Lode-dependent Yld91 function for anisotropic-asymmetric hardening modeling of metals under non-associated flow rule

The accurate characterizations of anisotropic hardening and tension-compression asymmetry are vital for sheet metal forming simulation. An anisotropic-asymmetric function is newly proposed by additive coupling of two Yld91 anisotropic functions via a Lode-dependent weight function (LAA-Yld91). The parameter evolution of LAA-Yld91 with respect to plastic compliance factor is described by the back propagation neural network optimized by ant colony optimization algorithm. Both the evolutionary exponent and weight function in the newly proposed function are applied to regulate the yield surface curvature. The accuracy and flexibility of the LAA-Yld91 function are evaluated by its application to Ti-6Al-4V, DP980 and AA 5754-O to characterize anisotropic -asymmetric hardening. The applications for the three metals illustrate that the LAA-Yld91 function can precisely characterize the evolution of anisotropic-asymmetric hardening behavior at plane strain tension, uniaxial tension and uniaxial compression along rolling direction, diagonal direction and transverse direction as well as equibiaxial tension and compression. It is therefore recommended to depict the anisotropy and strength differential effect and their evolution with plastic deformation for metal forming.