Recent Developments in Damage and Failure Modeling with LS-DYNA

Transcription

1 Recent evelopments in amage and Failure Modeling with LS-YNA r. André Haufe ynamore GmbH Frieder Neukamm, r. Markus Feucht aimler AG Paul ubois Consultant r. Thomas Borvall ERAB 1

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 esign to the point 2

3 Technological challenges in the automotive industry amage E Safety requirements Weight New materials Composites High strength steel Light alloys Polymers New power train technology σ σ ε max Cost effectiveness Anisotropy c b a esign to the point Failure E Plasticity η E( ε ) e ebonding Fracture growth σ fail = true σ σ σ σ y 3

4 Motivation Lightweight steel/aluminium design! Can we predict failure modes (brittle, ductile, time delayed)? 22MnB5 CP800 stress TWIP TRIP800 ZE340 Aural strain 4

5 Motivation Material behavior dependent on local history of loading Micro-alloyed steel Hot-formed steel stress strain stress strain 0,00 0,05 0,10 0,15 5

6 Material models along the process chain Forming Simulation Correct description of yield locus Anisotropic yield locus: Typical models: Barlat89, Barlat2000, Hill48, Yoshida, Transfer of Variables Plastic Strain Thickness amage Crash Simulation Energy absorption Prediction of structural folding patterns Strain rate dependent models (including damage) Typical models: von Mises, Gurson, Gurson-JC, 6

7 Von Mises with damage 7

8 Von Mises plasticity with damage in LS-YNA (MAT_81/82) Enhancement of *MAT_PIECEWISE_LINEAR_PLASTICITY(#024) with damage. Instead of abrupt failure (#024) continuous softening by damage formulation (#081/082) Elasto - Visco - Plasticity with isotropic Hardening and amage: No regularisation & damage/failure independent of state of stress!! A d = with A 0 = scalar (isotropic failure) p = ( ε ) = p ε EPPF EPPFR EPPF ( ) σ = 1 C ep : ε MAT_024: only abrupt failure MAT_081:damage, linear or nonlinear softening linear softening nonlinear softening FAIL EPPF EPPFR 8

9 The Gurson model 9

10 The Gurson-model in LS-YNA The yield function is given as 2 σ 2 e * q trσ * Φ ( σ, σ = + 2 M, f ) 2q1f cosh 1 ( q1f ) = 0 2 σm 2σ M The effective void volume fraction is defined according to f f fc * f ( f ) = 1/ q + 1 fc fc ( f fc ) f > fc ff fc For the matrix material associative von Mises plasticity is assumed for the undamaged state. Yield is NOT isochoric though! q 1 and q 2 are free parameters of the model to fit the yield surface to experimental data. f c is the critical void volume fraction above which the voids start to combine and grow. * Failure is being initiated at f ( f F ) = 1 q 1 Undamaged Gurson yield surface σ e = equivalent von Mises stress σ M = yield stress (matrix) σ = stress tensor f c = critical void volume fraction 10

11 The Gurson-model in LS-YNA The growth of the void volume is and can be considered as damage. f = f + f N G Nucleation of new voids intension: where A pl f ε ε N 1 M N A = exp s 2π 2 N sn ε N s N ε pl M pl N M f 2 = Aε ε N = mean nucleation strain ε pl M = eff. pl. strain (matrix) s N = std. deviation σ amaged Gurson yield surface (needs in hydrostatic loading) Growth of existing voids: where f = V V voids voids + V matix f G = (1 f ) ε pl kk Typical Gurson stress-strain curve ε 11

12 Gurson enhanced by JC-failure model Void growth in the standard Gurson model is triggered by volumetric straining (see also VGTYP for differences between tension and compression for nucleation of new voids). Hence for pure shear loading softening and subsequent failure is not taking place. The Johnson-Cook enhancement adds a failure criterion that is invoked between two defined triaxiality values and triggers sudden failure via element erosion. The definition of triaxiality play a major role: efinition of failure strain λ tri σii = 3 σ vm ( ) ( ) εf = exp 3 λtri 1+ 4 lnε Λ where L < λ < L 1 tri 2 with L 1 and L 2 being user defined lower and upper triaxiality bounds and 1 4 are user defined Johnson-Cook failure parameters. Λ is the user defined curve LCAM that defines a scalar value vs. element length and hence acts a regularisation means. Failure (i. e. element erosion) is initiated iff: σ f = εp < ε 1 no failure f 1 failure ( element erosion) Typical GJC stress-strain curve ε 12

13 The Gurson_JC-model Interaction between submodels by definition of L1 and L2 Remember: L1 and L2 are triaxiality values. Triaxilality is defined as λ tri σii = 3 σ vm Hence positive values define tension, negative define compression. Gurson Gurson & JC Gurson The following holds for the JC-corridor: λ < 2 tri L Only Gurson is active L2 λ L1 tri < λ L1 tri Gurson and JC-criteria is active Only Gurson is active L2 λ tri L1 13

14 Produceability to Serviceability 14

15 Closing the process chain Forming simulation Crash simulation Hill based models Anisotropiy of yield surface Kinematic/Isotropic hardening Failure by FL (post-processing) No computation of damage??? v. Mises or Gurson model Strain rate dependency Isotropic hardening amage evolution Failure models (damage variable necessary!!) σ II σ II σ II σ I σ I σ III σ III σ III σ I 15

16 ifferent ways to realize a consistent modeling One Material Model for Forming and Crash Simulation Requirements for Forming Simulations: Anisotropy, Exact escription of Yield Locus, Kinematic Hardening, etc. Requirements for Crash Simulation: ynamic Material Behavior, Failure Prediction, Energy Absorption, Robust Formulation Leads to very complex model Modular Concept for the escription of Plasticity and 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_A.(damage) 16

17 Produceability to Serviceability Anisotropy Yield locus amage ynamic effects Forming simulation Mapping Crash simulation Barlat σ,ε pl Gurson σ,ε pl,t f Fortran-Program σ, f 0 ε pl,0, t0, 0 Gurson background Incompatible Models: Isochoric plastic behavior Schmeing, Haufe & Feucht [2007] Neukamm, Feucht & Haufe [2007] 17

18 Produceability to Serviceability: Modular Concept Forming simulation Mapping Crash simulation Material model ε pl, t ε pl,,t 0 0 Material model σ, ε pl amage model σ,ε pl amage model Modular Concept: Proven material models for both disciplines are retained Use of one continuous damage model for both 18

19 Produceability to Serviceability: Modular Concept Current status in 971R5 Forming simulation Mapping Crash simulation Barlat σ,ε pl GISSMO σ,ε pl,t Fortran-Program σ, t 0 ε pl,0, 0 Mises σ,ε pl GISSMO Ebelsheiser, Feucht & Neukamm [2008] Neukamm, Feucht, ubois & Haufe [ ] 19

20 GISSMO a short description Effective stress concept (similiar to MAT_81/224 etc.) J. Lemaitre, A Continuous amage Mechanics Model for uctile Fracture Overall Section Area containing micro-defects S Reduced ( effective ) Section Area S ˆ < S Measure of amage = S Sˆ S Reduction of effective cross-section leads to reduction of tangential stiffness Phenomenological description σ * ( ) = σ 1 20

21 GISSMO - a short description uctile damage and failure amage Evolution Failure Curve amage overestimated for linear damage accumulation Crash Mises Gurson GISSMO Forming triaxiality Neukamm, Feucht, ubois & Haufe [ ] 21

22 GISSMO a short description Engineering approach for instability failure t 1 2 n ψ Evolution of Instability Material Instability F = n ε v, loc ( 1 ) n F 1 ε v Tensile Flachzugprobe test specimen IN EN IN EN ,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15 0,10 0,05 Simulation Versuch 0,00 0,00 0,05 0,10 0,15 0,20 0,25 0,30 Crash Mises Gurson Forming Material Instability triaxiality Neukamm, Feucht, ubois & Haufe [ ] 22

23 REMARK: Failure criterion for plane stress and 3 solids Shells (2) Solids (3) Bruchdehnung Triaxialität Lode Parameter Bruchdehnung Triaxialität Lode Parameter Bruchdehnung For shells (2 with the assumption of plane stress ) triaxility and Lode angle depend on each other. fracture strain is a function of the triaxiality Triaxialität For Solids (3) both the Lode angle and triaxiality are independent fracture strain is a function of triaxiality and Lode angle Baseran [2010] 23

24 GISSMO a short description Inherent mesh-size dependency of results in the post-critical region Simulations of tensile test specimen with different mesh sizes element size Engineering Stress 0,4 0,2 Influence of damage in post-critical region Experiment 0,5mm 1mm 2,5mm Regularization of mesh-size dependency 0,0 0,0 0,1 0,2 0,3 0,4 0,5 Engineering Strain 24

25 GISSMO a short description Generalized Incremental Stress State dependent damage MOdel MGTYP: Flag for coupling (Lemaitre) * σ ( ) = σ 1 CRIT, FAEXP: Post-critical behavior * σ = σ 1 1 CRIT CRIT FAEXP True Stress True Stress m=2 m=5 GISSMO dmgtyp2 m=8 MAT_ True Strain 0 0 True Strain 25

26 GISSMO Identification of damage parameters: Range of experiments and simulations To be considered: 8 Specimen geometries 5 iscretisations 26

27 GISSMO Equivalent plastic strain vs. triaxiality ε f 2,0 1,8 1,6 Element size 1mm 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 triaxiality 27

28 GISSMO vs. Gurson vs. 24/81 Comparison of experiments and simulations Versuch GISSMO Gurson constant (v. Mises) Mini-Flachzugproben ungekerbt Mini-Flachzugproben Kerbradius 1mm Scherzugproben Kerbradius 1mm, 15 Small tensile test specimen Notched tensile specimen, notch radius 1mm Shear test, inclined 15 0,50 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0,0 0,2 0,4 0,6 0,8 0,6 0,5 0,40 0,4 0,30 0,3 0,2 0,20 0,1 0,10 0,0 0,00-0,10 0,10 0,30 0,50 0,00 0,05 0,10 0,15 0,20 0,60 Tensile Flachzugproben specimen IN EN EN ,60 Shear Scherzugproben test, straight Kerbradius 1mm, 0 12 Arcan 0,50 0, ,40 0,40 8 0,30 0,30 6 0,20 0,20 4 0,10 0,10 2 0,00 0,00 0,10 0,20 0,30 0,40 0,00 0,00 0,05 0,10 0,15 0,20 0 0,0 0,5 1,0 1,5 28

29 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 amage Parameters is more straight-forward 29

30 Example: tension rod GISSMO input instability damage 30

31 Example: Arcan shear test damage triaxiality damage instability 31

32 GISSMO eep-draw simulation of cross-die using GISSMO Constant failure criterion Linear damage accumulation Failure not predicted correctly GISSMO-Criterion Linear accumulation of damage Possibly overestimated damage GISSMO-Criterion Nonlinear damage accumulation Rupture predicted correctly 32

33 Process chain with GISSMO Forming simulation: *MAT_36 (Barlat 89) *MAT_A_EROSION (GISSMO) Plast. strains Thickness distribution amage Mapping Crash Simulation: *MAT_24 (Mises) *MAT_A_EROSION (GISSMO) 33

34 Summary Features of GISSMO: The use of existing material models and respective parameters The 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 Automatic method for identification of parameters is to be developed Offers features for a comprehensive treatment of damage in forming simulations Available in LS-YNA V9.71 R5 Verification und validation of concept are under way 34

35 Threepart failure concept 35

36 amage and failure concept New implementation of a threepart failure model By using the basic software architecture available since the implementation of GISSMO another client driven threepart failure and damage model has been implemented. The model will be available in *MAT_A_EROSION starting with LS-YNA V971 R5. The concept allows (theoretically) the combination with any available constitutive model in LS-YNA. Hence the same idea for closing the gap between forming and crash simulations apply. The individual criteria deliver strain rate dependent failure accumulation that is being input in tabulated from. Using the accumulated data in subsequent simulations (multi-stage) simulations, the well established method of using the YNAIN-files is chosen. Hence *INCLUE_STAMPE_PART will be able to handle the new option. Basis material model: e.g. MAT_24 σ II σ II Yield stress ε σ I σ III σ I Plastic strain σ III 36

37 amage and failure concept Three individual criteria may predict failure in thin sheet metal. Post-critical behavior is defined by allowance of an additional displacement in each element. The element is deleted if a defined number of integrations points is flagged as failed. uctile failure Shear failure Instability criteria For the ductile initiation option a function p p p ε = ε ( η, ε ) represents the plastic strain at onset of damage (P1). This is a function of stress triaxiality defined as η = p / q with p being the pressure and q the von Mises equivalent stress. Optionally this can be defined as a table with the second dependency being on the effective plastic strain p rate ε. The damage initiation history variable evolves according to ω ε p = 0 p dε ε p For the shear initiation option a function p p p ε = ε ( θ, ε ) represents the plastic strain at onset of damage (P1). This is a function of a shear stress function defined as θ = ( q + k p) / τ S with p being the pressure, q the von Mises equivalent stress and τ the maximum shear stress defined as a function of the principal stress values τ = ( σ major σ minor ) / 2 Introduced here is also the pressure influence parameter k S (P2). Optionally this can be defined as a table with the second dependency being on the effective plastic strain p rate ε. The damage initiation history variable evolves according to ω ε p = 0 p dε ε p For the MSFL initiation option a function p p p = (, ) ε ε α ε represents the plastic strain at onset of damage. This is a function of the ratio of principal plastic strain rates defined as α = ε / ε p minor p major The MSFL criterion is only relevant for shells and the principal strains should be interpreted as the in-plane principal strains. The damage initiation history variable evolves according to: ω = max p ε t T p ε 37

38 Failure mechanism in sheet metal deformation uctile failure criteria Shear failure criteria Instability failure criteria ε ε S ε I σ η σ θ σ α = ε 2 ε 1 fail rupt ε ε ε fail rupt ε ε ε fail rupt ε ε ε 38

39 Thank you for your attention! ynamore GmbH Industriestraße Stuttgart Germany 39