Inelastic Constitutive Equation on the Basis of Distribution Function of Yield Stress : (Basic Equation and Parameter for Work Hardening and Softening)

Abstract

In this paper, we propose the distribution function of the yield stress to characterize the inelastic behavior of metals. This inelastic model consists of infinitely small cells which have perfectly elastoplastic properties. The distribution function of the yield stress means the content of infinitely small cells. The integral constituitve equation for this model is derived under the combined stress state. To give the effect of the work hardening and softening to the model, we propose the scalar parameter which is the integrated value of inner products of incremental plastic strain vectors along the plastic strain path. This parameter is elaborated by the experimental data of the tensile stress-strain curve and the uniaxial cyclic curves for SUS 304 stainless steel. Biaxial stress-strain relations are calculated with the constitutive equation, including this parameter. It is shown that the work hardening and softening phenomena can be simulated with this constitutive equation and this parameter.