An internal variable constitutive model for hot working of metals

Abstract

A set of internal variable type constitutive equations which model large elastic-viscoplastic deformations of metals at high temperatures is formulated. For a first-order representation of large deformation constitutive behavior we use a scalar as an internal variable to represent the isotropic resistance to plastic flow offered by the internal state of the material. Hot compression tests on an iron-2% silicon alloy and a commercially pure aluminum have been conducted. Based on these experiments, specific viscoplastic constitutive functions are proposed, and the values for the materials parameters appearing in these functions are determined. The constitutive equations with these functions and material parameters accurately reproduce the basic tests and also accurately predict the response of the metal to some critical experiments which were not used to determine the material parameters in the constitutive functions. Although the use of a single scalr internal variable limits the constitutive equations to describing the deformation behavior of initially isotropic metals up to deformation levels where significant internal damage and polycrystal texturing has not developed, the constitutive equations presented here should be useful for obtaining an improved analysis of various hot deformation processing operations of metals.