Void nucleation models and their implications for the material behavior of rubber-modified epoxies

초록

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 hydrostatic stresses as well as for positive hydrostatic 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 derived 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-modified epoxies. The cavitation and; the deformation behavior were analyzed around a crack tip under Mode I plane strain conditions. In the analyses, the cavitation of rubber particles was considered via three different void nucleation models. The numerical results indicate that a circular cavitation zone can be obtained with void nucleation controlled by the macroscopic hydrostatic stress. The results also imply that the mean value and the standard deviation for the macroscopic hydrostatic stress-controlled void nucleation model can be determined by comparing the sizes of a plastic zone and a cavitation zone with those observed in experiments.

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