A Class of Upper Bound Solutions for Plane-Strain Extrusion

In the present investigation a class of upper bound solutions are proposed for plane-strain extrusion through square dies at different area reductions. The variation of normalized mean extrusion pressure with area reduction has been computed for a number of die geometries and for different values of friction conditions at the interfaces. A non-linear optimization procedure for calculation of the best upper bound is used. The method eliminates the constraints by a simple change of variables thus transforming the usual constrained problem to an unconstrained problem so that more complex velocity fields may be analyzed by the proposed procedure. The results are compared with slipline field analysis.