Hill-1948、Hill-1979、Hill-1990、和Hill-1993屈服函数在金属板材塑性力学性质的描述中广泛采用，但Hill屈服函数系列存在一些难愈克服的局限性（如： Hill-1948无法同时描述好板材屈服应力和q-值沿板面的变化）。本申请项目的研究内容：1）建立广义Hill-1979、Hill-1993屈服函数，放弃要求主应力方向与板材正交对称轴方向一致的条件；2）建立广义Hill-1990屈服函数，拟合好Lode应力参数和Lode应变参数之间关系；3）利用晶粒的立方对称性，推导立方晶粒正交板材的广义Hill屈服函数；4）通过Taylor-Bishop-Hill物理模型和实验测量验证广义Hill屈服函数，了解板材塑性实验中出现的两个“非正常”行为。由于汽车、飞机等钣金件塑性成形的尺寸精度要求高，建立广义Hill屈服函数具有理论和应用价值。

The Hill-1948, Hill-1979, Hill-1990, and Hill-1993 yield functions are used widely in plasticity of sheet metals. But the family of the Hill yield functions exists some limitations (e.g., the Hill-1948 cannot describe the anisotropies of yield stresses and q-values on sheet metals very well). The studying contents of the project are： 1) establish the general Hill-1979 and the general Hill-1993 yield functions to relax the restriction that the loading has to be coaxial with the orthotropy of the sheet metals; 2) establish the general Hill-1990 yield function to fit the relation between the Lode’s stress parameter and the Lode’s strain parameter very well; 3) derive the family of general Hill yield functions on orthorhombic sheets of cubic crystallites by using the cubic symmetries of crystals; 4) verify the general Hill yield functions by the Taylor-Bishop-Hill model and the experimental measurement and understand two‘anomalous’ behaviors of sheet metals in tests. Because the high precision of the sizes is required in the plastic forming processes of automobile, aircraft and other sheet metal parts, the derivation of general Hill yield functions has theoretical and application values.