Computational investigation into the role of localisation on yield of a porous ductile solid

Abstract

In ductile materials containing micro-voids, diffuse plasticity or localisation of plastic strain in narrow bands bridging the ligaments between voids can both occur as precursors to failure. In particular, localisation of plastic strain leads to coalescence through the formation of void sheets or plastic collapse of the ligament. If yielding is defined as the point in macro stress space at which the macroscopic plastic dissipation becomes large, either diffuse plasticity or localisation can cause yielding. Appropriate combinations of triaxiality T and Lode parameter L can cause localisation to occur earlier, and thereby modify the yield surface significantly. This is more likely to happen at high values of porosity. The competition between the two modes of yielding has been captured by a recently proposed multi-surface yield framework (Keralavarma, S. M., 2017, “A multi-surface plasticity model for ductile fracture simulations,” Journal of the Mechanics and Physics of Solids, 103, pp. 100–120), where the competition between the Gurson criterion for yielding by diffuse plastic flow and a criterion for localized yielding within discrete coalescence bands leads to a piecewise smooth yield locus with sharp vertices. In the present work, we generate yield surfaces computationally by using a voided, cuboidal unit cell and a computational homogenisation framework that allows for both macro deformation gradient and macro Cauchy stress control. The basic aim is to see how the multi-surface framework of yield compares with macro yield loci generated computationally using a formulation where both finite deformations and void shape changes are allowed. We show, for spherical, prolate and oblate initial voids, that localisation inevitably hastens macro yield and adds sharp vertices to the yield locus, for a wide range of L and T. The multi-surface framework, at least for spherical initial voids, is remarkably successful in capturing this competition.