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.

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.

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.

Universal Weight Function Consistent Method to Fit Polynomial Stress Distribution for Calculation of Stress Intensity Factor

2010 ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Wall Thickness ◽  
Function Method ◽  
Polynomial Equation ◽  
Evaluation Procedure ◽  
Weight Function Method

Procedures for analytical evaluation of flaws in nuclear pressure boundary components are provided in Section XI of the ASME B&PV Code. The flaw evaluation procedure requires calculation of the stress intensity factor. Engineering procedures to calculate the stress intensity factor are typically based on a polynomial equation to represent the stress distribution through the wall thickness, where the polynomial equation is fitted using the least squares method to discrete data point of stress through the wall thickness. However, the resultant polynomial equation is not always an optimum fit to stress distributions with large gradients or discontinuities. Application of the weight function method enables a more accurate representation of the stress distribution for the calculation of the stress intensity factor. Since engineering procedures and engineering software for flaw evaluation are typically based on the polynomial equation to represent the stress distribution, it would be desirable to incorporate the advantages of the weight function method while still retaining the framework of the polynomial equation to represent the stress distribution when calculating the stress intensity factor. A method to calculate the stress intensity factor using a polynomial equation to represent the stress distribution through the wall thickness, but which provides the same value of the stress intensity factor as is obtained using the Universal Weight Function Method, is provided in this paper.

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.

Weight Function Method With Segment-Wise Polynomial Interpolation to Calculate Stress Intensity Factors for Complicated Stress Distributions

2012 ◽  
Author(s):  
Yinsheng Li ◽  
Hiroto Itoh ◽  
Kunio Hasegawa ◽  
Steven X. Xu ◽  
Douglas A. Scarth
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Polynomial Interpolation ◽  
Distribution Area ◽  
Stress Distributions ◽  
Weight Function Method

Many solutions of the stress intensity factor have been proposed in recent years. However, most of them take only third or fourth-order polynomial stress distributions into account. For complicated stress distributions which are difficult to be represented as third or fourth-order polynomial equations over the stress distribution area such as residual stress distributions or thermal stress distributions in dissimilar materials, it is important to further improve the accuracy of the stress intensity factor. In this study, a weight function method with segment-wise polynomial interpolation is proposed to calculate solutions of the stress intensity factor for complicated stress distributions. By using this method, solutions of the stress intensity factor can be obtained without employing finite element analysis or difficult calculations. It is therefore easy to use in engineering applications. In this method, the stress distribution area is firstly divided into several segments and the stress distribution in each segment is curve fitted to segment-wise polynomial equation. The stress intensity factor is then calculated based on the weight function method and the fitted stress distribution in each segment. Some example solutions for both infinite length cracks and semi-elliptical cracks are compared with the results from finite element analysis. In conclusion, it is confirmed that this method is applicable with high accuracy to the calculation of the stress intensity factor taking actual complicated stress distributions into consideration.

Weight Function Method With Segment-Wise Polynomial Interpolation to Calculate Stress Intensity Factors for Complicated Stress Distributions

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Yinsheng Li ◽  
Kunio Hasegawa ◽  
Steven X. Xu ◽  
Douglas A. Scarth
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Polynomial Interpolation ◽  
Distribution Area ◽  
Stress Distributions ◽  
Weight Function Method

Many solutions of the stress intensity factor have been proposed in recent years. However, most of them take only third or fourth-order polynomial stress distributions into account. For complicated stress distributions which are difficult to be represented as third or fourth-order polynomial equations over the stress distribution area such as residual stress distributions or thermal stress distributions in dissimilar materials, it is important to further improve the accuracy of the stress intensity factor. In this study, a weight function method with segment-wise polynomial interpolation is proposed to calculate solutions of the stress intensity factor for complicated stress distributions. By using this method, solutions of the stress intensity factor can be obtained without employing finite element analysis or difficult calculations. It is therefore easy to use in engineering applications. In this method, the stress distribution area is firstly divided into several segments and the stress distribution in each segment is curve fitted to segment-wise polynomial equation. The stress intensity factor is then calculated based on the weight function method and the fitted stress distribution in each segment. Some example solutions for both infinite length cracks and semi-elliptical cracks are compared with the results from finite element analysis. In conclusion, it is confirmed that this method is applicable with high accuracy to the calculation of the stress intensity factor taking actual complicated stress distributions into consideration.

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.

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.

Universal Weight Function Consistent Method to Fit Polynomial Stress Distribution for Calculation of Stress Intensity Factor

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Wall Thickness ◽  
Function Method ◽  
Polynomial Equation ◽  
Evaluation Procedure ◽  
Weight Function Method

Procedures for the analytical evaluation of flaws in nuclear pressure boundary components are provided in Section XI of the ASME B&PV Code. The flaw evaluation procedure requires calculation of the stress intensity factor. Engineering procedures to calculate the stress intensity factor are typically based on a polynomial equation to represent the stress distribution through the wall thickness, where the polynomial equation is fitted using the least squares method to discrete data point of stress through the wall thickness. However, the resultant polynomial equation is not always an optimum fit to stress distributions with large gradients or discontinuities. Application of the weight function method enables a more accurate representation of the stress distribution for the calculation of the stress intensity factor. Since engineering procedures and engineering software for flaw evaluation are typically based on the polynomial equation to represent the stress distribution, it would be desirable to incorporate the advantages of the weight function method while still retaining the framework of the polynomial equation to represent the stress distribution when calculating the stress intensity factor. A method to calculate the stress intensity factor using a polynomial equation to represent the stress distribution through the wall thickness, but which provides the same value of the stress intensity factor as is obtained using the Universal Weight Function Method, is provided in this paper.

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