A constitutive model for isotropic, porous, elastic-viscoplastic metals

Abstract

A complete rate and temperature dependent constitutive model for the high temperature deformation of isotropic, moderately porous metallic materials is formulated. The essential new feature of the constitutive model is a new potential function for the viscoplastic stretching. This viscoplastic potential contains one undetermined scalar valued function of the material strain rate sensitivity and the volume fraction of voids. The form of this function is determined by fitting certain predictions from the model to results obtained from full finite element periodic unit cell calculations of initially spherical holes in a viscoplastic medium. Finite element calculations are carried out for two sets of material constants, one representing the highly rate dependent behaviour of a real material (Fe-2%Si) under hot-working conditions, and the other representing the rate independent limit of a perfectly plastic material. The fit of the new potential to the finite element calculations for a large range of void volume fractions and stress triaxialties is shown to be very good. It is also shown that the predictions from the potential proposed in this paper are in better agreement with the numerical unit cell calculations than the predictions from other existing models in the literature. The constitutive model presented here should find use in modeling hot workability of metals, and also in modeling the late stages of densification of metallic powders by hot isostatic pressing.