A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids

Abstract

This study deals with the modeling of anisotropic damage in ductile materials resulting from the growth of micro-voids up to coalescence. The emphasis is put on the change in size, shape and distribution of the voids under axisymmetric loadings. A numerical study based on unit cell calculations of a void in a creeping matrix at different stress triaxialities is presented and discussed. Based on the main trends observed in the numerical simulation, a model of anisotropic damage is then proposed. This model is developed in three steps. The case of isotropic voided power-law materials is discused first. This model is extended to the case of power-law materials containing axisymmetric prolate ellipsoidal cavities. Then the evolution in distribution of the voids is taken into account by a simple model in which the voided material is seen as a lamination of the unvoided matrix together with porous layers. The proposed model contains three damage parameters, the porosity, the void aspect-ratio and the distribution aspect-ratio. Its predictions are in good agreement with the FEM simulations.