A Theory of Non-Linear Anisotropic Hardening

A yield function is derived which accounts for translation, contraction and rotation of the yield surface in the progress of plastic deformation for non-linear work-hardening materials. The present theory removes the restrictive condition of a rigid translation implicit in linear work-hardening by the kinematic hardening rule. The function proposed is shown to be in good agreement with experimentally determined yield loci for 2 1/4 per cent Cr, 1 per cent Mo alloy steel at room temperature in a principal biaxial stress subspace and those for aluminium 1100 at room and elevated temperatures in a combined tension-torsion stress subspace. Parameters pertaining to translation are determined, in confirmation of the theory, from reversed yielding torsion tests on tubes of En 3B steel.