On the dead-zone formation and limit analysis in axially symmetric extrusion

For axisymmetric direct and indirect extrusion, a kinematically admissible velocity field based on a simple radial flow field combined with the asymptotic behaviour required of a real velocity field near a velocity discontinuity surface is proposed. The influence of the extrusion ratio on the shape of a dead zone and the extrusion pressure is investigated. The result obtained for the upper bound on the extrusion pressure is compared with other solutions. It is shown that using the asymptotic velocity field slightly improves the prediction of the extrusion pressure in comparison with the other solutions based on radial flow. The main advantages of the approach proposed are that it is applicable to a class of processes and that it accounts for the behaviour of a real velocity field in the vicinity of velocity discontinuity surfaces/maximum friction surfaces where various physical effects like local heating, recrystalization, and transformations occur.