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Design and Analysis

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

[+] Author and Article Information
Steven X. Xu

Kinectrics, Inc.,
800 Kipling Avenue, Unit 2,
Toronto, ON, M8Z 5G5, Canada

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received December 19, 2010; final manuscript received February 16, 2012; published online October 18, 2012. Assoc. Editor: Somnath Chattopdhyay.

J. Pressure Vessel Technol 134(6), 061204 (Oct 18, 2012) (11 pages) doi:10.1115/1.4006557 History: Received December 19, 2010; Revised February 16, 2012

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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Figures

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Fig. 1

Axial part-through-wall planar flaw in a cylinder

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Fig. 2

Circumferential part-through-wall planar flaw in a cylinder

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Fig. 3

Stress distribution acting over the crack depth

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Fig. 4

Fourth-order polynomial representation of stress distribution equation (58) with a/t = 0.2 using the universal weight function consistent method and the least squares method

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Fig. 5

Cubic polynomial representation of stress distribution equation (58) with a/t = 0.2 using the universal weight function consistent method and the least squares method

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Fig. 6

Finite element crack-tip mesh for a cylinder with an internal circumferential surface flaw of semi-elliptical shape with a/t =0.5, a/c = 0.2

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Fig. 7

Fourth-order polynomial representation of stress distribution equation (59) with a/t = 0.2 using the universal weight function consistent method and the least squares method

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Fig. 8

Fourth-order polynomial representation of stress distribution equation (59) with a/t = 0.5 using the universal weight function consistent method and the least squares method

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