Customizable Hill48 yield criterion framework for stress-state-dependent plastic anisotropy

The stress-state-dependent plastic anisotropy of sheet metals has recently attracted significant attention in metal plasticity community. However, existing phenomenological plasticity models still exhibit limitations or gaps in characterizing the stress state dependence of anisotropic yield strength and plastic flow, particularly under a wide range of loading conditions involving seven typical stress states spanning from equi-biaxial compression (EBC) to equi-biaxial tension (EBT). To address this issue, in this study, we proposed a modified Hill48 yield criterion framework with significantly enhanced flexibility by coupling the classic Hill48 yield function with stress adjustment factors (SAFs), referred to as M-Hill48-SAF. A continuous interpolation method based on a sixth-order polynomial were proposed to define the anisotropic SAF as a function of stress triaxiality, which can analytically describe the yield strength ranging from EBC to EBT. Using artificial materials, the adaptability and enhanced flexibility of the proposed model in capturing stress state dependence was systematically validated across seven distinct stress states. The predicted yield locus offers a unique advantage: it can be independently adjusted and customized at a specific stress state without influencing the others. Moreover, the model accurately captures yield evolution behavior under arbitrary loading directions across all seven stress states. The proposed model was further applied to several representative sheet metals, including high-strength steels (DP980 and QP1180), aluminum alloy (AA5754-O), magnesium alloy (AZ31), and titanium alloy (Ti-6Al-4V). Comparative analysis with several recently developed yield criteria confirms that the proposed model markedly enhances the prediction accuracy of strength characteristics across a broad range of stress states. Finally, the flexibility and customizability of the proposed model were discussed in relation to the availability of stress-state and loading-direction data, and their effects on the yield surface shape.