Autofrettage theory and fatigue life of open-ended cylinders

Abstract

Two new theories of autofrettage are presented for an open-ended, thick-walled cylinder which can take into account work-hardening in the presence of small plastic strains based upon equivalent uniaxial stress-strain data. They apply to an internally pressurised cylinder where the axial force is not reacted by the cylinder wall, as is the case with the closed-end or plane strain condition, but where a close fitting internal piston or plug is supported separately to contain the pressure. It is shown that solutions to the wall stress distributions depend upon the initial yield condition. Both the Tresca and von Mises flow rules are employed to determine applied and residual stress distributions for given elastic-plastic radii in the wall of the cylinder, assuming purely elastic unloading. Since the Tresca theory does not specifically account for the open-end condition the von Mises theory is taken to be the more realistic, particularly for cylinder diameter ratios ( W) in excess of ≈3, where the largest discrepancies between theories arise. It is reasoned, from previous experimental observations, that the greatest benefit autofrettage has on fatigue strength applies to an optimum pressure for which the equivalent residual stress in the bore has not involved reversed yielding. The onset of reversed yielding may be estimated most realistically with an account of the Bauschinger effect as supplied by the rule of kinematic hardening. In order to further appraise these theories they are employed to predict the fatigue life of fully autofrettaged W = 2, Ni-Cr-Mo cylinders. For this purpose the stress intensity factor calibration of Parker and Farrow is used and that of Bowie and Freese is modified to account for the presence of the residual stress. Comparisons made with available experimentally-determined fatigue lives confirm that a non-hardening assumption is acceptable with this cylinder geometry.