Modeling ductile fracture in metals involving two populations of voids – influence of continuous nucleation of secondary voids upon growth and coalescence of primary voids

Abstract

This paper is devoted to the study of the influence of the nucleation of small, secondary voids upon the growth and coalescence of large, primary cavities in porous ductile metals. For this purpose, a simple model is considered: a hollow sphere subjected to hydrostatic loading whereby the central hole simulates a large, primary void, and the presence of secondary voids in the surrounding matrix is accounted for by the Gurson–Tvergaard–Needleman homogenized model for plastic porous materials. Continuous nucleation of small voids in the matrix is described by the straightforward phenomenological formula proposed by Pineau and Joly. Initially, the problem is solved analytically, then numerically when a non-uniform distribution of secondary voids develops in the matrix. These elements are used to define a simplified model in which only a small number of internal parameters describe the growth of primary voids coupled with the nucleation, growth and coalescence of secondary voids. Comparisons between the results derived from this simplified model and those obtained through the numerical computations are used to demonstrate the accuracy of the proposed model.