Bifurcation and post bifurcation behaviour of internally pressurized elastic-plastic circular tubes under plane strain conditions

Abstract

The nonaxisymmetric bifurcation and post bifurcation behaviours of circular tubes subjected to internal pressure are investigated numerically in terms of the finite element method. It is assumed that tubes are made of elastic-plastic strain hardening material with smooth yield surface and that they deform under plane strain condition. Hill's uniqueness theory along with the Prandtl-Reuss equation and the separation of the variables are employed to obtain the bifurcation point and corresponding mode. The results indicate that the mode with longest wave length is critical and always follows the maximum pressure point for all cases investigated here. For thin to thick tubes, the post bifurcation behaviours are numerically investigated. The development of unloading region, stress and strain distributions, localization of the deformation and thinning of the tube are clarified.