Importance of the coupling between the sign of the mean stress and the third invariant on the rate of void growth and collapse in porous solids with a von Mises matrix

Abstract

Recently, Cazacu et al (2013a J. Appl. Mech. 80 64501) demonstrated that the plastic potential of porous solids with a von Mises matrix containing randomly distributed spherical cavities should involve a very specific coupling between the mean stress and , the third invariant of the stress deviator. In this paper, the effects of this coupling on void evolution are investigated. It is shown that the new analytical model predicts that for axisymmetric stress states, void growth is faster for loading histories corresponding to than for those corresponding to . However, void collapse occurs faster for loadings where than for those characterized by . Finite-element (FE) results also confirm these trends. Furthermore, comparisons between FE results and corresponding predictions of yielding and void evolution show the improvements provided by the new model with respect to Gurson's. Irrespective of the loading history, the predicted rate of void growth is much faster than that according to Gurson's criterion.