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.

在本文中，原始 Hill48 屈服模型在预测单轴拉伸屈服应力和r值进行了详细分析，然后提出了判断原始Hill48产量模型适用性的充要条件。在此基础上，考察了钢板DC04、DP980和铝合金AA5754-O对充要条件的近似满足。结果表明，可以利用充要条件对原始Hill48模型的预测误差进行定性分析。基于Hill48屈服函数的内在关系，在各向异性参数中引入主应力轴方向，建立了适合平面应力状态的修正Hill48模型。根据原始 Hill48 屈服模型在双轴拉应力中预测误差的变化，针对单轴应力状态和对称双轴应力状态之间的非对称双轴应力，提出了一种包含材料参数的指数插值方法。理论预测结果表明，修正后的模型能够准确捕捉定向屈服应力，r 值和产量轨迹。修改后的模型的主要优点是在应力张量中仍然保持简单的二次形式，并且可以通过使用关联流动法则显着提高铝合金等材料各向异性行为的预测精度。