Conical Flows in Metal Forming

Abstract

An improved velocity field based on the solution to an incompressible fluid flow is used to establish an upper bound approach for conical flows in metal forming. From a three parameter characterization of the equivalent stress-equivalent strain data on copper and aluminum, the effects of work hardening on forming stresses, maximum reduction ratios, optimum cone angles, and dead zone angles are studied for drawing, conventional, and hydrostatic extrusion. Results for a rigid-plastic material are obtained as a special case of the work hardening material. Experimental data are offered to show an excellent correlation with theory. A representation for the redundant work factor is developed that incorporates in it the effects of material properties and flow geometry. The existence of maximum pressure well inside the plastic region is pointed out and the possibility of introducing the forming fluid at some distance inside the die to facilitate better lubrication is examined.