Dilational Response of Voided Polycrystals

Finite-element (FE) cell model computations have been used to gain insights into the ductile response of porous polycrystals. Generally, the behavior of the matrix is described by a J ₂-plasticity model. In this article, we present a new computational approach to FE cell models for porous polycrystals deforming by slip based on crystal plasticity. The cell provides the homogenized dilational response, where the constitutive response of every integration point is based on a single-crystal visco-plasticity law. The calculations are performed for a body-centered cubic polycrystal with random texture. Axisymmetric tensile and compressive loadings are imposed corresponding to the fixed values of the stress triaxiality and to two possible values of the Lode parameter. The resulting numerical yield points are compared with those obtained using a J ₂-FE cell and an analytical model. The predictions confirm the combined effects of the mean stress and third-invariant on yielding recently revealed by the analytical model.