A statistical yield model for porous polycrystals

Abstract

The famous Gurson model and its modified versions, through which the constitutive relationship and the evolution of void volume fraction with strain can be derived, have been widely used in the study of deformation and damage behavior of porous materials. However, the Gurson-type models are based on the assumption that matrix around voids is homogeneous and isotropic. In fact, in actual polycrystalline materials, voids and surrounding grains are generally at the same scale level, so the matrix that can be felt by the void is inherently heterogeneous and anisotropic. In this sense, whether the Gurson model can accurately characterize the yield of porous polycrystals becomes a question that needs to be answered. In this work, a representative volume unit (RVU) model with a central void and randomly oriented and shaped grains is built. By performing crystal plasticity finite element simulations on this polycrystalline RVU, the yield behavior of the porous polycrystals under different triaxial stress states is systematically studied, with a focus on how the random orientations and morphologies of the grains around the void affect the overall initial yield of the porous polycrystals. On this basis, a statistical yield model which takes into account the random orientations and morphologies of the grains around the void is built. Compared with the classical Gurson model, this statistical yield model can well envelop almost all dispersed yield points of the polycrystalline RVUs at different stress triaxialities.