failure prediction. This work has been carried out within the commercial crashworthiness FEcode PAM-CRASH [1].The IMPACT project was initiated in 2000 and completed in 2003. New (and existing) material

failure laws for both thermo visco-elastic plastics and advanced metals were investigated withspecial emphasis to accurately predict both initial material failure and subsequent crackpropagation. Crack propagation should be accurately represented in order to evaluate its effect onthe structure integrity and crashworthiness; for this two techniques using adaptive meshing andelement splitting have been studied. The work also accounted for changes in material morphologythat result from the manufacturing process; this will influence failure limits for metal stampedparts due to the shaping operation.

2. Constitutive modelling of failure and solution strategies

Two different approaches are considered for material failure modelling. First, a micro-mechanical approach using 3D solid elements is used to provide a reasonably accurate predictionof the 3D stress distribution in the necking failure location and around a propagating crack. Ifsuitably fine meshing and appropriate material laws are selected then both failure initiation andcrack propagation can be represented; clearly this approach leads to large FE models and istherefore restricted to component failure analysis. The second approach is more practical for largescale crash analysis and uses conventional shell elements and macro-mechanical failure criteria toidentify the onset of material failure. This law cannot treat crack propagation and consequently

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A.K. Pickett et al. / International Journal of Impact Engineering 30 (2004) 853–872854

element splitting and energy-based criteria are applied for this phase of failure. The followingsections briefly outline both approaches.

2.1. Micro-mechanical models

The term ‘micro-mechanical models’ is used here to classify a modelling approach usingdetailed 3D solid elements which attempt to represent local necking, the formation of a crack andcrack propagation. During the course of the project phenomenological constitutive models withfailure criteria based upon micro-mechanical void growth using the Gurson model [5] and theGologanu model [6] were developed, together with the Lemaitre mezzo-scale damage mechanicsmodel [7] and the Wilkins failure criteria [8]; each of these models is briefly described below.

2.1.1. The Gurson damage model

In recent years the Gurson constitutive model [5] has been widely used to treat progressivemicrorupture of ductile metals. This model represents the commonly observed stages of ductilefracture, which include

(1) The formation of voids around inclusions and second phase particles.(2) The growth of voids due to plastic straining and hydrostatic stress.(3) The coalescence of growing voids leading to fracture.

These mechanisms are represented by introducing strain softening to the von Mises elasto-plastic yield surface to treat damage growth. The nucleation rate of micro-voids is expressed as aGaussian distribution over plastic strains. The mean effective plastic strain eN; the nucleatedmicrovoid volume fraction fN and standard deviation of this Gaussian distribution SN are threeGurson parameters that must be found. The growth is controlled by plastic strain and thehydrostatic state of stress. Additional parameters must be given for initial void content f0; thecritical microvoid volume fraction at the onset of coalescence fC and the critical fraction of voidsat which fracture occurs fF: Usually ‘inverse engineering’ techniques are used to determine theGurson parameters by correlating test and analysis results for failure load and cross sectiondimension changes which occur at the neck of a tensile coupon test.The Gurson model is a quadratic formulation of plastic potential which can also be used as a

yield function in which seq is the macroscopic equivalent stress, sM is the elasto-viscoplastic flowstress, sm is the mean stress (¼ ðs11 þ s22 þ s33Þ=3), q1 and q2 are two material constants and f � isthe Tvergaard and Needleman effective void volume fraction [9],

fevp ¼s2eqs2M

� j ¼ 0;

where

j ¼ 1þ ðq1f �Þ2 � 2q1f

� coshðvÞ; n ¼3

2q2

smsM

:

The microvoids volume fraction rate is expressed by

’f ¼ ’fgrowth þ ’fnucleation;

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A.K. Pickett et al. / International Journal of Impact Engineering 30 (2004) 853–872 855

where the growth of existing voids is given by

’fgrowth ¼ ð1� f Þ’ekk

and the void nucleation is controlled by plastic strain and takes the form,

’fnucleation ¼fN

SN

ffiffiffiffiffiffi2p

p exp �1

2

eM � eNSN

� �2( )

’eM:

The effective void volume fraction f � is then defined by

f �f for fp fc;

fc þð1=q1Þ � fc

fF � fcðf � fcÞ for f > fc;

8<:

where fc and fF are two additional, previously defined, fitting parameters.The main disadvantages of the model are determination of the Gurson parameters and, more

importantly, that damage is only a consequence of hydrostatic loading. Damage and failure dueto shear loading is not considered. Furthermore, studies in the IMPACT project on tensile loadednotched specimens have found that the optimal Gurson parameters vary with notch diameter; thiswould indicate that the Gurson parameters are not a constant, but may be a function of the stateof triaxial loading.

2.1.2. The Gologanu damage model

The Gologanu model extends the Gurson model by taking into account the changes inmicrovoid shape that occur during deformation. Indeed, the Gologanu model considers cavities ofellipsoidal form, whose shape and orientation can evolve. The plastic potential is a quadraticformulation which can also be used as a yield function in which sM is the elasto-viscoplastic flowstress, q1; a1 and a2 are material parameters introduced in order to converge the model with fullnumerical analyses of periodic arrays of voids; f � is the Tvergaard and Needleman’s coalescencefunction:

fevp ¼ Cjjs0 þ ZsHX jj2

s2M� j ¼ 0;

where

j ¼ 1þ ðq1f �Þ2 � 2q1f

� coshðnÞ; n ¼ ksH=sM; sH ¼ ð1� 2a2Þs11 þ a1s22:

The parameters k; Z; C and X depend on the geometry of the ellipsoid void, sH is the mean stressand the von Mises norm is given by,

jjsij jj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi3

2sijsij

r:

Numerically, in pure shear loading, there is no damage evolution and consequently no rupture. Inorder to introduce damage due to shearing the damage evolution law is modified to comprise ofthe sum of the classical law and a new part due to shear loading giving

’f ¼ ’fgrowth þ ’fnucleation þ ’fshear:

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In pure shear it is commonly accepted that the voids experience a rotation without any change ingrowth and it appears that nucleation can be generated. Consequently, the damage evolution lawdue to shearing takes the form of a statistical law, similar to the nucleation evolution law, buttaking into consideration the shearing strain and the shearing strain rate. It is defined by

’fshear ¼fS

SS

ffiffiffiffiffiffi2p

p exp �1

2

exy � eSSS

� �2

’exy

!:

The identification of the damage parameters controlled by the shearing strains is carried out bythe inverse method using an Arcan type test [10]. Fig. 1 shows the tensile simulation of a non-axisymmetric double V-notched specimen; (a) shows the initial finite element modelling; (b) and(c) are the damage distribution at the end of the process using the Gurson and Gologanu modelsrespectively and Table 1 gives the data for the constitutive models. Fig. 1d gives the orientationand shape evolution S at the end of the rupture process for an initial prolate void shape using theGologanu model. From Fig. 1 it can be seen that including changes in the void shape does allowanisotropic damage to be represented and more correctly captures the failure process. It should benoted, however, that the implementation here was only for shell element which limits accuracysince triaxial stresses, particularly in the necking zone, are neglected. A solid element would givebetter accuracy but would be computationally expensive; a further improvement could be to usean energy criterion to dissipate energy as each failed element is eliminated.

2.1.3. The Lemaitre damage model

The framework of continuum damage mechanics is used to describe the development of damageunder mechanical loadings, its progression up to the initiation of a macro-crack and finally thegrowth of this macro-crack during failure of the component. The original model for ductilefracture was established for isotropic damage conditions and later extended to include anisotropicdamage development [11,12]. The basic ingredient of the model is the damage law used either inmonotonic loadings for ductile fracture, or in cyclic loadings for low cycle or high cycle loadings.This damage law depends on the damage variable D which evolves between zero and the criticaldamage value Dc which corresponds to macro-crack initiation. The strain energy density releaserate Y ; which is the principle variable governing the phenomenon of damage is expressed by

Y ¼We

1� D:

The strain energy rate We is split into its shear and hydrostatic parts and leads to the followingexpression

We ¼ð1þ nÞ

2Eð1� DÞ/sijS/sijS�

n2Eð1� DÞ

/sijS2;

in which E is Young’s modulus, n Poisson’s ratio and

/sijS ¼ sij if sijX0 and /sijS ¼ 0 if sijo0:

Finally, the damage evolution during plastic straining is defined by the following expression

’D ¼Y

S

� �S

’ep if ep > eD;

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where Y is the strain energy density release rate, S and s are material coefficients, ep is the effectiveplastic strain and eD is the plastic strain at damage threshold.As the damage evolution is localised in the large plastic strain zone the evolution damage law

and the threshold parameters must be identified in sequence. A direct identification approach, or

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Fig. 1. Comparison of rupture mechanisms for the (a) Gurson and (c–d) Gologanu models.


local approach, is used essentially on uniaxial monotonic and cyclic tests, Fig. 2. For a betteridentification experiments in the largest possible domains of stress, strain, time and number ofcycles are needed [7]. An identification approach using inverse techniques is used to find thedamage parameters by correlating experimental and numerical macroscopic measurementsstrongly dependent on the parameters [13,14]. Tensile tests on thin notched specimens are used asmechanical tests to measure macroscopic responses and variations of inner radius and force withrespect to elongation of the specimen are used to correlate test and numerical models.In order to better represent the behaviour of an aluminium alloy, an anisotropic potential can

be used [15–17]; for the present study, a Hill 48 potential is considered. The above damage modelfor anisotropic materials has been implemented in 2D shell and 3D solid elements. The damageparameters were identified using the above procedures and are given in Table 2. These were thenapplied to a validation example consisting of the three points bending of an extruded aluminiumalloy section with an initial slit (starter crack) on the lower face to localise failure initiation, Fig. 3.This test was carried out dynamically and the numerical and experimental results are found to bein good agreement in terms of failure path and energy level, Fig. 4.

2.1.4. The Wilkins failure criteriaAn early continuum model for void nucleation is due to Argon, Ref. [18]. This model proposes

that the decohesion stress sc is a critical combination of the hydrostatic sm and the effective von

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-200

-50

200

-0.2 -0.1

0.1 0.2 0.3 0.4εp strain

2.∆εp

σ Stress [MPa]

100

Cycle 10Cycle120Cycle 200Cycle 400Cycle 600Cycle 830Cycle 1030Cycle 1290Cycle 1370Cycle 1495Cyce 1615Cycle 1735

300

-300

σmax (NR)

σmax (N0)

Fig. 2. Monotonic cyclic test to determine the Lemaitre damage parameters; smaxðN0Þ is the maximum stress at the first

cycle N0 and smaxðNRÞ is the maximum stress at the last cycle (failure) NR:

Table 1

Gurson and Gologanu parameters for the aluminium offset tensile notched specimen

Model q1 q�2 f0 fN SN eN fC fF S��

Gurson/Gologanu 1.5 1.0 10–4 0.05 0.9 0.03 0.05 0.1 0


Mises stress se

sc ¼ sm þ se:

In a similar approach Wilkins [8] proposed a failure criterion based of the summation of theincrement of plasticity, in this case two weighting functions, w1 and w2; are introduced toindependently weight damage due to the hydrostatic and deviatoric loading components; failure isassumed once the cumulative damage reaches a critical value Dc: The expression for cumulative

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Table 2

The Lemaitre damage parameters for 6014 T7 aluminium alloy

The Lemaitre model eD s S Dc

0.05 2 1.22 0.34

Fig. 3. FE model for the 3 point bending of an aluminium alloy (6014 T7) section with ‘starter crack’.

115000

330000

445000

For

ce (

N)

Displacement (mm)

0 5 10 15 20

0

0

0

rce

(N)

0 5 10 15

Lemaitre Shell

Lemaitre Solid

Test

Fig. 4. Experimental and simulation load versus displacement curves for shells and solids using the Lemaitre model.


damage (D) is

D ¼Z

w1w2 d%ep;

where, d%ep is the equivalent plastic strain, w1 is the hydrostatic-pressure weightingterm=ð1=1þ aPÞa; w2 is the deviatoric weighting term(=ð2� AÞb)

where A ¼ Maxs2

s3;s2

s1

� �; s1Xs2Xs3:

The hydrostatic stress is denoted P; and s1; s2 and s3 are the principle stress deviators; thematerial constants a; p and b are found from experimental testing which should, ideally, cover awide range of loading conditions ranging from pure hydrostatic to pure shear. Again, FEsolutions and ‘inverse engineering’ techniques are used to correlate test and simulation results anddetermine ‘best fit’ values for these constants.Within this work tensile parallel sided and notched specimens (8, 4 and 0.25mm diameter) have

been used to determine the model failure parameters; typical constants for 6014 T7 aluminiumalloy are given in Table 3. As a validation exercise the previous extruded aluminium exampleunder three point bending was studied. In this case a mesh of shell elements was used for most ofthe section with only 3D solids being used around the area of failure, Fig. 5, in order to reduceCPU time. Fig. 5 shows the comparison between experiment and simulation for impact force timehistories and direction of crack propagation. In general the results are encouraging and a goodagreement is found; in this case the difference between the Hill 48 and standard von Misesplasticity are not significant.An industrial application of the Wilkins failure model is shown in Fig. 6, which considers the

dynamic loading of an aluminium space frame structure. The mode of loading is side impact usinga 179mm diameter rigid post. The modelling used a hybrid approach in which most of thestructure used simple shell elements which were locally refined in critical areas with detailed 3Dsolid element meshes at which the failure criteria was applied. The failure parameters for theWilkins model were obtained from tensile tests on notched specimens. While this modellingapproach is costly in terms of preparation and CPU time it does provide predictive results and allof the main failure locations were correctly identified. Future work will consider the automatedmethods introduced in Section 3.1 which will have the potential to identify all possible failurelocations and restrict mesh refinement only to these zones.

2.1.5. Comparison of the micro-failure models

During the course of the work a comparison of the different micro-mechanical models has notbeen made; however, some general comments on the performance and usefulness of the individual

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Table 3

The Wilkins failure parameters for 6014 T7 aluminium alloy

The Wilkins model Dc a a b

0.74 2.1GPa 1.1 0.75


models can be made. The Gurson model can realistically represent failure provided the loadingstate in the coupon used to determine the Gurson parameters is similar to that in the rupture zoneof the structure and is predominantly hydrostatic. Improvements are possible using the Gologanumodel to take into account anisotropic damage; however, this model introduces several additionalparameters that are not easily identified. The Lemaitre model appears to give encouraging resultsand uses a well defined, if somewhat laborious cyclic testing procedure, to determine the modeldamage parameters. Finally, the Wilkins failure model is easily understood and relativelystraightforward to calibrate against appropriate test coupons; consequently, it has been wellreceived by industrial partners in the IMPACT project.

2.2. Macro-mechanical models

Modern crash simulation models typically use element edge lengths of 5–15mm. The previousmicro-mechanical failure laws are unsuitable for such meshes and alternative methods must besought. In the IMPACT project two different approaches were developed and tested:

1. Failure prediction based on the onset of local instability.2. Failure based on fracture curves.

The first approach has been applied to sheet metal components made of high strength TRIP,complex phase and dual phase steels, whereas the second was used for automotive plastics. Bothare briefly described below.

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Fig. 5. Experimental and numerical load versus displacement curves (Wilkins model).


2.2.1. Stability criteria for fractureFor sheet metal the onset of instability can be used as a fracture criterion. This loss of stability is

analysed by considering principal strains on a rectangular element of the sheet. Usually instability

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Fig. 6. Experimental set-up for space frame aluminium structure and comparison of the observed test and simulation

failure locations.


manifests itself by local thinning (necking) in a groove running perpendicular to the largerprincipal stress; an analytical solution to this stability problem is provided by Marciniak [19],Fig. 7a. At the onset of instability the local strains associated with this groove equal the globalstrains and can therefore be used as a measure of failure strains in a shell element, Fig. 7b. Afterinstability large local strains localise in the neck leading to a large difference between local andglobal strains, Fig. 7c.In the IMPACT project the CRACH algorithm [20] is used to determine instability limits; this

incorporates the following improvements to the original Marciniak model:

– A refined model of the geometry of the localised neck area is used.– A refined material model with anisotropic hardening including the ‘Bauschinger’ effect.– Inclusion of parameters to account for process history effects such as solution heat treatmentand age hardening.

In practice the part to be considered for crash failure analysis must first be simulated asa metal stamping problem. Information on the complete deformation history for eachelement is needed and stored during stamping; this is then mapped to the new crash meshprior to the crash simulation. During the crash simulation information on critical elements isexchanged between the crash simulation model and the CRACH algorithm to provide acontinuous update on the stability limits for the elements. If a state of instability is reached theelement is eliminated.The CRACH algorithm requires an extensive test program to characterise the dynamic failure

of pre-strained material. Specimens were prepared with different pre-strain conditions and thentested dynamically to failure. Most of this high strain rate testing work used a conventionalHopkinson bar; however, for the case of bi-axial loading a new dynamic multi-axial ‘bulge’ rig hasbeen developed that allows such deformation to be applied to high strength thin-sheet specimensat elevated strain rates (>100/s), Fig. 8. Also shown in Fig. 8 is an example of the failure of a100mm diameter TRIP steel specimen.

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Fig. 7. Local and global strains: (a) the Marciniak instability model, (b) onset of instability (local strains�globalstrains) and (c) fracture (local strainscglobal strains).


The side impact study, Fig. 9, illustrates the principle of this approach. The side structureanalysed and the loading set-up for the experiment and simulation model are shown in Fig. 9a andb. This test case imposes loading conditions of the B-pillar has been solely developed forvalidation purposes of the numerical model. During the test, the B-pillar has been deliberatelyloaded up to complete fracture. The simulation is performed with a detailed shell element modelhaving an average edge length of about 5mm. The prediction of failure is based on the onset ofinstability as predicted by the CRACH algorithm. Fig. 9c shows the test location of failure in theB pillar which is also observed in the numerical analysis.

2.2.2. Constitutive and failure model for plasticsTypical polymers used in automotive applications are ductile thermoplastics which are used for

a wide variety of applications including interior trim. These applications must meet certain energyabsorption requirements to minimise occupant injury. For this work two commercial plastics wereinvestigated:

1. HIFAX CR 1171 G 2116 from Basell Polyolefins: This is a semicristalline ‘filled’ polypropylene(PP) copolymer.

2. BAYBLEND T65 792 from Bayer: This is an amorphous ‘unfilled’ polycarbonate/acrylonitrile-butadiene-Styrene (PC-ABS) blend.

Clearly the mechanical behaviour of metals and plastics are very different; never-the-less, it hasbeen proposed that the elasto-plastic von Mises law is a reasonable basis to describe the non-linear response of plastics, Ref. [3]. The main difficulty is to provide a hardening law that cancorrectly describe the rate and temperature dependent behaviour of these materials. An example

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Fig. 8. Rig for the dynamic bi-axial bulge test and a failed specimen after loading.


stress–strain response for HIFAX (PP) is shown in Fig. 10. A simple law that reasonablycharacterises the form of the stress–strain curve for most plastics is the G’Sell model [21], withfour curve fitting parameters

s ¼ k½1� expð�weÞexpðhe2Þð’e=’e0Þ

m;

where s and e are the effective stress and strain, k is a scaling factor, ½1� expð�weÞ is a visco-elasticterm to describe the beginning of the stress–strain curve and ehe2 controls strain hardening at largestrains. Finally, ð’e=’e0Þ

m expresses the strain rate sensitivity as a power law. The material constantsk;w; h and m are determined for different temperatures and linear interpolation is used for anyother temperature state. G’Sell parameters for HIFAX and BAYBLEND were determined fromexperimental testing and are given in Table 4. Strain rate effects are included by determining thesefactors for different rates of loading and using linear interpolation for other strain rates.The high sensitivity of these materials to thermal changes suggests that temperature increase

due to internal material deformation should also be included. The adiabatic increase in

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Fig. 9. Side impact simulation and failure prediction using a macro-failure criteria: (a) the body in white structure, (b)

the loading set-up and (c) test and simulation results showing the critical location for failure. Note: The extreme loading

of the B-pillar has been deliberately conducted to complete fracture. These loading conditions, as well as the test setup,

are not part of the homologation process of a vehicle.


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0.00 0.05 0.10 0.15 0.200

5

10

15

20

25

v=500 mm/min v=100 mm/min v=50mm/min v=10mm/min v=1 mm/min

stre

ss (

MP

a)

strain (mm/mm)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

5

10

15

20

25

T= 20 °C T= 80 °C

Eng

inee

ring

Str

ess

(MP

a)

Engineering Strain(mm/mm)(b)

(a)

Fig. 10. Typical stress versus strain curves for PP: (a) strain rate dependence and (b) temperature dependence.

Table 4

G’Sell parameters for BAYBLEND and HIFAX for three temperatures

�15�C 20�C 85�C

BAYBLEND

k (Mpa) 66.725 55.249 34.497

w (dimensionless) 63.661 73.982 104.693

h (dimensionless) 1.264 1.308 1.349

m (dimensionless) 0.0182 0.0299 0.0319

HIFAX

k (Mpa) 0.044 0.027 0.015

w (dimensionless) 231 144 60

h (dimensionless) 1.79 0.73 0.54

m (dimensionless) 0.055 0.055 0.093


temperature can be expressed by the simple relation:

DT ¼ cQDep;

where DT is the temperature increment resulting from a plastic strain increment Dep for a materialwith heat capacity Q; c is a conversion constant usually assumed to be 0.9.Experimental testing has also shown that failure in plastics is highly dependent on rate of loading

and temperature. Consequently, a simple temperature and rate dependent failure criteria based onmaximum principle strain has been used. The required information is defined via a set of curves,Fig. 11a, from which failure for any strain rate and temperature condition may be interpolated.Fig. 11b shows the application of the plastic constitutive law, with failure, for a constant rate anddifferent temperature conditions. The abrupt point of failure is clearly seen in these curves.

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Fig. 11. Failure and stress–strain curves: (a) definition of failure and (b) stress–strain curves with failure (strain

rate=0.1 s�1).

Fig. 12. Geometry of the plastic honeycomb plate.


An example application of this model is the impact of a thermoplastic (BAYBLEND)honeycomb plate, Fig. 12, which is used for energy absorption in the A-pillars of a vehicle. Thehoneycomb plate was impacted with a sphere at different temperatures and with differentvelocities. Test and simulation results for the ductile impact case at 85�C and the brittle impactcase �35�C are shown in Fig. 13. The constitutive model and simple macro-failure criteria give agood prediction of the changes in failure modes for both high and low temperature impact cases.The impact force time histories are also in good agreement with test results.

3. Numerical techniques

Two special developments to facilitate application of the material models have been made.First, techniques to automatically convert single shell elements to a patch of fine solid elementshave been developed. This provides an automated procedure to locally apply micro-mechanicalmaterial models and limit CPU costs. In the case of macro-material modelling techniques havebeen developed to treat crack growth by splitting elements and allowing crack propagationdependent on energy based criteria. Both techniques are briefly illustrated.

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Fig. 13. Comparison of experimental and simulation results for deformation and impact force on the honeycomb

plastic panel: (a) 85�C (above) and (b) 35�C (below).


3.1. Remeshing: shells to solids

Generally shell elements having an edge legth of 5–15mm are appropriate for crash simulation.As mentioned previosly these elements are not suitable for micro-mechanical constitutive laws anddetailed 3D solid elements must be used. The two element types can be combined to reduce CPUcosts by using coarse shell elements with fine solid meshes only in areas of potential failure.Clearly a better approach is to automate this process and replace shell elements with solidselements only in areas that approach failure during the crash. Fig. 14 shows the conversion of oneshell element to a set of solids. For such a procedure the patch of solid elements of specific sizemust be generated and all constitutive variables, including damage variables, must be mappedfrom the shells to the solid elements. Special constraints are also introduced to tie existing shelland solid elements to the new solids. Fig. 14 shows the application of this technique to a simpleexample.

3.2. Shell element splitting

The macro-mechanical stability criterion presented in Section 2.2.1 is only valid up to the pointof fracture; thereafter the local stress distribution of a growing crack cannot be captured by thecoarse shell model. This crack growth phenomenon can be approximately treated by splittingelements, Fig. 15. The algorithm collects element information at nodal points and checks if thenode belongs to a propagating crack and must be considered for opening. The direction of crackopening is assumed to be normal to the direction of maximum principle strain; fictitious forces

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Fig. 14. Automatic switching from shell to solid elements and a simulation example.

Fig. 15. Principle idea of shell element splitting and an FE example.


control crack opening such that at full opening the Mode I fracture energy of the material over thearea represented is absorbed.

4. Conclusion

The IMPACT project undertook an extensive program to test dynamically a range ofautomotive materials, develop constitutive models and validate the failure modelling of thesematerials on components. In total four different constitutive failure laws for metals have beenstudied and evaluated which are suitable for micro-mechanical analysis. Furthermore, a newmacro-mechanical constitutive and failure law for rate and temperature dependent plastics and amacro-mechanical failure law based on instability fracture criteria for high strength steels havebeen developed and validated. Other novel developments have included automatic meshrefinement and shell element splitting techniques to treat crack propagation. The work has beenvalidated on several industrially relevant demonstrators where a good agreement between test andsimulation results for failure prediction has been found.

Acknowledgements

The enthusiastic support of the IMPACT project partners VW, BMW, AUDI, IDIADA,ALCAN, ESI Group, CCP, Magna Steyr, CRF and the Universities of Oxford, Valenciennes andCachan are gratefully appreciated. The partners would also like to thank the CEC for theirfinancial support of this project under the Framework V programme.

References

[1] PAM-CRASH. ESI Group, Rue Hamelin, BP 2008-16, 75761 Paris Cedex 16, France, http://www.esi-group.com.

[2] DYNA3D. Livermore Software Technology Corporation, http://www.lstc.com.

[3] Anderson TL. Fracture mechanics: fundamentals and applications, 2nd ed.. Boca Raton, FL: CRC Press; 1995.

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