Axi-symmetric tube extrusion through a flat-faced circular die: Numerical construction of slip-line fields and associated velocity fields

A numerical method of construction of axi-symmetric slip-line fields and their associated velocity fields [13–15] is applied to investigate the problem of axi-symmetric tube extrusion through smooth and rough flat-faced circular dies and the salient results presented in a computographic manner. A reasonably satisfactory agreement was observed between the estimated values of the non-dimensionalised specific extrusion pressures in each case when these were compared with the analytical and experimental work of Kudo [6] and that carried out by the authors. The deficiency in the technique used, the difficulties encountered and also some specific errors noticed during the construction of the fields, are highlighted and the results commented upon.     

Combined rod and tube extrusion: Numerical solution of axi-symmetric slip-line fields and associated velocity fields

Numerical method of construction of axi-symmetric slip-line fields and associated velocity fields in the form of computographic plots of axial and radial velocity components, earlier given by the authors for rod extrusion and tube extrusion, was extended to the solution of two types of combined rod and tube extrusions: (i) where the rod and tube are extruded in opposite direction to each other and (ii) where, both the rod and tube move in the same axial direction as the punch movement during the extrusion process. Computographic plots of slip-line fields and associated velocity fields in the (r, z) plane are given and the deficiencies noticed in the solutions are highlighted. The results of specific punch pressures are observed to compare well with those estimated, using simple upper bound analysis and the experimental work of the authors.     

Axi-symmetric tube extrusion/piercing using die–mandrel combinations: some experiments and a generalised upper bound analysis

A generalised upper bound technique is applied to the solution of working pressures in extrusion–piercing of hollow tubes starting from either solid circular or initially hollow billets by using axi-symmetric die–mandrel combinations of different shapes. Characteristic deformation modes during processing of these tubes made of tellurium lead and commercially pure aluminium were studied experimentally and the results presented. Estimates of working pressures based on the generalised upper bound analysis are compared with the experimental and with those estimated earlier from the slab method of analysis given in Chitkara and Aleem (International Journal of Mechanical Sciences, submitted for publication). These show good co-relations with each other and with the experiments.