On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals

Abstract

The paper is concerned with the structure of multiaxial stress-strain relations in time-dependent metal plasticity, as for transient creep and rate sensitive yielding. First, a general kinematical relation is developed between the macroscopic inelastic strain tensor and microstructural slip displacements, as modeled either by continuum shearing on crystallographic planes of individual grains or by the motion of discrete dislocation lines. It is assumed that at any given slipped state, the rate of slipping on a particular system is governed by the resolved shear stress on that system (or by the local “forces” on dislocation lines). This leads to the primary result of the paper: Components of the macroscopic inelastic strain rate tensor are derivable, at each instant in the course of deformation, from a potential function of stress. General features of the flow potential surfaces in stress space are discussed, and some specific functional forms are examined. Linear viscoelasticity and time-independent plasticity are developed as limiting cases of the flow potential formulation, and the appropriateness of a potential function for stationary creep is discussed.