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前言滑移线场理论在平面应变问题中已经得到了广泛的应用,但对于较复杂的塑性变形问题,如平板经过光滑模具的抽拉问题,过去一般都采用图解或数值方法求解,而无法用解析方法求解,因此难以分析结果,不易提高计算精度。本文利用作者提出的相似解析法,即根据塑性变形区内的速度场和滑移线场之间存在的几何相似性进行求解的方法,以及得出的由两条相等半径的圆弧滑移线所确定的滑移线场(简称等半径双圆弧滑移线场)的解析表达式,对上述问题进行求解,得到了满意的解析解答。
Introduction The slip line theory has been widely used in the plane strain problem. However, for the more complex plastic deformation problems, such as the drawing of the smooth plate through the flat plate, the past is usually solved graphically or numerically and can not be used Solve the analytical method, it is difficult to analyze the results, not easy to improve the calculation accuracy. In this paper, we use the similarity analysis method proposed by the author, that is, the method of solving according to the geometric similarity existing between the velocity field and the slip line field in the plastic deformation zone, and the method of solving the problem by two arcs of equal radius The analytical expression for the slip line field (ie, the equivalent radius double arc slip line field) is solved and the satisfactory analytical solution is obtained.