平面应变镦粗问题的摄动分析

Perturbation Analysis on the Problem of Plane-Strain Upsetting

通过引入速度势函数，将理想刚塑性体平面应变问题的控制方程化简为两个非线性偏微分方程．应用摄动方法，以摩擦因素（是摩擦系数和变形区几何参数的函数）为摄动参数，获得了平面应变镦粗问题的摄动解．在此基础上，研究了镦粗过程中的变形规律和应力分布规律，理论分析结果与由其它理论所得的结果符合较好．

The paper is concerned with the problem of plane－strain upsetting of an ideal plastic－rigid solid. It is shown that the governing equations for such a problem can be reduced to two nonlinear partial differential equations by introducing a velocity potential function' By a Applytng perturbation method to these equations by taking the friction factor,which is a function of the Coulomb coefficient of friction and the geometry parameter of deformation region,as perturbation parameter,the perturbation solutions are obtained. Based on these solutions,the deformation law and the distribution of stresses are investigated. The results of theoretical analysis are in good agreement with those of other theories.