THE SOLUTION OF AXI-SYMMETRIC PLASTIC DEFORMATION PROBLEMS FROM EQUILIBRIUM FORCE DIAGRAM CONSIDERATION AND THE APPLICATION OF THE METHOD TO THE EXTRUSION PROCESS

SUMMARY A method is proposed which provides the force for a given axi-symmetric plastic deformation process. The method is based on equilibrium considerations of the stress system arising from a kinematically admissible system of velocity discontinuities. The circumferential stress is denned by the Haar and von Karman assumption. This assumed pattern of velocity discontinuities is adjusted to give a minimum value of applied force. The method is considered in the context of the extrusion process and is shown to agree with an alternative upper bound solution, both solutions being in reasonable agreement with experimental results. By a comprehensive evaluation of the extrusion loads for various reductions, frictional conditions and cone angles, the method may be used to predict the formation of dead zones. Experimental results for the extrusion through lubricated 90° dies show reasonable agreement with such predictions.