Role of the Plastic Flow of the Matrix on Yielding and Void Evolution of Porous Solids

Abstract

In this paper, it is shown that yielding and void evolution in a porous metallic material is strongly influenced by the particularities of the plastic flow of the matrix. This is demonstrated by comparing the effective response of porous solids for which the matrix is described by Tresca and von Mises yield criterion, respectively. The effective response of the porous solid is calculated analytically using rigorous limit analysis theorems and upscaling techniques. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. For the first time it is demonstrated that if the matrix plastic response is governed by Tresca yield criterion, the overall response is softer, the combined effects of pressure and the third-invariant on yielding being much stronger than in a porous solid with von Mises matrix. Furthermore, the rate of void growth or collapse is much faster in a porous solid with Tresca matrix.