GISSMO Material Modeling with a sophisticated Failure Criteria

GISSMO Material Modeling with a sophisticated Failure Criteria André Haufe, Paul DuBois, Frieder Neukamm, Markus Feucht Dynamore GmbH Industriestraße 2 70565 Stuttgart http://www.dynamore.de

Motivation 2

Technological challenges in the automotive industry Safety requirements Weight New materials Composites High strength steel Light alloys Polymers New power train technology Cost effectiveness Design to the point 3

Technological challenges in the automotive industry Damage E Safety requirements Weight New materials Composites High strength steel Light alloys Polymers New power train technology max Cost effectiveness Anisotropy c b a Design to the point Failure E Plasticity E( ) e Debonding Fracture growth fail true y 4

Closing the process chain: Standard materials / state of the art Forming simulation Crash simulation 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 Mapping v. Mises or Gurson model Strain rate dependency Isotropic hardening Damage evolution Failure models (mapping of damage variable) II II I I III III III I 5

Preliminary considerations for plane stress 6

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? 7

Isotropic (scalar) damage Effective stress concept (similar to MAT_8/20/224 etc.) J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture Overall Section Area containing micro-defects S Reduced ( effective ) Section Area Sˆ S Measure of Damage D S Sˆ S Reduction of effective cross-section leads to reduction of tangential stiffness Phenomenological description σ * σ D 8

Plane stress condition Typical discretization with shell elements: xx yy yx xy Principle axis Plane stress Parameterised 2 3 σ 0 0 0 (, ) (, ) 2 0 3 k 2 0 0 σ 0 k 0 0 0 0 ( k) k vm 2 Definition of stress triaxiality: p ( k ) ( k ) 2 vm 3 ( k) k 3 ( k) k sign( ) 9

Haigh-Westergaard coordinates in principle stress space Lode angle I tr( ) σ 3 3 2 J s: s 2 Deviatoric plane 3 3 J 3 arccos.5 3 2 J 2 Definition of stress triaxiality: p vm 0

A toy to visualize stress invariants (downloadable from the www.dynamore.se) Crafting instructions page : Download the PDF-file Print on thick piece of paper Cut out where indicated Add four wooden sticks (5cm) Add some glue where necessary (engineers should find out the locations without further instructions all others contact their local distributor) Have fun!

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 2

Plane stress parameterised for shells Triaxiality p ( k ) ( k ) 2 vm 3 ( k) k 3 ( k) k sign( ) Bounds: Compression ( k ) lim lim sign( ) sign( ) k k 3 ( k) k 3 tension p vm compression Tension ( k ) lim lim sign( ) sign( ) k k 3 ( k) k 3 k Biaxial tension ( k ) 2 lim lim sign( ) sign( ) k k 3 ( k) k 3 3

How to define the accumulation of damage? A comparison of model approaches Investigation of failure criteria for the following case: Plane stress: 3 0 Small elastic deformations: Isochoric plasticity: Proportional loading: and 2 p 2 p2 3 p3 p p2 a b p2 p 2b a 2 b Damage or failure criteria p vm p vm 4 3 2 2 p 2 2 3 a a b a 2 b a a 4

How to define the accumulation of damage? A comparison of classical model approaches Some typical loading paths 5

How to define the accumulation of damage? A comparison of classical model approaches Some typical loading paths Four criteria Principal strain: max p max Equivalent plastic strain: 4 3 3 4 2 2 2 max p p b b max p 2 b b Thinning: max p3 p Diffuse necking: p3 2 b 2 2 2 b b b 2 b 2b p max 2 max b 6

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. 7

Failure models in the plane of major strain vs. b 8

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. 9

Failure models: equivalent plastic strain vs. triaxiality For uniaxial and biaxial tension different criteria lead to a factor of 2: 0.5 2, p, p p, p 2, p 2, p p, p 20

Johnson-Cook criterion (Hancock-McKenzie ) d d d pf 3 d 0 3 2 2 f 2 e 2 d e d 3 p vm Johnson-Cook and FLC are very close in the neighborhood of uniaxial tension. 2

Parametrized for 3D stress space 22

Compression Lode-angle: Extension- and Compression test III III Possible value for first principle stress II I III and 0 Compression II III and 0 I I 30 II I Extension II 30 View not parallel to hydrostatic axis View parallel and on hydrostatic axis (perpendicular to deviator plane) 23

3D-Stress state parameterised for volume elements 0 extension compression 0 0 0 0 4 0 0 4 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p vm 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 24

Invariants in 3D stress space Failure criterion extd. for 3D solids Stress domain in sheet metal forming Parameter definition m I 3 vm 27 J vm 3 mit 3 3 2 3 2 vm J s s s [Source: Wierzbicki et al.] or 30 0 or 0 or 30 25

Deriving GISSMO from that 26

Closing the process chain: UHS materials for press hardening Forming simulation Crash simulation Hill based models Ortho- or isotropic yield surface Isotropic hardening Feasibility by thinning or damage (calibration?!) Dependency on temperature Microstructural evolution (#244) Mapping v. Mises or Gurson model Strain rate dependency Isotropic hardening (locally) Damage evolution (locally) Failure models (mapping damage variable) II II II I I III III I III 27

Different ways to realize a consistent modeling One Material Model for Forming and Crash Simulation Modular Concept for the Description of Plasticity & Failure 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 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) 28

Produceability to Serviceability: Modular Concept Forming simulation Mapping Crash simulation Material model pl, t pl,, t 0 0 Material model, pl D Damage model D D D, pl Damage model Modular Concept: Proven material models for both disciplines are retained Use of one continuous damage model for both 29

Fortran-Program Produceability to Serviceability: Modular Concept Current status in 97R5 Forming simulation Mapping Crash simulation Barlat, pl,t, t 0 pl,0, 0 Mises, pl, pl GISSMO D D GISSMO Ebelsheiser, Feucht & Neukamm [2008] Neukamm, Feucht, DuBois & Haufe [2008-200] 30

GISSMO Failure criterion extd. for 3D solids Stress domain in sheet metal forming Parameter definition m I 3 vm 27 J vm 3 mit 3 3 2 3 2 vm J s s s [Source: Wierzbicki et al.] Xue Hutchinson Gurson std. f Xue Hutchinson Gurson std. [Experimental data by Wierzbicki et al.] 3

GISSMO - a short description Ductile damage and failure Damage evolution Failure curve Damage regularly overestimated for linear damage accumulation!! Crash Mises Gurson GISSMO Forming triaxiality Neukamm, Feucht, DuBois & Haufe [2008-200] 32

GISSMO a short description Engineering approach for instability failure t 2 n Instability evolution Instability curve definition n n F F v v, loc Tensile Flachzugprobe test specimen DIN EN DIN 200 EN 200 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,5 0,0 0,05 Simulation Versuch 0,00 0,00 0,05 0,0 0,5 0,20 0,25 0,30 Crash Mises Gurson Forming Material Instability triaxiality Neukamm, Feucht, DuBois & Haufe [2008-200] 33

GISSMO a short description Mesh size dependency: Simple regularisation Test program and calibration Inherent mesh-size dependency of results in the post-critical region Simulation (and calibration) of tensile test specimen with different mesh sizes 34

True Stress True Stress GISSMO a short description for the uniaxial case Generalized Incremental Stress State dependent damage MOdel DMGTYP: Flag for coupling (Lemaitre) DCRIT, FADEXP: Post-critical behavior * D * D D D CRIT CRIT FADEXP GISSMO dmgtyp2 m=2 m=5 m=8 MAT_024 0 0 True Strain 0 0 True Strain 35

GISSMO Non-proportional loading influence on failure behavior Failure strain depending on Loading state fail () Load path and pre-damage Accumulation of damage Failure fail m / eq 36

Non-Proportional Loading 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 f B C A D 0.577 0.333 p vm Triaxiality is no longer constant over the stress-strain path if lateral constraint is imposed or lifted. 37

Non-proportional loading criterion without triaxiality f d 0.4 d p f dt p f f p vm 0.577 0.333 38

Non-proportional loading criterion with triaxiality d f p d3.5 vm d d2e 0.66e p f dt p vm cte p f p vm f p vm 0.577 0.333 39

Comparison: Uniaxial tension with/without confinement f p vm 0.577 0.333 40

Input of GISSMO Input definition in LS-DYNA (/4) *MAT_PIECEWISE_LINEAR_PLASTICITY $ mid ro e pr sigy etan fail tdel 00 7.8000E-9 2.000E+5 0.300000 $ c p lcss lcsr vp 0.000 0.000 99 0.000... *MAT_ADD_EROSION $ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS 00 $ MNPRES SIGP SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM $ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD 0 0.3 2 0.2 2 2 $ SIZFLG REFSZ NAHSV 0 5 4 Standard material Input (i.e. MAT_24) Standard failure parameters (optional) GISSMO failure parameters If IDAMG= GISSMO is invoked. Further parameters are expected. DMGTYP=0: Damage is accumulated But not coupled to stresses, no failure. DMGTYP=: Damage is accumulated and coupled to flow stress if D>D crit. Failure occurs if D=. 43

Input of GISSMO Input definition in LS-DYNA (2/4) *MAT_PIECEWISE_LINEAR_PLASTICITY $ mid ro e pr sigy etan fail tdel 00 7.8000E-9 2.000E+5 0.300000 $ c p lcss lcsr vp 0.000 0.000 99 0.000... *MAT_ADD_EROSION $ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS 00 $ MNPRES SIGP SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM $ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD 0 0.3 2 0.2 2 2 $ SIZFLG REFSZ NAHSV 0 5 4 ID of curve defining equivalent plastic strain at failure vs. triaxiality. Damage will have values from 0 up to.0. Exponent for nonlinear damage accumulation: Standard material Input (i.e. MAT_24) Standard failure parameters (optional) GISSMO failure parameters 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. 44

Input of GISSMO Input definition in LS-DYNA (3/4) *MAT_PIECEWISE_LINEAR_PLASTICITY $ mid ro e pr sigy etan fail tdel 00 7.8000E-9 2.000E+5 0.300000 $ c p lcss lcsr vp 0.000 0.000 99 0.000... *MAT_ADD_EROSION $ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS 00 $ MNPRES SIGP SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM $ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD 0 0.3 2 0.2 2 2 $ SIZFLG REFSZ NAHSV 0 5 4 Standard material Input (i.e. MAT_24) Standard failure parameters (optional) GISSMO failure parameters Fading exponent as defined in: * D D CRIT DCRIT FADEXP Load curve defining element size dependent regularization factors vs. equiv. plastic strain to failure. SIZFLG=0 (default) Characteristic element is computed with respect to initial configuration. SIZFLG= Characteristic element updated in each increment (actual configuration, not recommended) 45

Input of GISSMO Input definition in LS-DYNA (4/4) *MAT_PIECEWISE_LINEAR_PLASTICITY $ mid ro e pr sigy etan fail tdel 00 7.8000E-9 2.000E+5 0.300000 $ c p lcss lcsr vp 0.000 0.000 99 0.000... *MAT_ADD_EROSION $ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS 00 $ MNPRES SIGP SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM $ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD 0 0.3 2 0.2 2 2 $ SIZFLG REFSZ NAHSV 0 5 4 Standard material Input (i.e. MAT_24) Standard failure parameters (optional) 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 d3plotdatabase. 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. 46

Sigma_technisch [GPa] GISSMO vs. Gurson vs. MAT_24/8 Comparison of experiments and simulations Mini-Flachzugproben ungekerbt eps_technisch Mini-Flachzugproben Kerbradius mm Small tensile test specimen Notched tensile specimen, notch radius mm Scherzugproben Shear test, inclined Kerbradius 5 mm, 5 0,50 0,60 0,50 0,40 0,30 0,20 0,0 0,00 0,0 0,2 0,4 0,6 0,8 0,6 Scherzugproben Kerbradius mm, 5 0,50 0,40 Versuch 0,30 GISSMO 0,20 Gurson 0,0 constant (v. Mises) 0,00 0,00 0,05 0,0 0,5 0,20 0,5 0,40 0,4 0,30 0,3 0,2 0,20 0, 0,0 0,0 0,00-0,0 0,0 0,30 0,50 0,00 0,05 0,0 0,5 0,20 0,60 Tensile Flachzugproben specimen DIN EN EN 0002 200 0,60 Shear Scherzugproben test, straight Kerbradius mm, 0 2 Arcan 0,50 0,50 0 0,40 0,40 8 0,30 0,30 6 0,20 0,20 4 0,0 0,0 2 0,00 0,00 0,0 0,20 0,30 0,40 0,00 0,00 0,05 0,0 0,5 0,20 0 0,0 0,5,0,5 47

Gurson vs. GISSMO regularized Regularization of element size dependency Gurson Resultant Failure Strain constant Failure energy depending on el. size Identification of damage parameters is difficult GISSMO Failure Strain constant Fracture energy constant Identification of Damage Parameters is more straight-forward 48

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 49

Thank you for your attention! 50