Closed Form Solutions for Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders in ASME Section XI Appendix A

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is pursued and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. It is expected that the equations developed in this paper will be added to the Appendix A procedures. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful in performing flaw growth calculations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.