当金属板材的压制方向、横向、板面垂直方向分别与参考坐标系的三个坐标轴xi(i=1,2,3)方向一致时,金属板材为正交材料。人们常采用Hill屈服准则,研究金属正交板材绕x2(或x1)轴作平面弯曲时变形和应力的关系。当正交金属板材绕参考坐标系的码轴旋转咖角后,金属板材的压制方向和横向不再与参考坐标系的x1和x2轴重合,正交板材成为斜板材。本文将推导出适用于斜板材的屈服函数,推导出斜板材绕x2轴作平面弯曲时变形和应力的关系,给出弯曲应力场与织构系数的关系,给出弯曲应力场随旋转角Ф变化的关系。
If the rolling, transverse, and normal directions of metal sheets are coincident with three axis xi (i=1,2,3 ) of a fixed Cartesian coordinate system, respectively, the metal sheets belong to orthorhombic sheets. Hill' s yield function is often used to analyze the relation of bending deformation and stress around x2=(or x1) for the or-thorhombic metal sheets. When the orthorhombic metal sheets have rotation angle Ф around x3, the rolling and transverse directions of the orthorhombic metal sheets are not coincident with axis x1 and x2 of the fixed Cartesian coordinate system yet respectively and the orthorhombic metal sheets become the skew metal sheets. In this article, we derived a yield function which is suitable to the skew metal sheets. We derived the relation between bending deformation and stress when the skew metal sheets are bended around x2, where the metal sheets are cubic tals. We gave the relation among bending stress, texture coefficients and angle Ф for skew metal sheets.