Anisotropic behaviour of porous, ductile media

Abstract

An orthotropic constitutive model for porous, ductile media is developed, which is centred on the micromechanical analysis of a cylindrical representative volume element (RVE) with elliptic cross-section containing a coaxial and confocal elliptic-cylindrical cavity. The constitutive model is obtained in the case of a rigid ideally plastic behaviour of the matrix material, whose yield condition obeys J 2 flow theory of plasticity with an associated flow rule. The following condition is assumed throughout: the longitudinal axis of the hollow cylindrical RVE is a principal direction of the macroscopic strain rate and stress tensors. Cases for which the principal directions of the macroscopic strain rate tensor in the RVE cross-section plane are aligned or rotated with respect to the ellipse axes are both considered. The constitutive behaviour is characterized by the homogenized yield domain in the macroscopic stress tensor space, by associated flow rules for the plastic components of the macroscopic strain rate tensor and by the evolution laws for the internal state variables. These are the void volume fraction, already appearing in Gurson's model, the aspect ratio of the cavity and its orientation in the RVE cross-section plane, assuming that during the deformation process, the void retains an elliptic shape. The theoretical results are compared with finite element computations of the RVE strength at plastic collapse to assess the capability of the model to describe the actual micromechanical response to the applied boundary conditions.