Dilatational Viscoplasticity of Cubic Polycrystals with Intergranular Cavities

Abstract

Theoretical predictions are derived for the viscoplastic response of polycrystalline solids containing a random distribution of intergranular porosity. The predictions follow from a nonlinear homogenization method based on a ‘generalized secant’ linearization of the viscoplastic crystal response, as proposed by Liu & Ponte Castañeda (J. Mech. Phys. Solids 52:467-495, 2004). The influence of crystallographic texture and porosity on the instantaneous response is investigated in the case of nonhardening power-law crystals with face-centered cubic symmetry. It is found that crystallinity of the matrix material has a minor effect, even when crystals exhibit a low strain-rate sensitivity. Thus, the assumption of matrix isotropy implicit in all standard theories of dilatational viscoplasticity should be appropriate for this class of materials.