Instability and Failure Prediction for Sheet Metal Forming ... · Instability and Failure...

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Instability and Failure Prediction for Sheet

Metal Forming Applications with LS-DYNA

André Haufe

LS-Dyna Info-Day 2011 – DYNAmore – Stuttgart – A. Haufe

2 LS-DYNA info-Day 2011 – 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


Motivation Lightweight steel/aluminium design!

Can we predict failure modes (brittle, ductile, time delayed)?

22MnB5

CP800

TRIP800

ZE340

Aural

TWIP


Micro-alloyed steel Hot-formed steel

Motivation Material behavior dependent on local history of loading

0

200

400

600

800

1000

1200

1400

1600

1800

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

technisch

te

chnis

ch

[MPa]

MN1-Rz-S1

MN1-Rz-S2

MN1-Rz-S3

MN1-Rz-S4

MN1-Rz-S5

MN1-Rz-S6

MN1-Rz-S7

MN1-Rz-S8

MN1-Rz-S9

MN1-Rz-S10

MN1-Rz-S11

MN1-Rz-S12

Technische Sigma-Epsilon-Kurve

0

100

200

300

400

500

600

700

800

900

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

te

ch

nis

ch

[M

Pa]

QH2-1-Fz-S1

QH2-1-Fz-S2

QH2-1-Fz-S3

QH2-1-Fz-S4

QH1-Fz-S1L

QH1-Fz-S1Q

QH1-Fz-S1D

Technische Sigma-Epsilon-Kurve

str

es

s

str

es

s

strain strain


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


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

Com

pre

ssio

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


Failure Prediction for UHSS:

Adding some damage


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


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 ,,

Re

arr

an

ge

his

tory

fie

ld

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


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

GISSMO – a short description Effective stress concept (similiar to MAT_81/224 etc.)


GISSMO Failure criterion for plane stress and extd. for 3D solids

Lode

Parameter-1

1

0

-0.5

0.5

0.50

-1-0.5

1Triaxialität

Bru

chdehnung

Triaxialität

Bru

chdehnung

-0.5 0 0.5 11

For shells (2D with the assumption of plane stress ) triaxility

and Lode angle depend on each other.

fracture strain is a function of the triaxiality

For Solids (3D) both the Lode angle and triaxiality are

independent

fracture strain is a function of triaxiality and Lode angle

Shells (2D) Solids (3D)

Lode Parameter

-1

1

0

-0.5

0.5

0.50

-1-0.5

1

Triaxialität

Bru

chdehnung

Baseran [2010]

3

1

2

27 2



1

3

m

vM vM

I

3

3

27

2 vM

J

3 1 2 3J s s smit


Stress domain in

sheet metal forming

GISSMO Failure criterion extd. for 3D solids

1 60or

0 0or

1 60or



1

3

m

vM vM

I

3

3

27

2 vM

J

3 1 2 3J s s smit


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 overestimated

for linear damage

accumulation

Failure Curve

GISSMO - a short description Ductile damage and failure

triaxiality

Wierzbicki et al. (and many more…) / Neukamm, Feucht, DuBois & Haufe [2008-2011]


Gurson

Mises

Forming

Crash

Evolution of Instability Material Instability

Material Instability

v

n

locv

Fn

F

11

,

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

Neukamm, Feucht, DuBois & Haufe [2008-2011]


GISSMO – a short description Inherent mesh-size dependency of results in the post-critical region

0,0

0,2

0,4

0,0 0,1 0,2 0,3 0,4 0,5

Engineering Strain

En

gin

ee

rin

g S

tre

ss

Experiment

0,5mm

1mm

2,5mm

Simulations of tensile test specimen with different mesh sizes

Regularization of

mesh-size dependency

element size

Influence of damage in

postcritical region


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 Generalized Incremental Stress State dependent damage MOdel


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


Forming simulation:

*MAT_36 (Barlat

89)

*MAT_ADD_EROSION

(GISSMO)

Crash Simulation:

*MAT_24 (Mises)

*MAT_ADD_EROSION

(GISSMO)

Plast. strains Thickness distribution Damage

Mapping

Process chain with GISSMO


Summary

Features of GISSMO:

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!

Instability and Failure Prediction for Sheet Metal Forming ... · Instability and Failure...

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