A Constitutive Stress–Strain Law for Metals with Sigmoidal Curves

Abstract

A formulation is proposed for true stress–true strain relationships in the plastic regime that exhibit sigmoidal shapes, such as those of certain metastable austenitic stainless steels (MASS). It contains two terms, broadly accounting for contributions to hardening from conventional plasticity and from mechanical stimulation of martensite formation. It is a continuous function, designed to cover the plastic strain range from zero up to several tens of percent. It is shown that it is suitable for capture of a range of curve shapes of this type—experimental data from tensile testing of a MASS alloy over a range of temperature, with good fidelity. The formulation incorporates six independent parameters, although there may be scope for limiting the range of values that they can have, facilitating convergence operations. Information is presented about how convergence is obtained. The equation is thus expected to be suitable for use in finite element method (FEM) models for simulation of plastic deformation in various scenarios, including indentation. Future work will involve exploration of the details of this.