Homogenized constitutive equations for porous single crystals plasticity

Abstract

Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. Classical models used to perform numerical simulations of ductile fracture, as the Gurson–Tvergaard–Needleman model and its extensions, are relevant for the case of large voids compared to the grain size, in which a homogenization of the material behavior over a large number of grains is used. Such modeling prevents assessing the effects of microstructure on both crack path and crack propagation resistance. Therefore, homogenized constitutive equations for porous single crystals plasticity are proposed, featuring void growth and void coalescence stages, hardening and void shape evolution. An original numerical implementation based on the coupling of Newton–Raphson and fixed point algorithms is described. In order to assess the accuracy of the proposed model as well as another one described recently in the literature, an extended database of porous unit-cell simulation results is gathered, investigating the effect of crystallographic orientations and hardening behavior for a FCC material. Strengths and weaknesses of both models are detailed with respect to the reference simulations, leading to the definition of the validity domain of the current model and to pinpoint necessary refinements.