A non-quadratic constitutive model under non-associated flow rule of sheet metals with anisotropic hardening: Modeling and experimental validation

Abstract

A non-associated flow rule (non-AFR) model is developed by adopting the Barlat89 yield function as the yield stress function and a modified Barlat89 yield function as the plastic potential function under plane stress conditions. Determination of parameters to calibrate the yield stress function requires four stresses, e.g. uniaxial yield stresses along 0°, 45°, 90° to the sheet metal rolling direction, RD, and the equi-biaxial yield stress. Four corresponding r-values (Lankford coefficients) under the same directions are used as calibration parameters for the plastic potential function. These functions capably describe anisotropic hardening behavior as well as variation of r-values during deformation. Uniaxial tensile tests, hydraulic bulge tests, and biaxial tensile tests were performed on a 980MPa steel in order to validate the non-AFR model, which are compared with other yield functions under both associated flow rule, AFR, and non-AFR conditions.