UBET analysis of process of extruding aluminum alloy ribbed thin-wall pipes through a porthole die

Using the upper bound element technique (UBET), a numerical model was proposed for analyzing the metal deformation behavior in the extrusion process of ribbed thin wall pipes through a porthole die. Optimization parameters were contained in the numerical model and determined through minimizing the total work of metal deformation. Taking the extrusion process of thin wall pipe with one rib as an example, the calculated results using the proposed model are as follows: the extrusion pressure p is linearly related to the extrusion ratio R by p = a+bR 0.683 , where a = 14.13, b = 0.911. When the length of the billet remaining in container is shorter than a quarter of the container diameter, the plastic region extends over the whole of the remained billet and the extrusion process reaches the state of funnel deformation. There exists an optimum depth of welding chamber in respect of the extrusion pressure, and to the calculated example the optimum depth is about 10% of the circumscribed diameter of portholes. To obtain more equitable metal flow in welding chamber, it is required to make the dividing planes in container to be consistent with corresponding welding planes in the chamber ( θ max i = θ′ max i ) through choosing different entering area for each of the portholes.