Cylinder under combined axial and torsion load

Abstract

A class of problems often encountered in metal forming involves forming a cylinder through combined axial load and a twist. Many investigators explored the process for a number of years and a classic solution was obtained by plasticity theory. In recent years, limit analysis was successfully used to analyse plastic deformation processes. The upper-bound analysis is designed so that the actual power or forming stress requirement is less than that predicated by the upper bound. Finding a lower upper-bound reduces the uncertainty of the actual power requirement. In the present work, actual power (tensile or torque) required to form a cylinder through combined axial load and a twist was estimated by the upper-bound technique. The power was minimized with respect to the axial velocity or angular velocity. In this manuscript, two cases where tension stress and shear stress are the prescribed independent process parameters are covered. Also, the friction effect at the clamped end is considered. The new solution coincides with the older but covers a range not provided in previous works.