An elasto-plastic finite-element analysis of sheet metal camber process

Abstract

This study aims to clarify the process conditions of the V-die bending of a sheet metal of steel. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of products after unloading, based on the tensile properties of the material and the geometry of the tools used. An elasto-plastic incremental finite-element computer code, based on an updated Lagrangian formulation (ULF), was developed to simulate the V-die bending of sheet metal. In particular, selective reduced integration (SRI) was adopted to formulate the stiffness matrix. The extended r-minimum technique was used to deal with the elasto-plastic state and contact problems at the tool–metal interface. A series of experiments were performed to validate the formulation in the theory, leading to the development of the computer codes. The predicted value of the punch load in the finite-element model agrees closely with the results of the experiments. The whole deformation history and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method.A special feature of this V-die bending process is the camber after unloading. The computer program successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank and the bending angle on camber process. The effects of all process variables on the final bending angle of the bent parts of the sheet after unloading were also evaluated. Results in this study clearly demonstrated that the code for simulating the V-die bending process was efficient.