Macroscopic response and microstructure evolution in viscoplastic polycrystals with pressurized pores

This paper presents a finite-strain homogenization model for the macroscopic behavior of porous polycrystals containing pressurized pores that are randomly distributed in a polycrystalline matrix. The porous polycrystal is modeled as a three-scale composite, where the pore size is taken to be much larger than the grain size, and the grains are described by single-crystal viscoplasticity. The instantaneous macroscopic response and corresponding field statistics in the material are determined using a generalization of the recently developed iterated second-order homogenization method, which employs the effective behavior of a linear comparison composite to estimate that of the nonlinear composite by means of a suitably designed variational approximation. Moreover, consistent evolution laws are derived for the pore pressure, pore geometry, and the underlying texture for the polycrystalline matrix. The model is then used to investigate porous ice polycrystals under a wide range of loading conditions. It is found that the pore pressure evolution has a strong effect on the material’s response under compressive loadings. More specifically, the macroscopic response of the porous polycrystals can be categorized into three different regimes: (i) a texture-controlled regime at low triaxialities, where the materials behave like solid polycrystals; (ii) a porosity-controlled regime at high triaxialities, where the materials behave like porous untextured materials; and (iii) a transition regime at intermediate triaxialities, where the materials exhibit a more complex behavior. This work highlights the importance of accounting for the interplay between porosity and matrix texture evolution in describing the constitutive response of porous polycrystals undergoing finite deformations.