Modelling in materials behavior of strength differential effect and yield locus evolution with non-associated flow rule

During numerical simulation of sheet metal forming, the accurate models to describe material yielding and hardening behavior by considering the anisotropy, non-uniform evolution of the yield surface and strength differential effect are vital to predict complicated deformation and forming defects such as fracture and springback. In the present work, a novel yield model with non-associated flow rule is proposed based on the frame of S-Y2009 criterion and coupled with normal stress components and the second deviatoric stress invariants, where the former is used to describe the anisotropy and non-uniform evolution of yield loci, and the later enables the description of SD effect. Different from some other models which identify the parameters via optimization algorithms, the proposed model adopts an analytical identification method from the stress-strain curve in various loading conditions, including uniaxial tension and compression along 0°, 45°, 90° to the rolling direction, and equi-biaxial tension and compression. The flexibility of the proposed model is validated for high strength steels, aluminum alloys and titanium alloys.