A new upper bound solution for axisymmetric direct extrusion considering Coulomb friction and generalized work functions

This paper provides a new upper bound solution for axisymmetric extrusion through a conical die. The most important distinguishing features of this solution, compared to available solutions, are the use of Coulomb friction and generalized work functions. In particular, a unified procedure is developed for evaluating the extrusion force for the work functions that yield the von Mises yield criterion, yield criteria closely approximating the Hershey-Hosford yield criteria, and a yield criterion that accounts for the strength-differential effect. The trial velocity field is intentionally chosen to be simple enough to emphasize the technique for constructing trial velocity fields that allow the extrusion force to be evaluated in the case of Coulomb friction. The possibility of a rigid region appearing in the die is taken into account. The numerical part of the solution reduces to evaluating an ordinary integral. The effect of various geometric and other process parameters on the extrusion force is revealed. Possible extensions of the solution are discussed.