Stress Strain Curves

Abstract

Traditionally, stress strain curves for example from tensile testing are described with empirical models with a number of adjustable parameters such as Hollomon, Ludwik, Voce and Swift. With such models it is difficult or impossible to generalize and extrapolate. A model in the form of Voce equation is derived from the same basic dislocation model used for the creep models with the values of constants computed. The derived model is used to describe stress strain curves for Cu including their temperature and strain rate dependence. The dynamic recovery constant ω plays a central to show how the work hardening deviates from a linear behaviour. The temperature dependence of ω is analyzed and shown to be related to that of the shear modulus. In the literature it is frequently assumed that dynamic recovery is controlled by cross-slip. However, the measured activation energy for dynamic recovery is many times smaller than the energy required to make partial dislocations brought together and form a constriction, which is necessary to enable cross-slip, so this is an unlikely possibility.