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

Instability and Failure Prediction for Sheet Metal Forming Applications with LS-DYNA André Haufe Dynamore GmbH Industriestraße 2 70565 Stuttgart http://www.dynamore.de LS-Dyna Info-Day 2011 – DYNAmore – Stuttgart – A. Haufe

Motivation LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 2

Technological challenges in the automotive industry Weight Composites High strength steel Safety requirements New materials Light alloys Polymers New power train technology Cost effectiveness Design to the point LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 3

Technological challenges in the automotive industry Weight Composites High strength steel Safety requirements New materials Light alloys Polymers Damage New power train E technology   Cost effectiveness  max Anisotropy Design to the point c b a Fracture growth Debonding Failure  Plasticity E  E ( ) e      fail true  y LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 4

Motivation Lightweight steel/aluminium design! Can we predict failure modes (brittle, ductile, time delayed)? 22MnB5 CP800 TWIP TRIP800 ZE340 Aural LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 5

Motivation Material behavior dependent on local history of loading Micro-alloyed steel Hot-formed steel 900 1800 800 1600 700 1400 600 1200 500 stress stress 1000 400 800  300  600 200 400 100 200 0 0 strain 0.00 0.10 0.20 0.30 0.40 0.50 strain 0,00 0,05 0,10 0   LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 6

Closing the process chain: Standard materials / state of the art Forming simulation Crash simulation  v. Mises or Gurson model  Hill based models  Anisotropiy of yield surface  Strain rate dependency  Isotropic hardening  Kinematic/Isotropic hardening  Damage evolution  State of the art: Failure by FLD (post-processing)  Failure models  NEW: Computation of damage (mapping of damage variable) (GISSMO) Mapping   II II  II  I  I  III    III III I LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 7

Preliminary considerations for plane stress LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 8

Plane stress condition  Typical discretization with shell elements: xx   yy  xy yx Principle axis Plane stress Parameterised           0 0  ( , ) 1 1 1     1         σ 0 k 0 ( , )    2 2 1        0   0 0 0  σ 3 3      k 0   2 1   0           2 1 ( k 1) k     0 1 vm    p ( k 1) ( k 1)        1 sign( ) Definition of stress triaxiality:      1    2 3 1 ( k 1) k 3 1 ( k 1) k vm 1 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 9

Haigh-Westergaard coordinates in principle stress space 1 tr( ) I    σ 1 Lode angle 3 3    2 J : s s 2   1 3 3 J Deviatoric     3 arccos   plane 1.5 3  2 J  2 p   Definition of stress triaxiality:  vm LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 10

A toy to visualize stress invariants (downloadable from the www.dynamore.se) page 1: Crafting instructions • 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! LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 11

A toy to visualize stress invariants (downloadable from the www.dynamore.se) Crafting instructions page 2: • Page 2 of the set may be added for further clarification of the triaxiality variable. Final shape of toy LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 12

Plane stress parameterised for shells    p ( k 1) ( k 1)        1 Triaxiality sign( )      1    2 3 1 ( k 1) k 3 1 ( k 1) k vm 1 Bounds: Compression p    ( k 1) 1         lim lim sign( ) sign( ) vm   1 1   3 3 1 ( k 1) k k k tension compression Tension k  ( k 1) 1       lim lim sign( ) sign( )   1 1   3 k k 3 1 ( k 1) k Biaxial tension  ( k 1) 2        lim lim sign( ) sign( )   1 1   3 k 1 k 1 3 1 ( k 1) k LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 13

How to define the accumulation of damage ? A comparison of model approaches Investigation of failure criteria for the following case: 0  Plane stress: 3       and  Small elastic deformations: 1 p 1 2 p 2 Damage or failure criteria  Isochoric plasticity: 3 p 3 p 1 p 2 4 2 2 1 b b     Proportional loading: a p p 1 3  2 1 1 2 b     a 2 2 1 a a b  2 b vm 1 2 1 p p p 1 a 3 1 a 2 a vm LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 14

How to define the accumulation of damage ? A comparison of classical model approaches Some typical loading paths LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 15

How to define the accumulation of damage ? A comparison of classical model approaches Some typical loading paths Four criteria Principal strain: 1 max p 1 1 max Equivalent plastic strain: 4 3 2 max 2 1 b 2 b p p 1 max p 1 3 4 1 b 2 b Thinning: p 3 max max p 3 p 1 2 1 b 2 1 b Diffuse necking: 2 2 1 b b p 1 max 1 b 2 b 2 b 2 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 16

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

Failure models in the plane of major strain vs. b LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 18

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. LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 19

Failure models: equivalent plastic strain vs. triaxiality For uniaxial and biaxial tension different criteria lead to a factor of 2: 0.5 2, p 1, p p 1, p 2 1, p 2, p p 1, p LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 20

Johnson-Cook criterion (Hancock-McKenzie ) p d 3 d d e vm pf 1 2 d 0 1 3 d 3 2 1 d e 2 2 1 f Johnson-Cook and FLC are very close in the neighborhood of uniaxial tension. LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 21

Parametrized for 3D stress space LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 22

Lode-angle: Extension- and Compression test   III III Possible value for first principle stress    II III      and 0 I II III   and 0 I Compression Compression  Extension   II  II   I       I 30     30 View not parallel to hydrostatic axis View parallel and on hydrostatic axis (perpendicular to deviator plane) LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 23

3D-Stress state parameterised for volume elements 0 1 0 0 1 F 1 0 0 0 0 1 1 4 0 0 1 1 0 0 1 extension 0 0 0 2 1 0 0 1 4 0 0 0 0 0 0 compression 0 0 1 0 0 0  0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 2 p    vm LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 24

Invariants in 3D stress space Failure criterion extd. for 3D solids Parameter definition  I    m 1   3 vM vM 27 J    Stress domain in 3 J s s s mit  3 3 1 2 3 sheet metal forming 2 vM [Source: Wierzbicki et al.]        1 or 30      0 0 or      1 or 30 LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 25

Failure Prediction for UHSS: Adding some damage LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 26

Closing the process chain: Standard materials / state of the art Forming simulation Crash simulation  v. Mises or Gurson model  Hill based models  Anisotropiy of yield surface  Strain rate dependency  Isotropic hardening  Kinematic/Isotropic hardening  Damage evolution  State of the art: Failure by FLD (post-processing)  Failure models  NEW: Computation of damage (mapping of damage variable) (GISSMO) Mapping   II II  II  I  I  III    III III I LS-DYNA info-Day 2011 – Stuttgart – A. Haufe 27