Validation of recent analytical dilatational models for porous polycrystals using crystal plasticity finite element models with Schmid and non-Schmid activation laws

Abstract

Recent analytic criteria for isotropic porous materials developed by Cazacu et al. (2013) revealed the importance of considering specificities of plastic behavior in the matrix. On one hand it was shown that if the matrix material is governed by the von Mises criterion, the yield surface of the porous material should be centrosymmetric and, with the exception of hydrostatic and purely deviatoric loadings, there are combined effects of the mean stress and third-invariant of the stress deviator on void growth or collapse; but on the other hand if the matrix plastic deformation displays strength differential (SD) effects, the response is also sensitive to third-invariant and there is a lack of symmetry of the yield surface of the porous material. In this paper, we use a unit cell modeling approach in conjunction with a crystal plasticity finite element model to verify these theoretical predictions. It is assumed that each porous polycrystal contains a regular array of initially spherical voids and a random initial texture. At the grain-level, we consider that plastic deformation is governed by Schmid law and a recent non-Schmid formulation by Savage et al. (2017a) that intrinsically accounts for tension–compression asymmetry in a physical sense. Unit cell FE calculations are performed for axisymmetric tensile and compressive loadings corresponding to a fixed value of the stress triaxiality and the two possible values of the Lode parameter. The resulting numerical points representing the homogenized yield surfaces and void growth/collapse curves are found to be in agreement with the analytical model's predictions.