An upper-bound analysis of axisymmetric extrusion assisted by cyclic torsion

Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation are of engineering interest in view of their advantages with respect to monotonic loading processes. The present work is aimed at the analysis of an axisymmetric extrusion process assisted by cyclic torsion, which can be induced by a cyclically rotating die with a specified rotation amplitude and frequency. The material is assumed to be rigid-perfectly plastic and the upper-bound analysis for a kinematically admissible flow field is presented. The field parameters are specified from the condition of minimum plastic dissipation. The evolution of the extrusion force and torsional moment is studied and the corresponding plastic flow field is specified, with process control parameters such as the ratio of extrusion and rotation rates, and the amplitude of die rotation. For increasing rotation frequency, it is shown that localization of plastic flow occurs in the bottom zone close to the rotating die. The analysis allows for specification of process control parameters and their relation to extrusion force, torsional moment, and the associated plastic dissipation for varying reduction ratios.