This article describes a theoretical model of the generalized kinematic velocity field for the axisymmetrical flow of a bi-component (metal-quasi-liquid lubricant) system that can be applied to dies with either straight or curved profiles. The differentiation of the derived analytical dependencies of the velocity of any point within the deformation zone enables the determination of the deformation strains. It is shown that the proposed model describes quite accurately the form - and is satisfactory in respect of the dimensions - of the plastic zone in the hot hydro-extrusion of hardening alloy AlCu4Mg1. At the same time the model confirms the dependency of the variation of the deformation on the die geometry that has been noted in other published works. It is found that the most favourable distribution of the deformation at the exit of the plastic zone is achieved by use of a sigmoidal die profile. A program has been developed for the numerical solution of the theoretical model. After further improvement of the model, with the inclusion of the necessary optimization, it might find application in the computer-aided design of dies having optimal geometrical parameters. © 1990.
Petzov, G. G., Jelezov, K. D., & Tzoneva, M. G. (1990). Model of the kinematic field in the axisymmetrical high-temperature extrusion of a bi-component (metal-lubricant) system. Journal of Materials Processing Tech., 21(2), 131–142. https://doi.org/10.1016/0924-0136(90)90002-C