A new anisotropic-asymmetric yield criterion covering wider stress states in sheet metal forming

The stress state-dependent plastic anisotropy of sheet metals has drawn significant attention. Nevertheless, existing phenomenological plasticity models limitedly capture the distinctive yield strengths and plastic flow (r-values) under a wide range of stress states covering uniaxial tension (UT), equi-biaxial tension (EBT), uniaxial compression (UC), plane strain tension (PS), and pure shear (SH). This study aims to propose a new anisotropic-asymmetric plasticity model with enhanced flexibility based on the non-associated flow rule. The yield function is formulated based on the additive coupling of two stress potentials: coupling between a new anisotropic pressuresensitive fourth-order polynomial function, and an isotropic stress invariant-based function. Then, all the anisotropic/asymmetric parameters of the yield function can be analytically identified from 7 yield stresses measured from UT tests along 0 & DEG;, 45 & DEG;, and 90 & DEG; to the rolling direction (RD), UC tests along 0 & DEG; and 90 & DEG; to the RD, EBT test, and SH test along 45 & DEG; to the RD. Within the scheme of no-associated flow rule, a new asymmetric fourth-order plastic potential function is proposed to analytically describe the plastic flow of sheet metals under UT, UC, EBT and SH. The additively coupled stress invariant-based term is introduced to adjust the yield stresses and plastic flow under biaxial tension including PS, which leads to an independent description of the yield stresses and plastic strain directions under SH and PS states. Various automotive sheet metals such as advanced high-strength steels, aluminum alloy, and magnesium alloy with strong asymmetry and anisotropy are investigated to verify the proposed yield criterion. The results demonstrate remarkable flexibility and accuracy of the proposed yield criterion against other existing models. Evolving yield surface and plastic potential of a quenching and partitioning steel are accurately captured by the proposed anisotropic-asymmetric yield criterion. Besides, the advantages of new model are further discussed in terms of the proof of yield surface convexity, identified parameters, and the regulation between anisotropy and isotropy in comparison with existing multiplicative coupling method.