Twisting and expansion of a hole in a non-uniform disk

Abstract

Finite and infinitesimal deformation of an infinitely extended, axisymmetric disk of a non-uniform initial thickness with a circular hole is considered. The disk is loaded along the interior surface of the hole by pressure and twisting moment of non-decreasing magnitudes. A state of plane stress is assumed and the incremental theory of plasticity is used. The material of the disk is assumed to be rigid-plastic for finite deformation and elastic-plastic for infinitesimal deformation. The analyses are based on the Tresca yield criterion and the isotropic hardening law, and emphasis is placed on the effects of the twisting moment, hardening parameter and loading path on the solution. Detailed results and comparisons are given for an initially uniform and an initially conical disk. Finally, comparison is made between solutions for elastic-plastic and rigid-plastic disks, revealing that the stress field is only slightly affected by the elastic strains.