Three-dimensional axisymmetric flow in perfectly plastic metals

Abstract

A method is presented for solving the three-dimensional axisymmet-ric field equations for a perfectly plastic material which obeys the von-Mises yieldcriterion and the Levy-Mises flow law. The method is used for the particular case inwhich a small axisymmetric perturbed flow is superposed on a uniform flow withoutflow reversal taking place. The method then leads to solving a fourth order differen-tial equation for the velocity potential. The special case of a thick cylindrical shellunder compressive flow is examined. The solution so obtained, being derived fromthe three dimensional theory, includes a correct treatment of transverse shear distor-tion. A preferred mode of instability is identified having a wave-length in reasonableagreement with that obtained experimentally by other workers.