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 stainless steel alloys applicable at normal and elevated temperatures. The relation utilizes an approximation of the closed form inversion of a highly accurate three-stage stress-strain relation recently obtained from the Ramberg-Osgood equation. The three stage inversion is formulated using an appropriate rational function assumption to approximate the fractional deviation of the actual stress-strain relation from an idealized linear elastic behaviour. The temperature dependence on the stress-strain relation is then introduced by modifying the basic mechanical properties of stainless steel to account for the temperature effects. The proposed approximate inversion is applicable over the full-range of the stress well beyond the elastic region up to the ultimate stress. Moreover, the inversion can be applied to both tensile and compressive stresses. The proposed approximate inversion is tested over a wide range of material parameters as well as a wide range of temperatures. It is shown that the new expression results in stress-strain curves which are both qualitatively and quantitatively in excellent agreement with experimental results and the fully iterated numerical solution of the full-range stress-strain relation for normal as well as elevated temperatures.