Laws for Work-Hardening and Low-Temperature Creep

TLDR

The true stress–strain curves of polycrystalline aluminum, copper, and stainless steel can be represented by an exponential approach to a saturation stress over a wide range. The study extends Voce’s empirical work‑hardening law to include temperature and strain‑rate dependence and grounds it in dislocation storage and dynamic recovery. The authors derive a differential equation for transient creep from the extended work‑hardening law, linking it to dislocation storage and dynamic recovery. The formalism applies to steady‑state creep across the same temperature and strain‑rate range, predicts a strongly temperature‑dependent creep‑rate exponent and weakly stress‑dependent activation energy, matches available data near half the melting temperature, and suggests no new mechanisms are needed at higher temperatures.

Abstract

The true stress-strain curves of polycrystalline aluminum, copper, and stainless steel are shown to be adequately represented by an exponential approach to a saturation stress over a significant range. This empirical law, which was first proposed by Voce, is expanded to describe the temperature and strain-rate dependence, and is put on a physical foundation in the framework of dislocation storage and dynamic recovery rates. The formalism can be applied to the steady-state limit of creep in the same range of temperatures and strain rates; the stress exponent of the creep rate must, as a consequence, be strongly temperature dependent, the activation energy weakly stress dependent. Near half the melting temperature, where available work-hardening data and available creep data overlap, they match. Extrapolation of the proposed law to higher temperatures suggests that no new mechanisms may be necessary to describe high-temperature creep. A new differential equation for transient creep also follows from the empirical work-hardening law.