A mixed finite element formulation for ductile damage modeling of thermoviscoplastic metals accounting for void shearing

The modeling of ductile damage in engineering metallic materials is an essential step in a design process. In this paper, a mixed finite element formulation is developed to predict ductile damage in thermoviscoplastic porous metals. The novel aspect of the model is the enhancement of Gurson’s plasticity formulation with a void shearing mechanism capable describing thermoviscoplastic flow stress and thermal diffusion. Thus, the model accounts for void growth, nucleation and coalescence; strain and strain-rate hardening; thermal softening; heating by plastic work; thermal diffusion; localized shear banding; and material strength degradation. Associative plasticity and small strains are assumed. Both strong and weak forms describing the material complex behavior are presented. Time discretization by means of backward Euler and Newmark- $$\beta $$ schemes is employed together with Galerkin finite element approximations, leading to a fully discrete set of nonlinear coupled algebraic equations. Two dynamic fracture problems involving ductile failure of plates under a plane strain assumption are numerically analyzed. The effects of the strain rate, thermal diffusion and void shearing mechanism are investigated in detail and shown to be significant. Results show that the present approach can reproduce plastically induced damage, localized shear banding, heating, porosity-induced stress degradation and crack-type damage evolution. The numerical performance is also reported in order to illustrate the convergence of the method.