Explicit full-range stress–strain relations for stainless steel at high temperatures

This paper presents a new explicit stress–strain relation for stainless steel at high temperatures. The relation is an approximation of the closed form inversion of an existing two-stage stress–strain relation based on a modified Ramberg–Osgood equation with corresponding temperature-dependent parameters. This new expression for the stress σσ, as an explicit function of the total strain ϵϵ, is obtained by making a modified power law assumption on the fractional deviation of the actual stress–strain curve from an idealized linear elastic behaviour. The validity of the inverted expression is tested over a wide range of material parameters and a wide range of temperatures. The tests show that the new expression results in stress–strain curves which are both qualitatively and quantitatively consistent with the fully iterated numerical solution of the full-range stress–strain relation for normal as well as high temperatures.