Plastic deformation and instability in thin-walled tubes under combined loading : a general theory. Part II

Abstract

This analysis concerns closed-ended tubes of circular section which are loaded by internal fluid pressure together with an external axial force. These may be applied in proportions that can be varied at will by servo-control during a single experiment. More generally it is envisaged that the servo-control can respond to changes in tube radius when these are monitored by a diametral extensometer. A main objective is to determine how the choice of control affects the regime of homogeneous deformation. Another is to consolidate an understanding of the transition to inhomogeneous deformation mediated by eigenmodes. The general approach is along similar lines to part I and takes the analysis appreciably farther in important respects. The constitutive basis is broadly classical, but yield functions spanning the whole of stress space are not called upon, primarily because of the extreme scarcity of good experimental data. There are counter-balancing benefits from this abstention : (i) the governing equations can be handled far more readily ; (ii) the structure of the mathematics as a whole is more transparent ; (iii) the final conclusions are valid for materials whose path-dependent behaviour is much more complex than can be accommodated by the simple theories reviewed in Part I.