On the plastic equation of state with one structure variable

Abstract

Summary. --The general expression for a plastic equation of state with one structure variable and with a scaling relationship is presented. It is demonstrated that this equation can be written, in general, in terms of stress, plastic strain rate and a function of plastic strain. Finally, the results are compared with previous formulations of the problem presented in the literature to show that they are particular cases of the general formalism presented.PACS 46.20 -Continuum mechanics.1. -Introduction.Hart [1] has developed the concept of the mechanical equation of state, based on the following arguments: ,(Of the three deformation variables z, ~ and ~, where z is the applied stress, s the plastic strain-rate and ~ the plastic strain, the two that are uniquely indicative of the mechanical state of the specimen are the first two, ~ and ~. If the imposed strain-rate ~ is stated, the corresponding stress z to produce ~ is a measure of the current state of the mechanical strength of the specimen. In fact, the mechanical state of the specimen at any instant is fully specified by the set of all possible pairs of values of ~ and ~ of which it is immediately capable. The situation is completely different with the plastic strain. Even when an arbitrary reference state is chosen, the plastic deformation depends on the actual deformation path rather than only on (*) The authors of this paper have agreed to not receive the proofs for correction.