剪切角是金属切削中一个重要的物理量 .本文从传统的弹性理论和塑性理论出发 ,由变分原理导出了材料符合 Prandtl- Reuss流动规律和 von Mises屈服判据的修正拉格朗日有限元刚度矩阵方程式 ,并从相应的等效流动应力场中直接获取剪切角 .实验结果表明 ,理论分析与实验值相吻合 . Shear angle is an important physical quantity in metal cutting.In this paper, based on the traditional theory of elasticity and plasticity, the modified Lagrangian finite element method is derived by the variational principle and the Prandtl-Reuss flow rule and von Mises yield criterion Stiffness matrix equation and obtain the shear angle directly from the corresponding equivalent flow stress field.The experimental results show that the theoretical analysis agrees well with the experimental data.