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.
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.
Article A-3000 of Appendix A in Section XI of the ASME Boiler and Pressure Vessel Code provides linear elastic fracture mechanics based calculation procedures for the determination of stress intensity factors. The 2015 Edition of ASME Section XI implements a number of significant improvements in Article A-3000. Major improvements 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 closed-form equations for stress intensity factor influence coefficients for circumferential ID surface cracks. 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. Closed-form equations for stress intensity factor influence coefficients for axial ID surface cracks have been under development. Tabular data of influence coefficients for the cylinder geometry provided in API 579-1/ASME FFS-1 2007 are used as data source. A set of closed-formed equations for an axial semi-elliptical ID surface crack with depth a and length 2c in a cylinder were previously reported in a 2014 PVP paper. The smallest value for a/c is 0.03125 in the tabular data that were used to fit the equations. For practical applications, it is desirable to use axial flaw equations that allow a/c to approach zero without extrapolation. This issue is addressed in the current PVP paper.
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. 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 implements a number of significant improvements in Article A-3000. Major improvements 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 closed-form equations for stress intensity factor influence coefficients for cylinder geometries. 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. A review of improvements that have been implemented in Article A-3000 of Appendix A in the 2015 Edition of ASME Section XI is provided in this paper. Example calculations are provided for illustration purpose.
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.
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