Linear elastic fracture mechanics based flaw evaluation procedures in Section XI of the ASME Boiler and Pressure Vessel Code require calculation of the stress intensity factor (KI). The 2015 Edition of ASME Section XI  implemented a number of significant improvements in Article A-3000, including closed-form equations for calculating stress intensity factor influence coefficients (Gi) for circumferential flaws on the inside surface of cylinders. In the 2017 Edition , closed-form equations for axial flaws on the inside and outside surfaces of cylinders have been implemented.
In this paper, closed-form equations are developed for circumferential cracks on the OD surface of cylinders, based on tabular data from API 579 (2007 Edition) . The equations presented, represent a complete set of Ri/t, a/t, and a/ℓ ratios. 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 the applied stress. 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.