A Gurson-type model accounting for void size effects

Abstract

In this paper we present an extension of the Gurson model of cavity growth which includes the void size effect. To this end, we perform the limit analysis of a hollow sphere made up of a Fleck and Hutchinson’s strain gradient plasticity material. Based on the trial velocity field of Gurson, we derive an approximate closed form expression of the macroscopic criterion. The latter incorporates the void size dependency through a non dimensional parameter defined as the ratio of the cavity radius and the intrinsic length of the plastic solid. The accuracy of this approximate criterion is demonstrated by its comparison with numerical data. In the last part of the paper we present a complete plasticity model involving the damage rate and a power-law strain hardening of the matrix. It is shown that the cavity size effect has a strong dependency on damage growth as well as on the stress strain response.