An improved Gurson-type model for hardenable ductile metals

Abstract

The aim of this paper is to improve the modelling of strain hardening within the framework of the famous Gurson model for porous ductile metals. Indeed, although the original derivation of this model, for an ideal-plastic matrix, was based on a micromechanical analysis of some representative volume element, namely a hollow rigid-plastic sphere loaded axisymmetrically, the extension to the case of a hardenable matrix was of purely phenomenological and macroscopic nature, and this entailed a number of drawbacks. The phenomenological model was incompatible with the classical, exact solution to the problem of a hollow rigid-hardenable sphere loaded hydrostatically; also, the prediction that for any loading path corresponding to a fixed triaxiality, the curve representing porosity as a function of equivalent strain depended only on the initial porosity and the triaxiality but not on the hardening exponent, was incorrect. A new model solving these difficulties, based on an approximate analysis of a hollow rigid-hardenable sphere subjected to some axisymmetric loading, is proposed. Two types of hardening are considered: isotropic, as in Gurson's original model, and kinematic, as in Mear and Hutchinson's variant of Gurson's model. Comparisons with some finite element simulations evidence the improvements brought.