Upper bound analysis and finite element simulation of bi-metallic tube backward extrusion

In this paper, the process of bi-metallic tube backward extrusion through a conical punch, by means of upper bound method and finite element method is investigated. A cylindrical admissible velocity field is developed and by calculating the internal, shear and frictional powers, the extrusion force is estimated. The extrusion process is also simulated by using the finite element code, ABAQUS. Analysis and simulations are done for two types of bi-metallic tubes: aluminum as core, copper as sleeve (Al-Cu) and copper as core, aluminum as sleeve (Cu-Al). The extrusion force from the upper bound method is compared with the Finite Element results. This comparison shows that the upper bound predictions are in good agreement with the Finite Element results. The results also show that, the extrusion force in the case of Al-Cu tube is smaller than Cu-Al tube and in both types of bi-metallic tubes, the aluminum leaves the deformation zone sooner than the copper. Finally the effects of various extrusion parameters, such as the friction factor, reduction in area and semi-punch angle upon the extrusion force are investigated and the optimum semi-punch angle is determined.