The use of upper-bound solutions for the determination of temperature distributions in fast hot rolling and axi-symmetric extrusion processes

Abstract

By using realistic upper-bound solutions it is possible to estimate instantaneous temperature distributions throughout a mass of material which is fast being plastically deformed. For a particular hot rolling process an estimate of this distribution has been made and, in part to justify the use of the method employed, the results of calculations of the deformation of an initially square grid and a calculation of the necessary roll torque and roll pressure distribution are given. Two particular instances of axi-symmetric processes are examined, both of 0·75 reduction. Firstly, for extrusion through a square die two forms of velocity field are presented and the results predicted therefrom are compared. Secondly, extrusion through a smooth conical die is examined.