A new formulation for three-dimensional extrusion and its application to extrusion of clover sections

Abstract

The metal flow in the extrusion process is an important factor in controlling the mechanical property of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of complicated sections due to the difficulty in representing the geometry of the die surface and in expressing the corresponding velocity field. In this study a new kinematically admissible velocity field for a generalized three-dimensional flow is derived, in which the flow is bounded by the die surface expressed by an analytic function. Then, by applying the upper-bound method to the derived velocity field, the flow pattern as well as the upper-bound extrusion pressure are obtained. As a computational example, extrusion of clover sections from round billets is chosen. A new method of die surface representation is proposed by which there is a smooth transition of die contour from the die entrance to the die exit. Computation is carried out for work-hardening materials such as aluminium and steel. The analysis takes into account the effect of product shape complexity, lubrication condition and reduction of area on extrusion pressure, average effective strain and distribution of effective strains on the cross-section of the extruded product.