Further Developments in Anisotropic Plasticity

Abstract

A simple extension of Hill’s formulation for anisotropic plasticity which accounts for the distortion of the yield surface, Mij, the strength differential between tension and compression, αi and the effective size of the loading surface, k, has been proposed. These material parameters, Mij, αi, and k, define the initial state of the material and vary with plastic deformation. The parameters describing the anisotropic state are determined from uniaxial tension and compression tests along the principal axes. It is shown that the yield stresses in tension and compression along the three principal axes are related by a constraint equation when the condition of incompressibility is imposed. Experimental data obtained from several anisotropic materials are reasonably consistent with the constraint equation. The anisotropic plasticity formulation is also shown to describe the yield surface of different HCP metals more closely than the Hill’s theory. Based on the proposed formulation, finite element calculations have been made for the notched and the three-point bend specimens. The calculated load-deflection relationships are in good agreement with the experimental results.