Abstract

An upper-bound solution based on a kinematically admissible velocity field is proposed for the axi-symmetric extrusion through conical dies. The pattern chosen uses a double triangle arrangement of velocity discontinuities. The solutions are optimized using a digital computer programme which incorporates terms to accommodate the work of circumferential straining and the effects of die friction. Analysis of the results for a full range of cone angles, reductions and frictional conditions provides useful predictions relating to the formation of dead zones. Such an analysis is given in detail for a 90° die. The solution is extended to incorporate strain-hardening characteristics of the material. The ensuing results yield information as to the type of hardness distribution across the extruded product with particular reference to the effects of die geometry and area reduction.

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