Ductile material failure in LS-DYNA

Mikael Schill

Introduction/Motivation

■ The automotive industry is facing demands on emissions which has lead to a weight reduction race of the BIW

■ The weight is reduced by using optimized material behaviour, e.g. high strength steels, but also mixingdifferent material types.

Introduction/Motivation

■ The cars consist of several different materials withvarious material behaviour

Introduction/Motivation

■ The material shows different types of failures

■ Failure of subsystems, e.g. connections

■ Manufacturing history has an influence on the failure

The tensile test

P P

sy

su

s

e 0

lnLL

AP

=

=

ε

σDiffuse necking

At the point of necking, the hardening of the material can no longer compensate for the decrease in area and increase in load.The softening behavior is due to the engineering measures, instead true values of stress and strain should be used.

General problem

■ Beyond the point of necking, the model shows softening.■ The solution is not unique.■ The solution will be mesh dependent – Regularisation is

necessaryTe

chni

cal s

tress

x

Failure criteria

■ However, the failure criteria theoretical basis can be found in failure models such as instability, damage etc.

Definition: Failure criteria determines a point offailure and does not model the actual failurebehaviour.

Tech

nica

l stre

ss

x

Fracture models

Continuum Damage Mechanics (CDM)

■ The concept of damage assumes growth of voids in the material ■ The voids reduces the effective area■ When the effective area equals the nominal area, then the material

fails.■ Since the true stress is related to the nominal area, it will decrease.

Thus,the material exhibits softening.

= deformed or current cross section

= effective cross section

= Damage

= True stress

= True effective stress

defect effA A A= -

𝐷𝐷 = 1 −𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒𝐴𝐴

=𝐴𝐴𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒𝑑𝑑𝑑𝑑𝐴𝐴

𝐴𝐴

𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒

𝜎𝜎 =𝐹𝐹𝐴𝐴

𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒 =𝐹𝐹

𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒=

𝜎𝜎1 − 𝐷𝐷

Damage coupling

■ The damage can be used as a failure criteria if it is uncoupled from the stress.

■ Thus, no softening will occur due to the damage■ If the damage is coupled to the stress, the material will

exhibit softening

σ

ε

Stress-strain relationship

Uncoupled

Coupled

GISSMO■ Generalized Incremental Stress State dependent damage Model■ Need for a generalized failure model which can be used in all

product simulations

GISSMO

Barlat Mises00,0 ,, tplεσ

plεσ ,

Mapping

tpl ,,εσ

D DGISSMO

plεσ ,

Forming simulation Crash simulation

Ebelsheiser, Feucht & Neukamm [2008]Neukamm, Feucht & Haufe [2008]

Developments for the process chain forming-to-crash

GISSMO can be added to ”any” material model

GISSMO damage evolution

■ User input failure curve■ Any history variable in rate equation

Gurson

Mises

FormingCrash

GISSMO

Damage Evolution

Damage overestimated for linear damage accumulation

Failure Curve

Gurson

Mises

FormingCrash

Evolution of Instability Material Instability

Material Instability

( )v

n

locv

FnF εε

∆=∆− 11

,

Flachzugprobe DIN EN 12001

0,000,050,100,150,200,250,300,350,400,450,50

0,00 0,05 0,10 0,15 0,20 0,25 0,30

Simulation

Versuch

Tensile test specimen DIN EN 12001

Neukamm, Feucht & Haufe [2008]

GISSMO – Stress Coupling

■ Optional material instability determines where the coupling starts

GISSMO Damage Model – step by step

■ Material instabilility, F, evolves with plastic strain through

■ At the instability limit εloc(η) F=1 and the material is assumed to reach a point of instability.

■ Damage evolves through

pn

loc

FnF εηε

)11(

)(−

=

GISSMO Damage Model – step by step

■ Beyond the point of instability, the stressescan be coupled to the damage through:

■ DCRIT is the D value at Material instability

GISSMO Damage Model – step by step

■ Damage is increasingthrough:

■ When the material is fully damaged, D=1, the stress in the integration point is 0.

■ When a user definednumber of integration points has failed, the element is deleted.

Mesh Regularisation

■ Regularisation curve that scales the failure strains as a function of the element size.

GISSMO - Input

■ The input to GISSMO can be determined through:■ Analytical criteria

■ An analytical failure model is transferred to GISSMO input

■ Experiments■ Parameters are determined from experiments through inverse

modeling

■ Combination■ A limited number of

tests are performed andused in combination withan analytical criteria.

GISSMO Test specimen examples

Increasing triaxiality

GISSMO Parameter calibration – Test data preparation

■ If necessary, the test data needs to be filtered to get a smooth result■ Any engineering measure will do for the optimization, e.g. engineering

stress/strain or Force/displacement.■ The point up to ultimate strength is determined by the yield surface and the

hardening.■ Thus, only the softening part is used in the optimization.

ECRIT

FADEXP,DMGEXP

LSCDG

Model calibration

Andrade, Haufe, Feucht, Basaran and Du Bois, “Zur aktuellen Modelltechnik für dieVersagensprognose von Aluminium-Strangpressprofilen mit LS-DYNA”, crashmat 2012 –Franhofer EMI, Freiburg

Multi-part failure concept: DIEM - Damage Initiation and Evolution Model

Failure mechanism in sheet metal deformation

Ductile failure criteria

DDε

η

DSε

θ

DIε

2

1

εα ε=

Shear failure criteria Instability failure criteria

Multiple individual criteria may be mixed to predict failure in thin sheet metal. Integration point is considered as failed if either of the selected criteria reaches a value of 1

(DCTYP=0) or if the value gained by multiplying the individual damage thresholds values reaches 1 (DCTYP=1).

Post-critical behavior is defined by allowance of an additional displacement in each element. The element is deleted if a defined number of integrations points is flagged as „failed“.

Ductile failure (DITYP=0) Shear failure (DITYP=1) Instability criteria (DITYP=2)For the ductile initiation option a function

( , )p p pD Dε ε η ε=

represents the plastic strain at onset of damage (P1). This is a function of stress triaxiality defined as

/p qη = −with p being the pressure and q the von Mises equivalent stress. Optionally this can be defined as a table with the second dependency being on the effective plastic strain rate .

pε

The damage initiation history variable evolves according to

0

p p

D pD

dε εωε

= ∫

For the shear initiation option a function ( , )p p p

D Dε ε θ ε=

represents the plastic strain at onset of damage (P1). This is a function of a shear stress function defined as

( ) /Sq k pθ τ= +with p being the pressure, q the von Mises equivalent stress and τ the maximum shear stress defined as a function of the principal stress values

( )major minor / 2τ σ σ= −Introduced here is also the pressure influence parameter kS(P2). Optionally this can be defined as a table with the second dependency being on the effective plastic strain rate . The damage initiation history variable evolves according to

pε

0

p p

D pD

dε εωε

= ∫

For the MSFLD initiation option a function

( , )p p pD Dε ε α ε=

represents the plastic strain at onset of damage. This is a function of the ratio of principal plastic strain rates defined as

minor major/p pα ε ε=

The MSFLD criterion is only relevant for shells and the principal strains should be interpreted as the in-plane principal strains. The damage initiation history variable evolves according to:

maxp

D t T pD

εωε≤=

Damage initiation and failure concept

Evolves only for negative pressures, thus does not consider compression.

Multiple individual criteria may be mixed to predict failure in thin sheet metal. Integration point is considered as failed if either of the selected criteria reaches a value of 1

(DCTYP=0) or if the value gained by multiplying the individual damage thresholds values reaches 1 (DCTYP=1).

Post-critical behavior is defined by allowance of an additional displacement in each element. The element is deleted if a defined number of integrations points is flagged as „failed“.

FLD failure (DITYP=3)

This initiation option is very similar to DITYP=2, the only difference being the damage initiation history variable that here evolves as

and where plastic strain here refers to the non-modified ditto, i.e, it considers damage initiation both in tension and compression.

For the evolution of the associated damage variable D we introduce the plastic displacement which evolves according to

0

p p

D pD

dε εωε

= ∫

with l being a characteristic length of the element. Fracture energy is related to plastic displacement asfollows:

DIε

2

1

εα ε=

Damage and failure concept

Damage evolution and element erosion After failure initiation damage evolution is invoked that is based on classical scalar damage.

The measurement that defines the further evolution is additional relative displacement of the element, hence a basic regularization method is applied.

The failure plastic displacement can be input as a table of damage and triaxiality. Thus, the damage evolution is non-linear

pinputu∆

0 11

Dpp

ele D

ul

ωε ω

<= ≥

Ad

A0

F

, ,

,max ,( )p p init p p init

pp p init p

input

u u u uD D uu u u

− −= = =

− ∆

D = scalar → isotropic behavior

( )1 :epD= −σ C ε

0

dADA

=

with 0.0 1.0D≤ ≤

Idea of scalar damage

σ

pεp

input

ele

ul

∆

DETYP: Damage evolution typeEQ.0.0: Linear softening, evolution of damage is a function of the plastic displacement after the initiation of damage.EQ.1.0: Linear softening, evolution of damage is a function of the fracture energy after the initiation of damage.

Damage evolution and failure concept

Comparison DIEM and GISSMO

■ GISSMO only has one initiation and failure criteria where DIEM has severalthat evolve simultaneously.

■ In GISSMO, the damage starts to evolve from the beginning while D starts to evolve after intitiation in DIEM.

■ In the MSFLD and FLD criteria of DIEM, only the middle surface is regarded. In GISSMO, all integration points are evaluated for instability.

■ In DIEM, the damage evolution can be defined as a table (damage, triaxialityand plastic displacement) where in GISSMO it is governed by DMGEXP.

■ In GISSMO, the mesh regularization is handeled by scaling the failure curve. In DIEM, a plastic displacement is used which is scaled by the element length, thus linear.

■ Input to DIEM and GISSMO is based on the same principles. Thus, calibrationis similar between the two methods.

Comparison DIEM and GISSMO

From Andrade, Feucht and Haufe ”On the Prediction of Material Failure in LS-DYNA: A Comparison Between GISSMO and DIEM”, 13th International LS-DYNA Conference

Conclusions

■ Diffuse necking■ Maximum Force criteria■ Described by the yield criterion and the hardening of the material

■ Beyond the point of diffuse necking, the solution becomes mesh dependent. ■ Failure criteria determines the point of failure, while a failure model also describes

the failure, i.e. Damage■ General failure criteria can be added to any material model through *MAT_ADD

EROSION■ GISSMO – General Damage model that can be added to any material model■ Input to GISSMO can be based on either experiments or analytical failure models.■ DIEM – Ductile, shear and instability failure model that can be added to “any” material

model in LS-DYNA. ■ Multiple DIEM failures can be combined and failure will be based on a multiplicative or

maximum value.■ Identification of GISSMO/DIEM parameters are made through inverse modeling

Thank you!

Mikael Schillmikael@dynamore.se

Thomas Johanssonthomas.johansson@dynamore.se