An upper bound analysis of the geometric shape of the deformation zone in drawing process of the metal plates through wedge-shaped die

In the present paper, drawing process of metal plates through a wedge-shaped die, by proposing new velocity field, has been analyzed by upper bound method and simulated by finite element method (Abaqus software). Among the important cases in upper bound analysis of the forming processes is selection the appropriate boundaries for the deformation zone and offering admissible velocity field that in addition to satisfy the incompressibility condition and boundary conditions, is consistent by the behavior of metal flow in the deformation zone. The entrance boundary of deformation zone has been assumed exponential curve surface and boundary at exit has been assumed cylindrical surface. In the past analyses, metal flow lines in the deformation zone have been assumed straight but in reality it is not. In the present work, velocity field and also geometric shape of the deformation zone, justify that metal flow lines are non-straight. Base on proposed velocity field, internal powers, shear and frictional and also total power have been calculated. Then, according to the plate pulling velocity, required drawing force has been obtained. Finally, analytical results have been compared with the obtained results of FEM. In order to validate the present analysis, obtained results have been compared with other researchers. Also, the effect of various parameters, such as percentage reduction in thickness and shear friction constant on the drawing force and die optimum angle have been investigated.