On the macroscopic strength criterion of ductile nanoporous materials

Abstract

This work investigates the void surface effects on the macroscopic yield criterion of ductile materials embedded with nanosized spherical cavities. The solid matrix is treated as an isotropic, von Mises, incompressible and rigid-perfectly plastic material. Based on the trial velocity field proposed by Gurson and the first-order Taylor approximations of the equivalent volume strain rate, surface strain rate and curvature change rate, a limit analysis is conducted for the spherical representative volume element under the application of an arbitrary macroscopic strain rate loading. The void surface effects enter into the mechanics and physics of the yield criterion through a plastic surface model of the Steigmann–Ogden type. In addition to the plastic dissipation in the solid matrix that is conventionally included in the classical solution, those due to residual surface stress, surface tensile strength and surface bending strength are also taken into account in order to address the void surface effects. A closed-form plastic dissipation is provided, based on which analytical parametric equations are developed for the macroscopic mean and equivalent stresses. The governing parameters of void surface plasticity are three dimensionless ratios among surface material properties, void radius and the bulk yield strength. The inclusion of residual surface stress leads to a simple translation of the classical yield surface along the mean stress axis. For the surface tensile strength, the yield surface experiences a bidirectional expansion. In contrast, the surface bending strength tends to expand the yield surface only along the equivalent stress axis.