Strain-Hardening and Strain-Rate Effects in Plastic Flow Through Conical Converging Dies

An upper-bound solution for energy expended to cause the flow of strain-hardening material through conical converging dies is presented. A linear strain-hardening coefficient is considered. The solution is adapted for determination of the required drawing force in wire drawing and the required ram force for extrusion. A simplified equation is then recommended, utilizing an expression for the average effective strain. The accuracy of the simplified equation was checked and found to agree within 1–2 percent with the upper-bound solution for all practical values of reduction, cone angle, and strain-hardening coefficients.