A constitutive model with three plastic constants: The description of anisotropic workhardening

Constitutive relations are suggested with three plasticity constants for numerical modeling of anisotropic workhardening characterized by translation, reshaping and turning of the subsequent yield surface. The yield surface is assumed in the shape of an ellipsoid of revolution in a vector space of stress deviators, its axes of revolution coinciding with the plastic deformation vector. The yield condition is expressed through the parameters of dimensions, location, and orientation of the hyperellipsoid, and is a natural development of the equation for a spherical yield surface considered by the conventional theory of combined isotropic-kinematic hardening. Methodology is also suggested for determining plastic constants though proportional loading experiment. Properties of the constitutive model are analyzed for proportional loading, and a table is constructed illustrating qualitatively different types of evolution of the subsequent yield surface with respective numerical values of plastic constants determining them. The effectiveness of the constitutive model suggested is confirmed by the examples of numerical modeling with experimental results available in the literature.