A macroscopic constitutive law for porous solids with pressure-sensitive matrices and its implications for plastic flow localization and crack tip behavior.

Abstract

A macroscopic yield criterion for porous solids with pressure-sensitive matrices modelled by Coulomb's yield criterion is obtained by generalizing Gurson's yield criterion with consideration of the hydrostatic yield stress of a spherical thick-walled shell and fitting the finite element results of a voided cube. The macroscopic yield criterion for the special case of pressure-insensitive matrices becomes a new accurate variant of Gurson's yield criterion, especially at large void volume fractions. Based on the macroscopic yield criterion, a plastic potential function for porous solids is derived for either plastic normality or non-normality flow of pressure-sensitive matrices. In addition, the elastic relation, the hardening rule, the consistency equation and the void volume evolution equation are presented to complete a set of constitutive relations for porous solids with rate-dependent pressure-sensitive matrices. An evolution equation for the flow stress is proposed to model the intrinsic strain softening and subsequent hardening of the matrices, and a simple power law is used to model the strain-rate sensitivity of the matrices. Furthermore, another set of constitutive relations for porous solids with rate-dependent kinematic-hardening matrices is formulated by modifying a continuum model based on Gurson's yield criterion. By employing the two sets of constitutive relations, plastic flow localization is analyzed under plane strain tension, axisymmetric tension and plane stress biaxial loading. The results show complex interactions of void volume inhomogeneity, pressure-sensitive yielding, plastic normality or non-normality, intrinsic strain softening, plastic potential surface curvature and different loading conditions. Moreover, the first set of constitutive relations is used to simulate the material behavior near a blunted crack tip in rubber-toughened epoxies by finite strain finite element methods. This investigation is the first computational study for the crack-tip fields of rubber-toughened epoxies. The finite element results show significant effects of the volume fraction of rubber particles, the pressure-sensitive yielding of epoxies and the intrinsic strain softening of epoxies on the stress and strain fields as well as the void volume distributions near the crack tip.