Micromechanics Computational Cell Microstructure idealization Ductile fracture Modeling

Micromechanics: Computational Cell Microstructure idealization Ductile fracture Modeling idealization Array of voids Computational cell |7| Finite element model Brown University

Micromechanics: Stress State Macroscopic stresses: Triaxiality: Lode parameter: The influence of Lode parameter is negletted in this study – it is not possible to obtain a wide range of Lode parameters when working with sheet metal Brown University

Void Dilation Equations 0, 20 Ferrite Void Volume Fraction 0, 2 0, 15 0, 1 0, 05 0 0 0, 15 0, 3 0, 45 0, 15 Martensite 0, 10 0, 05 0, 00 0, 6 Macroscopic strain 0, 15 0, 30 0, 45 0, 60 Macroscopic strain 0. 25 0. 50 0. 75 1. 00 1. 25 1. 50 |2| Brown University

8 Proportionality constant Void Dilation Equations 6 4 2 Ferrite 0 0 0, 5 1 1, 5 2 10 8 6 4 2 Martensite 0 0 Triaxiality [Contd. ] 0, 5 1 1, 5 2 Triaxiality Void dilation equation: Ferrite Void dilation equation: Martensite |3| Brown University

1, 7 1, 6 Void Elongation Ratio Void elongation ratio Void Elongation Equations 1, 5 1, 4 1, 3 1, 2 1, 1 1 0, 00 Ferrite 0, 05 0, 10 Strain 0, 15 1, 4 1, 3 1, 2 1, 1 1 0, 00 0, 20 Martensite 0, 05 0, 10 Strain 0, 15 0, 20 1) Micro void elongation is prominent at low triaxialities for both ferrite and martensite 2) The void in ferrite tend to elongate rapidly when compared to the void in martensite for a given macroscopic strain at high triaxialities 3) The evolution of void elongation ratio is almost linear (similar to the evolution of void dilation) with respect to the macroscopic strain |4| Brown University

Void Elongation Equations 4 Proportionality Constant 4 [Contd. ] 3 2 1 Ferrite 0 0 0, 5 1 Triaxiality 1, 5 3 2 1 Martensite 0 2 0 0, 5 1 Triaxiality 1, 5 2 Evaluating proportionality functions The proportionality functions are obtained by plotting slopes of void elongation evolution curves with respect to the triaxialities at which they are obtained |5| Brown University

Microscopic Damage Mechanisms undeformed cell dilated void initial void elongated void initial void Void Dilation Void Elongation Coalescence of dilated voids Coalescence of elongated voids |6| Brown University

Modified Le. Maitre Model Stress rate and elastic strain rate Isotropic visco-plastic constitutive equation Damage evolution equation Void elongation evolution |7| Brown University