Axi-symmetric tube extrusion through a smooth conical or cosine die and over a conical or ogival mandrel: numerical construction of axi-symmetric slip-line fields and associated velocity fields

Abstract

The numerical method of construction of axi-symmetric slip-line fields and their associated velocity fields suggested earlier for rod extrusion (Chitkara NR, Butt MA. Axi-symmetric rod extrusion through smooth conical, cosine and lat-faced dies, International Journal of Mechanical Sciences, submitted) and tube extrusion (Chitkara NR, Butt MA. Axi-synnetric tube extrusion through a flat-faced circular die: International Journal of Mechanical Sciences, 1997;39(3);341–366) is employed to construct slip-line fields and their associated velocity fields for a few cases of forward tube extrusion through smooth, rigid conical and cosine dies and over a smooth rigid conical or ogival mandrel. The computographic plots of slip-line fields and associated velocity fields are given in the form of weighted and directed velocity vectors as are the normal pressure distribution on both the die and the mandrel surfaces. The values of the non-dimensionalised mean extrusion pressures, ρ ̄ /2k are compared in each case with a similar case of plane strin extrusion and the results commented upon.