A generalized upper bound solution for extrusion of bi-metallic rectangular cross-section bars through dies of any shape

In this paper, a generalized upper bound solution is developed for extrusion of bi-metallic rectangular cross-section bars through dies of any shape. The internal, shearing and frictional power terms are derived and they are used in the upper bound model. By using the developed upper bound model, the extrusion pressures for two types of die shapes, an optimum wedge shaped die as a linear die profile and an optimum streamlined die shape as a curved die profile, are determined. The corresponding results for those two die shapes are also determined by using the finite element code and compared with the upper bound results. These comparisons show a good agreement.