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

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 α-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 proposed 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.