Upper bound loads for extrusion through circular dies

Extrusion dies having circular shapes are considered and by using circular arcs along which a constant magnitude velocity discontinuity occurs, it is shown that upper bounds to the extrusion load may quickly and easily be obtained. The four symmetrical shapes of die:convex, concave, bell-mouthed and convex — wedge shaped, are examined and an example of an unsymmetrical pair of convex dies of unequal curvature.