GISSMO Material Modeling with a sophisticated Failure …€¦ · GISSMO – Material Modeling with...

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GISSMO – Material Modeling with

a sophisticated Failure Criteria

André Haufe, Paul DuBois, Frieder Neukamm, Markus Feucht

LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe

2 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe

Motivation


Weight Composites

High strength steel

Light alloys

Polymers

Safety requirements

Cost effectiveness

New materials

Design to the point

New power train

technology

Technological challenges in the automotive industry


Technological challenges in the automotive industry

Damage

max

E

Failure

fail true

E

Anisotropy c

a

b

( )eE

y

Fracture growth Debonding

Weight Composites

High strength steel

Light alloys

Polymers

Safety requirements

Cost effectiveness

New materials

Design to the point

New power train

technology

Plasticity


Mapping

Forming simulation

Closing the process chain: Standard materials / state of the art

v. Mises or Gurson model

Strain rate dependency

Isotropic hardening

Damage evolution

Failure models

(mapping of damage variable)

II

I

III

Hill based models

Anisotropiy of yield surface

Kinematic/Isotropic hardening

State of the art: Failure by FLD

(post-processing)

NEW: Computation of damage

(GISSMO)

II

IIII

II

I

III

Crash simulation


Preliminary considerations

for plane stress


Some thoughts on damage formulations

Is path dependence critical for the target application (crashworthiness)?

Is a phenomenological model good enough?

Should we take orthotropic effects into account (i.e. tensorial damage)

or is a scalar formulation fine?

Shall we accumulate the damage value based on the stress state

or on the strain state?

Shall the damage accumulation be isotropic, orthotropic or at least

pressure dependent?


J. Lemaitre, A Continuous Damage

Mechanics Model for Ductile Fracture

Overall Section Area

containing micro-defects

Reduced (“effective“)

Section Area

SS ˆS S

SSD

ˆ

Measure of

Damage

Reduction of effective cross-section leads to

reduction of tangential stiffness

Phenomenological description D 1*

σσ

Isotropic (scalar) damage Effective stress concept (similar to MAT_81/120/224 etc.)


Plane stress condition

Principle axis

0

0

0

3

2

1

σ0

),(

),(

3

2

1

Plane stress

1

1

2

1

0 0

0 0

0 0 0

1 ( 1)vm

k

k k

σ1

12 k

Definition of stress triaxiality:

11

2

1

( 1) ( 1)sign( )

3 1 ( 1)3 1 ( 1)vm

p k k

k kk k

Parameterised

xx

yyxy

yx

Typical discretization with shell elements:


Haigh-Westergaard coordinates in principle stress space

1

2

3

1.5

2

1tr( )

3 3

2 :

1 3 3arccos

3 2

I

J

J

J

σ

s s

Deviatoric

plane

Lode angle

vm

p

Definition of stress triaxiality:


A toy to visualize stress invariants (downloadable from the www.dynamore.se)

• Download the PDF-file

• Print on thick piece of paper

• Cut out where indicated

• Add four wooden sticks (15cm)

• Add some glue where necessary

(engineers should find out the locations without

further instructions – all others contact their

local distributor)

• Have fun!

Crafting instructions page 1:


A toy to visualize stress invariants (downloadable from the www.dynamore.se)

• Page 2 of the set may be added for further

clarification of the triaxiality variable.

Crafting instructions page 2:

Final shape of toy


Plane stress parameterised for shells

Triaxiality

11

2

1

( 1) ( 1)sign( )

3 1 ( 1)3 1 ( 1)vm

p k k

k kk k

Bounds:

k

vm

p

1 1

( 1) 1lim lim sign( ) sign( )

33 1 ( 1)k k

k

k k

1 1


33 1 ( 1)k k

k

k k

1 11 1


33 1 ( 1)k k

k

k k

Compression

Biaxial tension

Tension

tension compression


How to define the accumulation of damage ? A comparison of model approaches

Investigation of failure criteria for the following case:

Plane stress:

Small elastic deformations:

Isochoric plasticity:

Proportional loading:

3 0

1 1 2 2p pand

2 1

2 1p p

a

b

3 3 1 2p p p

1 2

2

ba

b

2 21

2 21

2

41

3

1

1

3 1

p p

vm

vm

b b

a a

p a

a a

Damage or failure criteria


How to define the accumulation of damage ? A comparison of classical model approaches

Some typical loading paths


How to define the accumulation of damage ? A comparison of classical model approaches

Some typical loading paths

1 max 1 1 max

2max2 2

1 max 1 2

3max max3 1

2

1 max 2

4 31

3 4 1

2 1 2 1

2 11 2 2

p

p p p

pp p

p

b bb b

b b

b bb b b

Four criteria

Principal strain:

Equivalent plastic strain:

Thinning:

Diffuse necking:


Failure models in the plane of principal strain

Failure strain under

uniaxial tension is

set the same in all

4 criteria.

Thinning and FLD predict

no failure under pure

shear loading.


Failure models in the plane of major strain vs. b


Failure models in the plane equivalent plastic strain vs. b

Calibrating different criteria

to a uniaxial tension test

can lead to considerably

different response in other

load cases.


Failure models: equivalent plastic strain vs. triaxiality

2, 1, 1,

1, 2, 1,

0.5

2

p p p p

p p p p

For uniaxial and biaxial tension

different criteria lead to a factor

of 2:


Johnson-Cook criterion (Hancock-McKenzie )

3

1 2

1

3

12

2 1

0

32

vm

pd

pf

f

d d e

d

d

d e

Johnson-Cook and

FLC are very close in

the neighborhood of

uniaxial tension.


Parametrized for 3D stress space


Lode-angle: Extension- and Compression test

I

III

II

0

II III

Iand

View parallel and on hydrostatic axis

(perpendicular to deviator plane)

Possible value for first

principle stress

I

III

II

Compression

0

II III

Iand

View not parallel to hydrostatic axis

Extension

30

30

Co

mp

ressio

n


1 01

1

1

0 0

10 04

10 0

4

1

1

0 0

0 0

0 0 0

1

1

0 0

10 02

0 0 0

1 0 0

0 0 0

0 0 0

1

1

0 0

0 0 0

0 0

1

0 0 0

0 0 0

0 0

1

1

1

0 0

0 0

10 0

2

3D-Stress state parameterised for volume elements

compression

extension

vm

p

F


Parameter definition

1

3

m

vM vM

I

3

3

27

2 vM

J

3 1 2 3J s s smit

[Source: Wierzbicki et al.]

Stress domain in

sheet metal forming

Invariants in 3D stress space Failure criterion extd. for 3D solids

1 30or

0 0or

1 30or


Deriving GISSMO from that…


Forming simulation

Closing the process chain: UHS materials for press hardening

v. Mises or Gurson model

Strain rate dependency

Isotropic hardening (locally)

Damage evolution (locally)

Failure models

(mapping damage variable)

II

I

III

Hill based models

Ortho- or isotropic yield surface

Isotropic hardening

Feasibility by thinning or

damage (calibration?!)

Dependency on temperature

Microstructural evolution (#244)

II

IIII

II

I

III

Crash simulation

Mapping


Different ways to realize a consistent modeling

One Material Model for Forming and

Crash Simulation

Requirements for Forming Simulations:

Anisotropy, Exact Description of Yield

Locus, Kinematic Hardening, etc.

Requirements for Crash Simulation:

Dynamic Material Behavior, Failure

Prediction, Energy Absorption, Robust

Formulation

Leads to very complex model

Modular Concept for the Description

of Plasticity & Failure

Plasticity and Failure Model are treated

separately

Existing Material Models are kept

unaltered

Consistent modeling through the use of

one damage model for forming and crash

simulation

*MAT_ADD….(damage)


Produceability to Serviceability: Modular Concept

Damage model

Material model Material model 00, , tpl

pl ,

Mapping

tpl ,

D D Damage model

pl ,

Forming simulation Crash simulation

D D

Modular Concept:

Proven material models for both disciplines are retained

Use of one continuous damage model for both


GISSMO

Barlat Mises 00,0 ,, tpl

pl ,

Mapping

tpl ,,

Fo

rtra

n-P

rog

ram

D D

GISSMO

pl ,

Forming simulation Crash simulation

Ebelsheiser, Feucht & Neukamm [2008]

Neukamm, Feucht, DuBois & Haufe [2008-2010]

Produceability to Serviceability: Modular Concept Current status in 971R5


Parameter definition

1

3

m

vM vM

I

3

3

27

2 vM

J

3 1 2 3J s s smit

[Source: Wierzbicki et al.]

Stress domain in

sheet metal forming

Xue

Hutchinson

Gurson std.

Xue

Hutchinson

Gurson std.

f

[Experimental data

by Wierzbicki et al.]

GISSMO Failure criterion extd. for 3D solids


Gurson

Mises

Forming Crash

GISSMO

Damage evolution

Damage regularly

overestimated for linear

damage accumulation!!

Failure curve


GISSMO - a short description Ductile damage and failure

triaxiality


Gurson

Mises

Forming

Crash

Material Instability

11

,

nv

v loc

nF F

Flachzugprobe DIN EN 12001

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

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

Simulation

Versuch

Tensile test specimen DIN EN 12001

GISSMO – a short description Engineering approach for instability failure n

t

1

2

triaxiality


Instability evolution Instability curve definition


GISSMO – a short description

Inherent mesh-size dependency of results

in the post-critical region

Simulation (and calibration) of tensile test

specimen with different mesh sizes

Mesh size dependency: Simple regularisation Test program and calibration


DMGTYP: Flag for coupling (Lemaitre)

D 1*

DCRIT, FADEXP: Post-critical behavior

0

0

True Strain

Tru

e S

tre

ss

GISSMO dmgtyp2

MAT_024

0

0True Strain

Tru

e S

tre

ss

m=2

m=5

m=8

FADEXP

CRIT

CRIT

D

DD

11*

GISSMO – a short description for the uniaxial case Generalized Incremental Stress State dependent damage MOdel


Failure strain depending on

Loading state

Load path and pre-damage

Accumulation of damage

)( fail

fail

eqm /

Failure

GISSMO Non-proportional loading influence on failure behavior


Non-Proportional Loading

vm

p

f

0.577 0.333

Triaxiality is no longer constant

over the stress-strain path if

lateral constraint is imposed or

lifted.

Compare 4 load paths:

A uniaxial tension

B uniaxial tension with lateral confinement

C uniaxial tension with/without confinement

D uniaxial tension without/with confinement

A B C D

A B

C

D


Non-proportional loading criterion without triaxiality

1 0.4

1

f

p

p ff

d

d dt

vm

p

f

0.577 0.333


Non-proportional loading criterion with triaxiality

3 1.5

1 2 0.66

1

vm vm

vm

p pd

f

pcte

p

p ff

d d e e

d dt

vm

p

f

0.577 0.333


Comparison: Uniaxial tension with/without confinement

vm

p

f

0.577 0.333


Input of GISSMO

*MAT_PIECEWISE_LINEAR_PLASTICITY

$ mid ro e pr sigy etan fail tdel

100 7.8000E-9 2.1000E+5 0.300000

$ c p lcss lcsr vp

0.000 0.000 99 0 1.000

...

*MAT_ADD_EROSION

$ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS

100

$ MNPRES SIGP1 SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM

$ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD

1 0 11 0.3 2 0.2 2 12

$ SIZFLG REFSZ NAHSV

0 5 4

Standard material

Input (i.e. MAT_24)

Input definition in LS-DYNA (1/4)

Standard failure

parameters (optional)

GISSMO failure

parameters

If IDAMG=1 GISSMO is invoked.

Further parameters are expected.

DMGTYP=0: Damage is accumulated

But not coupled to stresses, no failure.

DMGTYP=1: Damage is accumulated

and coupled to flow stress if D>Dcrit.

Failure occurs if D=1.


Input of GISSMO



100 7.8000E-9 2.1000E+5 0.300000

$ c p lcss lcsr vp

0.000 0.000 99 0 1.000

...

*MAT_ADD_EROSION


100



1 0 11 0.3 2 0.2 2 12


0 5 4

Standard material

Input (i.e. MAT_24)


Standard failure


GISSMO failure

parameters

ID of curve defining equivalent plastic

strain at failure vs. triaxiality.

Damage will have values from 0 up to 1.0.

ECRIT: Equiv. plastic strain at instability onset.

If negative a curve is expected that defines

ECRIT vs. traiaxiality.

If ECRIT=0 the ordinate value Dcrit is used.

Exponent for nonlinear damage

accumulation:


Input of GISSMO



100 7.8000E-9 2.1000E+5 0.300000

$ c p lcss lcsr vp

0.000 0.000 99 0 1.000

...

*MAT_ADD_EROSION


100



1 0 11 0.3 2 0.2 2 12


0 5 4

Standard material

Input (i.e. MAT_24)


Standard failure


GISSMO failure

parameters

Fading exponent as defined in:

SIZFLG=0 (default) Characteristic element is

computed with respect to initial configuration.

SIZFLG=1 Characteristic element updated in each

increment (actual configuration, not recommended)

Load curve defining element size dependent

regularization factors vs. equiv. plastic strain to

failure.

FADEXP

CRIT

CRIT

D

DD

11*


Input of GISSMO



100 7.8000E-9 2.1000E+5 0.300000

$ c p lcss lcsr vp

0.000 0.000 99 0 1.000

...

*MAT_ADD_EROSION


100



1 0 11 0.3 2 0.2 2 12


0 5 4

Standard material

Input (i.e. MAT_24)


Standard failure


GISSMO failure

parameters

Reference element size for which the failure

parameters were calibrated. This may be used

when mapping of failure parameters from finer

to coarser meshes is necessary.

Number of additional history variables written to d3plot-

database. Please keep in mind, that this additional.

history variable are added to the standard variables of

the corresponding material model. I.e. the sum of both

history variable sets needs to be defined in

*DATABASE_EXTEND_BINARY. The number of the

history variables used in the material model (i.e.

MAT_24 in this example) is written to d3hsp-file.


Flachzugproben DIN EN 10002

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,00 0,10 0,20 0,30 0,40

Mini-Flachzugproben ungekerbt

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,0 0,2 0,4 0,6 0,8

Mini-Flachzugproben Kerbradius 1mm

0,0

0,1

0,2

0,3

0,4

0,5

0,6

-0,10 0,10 0,30 0,50

Arcan

0

2

4

6

8

10

12

0,0 0,5 1,0 1,5

Scherzugproben Kerbradius 1mm, 0°

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,00 0,05 0,10 0,15 0,20


0,00

0,10

0,20

0,30

0,40

0,50

0,00 0,05 0,10 0,15 0,20


0,00

0,10

0,20

0,30

0,40

0,50

0,00 0,05 0,10 0,15 0,20

eps_technisch

Sig

ma_

tech

nis

ch [

GP

a]

Versuch

GISSMO

Gurson

constant (v. Mises)

Small tensile test specimen Notched tensile specimen, notch radius 1mm Shear test, inclined 15

Tensile specimen DIN EN 12001 Shear test, straight

GISSMO vs. Gurson vs. MAT_24/81 Comparison of experiments and simulations


GISSMO

Failure Strain constant

Fracture energy constant

Identification of Damage Parameters

is more straight-forward

Gurson

Resultant Failure Strain constant

Failure energy depending on el. size

Identification of damage parameters

is difficult

Gurson vs. GISSMO – “regularized” Regularization of element size dependency


Summary

Use of existing material models and respective parameters

Constitutive model and damage formulation are treated separately

Allows for the calculation of pre-damage for forming and

crashworthiness simulations

Characterization of materials requires a variety of tests

Offers features for a comprehensive treatment of damage

in forming simulations and allows simply carrying aver to crash

analysis


Thank you for your attention!

GISSMO Material Modeling with a sophisticated Failure …€¦ · GISSMO – Material Modeling with...

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Transcript of GISSMO Material Modeling with a sophisticated Failure …€¦ · GISSMO – Material Modeling with...