An Applied Analytical Method for the Forward Extrusion of Metals

An applied analytical formulation was developed to deal with the forward extrusion of non-symmetric sections based on the upper bound method. This method of solution has been developed as an alternative to finite element method with the advantages of less time consumption and expense. The deforming region where the material flow occurs was formulated in a new and more realistic fashion by streamlines and stream surfaces. Streamlines and stream surfaces were defined parametrically for the material flow and the development of the kinematically admissible velocity field. The newly developed velocity field incorporated features such that the real physical aspects of the problem were followed more closely than before. The internal, shear and frictional power terms were obtained from the upper bound solution. Using the present method of analysis, the pattern of material flow and the relative extrusion pressure were computed. Results compared to previous works indicated substantial improvements. Experimental and numerical investigations were carried out, and the proposed theoretical model was verified. Close agreement was observed between the analytical results and those from the simulation and the experiment.