A generalized velocity field for plane strain backward extrusion through punches of any shape

In this paper, the process of plane strain backward extrusion process through arbitrarily curved punches, by means of the upper bound method and the finite element method is investigated. A generalized velocity field is developed and by calculating of the internal, shear and frictional powers, the extrusion force is estimated. Then, by using the developed analytical model, optimum punch lengths which minimize the required extrusion forces, are determined for a wedge shaped punch and a streamlined punch shape. The corresponding results for those two punch shapes are also determined by using a finite element code and compared with the upper bound results. This comparison shows that the upper bound predictions are in good agreement with the FE results.