Analytical modeling of anisotropic-strength differential hardening with low strength under plane strain tension for WE43 alloy

Accurately characterizing the evolution characteristic of hardening behavior is helpful for the design of metal forming processes. To depict the direction- and stress state-related evolving characteristic, the study proposes an anisotropic-strength differential (SD) hardening model with the form of the first stress invariant, third deviatoric stress invariant, and non-quadratic Hershy-Hosford function. The material parameters can be analytically determined by four hardening curves under the typical stress states. Through adopting a geometry-inspired numerical convex analysis approach, the limits of the convexity-related parameters are efficiently computed to present the determined convexity domain. The established SD hardening model is employed to explain the deformation history-related hardening behavior of WE43 alloy under various stress states. These predicted results have a high consistency with the actual yield stresses. The proposed yield function shows a higher superiority than the existing model in the aspect of characterizing the low strength under plane strain tension (PST). The SD hardening model is extended to the anisotropic form under non-associated flow rule, where the Hill48 yield function is utilized as the plastic potential function. The predicted results indicate that the established model can accurately capture the anisotropic and SD effects of WE43 alloy. This implies the tremendous potential to model the anisotropic-SD hardening performance with low strength under PST for other materials.