Influence of continuous nucleation of secondary voids upon growth and coalescence of cavities in porous ductile metals

We study the influence of the nucleation of secondary small voids upon growth and coalescence of primary large cavities in porous ductile metals. To do so, we consider a simple model, the loading of a hollow sphere subjected to hydrostatic loading whereby the sphere simulates a big, primary void, the presence of secondary voids in the surrounding matrix being accounted for by the Gurson-Tvergaard-Needleman homogenized model for plastic porous materials. Continuous nucleation of small voids in the matrix is described by a simple phenomenological formula proposed by Pineau and Joly for the evolution of porosity due to nucleation. The problem is solved analytically at initial time and numerically at later times, when a nonuniform distribution of secondary voids develops in the matrix. These elements are used to define a simplified model with only a small number internal parameters, describing growth of primary voids coupled with nucleation, growth and coalescence of secondary ones. This study opens the way to the analysis of coalescence of primary voids assisted by secondary ones.