Abstract

A macroscopic yield criterion for porous solids with pressure-sensitive matrices modeled by Coulomb’s yield criterion was obtained by generalizing Gurson’s yield criterion with consideration of the hydrostatic yield stresses for a spherical thick-walled shell and by fitting the finite element results of a voided cube. The macroscopic yield criterion is valid for negative mean normal stresses as well as for positive mean normal stresses. From the yield criterion, a plastic potential function for the porous solids was derived either for plastic normality flow or for plastic non-normality flow of pressure-sensitive matrices. In addition, elastic relations, an evolution rule for the plastic behavior of the matrices, a consistency equation and a void volume evolution equation were presented to complete a set of constitutive relations. The set of constitutive relations was implemented into a finite element code ABAQUS to analyze the material behavior of rubber-toughened epoxies. The cavitation and the deformation behavior were analyzed around a crack tip under three-point bending and around notch tips under four-point bending. In the numerical analyses, the cavitation of rubber particles was considered via a stress-controlled void nucleation model. The numerical results indicate that a reasonable cavitation zone can be obtained with void nucleation being controlled by the macroscopic mean normal stress, and a plastic zone is smaller around a notch tip under compression than under tension. These numerical results agree well with corresponding experimental results on the cavitation and plastic zones.

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