A general yield function with differential and anisotropic hardening for strength modelling under various stress states with non-associated flow rule

Sheet metal experiences various stress states during plastic deformation, including uniaxial compression, shear, uniaxial, plane strain and equibiaxial tension, but the existing yield functions cannot precisely model the differential strain hardening behaviour under different stress states. In this research, a stress invariant-based yield function is proposed to illustrate differential hardening by an analytical appraoch under distinct stress states (eg. from uniaxial compression to equibiaxial tension). The convex domain of the proposed function is computed by a simple geometry-inspired numerical convex analysis method. The parameters of the function are analytically computed by hardening behaviours under four different stress states from uniaxial compression to equibiaxial tension, such as uniaxial tension, equibiaxial tension, shear and plane strain tension. The proposed function is utilized to describe the plastic behaviour of AA7075 T6, a high strength steel QP1180, and a magnesium alloy AZ31 under the four different stress states from the onset of plastic deformation to fracture. Simulations with the proposed function are conducted to predict the load response of experiments in shear and notched tensile tests. The function is further extended into anisotropic hardening by interpolation method with the Barlat’91 linear transformation tensor. The result shows that the experimental responses are precisely predicted from the proposed yield function under various stress states in the entire range of plastic deformation. The application to BCC, FCC and HCP metals suggests that the proposed function is capable of precise modelling of differential hardening behaviours under four different stress states and strength differential effect and its evolution.