Analysis of elliptical cup drawing process of stainless sheet metal

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.