Directional distortional hardening in metal plasticity within thermodynamics

This paper presents a complete theory for metal plasticity that includes isotropic, kinematic, and directional distortional hardening, within the framework of thermodynamics. Directional distortion is defined here as the formation of a region of high curvature on the yield surface, approximately in the direction of loading, and a region of flattening approximately in the opposite direction, as observed in experiments on various types of metals. The distinguishing features of this theory are the introduction of a fourth order tensor-valued internal variable, whose evolution in conjunction with a directional scalar multiplier describes the evolving directional distortion, and the fact that the hardening laws for all internal variables are derived on the basis of sufficient conditions to satisfy the thermodynamic requirement of positive dissipation. The applicability of the theory is illustrated by fitting experimental data on distorted yield surfaces in the course of plastic deformation.