Autofrettage of open-end tubes - Pressures, stresses, strains, and code comparisons

Autofrettage is used to introduce advantageous residual stresses into press ure vessels. The Bauschinger effect can produce less compressive residual h oop stresses near the bore than are predicted by "ideal'' autofrettage solu tions. A recently developed numerical analysis procedure is adopted and ext ended. The ratio of calculated autofrettage pressure (numerical)/ideal auto frettage pressure (Tresca criterion and plane stress) is calculated and ver ified against available solutions. The case of open-end conditions based up on von Mises and engineering plane strain (constant axial strain with zero net axial force) is examined in detail. The ratio in this case varies betwe en unity, and 2/root3, but exhibits ver-v significant variations from the p lane stress case when the diameter ratio of the tube exceeds 1.8. Results a re within 0.5 percent of available analytical, numerical, and experimental results. A simple numerical fit allows all autofrettage pressures to be rep licated to within 0.5 percent. The true plane strain pressure ratio is exam ined and shown to be inappropriate in modeling engineering plane strain. A number of residual hoop and a-vial 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 perce ntage overstrain levels. These comparisons indicate that Bauschinger effect is evident when the ratio autofrettage radius/bore radius exceeds 1.2, irr espective of diameter ratio. To assist designers the important values of re sidual hoop stress at the bore are summarized in a composite plot and a num erical fit is provided. The accuracy of the current ASME code rising pressu re criteria is assessed. The code is shown to be generally and modestly con servative. A design procedure is proposed which appears capable of extendin g 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 tu be of radius ratio 2 at the peak of the autofrettage cycle rising von Mises criterion with open-end, closed-end, and plane strain conditions. These ar e compared with available solutions; general agreement is demonstrated, wit h agreement within 2 percent with an accepted simple formula in the case of open ends. ASME code predictions of percentage overstrain based upon strai ns at the peak of the autofrettage cycle are generally within 6 percent of numerical predictions. This is in turn produces an agreement within approxi mately 3 percent in residual bore hoop stress calculation. This discrepancy is generally conservative, becoming nonconservative only at overstrain lev els exceeding 80 percent. Strain during removal of autofrettage pressure, i n the presence of Bauschinger effect, is also calculated. This shows that t he 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. Th ese latter results show similar agreement with the ASME code as in the peak -strain analysis and permit correction of estimates of percentage overstrai n based upon permanent bore enlargement.