Limitation analysis of the Hill48 yield model and establishment of its modified model for planar plastic anisotropy

In this paper, the limitations of the original Hill48 yield model in predicting uniaxial tensile yield stresses and r-values were analyzed in detail, and then the necessary and sufficient conditions for judging the applicability of the original Hill48 yield model were proposed. On this basis, the approximate satisfactions of the steel sheet DC04, DP980 and the aluminum alloy AA5754-O to the necessary and sufficient conditions were investigated. The results show that the necessary and sufficient conditions can be used to qualitatively analyze the predicted error of the original Hill48 model. Based on the inherent relationship of Hill48 yield function, the direction of principal stress axis was introduced into the anisotropic parameters, and a modified Hill48 model suitable for plane stress state was developed. According to the variation of the predicted error of the original Hill48 yield model in biaxial tensile stress, an exponential interpolation method including material parameter was proposed to correct the asymmetric biaxial stress between uniaxial stress state and symmetric biaxial stress state. The theoretical predicted results show that the modified model can accurately capture the directional yield stresses, r-values and yield locus. The main advantage of the modified model is that it still maintains a simple quadratic form in the stress tensor, and can significantly improve the predicted accuracy of anisotropic behavior of aluminum alloy and other materials from the use of associated flow rule.