Stress intensity factor evaluation of a circumferential crack in a finite length thin-walled cylinder for arbitrarily distributed stress on crack surface by weight function method

Propagation of a critical unstable crack under the action of static or varying stresses is determined by the intensity of strain field at tips of the crack. Stress intensity factor (SIF) is an important parameter in fracture mechanics, which is used as a criterion to judge the unstable propagation of a crack and plays an important role in calculating crack propagation life. SIF is related to both geometrical form and loading condition of a structure. In the paper, a weight function method is introduced to study crack propagation of center through cracks and edge cracks in a finite-size plate. In addition, finite element method, linear regression, and polynomial interpolating technique are used to simulate and verify the proposed method. Comparison studies among the proposed and current methods are performed as well. The results show that the weight function method can be used to calculate SIF easily.

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

ASME 2010 Pressure Vessels and Piping Conference: Volume 1 ◽

10.1115/pvp2010-25728 ◽

2010 ◽

Cited By ~ 1

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.

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

Volume 1A: Codes and Standards ◽

10.1115/pvp2013-97522 ◽

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.

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

Volume 1: Codes and Standards ◽

10.1115/pvp2012-78719 ◽

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.

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

Journal of Pressure Vessel Technology ◽

10.1115/1.4025816 ◽

2014 ◽

Vol 136 (2) ◽

Cited By ~ 1

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.

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