Plastic anisotropy of sheet metals under plane strain loading: A novel non-associated constitutive model based on fourth-order polynomial functions

Constitutive modeling of sheet metals under plane strain state is important but challenging. Recent studies report that the yield strength and plastic strain rate of sheet metals in the plane strain mode exhibit strong anisotropy. To address the plane strain anisotropy, fourth-order polynomial functions (Poly4) of the stress tensor were applied to the yield stress and plastic potential functions under the non-associated flow rule (NAFR-Poly4). The yield stresses under near-plane strain (NPS) measured along three angles from the sheet rolling direction were used for an analytical determination of the parameters of the yield stress function and the commonly applied yield stresses under uniaxial tension (UT) and equi-biaxial tension (EBT). In addition, the plastic strain rates under UT, NPS, and EBT were used to determine the parameters of the polynomial plastic potential. Compared with experimental results under a wide range of loading conditions, the proposed NAFR-Poly4 model predicts the anisotropic NPS deformation of a dual-phase steel and an aluminum alloy with remarkably improved accuracy over the other existing models. The NPS yield stresses of the dual-phase steel are accurately predicted with a reduced average plastic flow deviation of 2.8° by NAFR-Poly4 compared to 7.1° by the Yld2k-2d model under AFR.