Plastic Flow through Taper Dies: A Threedimensional Analysis

The plastic flow of metal in the extrusion process is an important factor in controlling the mechanical properties of the extruded products. It is, however, difficult to predict the metal flow in three dimensional extrusions of sections due to the involvement of re-entrant corners. The present study is to find an upper bound solution for the extrusion of triangular sectioned through taper dies from round sectioned billet. A discontinuous kinematically admissible velocity field (KAVF) is proposed. From the proposed KAVF, the upper bound solution on non-dimensional extrusion pressure is determined with respect to the chosen process parameters. The theoretical results are compared with experimental results to check the validity of the proposed velocity field. An extrusion setup is designed and fabricated for the said purpose, and all extrusions are carried out using circular billets. Experiments are carried out with commercially available lead at room temperature