Improvements in Article A-3000 of Appendix A for Calculation of Stress Intensity Factor in Section XI of the 2015 Edition of ASME Boiler and Pressure Vessel Code

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Steven X. Xu ◽  
Russell C. Cipolla ◽  
Darrell R. Lee ◽  
Douglas A. Scarth
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Pressure Vessel ◽  
Nuclear Power ◽  
Evaluation Procedures ◽  
Influence Coefficients

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.

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

2014 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Nuclear Power ◽  
Cubic Equation ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Surface Flaws

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.

Technical Basis for Proposed Weight Function Method for Calculation of Stress Intensity Factor for Surface Flaws in ASME Section XI Appendix A

2011 ◽  
Author(s):  
Steven X. Xu ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Flaw Location ◽  
Technical Basis

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. A method for calculating the stress intensity factor is provided in Appendix A of ASME Section XI. This method consists of a two-step process. In the first step, the stress distribution, as calculated in the absence of the flaw, is obtained at the flaw location. For a surface flaw, the stress distribution at the flaw location is then fitted to a third-order polynomial equation. In the second step, the fitted polynomial representation of the stress distribution is used with standardized influence coefficients to calculate the stress intensity factor. 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 is proposed in this paper for implementation into Appendix A of ASME Section XI. Universal Weight Function coefficients are determined from standardized influence coefficients through closed-form equations. Closed-form equations for calculation of the stress intensity factor are provided. The technical basis and verification for this alternate method for calculation of the stress intensity factor are described in this paper.

Technical Basis for Application of Weight Function Method for Calculation of Stress Intensity Factor for Surface Flaws Proposed for ASME Section XI Appendix A

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Steven X. Xu ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Flaw Location ◽  
Technical Basis

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. A method for calculating the stress intensity factor is provided in Appendix A of ASME Section XI. This method consists of a two-step process. In the first step, the stress distribution, as calculated in the absence of the flaw, is obtained at the flaw location. For a surface flaw, the stress distribution at the flaw location is then fitted to a third-order polynomial equation. In the second step, the fitted polynomial representation of the stress distribution is used with standardized influence coefficients to calculate the stress intensity factor. 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 is proposed in this paper for implementation into Appendix A of ASME Section XI. Universal weight function coefficients are determined from standardized influence coefficients through closed-form equations. Closed-form equations for calculation of the stress intensity factor are provided. The technical basis and verification for this alternate method for calculation of the stress intensity factor are described in this paper.

Comparison of the Stress Intensity Factor Influence Coefficients for Axial ID Surface Cracks in Cylinders of RSE-M and API 579-1

2015 ◽  
Author(s):  
Patrick Le Delliou ◽  
Stéphane Chapuliot
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Crack Depth ◽  
Wall Stress ◽  
Surface Point ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Wide Range

Analytical evaluation procedures for determining the acceptability of flaw detected during in-service inspection of nuclear power plant components are provided in Appendix 5.4 of the French RSE-M Code. Linear elastic fracture mechanics based evaluation procedures require calculation of the stress intensity factor (SIF). In Appendix 5.4 of the RSE-M Code, influence coefficients needed to compute the SIF are provided for a wide range of surface axial or circumferential flaws in cylinders, the through-wall stress field being represented by a cubic equation. On the other hand, Appendix C of API 579-1 FFS procedure provides also a very complete set of influence coefficients. The paper presents the comparison of the influence coefficients from both documents, focused on axial ID semi-elliptical surface flaws in cylinders. The cylinder and crack geometries are represented by three ratios: Ri/t, a/t, and a/c, where Ri, t, a, and c are respectively the inner radius, the wall thickness, the crack depth and one-half of the crack length. The solutions for the coefficients G0 and G1 at the deepest point and at the surface point are investigated. At the deepest point, the agreement between the solutions is good, the relative difference being lower than 2 %, except for the plate (Ri/t = ∞) at a/c = 0.125 and 0.0625 and a/t = 0.8 (around 5 %). At the surface point, the agreement between both solutions is not so good. At this point, the relative differences depend strongly on the a/c ratio, being larger for elongated cracks (with low a/c ratios). However, it must be recalled that the absolute values of the coefficients are low at the surface point for elongated cracks, and that for these cracks the critical point regarding the stress intensity factor is the deepest point.

Closed-Form Calculation of Stress Intensity Factor for an Axial ID Surface Flaw in Cylinder Subjected to Weld Residual Stresses

2013 ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Function Method ◽  
Current Method ◽  
Surface Flaw ◽  
Weight Function Method ◽  
Influence Coefficients

A method for calculating the stress intensity factor for linear elastic fracture mechanics based flaw evaluation is provided in Appendix A-3000 of ASME Section XI. In the 2010 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 influence coefficients. The influence coefficients are currently only provided for flat plate geometry in tabular format. The ASME Section XI Working Group on Flaw Evaluation is in the process of rewriting Appendix A-3000. Proposed major updates include the implementation of explicit use of Universal Weight Function Method for calculation of the stress intensity factor for a surface flaw and the inclusion of closed-form influence coefficients for cylinder geometry. The explicit use of weight function method eliminates the need for fitting polynomial equations to the actual through-thickness stress distributions at crack location. In this paper, the proposed Appendix A procedure is applied to calculate the stress intensity factors in closed-form for an axial ID surface flaw in a cylinder subjected to a set of nonlinear hoop weld residual stress profiles. The calculated stress intensity factor results are compared with the results calculated based on the current method in Appendix A using cubic equations to represent the stress distribution. Three-dimensional finite element analyses were performed to verify the accuracy of the stress intensity factor results calculated based on the current and proposed Appendix A procedures. The results in this paper support the implementation of the proposed stress intensity factor calculation procedure into ASME Code.

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

2016 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Inside Surface ◽  
Linear Elastic ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Elastic Fracture ◽  
Flaw Location

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.

Investigation of Calculating Stress Intensity Factor at Surface Point and its Inclusion in Engineering Standards

2018 ◽  
Author(s):  
Steven X. Xu ◽  
Greg Thorwald ◽  
Patrick Le Delliou ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Working Group ◽  
Surface Point ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Engineering Standards ◽  
Point G

Article A-3000 of Appendix A in ASME Section XI provides methods to calculate stress intensity factors that are used in Section XI linear elastic fracture mechanics based flaw evaluation procedures. The ASME Section XI Working Group on Flaw Evaluation has been in the process of rewriting Article A-3000 of Appendix A. The rewrite of Article A-3000 includes implementation of closed-form equations for stress intensity factor influence coefficients for cylinder geometries. Closed-form relations for stress influence coefficients G0 and G1 for axial flaws on the outside surface in cylinders were recently developed and implemented into the 2017 Edition of ASME Section XI Appendix A. The closed-form equations were implemented with one restriction on the application related to very long flaws. This restriction was taken as an interim approach to addressing a technical concern from the US NRC staff. NRC staff had technical concern on the large percentage fitting errors for the G1 influence coefficients at surface point for some very long flaws. An action was assigned within the ASME Section XI Working Group on Flaw Evaluation to investigate the accuracy of surface point G values for very long flaws. The intent of the investigation is to provide technical justification for using the closed-form equations with no restriction and to identify any issues in the source data or during the fitting process. This paper describes current results from this ongoing investigation.

Calculation of Stress Intensity Factor for Surface Flaws Using Universal Weight Functions With Piece-Wise Cubic Stress Interpolation

2012 ◽  
Author(s):  
Steven X. Xu ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Function Method ◽  
Linear Interpolation ◽  
Surface Flaw ◽  
Weight Function Method

Linear elastic fracture mechanics based flaw evaluation procedures in ASME Section XI require calculation of the stress intensity factor. The method to calculate the stress intensity factor that is provided in the 2010 Edition of Appendix A of ASME Section XI is to fit the stress distribution ahead of the crack tip to a polynomial equation, and then use standardized influence coefficients. In PVP2011-57911, 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 was proposed for implementation into Appendix A of Section XI. The alternate method provides closed-form solutions for the stress intensity factor. A numerical approximation is the assumed piece-wise linear variation of stress between discrete locations where stresses are known. For highly nonlinear stress distributions, piece-wise cubic interpolation of stress over intervals between discrete locations where stresses are known is an improvement over piece-wise linear interpolation. Investigation of a cubic interpolation of stress between discrete locations where stresses are known has been conducted. Closed-form equations for calculation of the stress intensity factor for a surface flaw were developed using the Universal Weight Function Method and generic piece-wise cubic interpolation of stress over intervals. Example calculations are provided to compare the results of stress intensity factors using piece-wise cubic interpolation with piece-wise linear interpolation.

Update on Stress Intensity Factor Influence Coefficients for Axial ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2015 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Stress Intensity Factors ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Tabular Data ◽  
Influence Coefficients

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.

Stress Intensity Factor Coefficients for Circumferential OD Surface Flaws in Cylinders for Appendix A of ASME Section XI

2018 ◽  
Author(s):  
Darrell R. Lee ◽  
Russell C. Cipolla ◽  
Michael C. Liu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Fourth Order ◽  
Stress Distributions ◽  
Linear Elastic ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Weld Residual Stress

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 [1] 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 [2], 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) [3]. 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.

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