The stresses and strains in a partly plastic thick tube under internal pressure and end-load

Abstract

Many solutions have been put forward from time to time for the stress distribution in a thick tube subjected to an internal pressure sufficient to cause yield at the interior, usually in connexion with the autofrettaging of gun barrels. These all give the same values for the radial and circumferential stresses, but differ as to the axial stresses according to the assumptions made in order to render a solution possible. The present paper reviews these solutions and presents an analysis making rather fewer assumptions; this is developed into a form suitable for practical application. The main defect of this analysis is the assumption (also made in all but one of the other solutions) that the strains at any stage depend only on the stress system then prevailing and not on how that stress system is reached. The only solution not open to this criticism is a graphical one, not capable of presentation in general form; a comparison of the results by this and the present solution in a particular case shows that the differences are insignificant. The strains are also evaluated, and it is shown that for open-end conditions Cook’s assumption that the axial stress is the mean of the radial and circumferential stresses leads to values of the exterior expansion which are not seriously in error.