A flexible yield criterion for strength modeling from biaxial compression to biaxial tension

Accurate strength modeling from equi-biaxial tension (EBT) to equi-biaxial compression (EBC) is critical for the plastic behavior prediction covering the wide-range of stress triaxiality encountered in sheet metal forming. To date, however, few yield criteria are available that can precisely model the initial yield and hardening behavior under six typical stress states between EBC and EBT, simultaneously. Furthermore, there is still a lack of a unified yield criterion for accurate strength modeling across various stress state ranges. To address the issues, a theoretical framework for constructing yield criteria dependent on stress states is provided and a new analytically described isotropic yield criterion is presented in this study. The flexibility in terms of the yield locus and application range is thoroughly explored to make the new yield criterion general. Subsequently, the isotropic yield criterion is extended into an analytically described anisotropic-asymmetric yield criterion. Furthermore, the extended yield criterion is applied to capture the initial yield behavior of DP980, AA5754-O, and AZ31 sheets, and the strain hardening behavior of QP1180 sheets at various stress states ranging from EBC to EBT along different loading directions. The predicted results from the extended criterion agree well with the corresponding experimental findings. The applications demonstrate that the proposed anisotropic-asymmetric yield criterion can effectively model the initial yield and hardening behavior of HCP, BCC, and FCC metal sheets under EBT, EBC, uniaxial tension (UT), plane strain tension (PST), shear (SH), and uniaxial compression (UC) in an analytical way.