A symmetric and asymmetric yield function based on normalized stress invariant suitable for sheet and bulk metals under various stress states

Sheet and bulk metals experience stress states in a wide stress state range under most of the static and dynamic service environments, but the existing yield functions cannot reasonably and accurately describe the strength or different hardening behaviors under those stress state ranges. In this paper, to accurately characterize the strength in a wide stress state range, a yield function is proposed that considers the effects of hydrostatic pressure and the third invariant and symmetric and asymmetric behavior. Experiments are carried out to characterize the plastic behavior of Al 6061 and high-strength 30CrMnSiNi2MoVE steel (30VE) between plane strain compression and plane strain tensile, and the strain hardening law is obtained by the inverse engineering approach. The strength of FCC metal Al 6061 and Al 7075-T6, BCC metal 30 V and QP1180, and HCP metal AZ31 is characterized by the proposed isotropic yield function to validate its effectiveness and flexibility and compared with the Yoon (2014), Lou (2020), and Lou (2022), Tresca, and Mises yield functions. Flowering, the proposed function is extended to model the different hardening behaviors and applied to model the evolution of yield surfaces of Al6061 and QP1180 at different strain levels. Finally, the proposed yield function is extended into anisotropic form by three different fourth-order linear transformation tensors to the second and third invariants, respectively. And applied to characterize the anisotropic behavior of different types of metals. The effectiveness of the proposed yield function's anisotropic form is validated by the FCC metals Al 2090-T3 and Al 5754-O, BCC metal DP980, and HCP metal AZ31B, pure textured magnesium, and Mg-0.5 % Th alloy; and compared with Yld2000–2d, Lou (2013), and Yoon (2014) yield functions. The result shows that the proposed yield function in the isotropic form provides higher flexibility and universality to model the strength and the different hardening behaviors of BCC, FCC, and HCP metals. The flexibility of the proposed yield function's anisotropic form can accurately characterize the anisotropic behavior of BCC, FCC, and HCP metals. Accordingly, the proposed yield function is not only recommended to model the strength and the different hardening behavior of isotropic sheet and bulk metal but also anisotropic. Since the yield function is the key to accurately predicting the plastic deformation and fracture behavior of engineering structures, it is suggested to use the proposed yield function to simulate the plastic and fracture behavior of sheet and bulk metal structures in both static and dynamic analysis.