A variationally consistent coupled isotropic elasto-plastic damage model for the analysis of LCF at finite strains

Transcription

1 A variationally consistent coupled isotropic elasto-plastic damage model for the analysis of LCF at finite strains O. Kintzel, J. Mosler GKSS Forschungszentrum Geesthacht Institute of Materials Research Materials Mechanics ECCM 2010 Paris, France May 16-21, 2010 PAGE 1

2 Outline Motivation Modeling of isotropic ductile-brittle damage Solution by means of a variationally consistent approach Numerical demonstration example Conclusion PAGE 2

3 Motivation Low cycle fatigue Fatigue damage caused by alternate loading at high stress levels Material degradation at local highly stressed zones, e.g. notches Ultimate structural failure by loss of load carrying capacity Aloha airline fatigue failure, 1988 PAGE 3

4 Motivation Evaluation of LCF Experimental evaluation of smooth round bars (DLC-Specimen) (Khan, Vyshnevskyy & Mosler 2008/09, GKSS) LCF failure criterion: Mesocrack initiation, crack length = mm CT-Specimen Crack propagation DLC-Specimen Mesocrack initiation DLC-Specimen PAGE 4

5 Motivation Material alloy Al2024 Considered material: Sheets of Aluminium alloy 2024 Material anisotropy: L-direction: ductile S-direction: quasi-brittle L-direction S-direction Material degradation driven by elasto-plastic strain accumulation Damage locally by ductile fracture (microvoid growth and coalescence) In S-direction more localized and quasi-brittle PAGE 5

6 Motivation Modeling of damage process Micropores Microcracks Isotropic ductile-brittle damage law (strain equivalence (ductile part)) Introduction of a novel brittle damage indicator function Considering of a geometrically non-linear setting (finite strains) PAGE 6

7 Modeling Finite strain elasticity Elastic part of Helmholtz energy (Compressible Neo-Hookean) Volumetric part of the strain energy function (Ciarlet 1988) Elastic metric tensor: Plastic metric tensor: Mandel stress tensor: PAGE 7

8 Modeling Finite strain plasticity Von Mises-type yield function Plastic part of Helmholtz energy Kinematic hardening: Isotropic hardening: PAGE 8

9 Modeling Ductile-brittle damage decomposition Decomposition of the damage variable into ductile and brittle parts Damage process driven by elasto-plastic strain accumulation Decomposition of the energy release rate Ductile part: Brittle part: PAGE 9

10 Modeling Isotropic damage models Ductile damage model (Lemaitre 1992) Brittle damage (novel damage indicator function) (Kintzel & Mosler 2010) Brittle part of Helmholtz energy Damage threshold: Shift tensor (alternate threshold): PAGE 10

11 Solution The variational constitutive update Variational principle for standard dissipative materials (associative rules) e.g. (Ortiz & Repetto 1999), (Miehe 2002), (Mosler & Bruhns 2009) Novel extended principle for generalized standard solids (Mosler 2010) Helmholtz energy and dissipation de-coupled! PAGE 11

12 Solution The variational constitutive update Non-associative finite strain elasto-plasticity Time integration by a consistent backward Euler scheme (Mosler 2010) PAGE 12

13 Solution The variational constitutive update Application to current brittle damage framework (Kintzel & Mosler 2010) define thresholds at which fracture occurs instantaneously can be calibrated to microcrack growth (similar to Paris law) PAGE 13

14 Numerical example Geometry and definitions Three-dimensional computation of DLC-Specimen : Damage initiation (if threshold for plastic stored energy is reached) : Mesocrack initiation (if critical damage threshold is reached first) PAGE 14

15 Numerical example Results after optimization Results for number of cycles (Kintzel, Khan & Mosler 2010) axi-symm. Optimized material parameters: PAGE 15 symm. A

16 Conclusion Experimental testing of smooth round bars (DLC) and round notched bars (RNB), Microstructural analyses by means of imaging software Development of a novel fully coupled isotropic quasi-brittle damage model for simulation in S-direction Solution by means of a variationally consistent approach, new variational principle for generalized standard solids, non-associative evolution equations! Advantage: Physically and mathematically sound framework Comparison of experiment and simulation good agreement Contact: Olaf Kintzel (olaf.kintzel@gkss.de) PAGE 16