A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations

Abstract

A two surface stress space model is introduced with internal state variable repositories for fading memory of maximum plastic strain range and non-proportionality of loading. Evolution equations for isotropic hardening variables are prescribed as a function of these internal variables and accumulated plastic strain, and reflect dislocation interactions that occur in real materials. The hardening modulus is made a function of prior plastic deformation and the distance of the current stress point from the limit surface. The kinematic hardening rules of Mroz and Prager are used for the yield and limit surfaces, respectively. The structure of the model is capable of representing essential aspects of complex nonproportional deformation behavior, including direction of the plastic strain rate vector, memory of plastic strain range, cross-hardening effects, variation of hardening modulus, cyclic hardening or softening, cyclic racheting, and mean stress relaxation.