A Three-Stage Explicit Stress-Strain Relations for Stainless Steel Alloys Applicable in Tension and Compression at Elevated Temperatures

Presented in this paper is an explicit full-range stress-strain relation for stainlesssteel alloys applicable at normal and elevated temperatures. The relation utilizes an approxima-tion of the closed form inversion of a highly accurate three-stage stress-strain relation recentlyobtained from the Ramberg-Osgood equation. The three stage inversion is formulated using anappropriate rational function assumption to approximate the fractional deviation of the actualstress-strain relation from an idealized linear elastic behaviour. The temperature dependenceon the stress-strain relation is then introduced by modifying the basic mechanical propertiesof stainless steel to account for the temperature e ects. The proposed approximate inversionis applicable over the full-range of the stress well beyond the elastic region up to the ultimatestress. Moreover, the inversion can be applied to both tensile and compressive stresses. Theproposed approximate inversion is tested over a wide range of material parameters as well as awide range of temperatures. It is shown that the new expression results in stress-strain curveswhich are both qualitatively and quantitatively in excellent agreement with experimental re-sults and the fully iterated numerical solution of the full-range stress-strain relation for normalas well as elevated temperatures