A non-quadratic pressure-sensitive constitutive model under non-associated flow rule with anisotropic hardening: Modeling and validation

A non-associated flow rule (non-AFR) constitutive model is proposed to describe the evolving yield stress and plastic potential surfaces of sheet metal under plane stress conditions. The yield stress function is a multiplication of two yield functions, within the first part includes an asymmetric pressure-sensitivity that considers anisotropic and asymmetric yielding of sheet metals. This yield stress function can describe anisotropic hardening behavior by directly employing the hardening functions under seven different loading conditions, i.e., uniaxial tension along 0 degrees, 45 degrees, 90 degrees to the rolling direction (RD) of sheet metal, uniaxial compression along the same orientations and equi-biaxial tension without any interpolation or optimization procedure at a discrete level of equivalent plastic strain. The second part is a non-quadratic isotropic function, which is the sum of two isotropic yield functions with high flexibility in shaping the yield surface. A new plastic potential function is proposed to capture the differential Lankford coefficients (r-values) between uniaxial tension and compression obtained from mechanical testing. Eight parameters in the plastic potential function were calibrated from seven r-values under the same loading conditions and one yield stress as calibrating parameters for the yield stress function. The proposed constitutive model was validated by experimental data of three engineering sheet metals, i.e., one dual-phase steel DP980, one TRIP-assisted steel QP980 and one aluminum alloy AA5754-O and compared with several classical yield criteria. The evolving yield behavior was accurately described by the proposed non-associated flow rule (non-AFR) constitutive model.