7.4.1 Introduction

The processes of metal extrusion or drawing have been considered within the framework of classical time-independent plasticity theory (see Avitzur [1968]). The theory considered here is to describe the influence of the speed of the process (of the order of 100 m/s) on all the other involved parameters (Cristescu [1975], [1976]). We consider mainly wires which are very thin, less than 0.5 mm in diameter. Let us assume that the main mechanical properties of the material can be described with a viscoplastic constitutive equation. Since the elastic part of the strain will be neglected the simplest possible model is a Bingham-type constitutive equation of the form

where ? _m is the mean yield stress which depends on reduction and is an approximation of the isotropic work-hardening law of the material, and is the positive part. Thus the model is viscoplastic rigid.

A second assumption is that the circular conical die remains rigid during plastic flow and that in the domain where plastic flow takes place (domain II) the process is axi-symmetric. Assuming volume incompressibility the following velocity field components in spherical co-ordinate r, ?, ? can be obtained

in the domain II defined by r ₀ ?r ?r _f , 0 ? ???, 0 ? ? ?2 ?. According to (7.4.2) the material particles are moving radially towards the apex 0. Since in the domain I (for r>r ₀) the whole rod...