An analysis of forming limit in the elliptic hole-flanging process of sheet metal

A methodology for formulating a three-dimensional elasto-plastic finite element model, which is based on Prandtl-Reuss flow rule and Hillʹs yield criterion, respectively, associates with an updated Lagrangian formulation, is developed to simulate the elliptic hole-flanging process. An extended r-minimum algorithm is proposed to formulate the boundary condition, such as the yield of element, maximum allowable strain increment, maximum allowable rotation increment, maximum allowable equivalent stress increment, and tolerance for nodes getting out of contact with tool. The fractured thickness of a specimen in simple tension test is adopted as the fracture criterion in simulation. The numerical simulation results include relationship between punch load and punch displacement, variation of the workpiece thickness, distribution of stress, distribution of strain, and limit forming ratio. The finite element model is developed to simulate anisotropic of the elliptic hole-flanging process. The accuracy of the finite element program is based on a comparison between the simulation and experiment outcomes. According to the experimental data, the prediction of the phenomenon of necking of the elliptic hole-flanging process occurs at the inner periphery of elliptic hole is studied. The simulation dearly demonstrates the efficiency of the model to simulate the elliptic hole-flanging process. This study has provided an improved understanding of the elliptic hole-flanging process for improving the manufacturing processes and the design of tools.