Limit moment of local wall thinning in pipe under bendingLiang-hao Hana,*, Shu-yan Hea, Ying-pei Wangb, Ceng-dian Liub

aCAD, Institute of Nuclear Energy Technology, Tsinghua University, Beijing 100084, Peoples Republic of ChinabEast-China University of Science and Technology, Shanghai 200237, Peoples Republic of China

Received 5 February 1999; accepted 15 February 1999

Abstract

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipesurface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is veryimportant to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wallthinning pipe under pure bending is computed employing 3D elasticplastic finite element analysis. The results show that the limit momentof pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defectoverpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results fromfinite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wallthinning pipe under bending. q 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Limit moment; Local wall thinning; Pipe

Nomenclatureu half angle of local wall thinningb half neutral angleRo outer radius of pipeRi inner radius of pipeRm meaning radius of pipet pipe wall thicknessd depth of local wall thinningh (t 2 d)/tL longitudinal length of local wall thinningsf flow stressP axial loadM limit momentM0 limit moment of plain pipe

1. Introduction

Local wall thinning is a very common volume defect inpipe and pressure vessel, which can result from corrosionand mechanical damage. Local wall thinning impairs theload-carrying capacity of pipe. Current researches on localwall thinning mainly focus on pipe under internal pressure.

These researches have led to the development of analyticalmethods [1,2] for evaluating the remaining strength of pipewith local wall thinning. Amongst these methods, the mostwidely accepted method is ASME/B31.G [1], but it can onlybe used to evaluate corroded pipe under pressure, it cannotbe used for evaluating pipe under bending and axial load.However, in engineering practice, pipe especially oil andgas transmission, can be subjected to bending and axialloads. So it is very important to develop a method to eval-uate the effect of local wall thinning on the integrity of thepipe under bending and axial load.

In this article, the limit moment of local wall thinningpipe is analyzed employing finite element method, theresults from finite element analysis are compared with theresults from net-section collapse (NSC) criterion [4,5].

2. Limit load analysis based on NSC criterion

Net-section collapse failure (NSC) criterion, proposed byKanninen et al. [4], has interpreted pipe leak and break loadsas indicating critical net-stresses at crack initiation andmaximum load. In a way similar to Kanninens, the NSCcriterion is used to analyze the failure of a pipe with localwall thinning under bending by assuming a uniform bend-ing-stress distribution in this article (Fig. 1). When the pipereaches collapse failure the net-section stress of structureequals the flow stress sf .

International Journal of Pressure Vessels and Piping 76 (1999) 539542

0308-0161/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved.PII: S0308-0161(99)00031-9

* Corresponding author. Tel.: 1 86-10-6278-4809; fax: 1 86-10-6277-1150.

E-mail address: lhaohan@263.net (L.-H. Han)

For the sake of conservative estimation, local wall thin-ning is located such that the center of its projection ondiameter plane coincides with the plane of maximum bend-ing moment. From the equilibrium of axial force and ofbending moments, the limit load of pipe with local wallthinning was determined. For simplicity, one may assumethat pipe is a thin-walled cylinder, that is, t=Rp 1; underthis assumption, one of the parameters, t=R, is eliminatedfrom the analysis. The limit moment is readily written asfollows:

u 1 b , p

b p2

1 21 2 hu

p2

P2pRmts0

1

M < 2s0R2mt{2sinb 2 1 2 hsinu} 2

u 1 b . p

b