Accelerated void growth in porous ductile solids containing two populations of cavities

This paper presents an analytical and numerical study of accelerated void growth in porous ductile solids arising from the presence of two populations of cavities very different in size. It is based on the model problem of some hollow sphere made of porous plastic material and subjected to hydrostatic tension. The central hole plays the role of a typical big cavity of the first population while those dispersed in the matrix stand for the small cavities of the second one. The behavior of the matrix is supposed to obey Gursonʹs famous “homogenized” model for porous ductile solids (Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I — yield criteria and flow rules for porous ductile media. ASME J Engng Materials Technol 99, 2–15). The analytic solution of this model problem shows that the small voids located near the big one grow twice as fast as the latter void. This suggests that in a subsequent step, these small cavities may reach coalescence prior to the big ones, thus creating spherical shells of ruined matter around the cavities of the first population and leading to accelerated growth of the latter cavities; this scenario is in agreement with experimental evidence. Since this subsequent step is not amenable to a complete analytic solution, it is studied numerically. Finally, a simplified model reproducing the two steps of void growth (prior to coalescence of the small voids and after it has started) is developed on the basis of the analytical solution for the first step and some elements of a similar solution for the second one. The results derived from this simplified model are in good quantitative agreement with those obtained through the complete numerical simulations.