Inversion of three-stage stress-strain relation for stainless steel in tension and compression

Presented in this paper is a new stress-strain relation for stainless steel alloys that provides the stress as an explicit function of the strain. The relation is an approximate inversion of a recently proposed three-stage stress-strain relation based on a modified Ramberg-Osgood equation. The three-stage relation is a much more accurate formulation than the previous two-stage formulations and is applicable to both tensile as well as compressive stresses. The new relation is derived by making a rational function assumption on the fractional deviation of the actual stress-strain curve from an idealized linear elastic behaviour. The new expression is valid over the full range of the stress well beyond the elastic region. The validity of the inverted expression is tested over a wide range of material parameters. These tests demonstrate that, the new expression results in stress-strain curves which are both qualitatively and quantitatively in excellent agreement with the fully iterated numerical solution of the full-range stress-strain relation with a maximum error below 4%.