A non-quadratic constitutive model under non-associated flow rule of sheet metals with anisotropic hardening: Modeling and experimental validation. (December 2016) - Min, Junying; Carsley, John E.; Lin, Jianping; Wen, Yuanyuan; Kuhlenkötter, Bernd
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 980 MPa 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. Graphical abstract: Highlights: A non-associated flow rule (non-AFR) model is developed. The yield and plastic potential functions in the non-AFR model are non-quadratic. The non-AFR model capably describes anisotropic hardening and variation of r -values. The non-AFR model is validated and compared with other models.