Modeling stress anisotropy, strength differential, and anisotropic hardening by coupling quadratic and stress-invariant-based yield functions under non-associated flow rule

An accurate description of yield surface is essential for the high-fidelity numerical analyses of sheet metal forming processes. In this work, a simple coupling of anisotropic quadratic and isotropic stress-invariant-based yield functions is proposed under the non-associated flow rule. The quadratic part is the asymmetric Hill48 function, which describes the anisotropic hardening with explicitly calibrated parameters from stress-strain curves. A new stress-invariant-based yield function, as a second component, is developed to capture the shapes of yield surface for diverse metallic materials with enhanced flexibility. Finally, a yield function is established by multiplying the anisotropic quadratic and the isotropic stress-invariant-based parts, which satisfies the convexity requirement in terms of stress state. The proposed asymmetric anisotropic yield function is validated with automotive sheet metals including dual-phase steels, aluminum alloys and magnesium alloys. Results show that the new yield criterion can accurately predict the anisotropy in stress, strength differential effect and yield surface evolution (or anisotropic hardening) of the investigated sheet metals.