Autofrettage of Open-End Tubes—Pressures, Stresses, Strains, and Code Comparisons

Abstract

Autofrettage is used to introduce advantageous residual stresses into pressure vessels. The Bauschinger effect can produce less compressive residual hoop stresses near the bore than are predicted by “ideal” autofrettage solutions. A recently developed numerical analysis procedure is adopted and extended. The ratio of calculated autofrettage pressure (numerical)/ideal autofrettage pressure (Tresca criterion and plane stress) is calculated and verified against available solutions. The case of open-end conditions based upon von Mises and engineering plane strain (constant axial strain with zero net axial force) is examined in detail. The ratio in this case varies between unity and 2/(√3), but exhibits very significant variations from the plane stress case when the diameter ratio of the tube exceeds 1.8. Results are within 0.5 percent of available analytical, numerical, and experimental results. A simple numerical fit allows all autofrettage pressures to be replicated to within 0.5 percent. The true plane strain pressure ratio is examined and shown to be inappropriate in modeling engineering plane strain. A number of residual hoop and axial stress profiles is presented for radius ratio 2.0. Calculated pressures are used to determine residual hoop stress values for tube diameter ratios from 1.1 to 3.0 for the full range of percentage overstrain levels. These comparisons indicate that Bauschinger effect is evident when the ratio autofrettage radius/bore radius exceeds 1.2, irrespective of diameter ratio. To assist designers the important values of residual hoop stress at the bore are summarized in a composite plot and a numerical fit is provided. The accuracy of the current ASME code using pressure criteria is assessed. The code is shown to be generally and modestly conservative. A design procedure is proposed which appears capable of extending code validity beyond 40 percent overstrain (the limit of the current code) and of eliminating the small nonconservatism at very low overstrain. Hoop strain values are calculated at both the bore and outside diameter of a tube of radius ratio 2 at the peak of the autofrettage cycle using von Mises criterion with open-end, closed-end, and plane strain conditions. These are compared with available solutions; general agreement is demonstrated, with agreement within 2 percent with an accepted simple formula in the case of open ends. ASME code predictions of percentage overstrain based upon strains at the peak of the autofrettage cycle are generally within 6 percent of numerical predictions. This is in turn produces an agreement within approximately 3 percent in residual bore hoop stress calculation. This discrepancy is generally conservative, becoming non-conservative only at overstrain levels exceeding 80 percent. Strain during removal of autofrettage pressure, in the presence of Bauschinger effect, is also calculated. This shows that the difference in strain during the unloading phase is up to 8 percent (ID) and 6.3 percent (OD) compared with the predictions of elastic unloading. These latter results show similar agreement with the ASME code as in the peak-strain analysis and permit correction of estimates of percentage overstrain based upon permanent bore enlargement.