stream function

In this paper, the drawing process of multi-layer sheet metal through wedge shaped die has been analyzed using stream function and upper bound method. Typically a sandwich sheet contains three layers of metal, where the outer layers are of the same thickness and material and different from those of the inner layer. In this study, a new deformation model has been introduced in which inlet and outlet shear boundaries are considered flexible and the effect of work hardening of sheet layer materials has been considered. According to the suggested stream function, velocity field, strain rates and powers have been calculated. The optimized geometry of deformation zone and required drawing force has been determined depending on the process conditions. Analytical results, including drawing force and thickness of sheets in outlet of die have been compared with the finite element (FE) results. The FE results have a good agreement with the analytical results. Finally, the effects of friction factor and reduction in thickness have been investigated on the drawing force and the optimum die angle.