Lode-dependent anisotropic-asymmetric yield function for isotropic and anisotropic hardening of pressure-insensitive materials. Part I: Quadratic function under non-associated flow rule

Abstract

It is challenging to precisely model the complicated plastic deformation of metals, including anisotropy in strength and plastic deformation, strength differential effect, anisotropic hardening, etc. A new approach is proposed to extend anisotropic yield functions into asymmetric ones by introducing a Lode dependent function. The approach is applied to the Hill48 function with a Lode-dependent function in a form of the normalized third stress invariant. The proposed Lode -dependent anisotropic-asymmetric (LAA) is applied to characterize the anisotropic hardening behaviors under both tension and compression of QP1180, DP980, AA2008 T4 and & alpha;-Ti to verify its performance. The convexity of yield surface evolution with plastic deformation is investigated by a geometry-inspired numerical convex analysis method. The application shows that the pro-posed LAA function precisely characterizes the anisotropy in tension and compression and its evolution with plastic deformation. It is therefore suggested to model the anisotropic-asymmetric plastic behavior with its applications to metal forming.