Directional Distortional Hardening in Plasticity within Thermodynamics

This paper presents a complete theory for metal plasticity that includes directional distortional hardening, supplemented by the classical kinematic and isotropic hardenings. Starting from an isotropic yield surface, the distortional hardening will be modeled either by fourth-order tensor-valued internal variable multiplied by a scalar, a scalar-valued internal variable in conjunction with the back stress, or a second-order tensor-valued internal variable. These models are unique because the rate equations for all internal variables, including the fourth order tensor, are derived strictly on the basis of sufficient conditions for the satisfaction of the second law of thermodynamics for positive dissipation, in conjunction with a few simple and plausible assumptions about free energy storage and release in the material. The models are shown to fit experimentally found yield surfaces rather well, in particular the model with the fourth-order tensor. Furthermore, this model is shown to simulate stress controlled biaxial ratchetting better than the same model without distortion of the yield surface.