Instability and Failure Prediction for Sheet Metal Forming - - PowerPoint PPT Presentation

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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

3 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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

4 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Technological challenges in the automotive industry

Damage

 

max

 E

Failure

 fail true

E 



Anisotropy

c

a b   ( )

e

E    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

5 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Motivation

Lightweight steel/aluminium design! Can we predict failure modes (brittle, ductile, time delayed)?

22MnB5 CP800 TRIP800 ZE340 Aural TWIP

6 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Micro-alloyed steel Hot-formed steel

Motivation

Material behavior dependent on local history of loading

200 400 600 800 1000 1200 1400 1600 1800 0,00 0,05 0,10  

100 200 300 400 500 600 700 800 900 0.00 0.10 0.20 0.30 0.40 0.50  

stress stress strain strain

7 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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



I



III



II



I



III



Crash simulation

8 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Preliminary considerations for plane stress

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Plane stress condition

Principle axis

                    

3 2 1

   σ ) , ( ) , (

3 2 1

         

Plane stress

 

1 1 2 1

1 ( 1)

vm

k k k                    σ

1



1 2

  k 

Definition of stress triaxiality:

 

1 1 2 1

( 1) ( 1) sign( ) 3 1 ( 1) 3 1 ( 1)

vm

p k k k k k k                

Parameterised

xx



yy



xy



yx



Typical discretization with shell elements:

10 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Haigh-Westergaard coordinates in principle stress space

1 2 3 1.5 2

1 tr( ) 3 3 2 : 1 3 3 arccos 3 2 I J J J                 σ s s

Deviatoric plane Lode angle

vm

p   

Definition of stress triaxiality:

11 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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:

12 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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

13 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Plane stress parameterised for shells

Triaxiality

 

1 1 2 1

( 1) ( 1) sign( ) 3 1 ( 1) 3 1 ( 1)

vm

p k k k k k k                

Bounds:

k

vm

p   

1 1

( 1) 1 lim lim sign( ) sign( ) 3 3 1 ( 1)

k k

k k k   

 

      

1 1

( 1) 1 lim lim sign( ) sign( ) 3 3 1 ( 1)

k k

k k k   

 

     

1 1 1 1

( 1) 2 lim lim sign( ) sign( ) 3 3 1 ( 1)

k k

k k k   

 

      

Compression Biaxial tension Tension

tension compression

14 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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 1 1 2 2 p p

and      

2 1 2 1 p p

a b      

3 3 1 2 p p p

1 2 2 b a b   

2 2 1 2 2 1 2

4 1 3 1 1 3 1

p p vm vm

b b a a p a a a

Damage or failure criteria

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How to define the accumulation of damage ?

A comparison of classical model approaches Some typical loading paths

16 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

How to define the accumulation of damage ?

A comparison of classical model approaches Some typical loading paths

1 max 1 1 max 2 max 2 2 1 max 1 2 3 max max 3 1 2 1 max 2

4 3 1 3 4 1 2 1 2 1 2 1 1 2 2

p p p p p p p p

b b b b b b b b b b b

Four criteria Principal strain: Equivalent plastic strain: Thinning: Diffuse necking:

17 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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.

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Failure models in the plane of major strain vs. b

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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.

20 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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

• f 2:

21 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Johnson-Cook criterion (Hancock-McKenzie )

3

1 2 1 3 1 2 2 1

3 2

vm

p d pf f

d d e d d d e

Johnson-Cook and FLC are very close in the neighborhood of uniaxial tension.

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Parametrized for 3D stress space

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Lode-angle: Extension- and Compression test

I



III



II



II III I

and     

View parallel and on hydrostatic axis (perpendicular to deviator plane) Possible value for first principle stress

    

I



III



II



Compression

II III I

and     

View not parallel to hydrostatic axis Extension

30     30   

Compression

24 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

1

1 1 1

1 4 1 4

1 1 1 1

1 2

1 1 1 1 1 1 1

1 2

3D-Stress state parameterised for volume elements

compression extension

vm

p   



F

25 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Parameter definition

1

3

m vM vM

I      

3 3

27 2

vM

J   

3 1 2 3

J s s s 

mit

[Source: Wierzbicki et al.]

Stress domain in sheet metal forming

Invariants in 3D stress space

Failure criterion extd. for 3D solids

1 30

• r

      

• r

     1 30

• r

    

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Failure Prediction for UHSS: Adding some damage

27 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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



I



III



II



I



III



Crash simulation

28 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Produceability to Serviceability: Modular Concept

Damage model

Material model Material model

, ,t pl



pl

 ,

Mapping

t

pl,



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

29 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

GISSMO

Barlat

Mises

,

, , t

pl

 

pl

 ,

Mapping

t

pl,

, 

Rearrange history field

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

30 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

• J. Lemaitre, A Continuous Damage

Mechanics Model for Ductile Fracture

Overall Section Area containing micro-defects Reduced (“effective“) Section Area

S S  ˆ S

S S S D ˆ  

Measure of Damage

Reduction of effective cross-section leads to reduction of tangential stiffness  Phenomenological description

 

D   1

*

σ σ

GISSMO – a short description

Effective stress concept (similiar to MAT_81/224 etc.)

31 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

GISSMO

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

Lode Parameter

• 1

1

• 0.5

0.5 0.5

• 1
• 0.5

1

Triaxialität Bruchdehnung Triaxialität Bruchdehnung

• 0.5

0.5 1 1

• 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

• 0.5

0.5 0.5

• 1
• 0.5

1

Triaxialität Bruchdehnung

Baseran [2010]

    

         3 1 2 27

2

  

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Parameter definition

1

3

m vM vM

I      

3 3

27 2

vM

J   

3 1 2 3

J s s s 

mit

[Source: Wierzbicki et al.]

Stress domain in sheet metal forming

GISSMO

Failure criterion extd. for 3D solids

1 60

• r

      

• r

     1 60

• r

    

33 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Parameter definition

1

3

m vM vM

I      

3 3

27 2

vM

J   

3 1 2 3

J s s s 

mit

[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

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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]

35 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Gurson Mises Forming Crash

Evolution of Instability Material Instability

Material Instability

 

v n loc v

F n F     

 1 1 ,

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]

36 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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 Engineering Stress

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

37 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

DMGTYP: Flag for coupling (Lemaitre)

 

D   1

*

 

DCRIT, FADEXP: Post-critical behavior

True Strain True Stress

GISSMO dmgtyp2 MAT_024

True Strain True Stress

m=2 m=5 m=8

                   

FADEXP CRIT CRIT

D D D 1 1

*

 

GISSMO – a short description

Generalized Incremental Stress State dependent damage MOdel

38 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 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

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

Scherzugproben Kerbradius 1mm, 15°

0,00 0,10 0,20 0,30 0,40 0,50 0,00 0,05 0,10 0,15 0,20

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

39 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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

40 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

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

41 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe

Thank you for your attention!