Dilatational viscoplasticity of polycrystalline solids with intergranular cavities

Abstract

We propose constitutive models for polycrystalline aggregates with intergranular cavities and test them against full-field numerical simulations. Such conditions are prevalent in many engineering applications and failure of metallic components (e.g. HIPing and other forming processes, spallation under dynamic loading conditions, etc.), where the dilatational effects associated with the presence of cavities must be accounted for, and standard polycrystalline models for incompressible plasticity are not appropriate. On the other hand, it is not clear that the use of porous plasticity models with isotropic matrix behavior is relevant, particularly, when large deformations can lead to significant texture evolution and therefore to strong matrix anisotropy. Of course, finite strains can also lead to significant changes in the porosity and pore shape, resulting in additional anisotropy development. In this work, we make use of ‘variational linear-comparison’ homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, texture of the matrix phase, single-crystal anisotropy, etc.) and type of loading (triaxiality) on the dilatational viscoplastic behavior of voided polycrystals. The results are also compared with the predictions of isotropic-matrix porous plasticity models to assess the effect of the possible matrix anisotropy in textured samples.