ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

This paper presents a new stress-strain relation for stainless steel alloys that provides the stress as an explicit function of strain and temperature. 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 an appropriate modification to account for temperature dependence. This new expression for the stress as an explicit function of the total strain, and temperature 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 temperature-dependent expression is tested over a wide range of material parameters and a wide range of temperatures. The tests show that the new expression is both qualitatively and quantitatively consistent with the fully iterated numerical solution of the full-range temperature-dependent stress-strain relation at moderate and high temperatures.