A three-stage full-range stress–strain inversion for stainless steel alloys as an explicit function of temperature

Abstract

Presented in this paper is a new explicit full-range stress–strain inversion for stainless steel alloys which expresses the stress as an explicit function of strain and temperature. The relation utilizes an approximation of the closed form inversion of a highly accurate three-stage stress–strain relation recently obtained from a modified version of the Ramberg–Osgood equation. The inversion which is obtained by making a generalized rational function assumption on the fractional deviation of the actual stress–strain curve from an idealized linear elastic behavior is applicable both to tensile and compressive stresses. The temperature dependence is then accounted for by using modified mechanical properties which are functions of temperature. The paper also presents a new direct temperature dependent stress–strain relation based on material properties at normal temperature. While previous studies use temperature dependent material properties to account for the effect of temperature on the stress–strain relation, this paper proposes explicit formulation based on the material properties at normal temperatures. The explicit temperature dependence is introduced by modifying the form of the stress–strain relation which includes a factor with an appropriate temperature dependent function. The validity of the temperature-dependent expression is tested over a wide range of material parameters and a wide range of temperatures. It is demonstrated that the proposed expression is both qualitatively and quantitatively in excellent agreement with the fully iterated numerical solution of the full-range temperature-dependent stress–strain relation at moderate and high temperatures.