不锈钢材的橢圆杯拉伸成形分析(英文)

Analysis of elliptical cup drawing process of stainless sheet metal

采用Prandtl-Reuss塑流法则和Hill的屈服判据,结合有限变形理论及updated Lagrangian formulation的概念,将四边形四节点退化壳元素偶合到刚性矩阵中,组成三维有限元素的分析模式来处理板材成形问题。以材料拉伸试验所得的样片断裂面厚度为数值分析的破断准则,探讨椭圆杯拉伸成形过程中冲击荷载与冲程的关系、工件厚度分布、变形过程及成形极限等。由数值分析与实验结果得知,冲击荷载随着冲程的增加而增大,当载荷达到最大值后,样片随着冲程的增加而继续变形,直到拉伸完成为止。工件最小厚度集中在工件与压头长轴接触处,因长轴的曲率半径比短轴的小,故料片在长轴处承受了最大拉伸应力。经由椭圆压头周长与初始样片周长所定义的极限拉伸比得知,此椭圆杯成形的极限拉伸比为2.136。

Prandtl-Reuss flow rule and Hill’s yield criterion were adopted and combined with the concept of finite deformation theory, updated Lagrangian formulation, and a three-dimensional finite element analytical model was established by application of quadrilateral four-node degenerated shell elements coupling into a rigid matrix to deal with the sheet metal forming problems. The fractured thickness of a specimen obtained from a simple tension test was used to be the fracture criterion for the numerical analysis to explore the relationship between punch load and stroke, the thickness distribution, the deformation history and the forming limit of work-piece in the elliptical cup drawing process. The numerical analysis and experiment results show that the punch load increases with the increase of punch stroke, and when the load reaches its maximum, the blank continues to deform with the increase of the punch stroke, resulting in a reduced load until the extension is completed. The minimum thickness of the work-piece concentrates in the contact region of the work-piece and long axis of the punch due to the smaller radius of the curvature of the long axis than the short axis. So the blanks bore the maximum tensile stress in the long axis. Through the limit drawing ratio defined by perimeter of the elliptical punch, the limit drawing ratio of this elliptical cup drawing is defined to be 2.136.