Some theoretical and practical problems of the metal extrusion process are analysed in this Thesis.

Plane strain extrusion of ideal materials, i.e. materials for which the yield stress is constant, are examined^ in the first three Chapters, using the upperhound technique. It is proved in Chapter 1, that identical upper-bounds to the working load may be obtained for any kinematically admissible velocity field by considering the total energy dissipation rate, and by considering the force equilibrium of regions seperated by the tangential velocity discontinuity surfaces. A radial flow field is introduced in Chapter 2, which yields improved upper-bound results for a wide range of die angles and reduction ratios^ A method is suggested in Chapter 3 to consider the effect of Coulomb friction caused by non-uniform die normal pressure distributions.

In Chapters 4 to 6, an approximate method is developed for estimating the ram pressure required for plane strain extrusion of real materials, i.e. materials the yield stress of which is dependant on strain, strain rate and temperature. In the same way as for the upperbound method, the proposed approximate method is based on an assumed velocity field. The method is developed in steps. In Chapter 4, strain hardening properties are considered, in Chapter 5 strain hardening and strain-rate effects and In Chapter 6 strain hardening, strain rate, initial temperature and subsequent variations in temperature due to die friction and heat conduction. Calculated ram pressures, for extruding pure lead and alum-^ inium, show satisfactory agreement when compared with experimental results obtained by several different researchers. Calculations show the effect of the process variables:​ die geometry, reduction ratio, material propter ties, initial billet temperature, and size.

Metal flow study, for the purpose of determining the properties of the extruded products, was undertaken, Chapter 7, covering a large number of different die arrangements using sections cut from partially extruded billets "built from different coloured plasticine layers.

The variation of shear stress with temperature and shearing velocity is determined experimentally. Chapter 8, for high purity, commertially pure lead and for lead-tin alloys. The exponent of the shearing stress-shearing velocity relation is found to be approximately equal to the exponent of the empirical effective stress-effective strain rate relation.

Empirical relations are derived in Chapter 9, relating the extrusion pressure and ram speed for pure lead and lead-tin alloys at different temperatures. Experimentally measured ram pressures show satisfactory agreement when compared with calculated results obtained using the method developed in Chapter 6.

Large friction force in the vicinity of the die orifice is suggested in Chapter 10 as a possible cause of circumferential surface cracks on the extruded product.

The equipment designed for executing the experiments are described in Chapter 11.