Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

Abstract

Analytical evaluation procedures for determining the acceptability of flaws detected during in-service inspection of nuclear power plant components are provided in Section XI of the ASME Boiler and Pressure Vessel Code. Linear elastic fracture mechanics based evaluation procedures in ASME Section XI require calculation of the stress intensity factor. In Article A-3000 of Appendix A of the 2013 Edition of ASME Section XI, the calculation of stress intensity factor for a surface crack is based on characterization of stress field with a cubic equation and use of stress intensity factor influence coefficients. The influence coefficients are only provided for a flat plate geometry. The ASME Section XI Working Group on Flaw Evaluation is in the process of rewriting Article A-3000 of Appendix A. Major updates include the implementation of an alternate method for calculation of the stress intensity factor for a surface flaw that makes explicit use of the Universal Weight Function Method and does not require a polynomial fit to the actual stress distribution, and the inclusion of stress intensity factor influence coefficients for the cylinder geometry. Tabular data of influence coefficients for the cylinder geometry are available in API 579-1/ASME FFS-1 2007. Effort has been made to develop closed-form relations for the stress intensity factor influence coefficients for the cylinder geometry based on API data. With the inclusion of the explicit weight function approach and the closed-form relations for influence coefficients, the procedures of Appendix A for the calculation of stress intensity factors can be used more efficiently. The development of closed-form relations for stress intensity factor influence coefficients for axial ID surface flaws in cylinders is described in this paper.

Data-Driven Stress Intensity Factor Solutions for Axial Outside Surface Cracks in Thick-Wall Cylinders

“…This paper briefly reviewed the tabular data of the stress intensity factor given in API 579 for axial semi-elliptical surface cracks in pressurized cylinders and the corresponding curve-fit closed-form solutions of the influence coefficients G0 and G1 of the stress intensity factor that were obtained by Xu et al [16,17] at the deepest and surface points. It was found that the closedform solutions of G0 and G1 are only applicable to the API selected cylinder sizes.…”

“…Noted that Xue et al [16,17] obtained the curve-fit closedform solutions of the influence coefficients G0 and G1 of the K factor for both axial inside and outside semi-elliptical surface cracks in pressurized cylinders, and sooner those closed-form solutions of K were adopted by ASME BPVC Section XI [2] in its 2021 version. Even so, the closed-from solutions of G0 and G1 can be only used in the ECA for the API selected cylinder sizes, i.e., Ri/t=1, 3, 5, 10, 20, 60 and 100.…”

“…Thus, a closed-form solution of stress intensity factor was desired for engineering application. Accordingly, based on the tabular data of the K factor given in API 579, Xue et al [16,17] employed the nonlinear regression method, and obtained a set of curve-fit solutions of the influence coefficients G0 and G1 for axial inside and outside semi-elliptical surface cracks for the API selected cylinder sizes. Those closed-form solutions of the K factor are applicable to any crack sizes for API selected cylinder sizes, but interpolations are still needed for other cylinder sizes with an arbitrary Ri/t ratio.…”

Data-Driven Stress Intensity Factor Solutions for Axial Outside Surface Cracks in Thin-Walled Cylinders

“…The tabular data of the K factor in API 579 [1] have been obtained extensive applications in the FFS evaluation of pressure vessels. For convenient use of the API tabular data, Xu et al [10,11] employed the nonlinear regression method and obtained a set of curve-fit closed-from solutions of the influence coefficients G0 and G1 for axial inside and outside semi-elliptical surface cracks at the deepest and surface points for the API selected cylinder sizes. For other cylinder sizes, however, three-parameter interpolations are still needed to determine the G0 and G1 values.…”

Fatigue Life Models for Pipelines Containing Dents and Gouges

“…Thus, a closed-form solution of stress intensity factors was desired for practical applications. Accordingly, based on the tabular data of the K factor given in API 579, Xue et al [42,43] employed the nonlinear regression method, and obtained a series of curve-fitting solutions of the influence coefficients G0 and G1 for axial inside and outside semi-elliptical surface cracks for each API selected cylinder size. The closed-form solutions of the K factors are applicable to any crack size for the API selected cylinder sizes, but an interpolation is still needed for other cylinder sizes with an arbitrary Ri/t ratio.…”