Anisotropic ductile damage fully coupled with anisotropic plastic flow: Modeling, experimental validation, and application to metal forming simulation

The main goal of this paper is the modeling, numerical simulation, and experimental validation of the anisotropic ductile damage effects on initially anisotropic plastic flow with mixed (isotropic and kinematic) nonlinear hardening under large plastic strains for metal forming processes simulation. A symmetric second-rank damage tensor together with a symmetrized fourth-rank damage-effect tensor is used to describe the anisotropic ductile damage evolution and its effect on the large plastic flow with hardening. Following the concept of effective state variables in the framework of the total energy equivalence assumption, the “Murakami” fourth-rank damage-effect tensor is chosen to describe the anisotropic damage effect on the elastic-plastic behavior including the mixed hardening. The “Lemaitre” ductile anisotropic damage evolution relationships, where the principal directions of the damage rate tensor are governed by those of the plastic strain rate tensor, are used. As difference with the works cited above, the nonlinear mixed isotropic and kinematic hardening is taken into account considering the full and strong damage effects through the effective state variables deduced from the total energy equivalence assumption initially proposed by Saanouni et al. The non-associative plasticity theory is considered, and the “ Hill 1948 ” quadratic (equivalent) stress norm is used to describe the large plastic anisotropic flow accounting for mixed isotropic and kinematic hardening with anisotropic damage effects. The formulation is performed assuming finite plastic strains and small elastic strains through the so-called rotated frame formulation. The obtained model was implemented into ABAQUS/Explicit® FE software thanks to the user’s developed subroutine VUMAT. The numerical aspects related to the time discretization of the fully coupled anisotropic constitutive equations are carefully described. Finally and for the validation purpose, the model is identified using an appropriate experimental data base concerning the grade 316L stainless steel to simulate numerically some metal forming processes.