Inversion of a full-range stress–strain relation for stainless steel alloys

Abstract This paper presents an approximate inversion of the stress–strain relation for stainless steel alloys. Using currently available stress–strain relations based on a modified Ramberg–Osgood equation, a new expression for the stress σ as an explicit function of the total strain e is obtained. The new expression is valid over the full-range of the stress well beyond the 0.2 % proof stress σ 0.2 , defined as the stress level corresponding to the plastic strain value of 0.2 % . The validity of the inverted expression is tested over a wide range of material parameters. 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.