Determining the Drawing Force in a Wire Drawing Process Considering an Arbitrary Hardening Law

Abstract

The present paper considers the wire drawing process through a conical die and provides an approximate solution for the drawing force, assuming an arbitrary hardening law. The solution is based on the upper bound theorem. However, this theorem does not apply to the stationary flow of strain-hardening materials. Therefore, an adopted engineering approach is to replace the original material model with a non-homogeneous, perfectly plastic model. The kinematically admissible velocity field is derived from an exact semi-analytical solution for the flow through an infinite channel, which increases the accuracy of the solution. The solution for the homogeneous perfectly plastic material compares with an available solution. The general solution is valid for any die angle. The numerical example focuses on the range of angles used in wire drawing. Since the material model is pressure-independent, it is straightforward to adopt the solution for calculating the force in extrusion.