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

Abstract

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. Article A-3000 of Appendix A in ASME Section XI prescribes a method to calculate the stress intensity factor for a surface or subsurface flaw by making use of the flaw location stress distribution obtained in the absence of the flaw. 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 for circumferential flaws on the inside surface of cylinders. Closed-form equations for stress intensity factor influence coefficients for axial flaws on the inside surface of cylinders have also been developed. Ongoing improvement efforts for Article A-3000 include development of closed-form relations for the stress intensity factor coefficients for flaws on the outside surface of cylinders. The development of closed-form relations for stress intensity factor coefficients for axial flaws on the outside surface of cylinders is described in this paper.

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

“…The machine learning method utilizes an artificial neural network (ANN), activation function and optimal learning algorithm to learn and to determine a general solution of K as a function of the cylinder size (t/Ri), aspect ratio (a/c), and crack depth (a/t) for an axial outside surface crack at its deepest and surface points. The proposed data-driven solutions of G0 and G1 for the axial outside surface cracks are validated by the curvefit solutions obtained by Xu et al [17].…”

“…For very long or infinite axial surface cracks, a/c0, the surface crack becomes a regular one-dimensional crack that is described by the crack depth only. From the tabular data of G0 and G1 that covers the Ri/t ratio of 1 to 1000 and the a/t ratio of 0 to 0.8, Xue et al [17] obtained the curve-fit solutions of G0 and G1 as a function of a/t and Ri/t with a high accuracy. This paper will not further consider these kinds of simple cracks.…”

“…For an analysis of crack initiation, growth, or failure, the ECA analysis only focuses on the deepest and surface points, and the new semi-elliptical surface crack shape will be determined by the crack increments estimated at these two points. As a result, Xue et al [17] determined the best curve fit of closed-form relation of G1 and G2 from the tabular data at those two points. For ASME Section XI applications, crack depth does not exceed one half of the crack length, i.e., a/c ≤ 1, and thus Xue et al [17] utilized API tabular data within these aspect ratios in their curve fitting.…”

“…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.…”

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.…”