General Stress-Strain Equation

Abstract

This paper presents a general stress-strain equation that expresses stress explicitly in terms of strain in a single continuous curve. It allows various features such as linear-elastic range, upper yield peak, plastic plateau, and smooth strain-hardening portion to be included. Any of these features can be excluded if desired. The shape of the curve described by the equation is identical, with positive and negative strains. The equation may be fitted to experimental data to represent the stress-strain behavior of a material and is therefore useful for describing experimental results in a succinct format. Comparison with experimental results shows that the equation can closely fit the stress-strain curves of steel at various temperatures—at temperatures where distinct yield peaks and plastic plateaus exit; as well as at temperatures where the stress-strain curves are smooth. Therefore the equation can be suitably extended to accurately model the temperature-dependent behavior of steel.