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Research Papers: Design and Analysis

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

[+] Author and Article Information
Yinsheng Li

Japan Nuclear Energy Safety Organization,
Toranomon 4-1-28, Minato-ku,
Tokyo 105-0001, Japan
e-mail: li-yinsheng@jnes.go.jp

Kunio Hasegawa

Japan Nuclear Energy Safety Organization,
Toranomon 4-1-28, Minato-ku,
Tokyo 105-0001, Japan
e-mail: hasegawa-kunio@jnes.go.jp

Steven X. Xu

Kinectrics, Inc.,
800 Kipling Avenue,
Unit 2 Toronto, ON M8Z 5G5 Canada
e-mail: Steven.XU@kinectrics.com

Douglas A. Scarth

Kinectrics, Inc.,
800 Kipling Avenue,
Unit 2 Toronto, ON M8Z 5G5 Canada
e-mail: Doug.Scarth@kinectrics.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received December 7, 2012; final manuscript received October 6, 2013; published online January 7, 2014. Assoc. Editor: Wolf Reinhardt.

J. Pressure Vessel Technol 136(2), 021202 (Jan 07, 2014) (10 pages) Paper No: PVT-12-1189; doi: 10.1115/1.4025816 History: Received December 07, 2012; Revised October 06, 2013

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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Figures

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Fig. 1

A semi-elliptical surface crack in a plate

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Fig. 2

Concept of the weight function method with segment-wise polynomial interpolation

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Fig. 3

Concept of segment division according to features of stress distributions

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Fig. 4

Axisymmetrical analysis model of a cylinder with a 360 deg. crack at the inner surface

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Fig. 5

Example of axisymmetrical analysis mesh of a cylinder with a 360 deg. inner surface crack with a/t = 0.6

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Fig. 6

Residual stresses used in this study

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Fig. 7

Segment divisions for the three residual stresses

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Fig. 8

Solutions of K for the three residual stress cases

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Fig. 9

Solutions of K using different approaches to segment division and curve fitting

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Fig. 10

Analysis model of a plate with a semi-elliptical surface crack

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Fig. 11

Singular element used at the crack tip

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Fig. 12

Example FEA mesh near the crack for a/l = 0.5 and a/t = 0.8

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Fig. 13

Solutions of K for semi-elliptical surface crack in the three residual stress cases

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