Material Model based on Non-associated Flow Rule with Higher-order Yield Function for Anisotropic Metals

Abstract

A new expression for the plastic constitutive model for materials with initial anisotropy is proposed. A plastic strain rate tensor should be permitted to follow, to a certain extent, the rotation of the stress rate tensor, which rotates instantly from the direction of the current stress tensor as in the case of plastic instability. For this purpose, a non-associated normality model, in which the plastic potential function is defined independently of the yield function, has been adopted in the proposed model. An explicit expression for the equivalent plastic strain rate, which is plastic-work-conjugated with the defined equivalent stress corresponding to the proposed yield function, is also presented. This is important for expressing a generalized work-hardening rule for materials with plastic flow stress anisotropy. The proposed theory is expected to overcome the serious problems in the associated plastic flow theory.