A general kinematically admissible velocity field for axisymmetric forging and its application to hollow disk forging

An approach for selecting general kinematically admissible velocity fields for axisymmetric forging problems is outlined. The approach accounts for the existence of a rigid zone at frictional interfaces and for the singular behavior of real velocity fields in the vicinity of maximum friction surfaces. The plastic work rate for a material obeying the von Mises yield criterion and its associated flow rule is expressed in terms of one arbitrary function of a single argument, its derivative, and anti-derivative. An upper bound solution for constrained forging is given. Comparison with an available upper bound solution is made and it is shown that the new kinematically admissible velocity field results in a more accurate solution at high friction. Other problems that can be treated are briefly discussed.