An analysis for drawing and extrusion of polygonal sections

Abstract

The material flow generated by drawing or extrusion of rigid plastic material through a converging die of regular polygonal cross-section has been analysed by an upper bound technique. A constant frictional stress is assumed to be acting over the entire interface between the die and the wire material. The solution predicts that the drawing stress is minimum at a particular value of convergence angle of die surfaces. With increase in the number of sides of the polygonal cross-section the drawing stress decreases till it approaches that required for the circular cross-section when the number of sides go to infinity. For large die angles dead-metal zones are formed along the die surfaces and the extrusion pressure for same reduction is little affected by the shape of the product. This result is similar to that found by Johnson [10] experimentally. The technique can be easily extended to an irregular polygonal section whose sides are tangent to a circle.