September, 2011

Vol.10, No. 3

Journal of Pipeline Engineering

Sa no m t f ple or c di op st y rib ut io n

incorporating The Journal of Pipeline Integrity

Great Southern Press

Clarion Technical Publishers

Journal of Pipeline Engineering Editorial Board - 2011

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Obiechina Akpachiogu, Cost Engineering Coordinator, Addax Petroleum Development Nigeria, Lagos, Nigeria Dr Husain Al-Muslim, Pipeline Engineer, Consulting Services Department, Saudi Aramco, Dhahran, Saudi Arabia Mohd Nazmi Ali Napiah, Pipeline Engineer, Petronas Gas, Segamat, Malaysia Dr Michael Beller, NDT Systems & Services AG, Stutensee, Germany Jorge Bonnetto, Operations Director TGS (retired), TGS, Buenos Aires, Argentina Dr Andrew Cosham, Atkins Boreas, Newcastle upon Tyne, UK Dr Sreekanta Das, Associate Professor, Department of Civil and Environmental Engineering, University of Windsor, ON, Canada Prof. Rudi Denys, Universiteit Gent – Laboratory Soete, Gent, Belgium Leigh Fletcher, Welding and Pipeline Integrity, Bright, Australia Roger Gomez Boland, Sub-Gerente Control, Transierra SA, Santa Cruz de la Sierra, Bolivia Daniel Hamburger, Pipeline Maintenance Manager, El Paso Eastern Pipelines, Birmingham, AL, USA Prof. Phil Hopkins, Executive Director, Penspen Ltd, Newcastle upon Tyne, UK Michael Istre, Engineering Supervisor, Project Consulting Services, Houston, TX, USA Dr Shawn Kenny, Memorial University of Newfoundland – Faculty of Engineering and Applied Science, St John’s, Canada Dr Gerhard Knauf, Salzgitter Mannesmann Forschung GmbH, Duisburg, Germany Prof. Andrew Palmer, Dept of Civil Engineering – National University of Singapore, Singapore Prof. Dimitri Pavlou, Professor of Mechanical Engineering, Technological Institute of Halkida , Halkida, Greece Dr Julia Race, School of Marine Sciences – University of Newcastle, Newcastle upon Tyne, UK Dr John Smart, John Smart & Associates, Houston, TX, USA Jan Spiekhout, Kema Gas Consulting & Services, Groningen, Netherlands Dr Nobuhisa Suzuki, JFE R&D Corporation, Kawasaki, Japan Prof. Sviatoslav Timashev, Russian Academy of Sciences – Science & Engineering Centre, Ekaterinburg, Russia Patrick Vieth, Senior Pipeline Engineer - Pipelines & Civil Engineering, BP America, Houston, TX, USA Dr Joe Zhou, Technology Leader, TransCanada PipeLines Ltd, Calgary, Canada Dr Xian-Kui Zhu, Senior Research Scientist, Battelle Pipeline Technology Center, Columbus, OH, USA

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The Journal of Pipeline Engineering incorporating

The Journal of Pipeline Integrity Volume 10, No 3 • Third Quarter, 2011

Contents

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Gianluca Mannucci and Giuseppe Demofonti ..................................................................................................... 133 Control of ductile facture propagation in X80 gas linepipe



Prof. Guy Pluvinage, Dr Mustapha Allouti, Dr Christian Schmitt, and Dr Julien Capelle . ..............................147 Assessment of a gouge, a dent, or a dent plus a gouge, in a pipe using limit analysis or notch fracture mechanics Dr Alfred M Pettinger and David W Sykora ...........................................................................................................161 Landslide risk assessment for pipeline systems in mountainous regions Hossein Abolghasem, Kaveh Arjomandi, and Dr Farid Taheri...............................................................................173 An effective optimization approach for designing cost-effective and reliable sandwich pipes for use in deep and ultra-deep water Antoon A Lefevre, Maurits Waaijenberg, Elliot Aylwin, and Hennie M Triel.......................................................181 Defect propagation from fatigue loading in 13%Cr pipelines

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OUR COVER PICTURE shows construction work under way on the Camisea pipeline across the Andes in Peru in 2003. Aspects of this project are discussed in the paper on pages 161-171.

The Journal of Pipeline Engineering has been accepted by the Scopus Content Selection & Advisory Board (CSAB) to be part of the SciVerse Scopus database and index.

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HE Journal of Pipeline Engineering (incorporating the Journal of Pipeline Integrity) is an independent, international, quarterly journal, devoted to the subject of promoting the science of pipeline engineering – and maintaining and improving pipeline integrity – for oil, gas, and products pipelines. The editorial content is original papers on all aspects of the subject. Papers sent to the Journal should not be submitted elsewhere while under editorial consideration. Authors wishing to submit papers should do so online at www.j-pipeng.com. The Journal of Pipeline Engineering now uses the ScholarOne manuscript management system for accepting and processing manuscripts, peer-reviewing, and informing authors of comments and manuscript acceptance. Please follow the link shown on the Journal’s site to submit your paper into this system: the necessary instructions can be found on the User Tutorials page where there is an Author's Quick Start Guide. Manuscript files can be uploaded in text or PDF format, with graphics either embedded or separate. Please contact the editor (see below) if you require any assistance.

The Journal of Pipeline Engineering aims to publish papers of quality within six months of manuscript acceptance.

Notes 4. Back issues: Single issues from current and past volumes are available for US$87.50 per copy.

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1. Disclaimer: While every effort is made to check the accuracy of the contributions published in The Journal of Pipeline Engineering, Great Southern Press Ltd and Clarion Technical Publishers do not accept responsibility for the views expressed which, although made in good faith, are those of the authors alone.

5. Publisher: The Journal of Pipeline Engineering is published by Great Southern Press Ltd (UK and Australia) and Clarion Technical Publishers (USA):

2. Copyright and photocopying: © 2011 Great Southern Press Ltd and Clarion Technical Publishers. All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without the prior permission in writing from the copyright holder. Authorization to photocopy items for internal and personal use is granted by the copyright holder for libraries and other users registered with their local reproduction rights organization. This consent does not extend to other kinds of copying such as copying for general distribution, for advertising and promotional purposes, for creating new collective works, or for resale. Special requests should be addressed to Great Southern Press Ltd, PO Box 21, Beaconsfield HP9 1NS, UK, or to the editor. 3. Information for subscribers: The Journal of Pipeline Engineering (incorporating the Journal of Pipeline Integrity) is published four times each year. The subscription price for 2011 is US$350 per year (inc. airmail postage). Members of the Professional Institute of Pipeline Engineers can subscribe for the special rate of US$175/year (inc. airmail postage). Subscribers receive free on-line access to all issues of the Journal during the period of their subscription.

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Editor: John Tiratsoo • email: [email protected] Clarion Technical Publishers, 3401 Louisiana, Suite 255, Houston TX 77002, USA • tel: +1 713 521 5929 • fax: +1 713 521 9255 • web: www.clarion.org Associate publisher: BJ Lowe • email: [email protected]

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Editorial The SciVerse Scopus database and the JPE

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• document download manager to easily download and organize multiple full-text articles simultaneously; • interoperability with other Scopus databases; • data export via bibiliographic managers such as RefWorks, EndNote and BibTeX. The database has been designed to help researchers and librarians to overcome many of the difficulties they have faced to date in easily accessing research and other published information. As Elesevier points out, researchers and others using the database can:

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E ARE DELIGHTED to announce that the Journal of Pipeline Engineering has been accepted into the SciVerse Scopus database. Launched in November, 2004, this is the largest abstract and citation database world-wide, and contains both peer-reviewed research literature and high-quality web sources. With over 18,000 peer-reviewed journals from more than 5,000 international publishers, the database is widely referenced as offering researchers and librarians a rapid, easy, and comprehensive way of supporting their research needs in the scientific, technical, medical, and social sciences fields; the coverage has recently been extended to include the arts and humanities. To be considered for inclusion in the database, journals and other publications are required to meet the following main eligibility criteria:

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We are pleased that the Journal of Pipeline Engineering has been seen by the Content Selection and Advisory Board to meet these criteria. The major Netherlands-based publishing company Elsevier, who manages SciVerse Scopus, says that the features and functionality of the database have been designed to support and improve researchers’ workflow, including: • a simple interface, which is also available on iPhones and similar handsets; • linking to full-text articles and other library resources; • author identifier to automatically match an author’s published research; • citation tracker to find, check, and track citations in real time; • affiliation identifier to automatically identify and match an organization with all its research output; • journal analyser to provide a quick insight into journal performance; • alerts, RSS, and HTML feeds to stay up-to-date;

• find out who is citing whom, and how many citations an article or an author has received; • analyse citations for a particular journal issue, volume, or year; • use this information to complete grant or other applications quickly and easily; • use the ‘refine results’ overview to quickly see the main journals, disciplines, and authors that publish in specific areas of interest; • uncover important and relevant articles that may otherwise have been missed; • check out the work and citations of other authors; • follow the ‘cited by’ and ‘reference’ links to track research trends and make connections.

As can be understood from the above, the database is hugely extensive, and integrating the Journal of Pipeline Engineering’s published content into it will take a little while longer. However, this process is under way, and we hope that by the end of this year all the papers that the Journal has published will be visible via SciVerse Sciopus, to the benefit of the contributors and to the wider pipelineengineering industry alike.

Third-party pips mechanical damage to the post THE annually-published report by CONCAWE on the Performance of European cross-country oil pipelines once again highlights the fact that third-party activities remain the main case of spillage incidents, although an increase in mechanical failures has been seen in recent years. The report is based on confidential input from over 70 oil pipeline companies in Europe, and annually provides a useful indicator of trends. For 39 years the association has Continued on inside back cover.

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Prague, 11–14 October, 2011 The Radisson Blu Hotel, Prague, Czech Republic

Courses





Conference





Exhibition

The PPIM Conference is recognized as the foremost international forum for sharing and learning about best practices in lifetime maintenance and condition-monitoring technology for natural gas, crude oil and product pipelines.

Plan to be there: www.clarion.org or call us at +1 713 521 5929

The international gathering of the global pigging industry!

Conference Organizers

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Control of ductile facture propagation in X80 gas linepipe by Gianluca Mannucci* and Giuseppe Demofonti Centro Sviluppo Materiali SpA, Rome, Italy

T

HE NEED TO CONVEY large quantity of gas from reservoirs located in remote areas to the consuming markets is pushing the development of a significant number of new long-distance high-pressure gastransmission pipelines. In order to be cost effective, these lines should be operated at high pressure (>10MPa) and constructed using large-diameter, high-grade steel linepipe such as API 5L X80 or greater. In addition, it is expected that these lines will convey rich gases – that is, gases rich in heavier components – as well as having to cross remote areas characterized by significant environmental constraints such as very low operating temperature.

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Ductile-fracture propagation control for these new lines is of primary importance, since a failure could cause a long and costly gas delivery service breakdown.The envisaged operating conditions (high grade, large diameter, high pressure, rich gas, low temperature) are such that the determination of minimum toughness requirements for arresting a propagating fracture is not a trivial issue. The paper presents the state-of-the-art about ductile-fracture control for X80 linepipe, looking at the available predictive methods, standards’ provisions, and the published full-scale burst-test database; it also mentions specific aspects such as the influence of separation on the fracture surface and the difference between the behaviours of spiral- and longitudinal-welded pipes. Finally the alternative to the linepipe material’s self-arrestability by the use of an external mechanical device – the so-called crack arrestor – is discussed.

H

IGH-PRESSURE GAS-transmission pipelines are a main option for exploiting remote gas fields and delivering gas at competitive prices to consumer markets. Technical and economical evaluations have proven that systems based on high-strength steels (HSS, that is steel equal or exceeding 555MPa specified minimum yield strength, SMYS) and high gas pressure (HP, that is pressures higher than 10MPa) allow pipeline solutions to compete on the ‘gas-to-market’ for distances greater than 3000km, possibly up to 5000km, for large transportation volumes [1, 2].

(for a defined flow). In addition, the use of HSS allows the wall thickness to be maintained in a proper range, without increasing the diameter-to-thickness ratio at an unsafe level, thus obtaining further cost savings.

Potential routes for gas export from giant mid-continental reservoirs to end users have been analysed by the majors. These analyses included route and material selections, definition of operating flow parameters, selection of optimum hydraulic diameters and wall thicknesses, sizing of intermediate gas compression stations, constructability and environmental impact analyses, etc. The main economic advantage of HP transportation as an option consists of a reduced number of intermediate compression stations

Background

This paper was first presented at the Pipeline Technology conference held in Ostend in 2009 and organized by the University of Gent. It is published here with the organizers’ and authors’ permission. *Author’s contact details tel: +39 (0)6505 5325 email: [email protected]

But limitations might occur in HSS linepipe applications if the important aspects related to their structural reliability are not fully clarified; among the technical topics still under discussion for HSS, the ductile-fracture propagation control is one of the most critical [3, 4].

A longitudinal crack or defect with critical dimension can cause a fracture to propagate along a pipeline in a ductile mode if the operating temperature is above the transition temperature of the linepipe steel. After the fracture initiation, decompression waves at various pressure levels propagate in the gas going back up the line; if the work performed by the gas (the driving force) on the crack flanks (i.e. flaps) in the broken zone is higher than the energy absorbed by both steel and backfill (the resistance force), the crack runs at constant speed corresponding to the energy balance and steady-state propagation conditions are achieved. If the steel toughness is high enough, the fracture will slow, turn in

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Fig.1. Fracture propagation on X80 pipes after a CSM full-scale burst (left) and view of the arrest at the E-glassfibre crack arrestor (manufactured by Europipe) after a CSM burst test on X100 pipes (right). propagation to that resisting it. The approach considers the gas decompression and the dynamic crack propagation as uncoupled processes, but both related to the crackpropagation speed.

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a spiral direction, and finally arrest. In order to limit the length of ductile-fracture propagation, linepipe steels having an appropriate toughness have to be used (Fig.1, left). As an alternative, where the pipeline steel is not able to provide the required toughness, external mechanical devices (the so-called crack arrestors, CA) should be used (Fig.1, right).

Charpy V-notch based predictive methods

The determination of the material toughness value required for arresting ductile fracture propagation has been historically based on the use of semi-empirical models in the form of predictive equations, which state the minimum required value of the Charpy V-notch (CVN) upper-shelf energy as a function of pipe geometry, grade, applied hoop stress, and the chemical composition (and temperature) of the gas. These semi-empirical predictive relationships have been developed using a combination of theoretical analyses and available burst-test data [5-9] by several organizations, including the Battelle Memorial Institute (BMI), the American Iron and Steel Institute (AISI), Centro Sviluppo Materiali (CSM), the High Strength Line Pipe Research Committee (HLP) of the Japanese Iron and Steel Institute (JISI), British Gas (BG), etc. The CVN-based predictive equations were named according to the relevant Institute, so we have Battelle, AISI, British Gas, Italsider/CSM, Mannesmann, Japan, Kawasaki, etc., equations, all of which were developed using the upper-shelf energy obtained by breaking the 2/3 Charpy-V specimen (extracted in transverse direction with respect to the pipe axis); the equations have converted 2/3 thickness Charpy-V energies to standard 10-mm x 10-mm Charpy-V energies historically by assuming constancy of the energy value per unit fracture-surface.

Among all the predictive equations, the Battelle two-curve method (BTCM) is generally considered as the most reliable. It was first proposed by Maxey [5], and it is based on the comparison of the force driving the ductile-fracture

The decompression process is treated as one-dimensional, adiabatic, and isentropic, and an analytical solution for an ideal gas is given. If the gas exhibits two-phase decompression behaviour, which is far from ideal, the BTCM can still be used providing that the gas-decompression curve is calculated using a dedicated gas-decompression model validated across the range of the gas’ chemical composition, temperature, and pressure of interest for the specific application. A number of decompression models [10-13] based on several different equations of state have been developed, and found to predict well the decompression behaviour observed both in full-scale burst tests on rich-gas pipelines and in shock-tube gas-decompression tests. It is, however, important to note that all the equations of state are empirical and should be examined to make sure the critical constants are appropriate for the temperature, pressure, and gas composition being considered. Among all the available models, the one developed by the Battelle Institute as a part of a PRCI project and named GASDECOM is the most used [12]. However, the capability of such code to correctly predict the decompression behaviour of rich gas at pressure values higher than those conventionally adopted in the existing gas pipeline networks (usually below 10MPa) has been questioned, and some research projects are continuing to work out new models able better to describe the behaviour of rich gas mixtures at high pressures (see, for instance, the PRCI project [14]). Finally, it has to be mentioned that recent interest is growing faster in steel pipelines able to deliver CO2 mixtures, that is CO2 containing impurities [17]. Governments and industry worldwide are in fact now proposing to capture CO2 from their power plants and to properly store it; fossilfuel power plants produce CO2 with varying combinations of impurities depending on the capture technology used,

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Fig.2. BTCM predictions for X80, 48-in x 18.3-mm pipeline operated at 12MPa with pure methane (left) and rich gas (right).

Coming back to the BTCM, in practical terms it consists of the determination of the variation of the fracture velocity with pressure for pressure levels higher than the arrest pressure. The driving (DC curve) and the resistance-force curves (RC curves) are compared as shown in Fig.2 (left), which considers an X80, 48-in outer diameter, 18.3-mm wall thickness gas pipeline pressurised with pure methane at an internal pressure of 12MPa (corresponding to 72% of SMYS). The relative position of the two curves determines the potential for sustained fracture propagation, or its arrest. If the two curves do not intercept (fracture curve RC 3, corresponding to 130J of Charpy V-notch energy) the decompression velocity is higher than the fracture velocity for all pressure levels, and an arrest occurs; if the curves intersect (fracture curve RC 1, 100J of Charpy V-notch Method EPRG BSE BTCM AISI

energy), crack propagation will continue indefinitely since at the intersection point the driving and resistance forces have the same value (only one of the two intersection points corresponds to a stable propagation); finally, the arrest/ propagation boundary is represented by a tangent between the two curves (fracture curve RC 2, 115J of Charpy V-notch energy) and is associated to the minimum arrest toughness value. If rich gas is considered instead of pure methane, the minimum toughness energy required to have an arrest substantially increases. Figure 2 (right) shows the BTCM predictions for the same pipeline as above pressurised at the same level of internal pressure but using rich gas (90% methane, 7% ethane, 2 % propane, 1% butane) instead of pure methane (GASDECOM has been used for calculating the gas-decompression curves in both cases); now the toughness arrest Charpy V-notch energy is 170J, which is almost 50% greater than the value for pure methane.

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and this has a strong impact on the minimum toughness energy required for an arrest [16]. It is becoming essential to work out reliable analytical models for calculating the gas-decompression behaviour of CO2 mixtures, since models such as GASDECOM are showing some limitations in this respect. Experimental validation results are so far limited, and additional experimental results would be useful to confirm the accuracy of the analytical methods.

The limits of applicability of the BTCM are given in Table 1 as reported in the ISO 3183 Standard [15]; it can be noted that it is recognized as the more appropriated method for medium- to high-strength steel linepipes up to grade X80, and it is the sole model which can take into account twophase gas mixtures via a proper gas-decompression model. Limit of applicability

Steel grade ≤ X80. P ≤ 8 MPa. OD ≤ 56”, WT ≤ 25.4mm. Single-phase gas. UF ≤ 80%SMSY. Steel grade ≤ X80. P ≤ 7 MPa. OD/WT = 40-115. Single-phase gas. If CVN predicted > 100 J correction by specialist advice is needed. Steel grade ≤ X80. P ≤ 12 MPa. OD/WT = 40-115. Single-phase and two-phases gases. If CVN predicted > 100 J correction by specialist advice is needed. Steel grade ≤ X70. OD ≤ 48”, WT ≤ 18.3mm. Single-phase gas. If CVN predicted > 100 J correction by specialist advice is needed.

Full Scale Burst Testing Results strongly dependent on pipes tested and difficult to extend to different testing conditions. Table 1. ISO 3183 Annex G guidance methods [15] (P = pressure, OD = outer diameter,WT = wall thickness, UF = usage factor, SMYS = specified minimum yield strength).

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The Battelle simplified equation (BSE) was obtained by best-fitting the BTCM results and, as a consequence, it has basically the same limitations. Due to the fact that only single-phase mixtures were considered, the BSE cannot be applied to rich gas. In addition, the predictive capability of the BTCM was afterwards successfully checked against higher-pressure tests, and this explains difference between the two in Table 1. All the other CVN-based equations have similar limitations as the BSE because most of the test results data used for their development were obtained for about 72% of SMYS, using lean gas and backfilled conditions. For the same reason these equations are only claimed to be applicable for pipes of conventional steels and for single-phase gas.

Alternative to conventional Charpy V-notch based predictive methods

• absorbed energy in a drop-weight tear test (DWTT) test (the Wilkowski approach and HLP method) • propagation absorbed energy in a CVN test (Leis’ correction factor) • crack-tip opening angle (CTOA) approach To solve the problem of the small dimensions of the CVN specimen, several researchers have considered whether larger specimens with a similar geometry would be appropriate: the Battelle DWTT specimen was considered the preferable candidate [18]. On the base of the capacity of the DWTT specimen to better represent the full-scale fracture conditions on pipe, Wilkowski et al. [19] indicated that an improvement in the predictions of the arrest / propagation event in a full-scale burst test exists when the DWTT specific energy is used as an alternative parameter to CVN as a measure of the propagation fracture resistance of the material. By comparing the absorbed energy in a brittle-notch DWTT specimen (that can be reasonably assumed as made by propagation energy only) with the energy absorbed in a standard pressed-notch DWTT specimen, Wilkowski derived an equivalent CVN energy to be used as material fracture resistance in BTCM. Different versions exist of such an approach: the most recent, the so-called Wilkowski 2000 minimum DWTT energy equation, when compared with full-scale burst-test results on high-grade pipes (i.e. X80 and higher) proved to be fairly able to capture the trend of the data (better than the CVN-based equations), even though the error cannot be ignored and should be considered in the analysis (Fig.3, left).

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The conventional Charpy V-notch (CVN) based methods previously described have proved to be non-conservative under conditions outside those used for their development as, for example, when high-pressure, rich-gas, low-temperature, high-grade, high-toughness linepipes are involved; in addition such semi-empirical relationships often do not provide a physically meaningful description of either the driving force for crack advance or the material resistance. Attention has thus been focussed on alternative methods involving a more physical description of the driving force acting at the crack tip, and a measurement of the toughness by alternative laboratory tests to the CVN test and more representative of the energy spent by the crack during the propagation in full-thickness conditions. The CVN test, although it is inexpensive and easy to carry out, in fact has a number of drawbacks with respect to the full-scale fracture conditions. Firstly, the thickness of the specimen is less than that of the pipe; secondly, the ligament is 8mm only (so the specimen cannot replicate the steady-state conditions occurring during a full-scale event); and thirdly, the standard CVN test provides a total energy to failure and does not distinguish between the initiation and propagation phases.

In this context, a few new parameters (and, consequently, the geometry of specimens and test methods) to quantify the real fracture resistance of steel pipe with respect to the fracture propagation event have been proposed through the years. The most relevant are based on:

In parallel to the work done by Wilkowski on DWTT specimens, the High Strength Line Pipe (HLP) Committee organized by the Iron and Steel Institute of Japan (ISIJ) did extensive work [20] in developing its own predictive model. The method is based on the comparison between the material-resistance curve and the gas-decompression

Fig.3. Comparisons of Charpy and DWTT energy values for X80 pipes in the full-scale test database [19] (left) and relation between DWTT absorbed energy and Charpy absorbed energy by HLP [20] (right).

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Fig.4. Leis CharpyV energy-correction equation [22] (left) and comparison between PICPRO and CSM’s full-scale burst-test results on X80, 56in diameter x 26mm wall thickness pipes (right). steels because of significant differences in their fracture behaviour as compared to that of the much lower toughness steels used in their empirical calibration. Based upon his experimental results, Leis defined a correction factor for the total energy absorbed by a standard CVN test to be used in conjunction with the BTCM (Fig.4, left). Below 95J, any minor non-linear effects were accounted for in the original calibration of the BTCM and, as a consequence, no further correction is needed. An improvement in the prediction capability of the BTCM with respect to arrest data of modern high-toughness steels occurred if such a correction factor is applied, even if a number of non-conservative mis-predictions remain for the arrest data of more-recent, very high toughness steels. The equation developed in fact indicates that the rate of correction drops as the toughness increases, whilst there is experimental evidence to the contrary. Therefore, the use of the equation should be limited in applications to very high toughness steels.

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curve, similar to BTCM discussed earlier. The novelty is that the material-resistance curve is expressed in terms of pre-cracked DWTT energy. A lot of effort has been spent to correlating the DWTT with CVN energy, and on investigating the effect of pipe thickness on DWTT energy (Fig.3, right). The original HLP model has been based upon data from seven full-scale burst tests carried out on one pipe grade (X70) and one geometry (1219mm OD, 18.3mm wall thickness), and its application to different cases is so far questionable; recently, the authors proposed modification of the method to correct the size effect of high-strength and high-toughness pipe, including X80 and X100 [21]. In the HLP method, the arrest energy is defined as the energy to arrest fracture in 24m on an even energy arrangement instead of on an increment energy arrangement, which is the traditional test method. Through the measurement of the propagation energy in instrumented CVN tests, Leis [22] postulated that CVNbased empirical models fail to correctly predict arrest toughness in applications involving modern high-toughness

Table 2. Range of X80 FSBT parameters (note: the quoted minima and maxima values are not necessarily from the same test).

The use of the crack-tip opening angle (CTOA) as the toughness parameter derives from the post-yielding fracture-

MIN

MAX

Diameter (inch)

42

56

Diameter (mm)

1067

1422

Wall thickness (mm)

12.5

26

CharpyV 1/1 (Joule)

83

278

DWTT energy (Joule/cm2)

251

976

Pressure (bar)

93.5

161

Hoop stress (MPa)

350

440

Design factor (%SMYS)

0.65

0.80

+6

+19.4

Test temperature (°C)

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Fig.5. X80 full-scale burst tests: comparison between actual test results and BTCM predictions. mechanics’ concept. The approach is based upon the balance between the capacity of the steel to resist the crack propagation, expressed by the CTOA critical value of the material, named CTOAc, and the driving force applied by the external loads, expressed by the CTOA applied, named CTOAa or CTOAmax [23]. The CTOA-based fracture criterion states that steady-state propagation of a ductile fracture is impossible if CTOAmax ≤ CTOAc. In practice, CTOAmax can be calculated with a suitable finite-element code, as for example CSM’s PICPRO code [24]. The PICPRO code is based on a bi-parametric fracture criterion, and includes both an actual gas-decompression model for both lean and rich gas decompression curve evaluation, and a semi-empirical soil-constraint model for taking into account the constraint effect of the surrounding environment on the crack tip. For the measurement of the CTOA critical value of the material, CTOAc, a suitable laboratory testing procedure has to be used. A suitable method was developed at the time of [25] called the two-specimen CTOA test (the TSC test) using steels with CVN energy up to about 200J and grades in the range up to X70 (with a few data about X80). Recent investigations have shown that for high-strength linepipe materials (≥ X80) the TSC test requires corrections, and a new version was developed [26]. Comparison between the CTOA-based predictions and the full-scale burst-test results show satisfactory results up to X80 grade pipe (Fig.4, right). For higher-strength pipe (such as X100 and X120), the revised TSC test is still not able to capture the real pipe fracture resistance; the main reason is that very high strength steels exhibit very low CTOA values which are difficult to measure with accuracy with the TSC test, which does not directly measure the angle at the crack tip but calculates it starting from measurement of the absorbed

energy. Recently, a specific effort has been made to develop simplified equations for both CTOAmax and CTOAc to be used for a less-refined analysis. By fitting the PICPRO results and comparing them with actual full-scale burst test results, a simplified analytical method has been developed which can be used for ductile fracture control in high-strength steel pipelines [27].

X80 full-scale burst-test database The CSM full-scale burst-test database has been used to identify full-scale burst-test data on large-diameter (≥ 36in), high-pressure (UF ≥ 50%SMYS) X80 pipes. It is fairly surprising to note that a relatively low number (only eight) tests on X80 pipes have been found1; as a matter of fact, more effort has been spent in recent years on X100 pipes (six full-scale burst tests published, and three tests due to be published). A total of 37 pipes were involved in the eight X80 tests: in 26 pipes cracks propagated, while in 11 cracks were arrested; the initiation pipes were not included in these numbers, nor were pipes that were not unaffected by the fracture event. The X80 tests were carried out over quite a long period, although the majority of the tests was carried out in the 1980s. The range of testing conditions is given in Table 2: all the tests were carried out using soil backfill; half tests were carried out using natural gas (lean gas) as the pressurising medium, and half the tests used air; no rich gas tests were found in the database. All the pipes involved were longitudinal welded, and the majority were manufactured by European pipe producers using plates produced following different manufacturing processes, including quenched-and-tempered (the older), control-rolled, and control-rolled plus accelerated cooled (the newer). Due

1 Two tests on 30-in diameter x 17.5-mm wall thickness longitudinally welded X80 pipes tested at about 40% SMYS [48] were not considered for size and usage factor restrictions mentioned above.

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Conserv. correction factor

Non-conserv. misprediction, %

Conserv. misprediction, %

Total error, %

BSE

1.36

35.1

0

35.1

BTCM

1.43

43.2

0

43.2

AISI

1.85

54.0

0

54.0

BTCM-Leis

1.35

29.7

0

29.7

Wilkowski 2000 DWTT

1.27

18.9

2.7

21.6

Fracture Arrest Approach

Table 3. Fracture arrest approaches accuracy for X80 grade steel pipe.

X80 fracture-arrest requirements

Among all the approaches previously described, the following have been considered and compared to the X80 full-scale burst-tests results, since they are the most promising for the X80 case under consideration: • • • • •

DWTT equation, the correction factor is equal to 1.27. All the CharpyV-based equations have a significant amount of error, the worst aspect of which is that all the error is on the wrong side, i.e. it is non-conservative mispredictions (in other words, the actual propagation pipes predicted as arrest). A better situation is with the Wilkowski 2000 DWTT equation, which exhibits the lowest correction factor and the lowest error. It has, however, to be pointed out that the BTCM, BSE, and AISI equations have been developed for lower-grade pipe and therefore their inability correctly to predict high-grade steel pipe data is justifiable. The Leis’ correction factor and the Wilkowski 2000 equation are much more recent and, as a consequence, they should have been better able to predict high-grade steel data.

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to the different manufacturing processes adopted for the plates’ production, the pipes exhibited different fracture behaviour during testing. Fracture appearance was in fact fully ductile for all the tested pipes considered, but different degrees of separation on the fracture surfaces were observed.

Battelle simplified equation BTCM AISI equation BTCM with Leis’ correction factor Wilkowski 2000 DWTT equation.

The CTOA-based approach, which proved to be quite satisfactory for X80 pipes, could not be applied to the X80 full-scale burst tests since some fundamental input data (such as the CTOAc value) were not generated at the time the tests were carried out. An example of comparison between X80 full-scale burst-test data and the predictive methods considered is shown in Fig.5 for the BTCM. Summarising, fracture arrest approaches accuracy for X80 grade steel pipe as shown in Table 3 with: • Conservative correction factor: multiplying factor which allows all the propagation points to be below the line; that is, with such a correction factor only the arrests are predicted. • Non-conservative misprediction: the ratio between predicted arrest and actual propagation points. • Conservative misprediction: the ratio between predicted propagation and actual arrest points. As can be seen, a correction factor is needed for all the approaches considered: for the CharpyV-based approach, it varies from 1.35 to 1.85; while for the Wilkowski 2000

Looking at Table 3, some comments can be made: • In terms of CharpyV energy, Leis’ correction factor does not provide significant benefit; BTCM remains so far the best method, providing that an adequate correction factor is applied (1.43 is the conservative correction factor for X80 pipe). • In terms of DWTT energy, the Wilkowski 2000 DWTT method is unique among those so far available, and can be used providing that an adequate correction factor is applied (1.27 conservative correction factor).

Standards’ provisions Standard codes for gas transmission pipelines such as ASME B31.8 [28], IGE/TD/1 [29], AS 2885-1997 [30], CSA Z662 [31], and DNV-OS-F101 [32] all indicate that pipelines should be designed with a sufficient toughness to arrest ductile fracture propagation. The European Pipeline Research Group (EPRG) has produced recommendations [33, 34] for ductile-fracture-arrest toughness which have been incorporated into DNV-OS-F101 as well as into the former edition of ISO 3183. The new revision of ISO Standard 3183 for linepipe [15] is the result of the harmonization of the requirements of previous API 5L and ISO 3183-1, 2, and 3 Standards, and also includes the new API 5L [35].

The Journal of Pipeline Engineering

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140

Fig.6. Risk of length of propagation for X80 pipes according to EPRG Guidelines [37].

It is important to note that, for X80 pipes, the EPRG recommendations are based on the Battelle simplified equation. As already mentioned, Table 1 summarizes the applicability limits of each method.

value (EPRG-CVNmin). This is supported by toughness data collected by EPRG at that time about actual pipe supplies, and a comparison of these data with the full-scale burst-test results [36, 37]. In practical terms, there is the risk that a pipe which meets EPRG-CVNmin will not arrest a running fracture. EPRG therefore developed a calculation route, based on probabilistic concepts, in order to determine the proportion of propagate pipes in a pipe order: by assuming that pipes in the pipeline are randomly distributed with respect to arrest/propagation properties, the relationship between the pipes purchased to EPRG-CVNmin and the length of any propagating fracture has been evaluated for a range of toughness levels and pipe grades. Figure 6 shows the results of these probabilistic calculations for X80 grade pipes, from which can be seen that the arrest probability within a few pipe lengths (three or five) can be estimated according how large is the mean toughness of the pipe with respect to EPRG-CVNmin. For typical ‘modern’ pipe where EPRG-CVNmin is exceeded by a “large margin” (i.e. the CVN mean > 2 times the EPRG-CVmin) there is a 95% probability that a fracture will arrest within three pipe lengths. On the contrary, in the event that pipes were supplied with a CVN mean equivalent or close to EPRG-CVNmin, there is a 95% probability that a fracture could propagate through many pipe lengths (i.e. > 10 pipe lengths).

The EPRG Guidelines deserve some additional comment: it is important to note that they are neither a best-fitting nor a lower-bound to the full-scale test results, but they are a judgement based on the assumption that 50% of the pipes in an order exceed 1.3 times the minimum EPRG-specified CVN

The use of other approaches is not excluded by ISO 3183-Annex G and can be used providing their suitability is proved. Users should also take all reasonable steps to ensure that the operating parameters, including gas composition and pressure, are comparable or consistent with the test condition

Ductile-fracture-arrest requirements are specified in a devoted Annex – Annex G - PSL 2 pipe with resistance to ductile fracture propagation – of the new ISO 3183 Standard. Annex G provides guidance on determining the CVN impact energy values for the arrest of ductile pipe fractures. It has to be noted that Annex G does not provide a unique route for determining the minimum fracture-arrest toughness value, but on the contrary it describes five different approaches that may be adopted for determining the pipe body CVN absorbed energy values to control ductile-fracture propagation in buried onshore gas pipelines. The five approaches are: • • • • •

EPRG Guidelines Battelle simplified equation (BSE) Battelle two-curve method (BTCM) AISI method Full-scale burst testing (FSBT).

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Fig.7. Earlier full-scale burst test on spiral pipes (left) and comparison between full-scale burst-test results and AISI predictions for spirally and longitudinally welded pipes [39] (right). if the fracture resistance of the seam weld is less than that of the pipe body, the crack may then propagate along the seam. There have been examples of full-scale burst tests on earlier spiral pipes where the fracture ran along the striprolling direction, unwrapping the pipe for quite a length (Fig.7, left).

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on which the respective Annex G guidance method was established. Application of the guidance methods to pipeline conditions outside the validity of the respective method can result in a non-conservative assessments of the resistance of the material to running fractures: this means that designer has the responsibility of choosing the most appropriate method and the consequent level of safety factor to be adopted.

Spirally vs longitudinally welded pipes

Future long-distance gas pipelines will be constructed using different types of pipe, that is to say that pipes other than those manufactured by UOE longitudinal welding could be used. In particular there is a growing interest in the use of spirally welded pipes since they are usually cheaper than those manufactured by UOE; however, currently limited experience of the use of spiral pipe in high-pressure gas pipelines could limit the use of such a pipe product.

One of the main concern when spiral pipes are considered with respect to longitudinally welded pipes is the orientation of the toughness-test samples with respect to the weld seam, and how the anisotropy (if any) of the coil can affect the result. From the point of view of fracture-propagation control, the semi-empirical predictive relationships presented above have been developed using a combination of theoretical analyses and available burst-test data which were mostly generated on longitudinally welded pipes. It has to be noted that the majority of studies and tests carried out in the last 30 years on fracture propagation in pipelines have generally considered longitudinally welded pipes, in which crack propagation is parallel to the rolling direction of the plate and the seam weld. For spirally welded pipes, since the direction parallel to the pipe axis is not the rolling direction, unlike the case for longitudinal-seam pipe, an improvement in the material’s fracture resistance can be anticipated which depends on the pipe’s helix angle [38]. In spirally welded pipe, a crack propagating longitudinally will intersect the seam weld, and

In order to clarify the point, a desk study on the matter was carried out by EPRG [39]. A comparison between tests carried out on spirally and longitudinally welded pipes tested in similar conditions was made to compare the behaviour of the two different pipe products. A total of 11 full-scale tests involving 27 spiral pipes were identified, in comparison to hundred of tests which involved longitudinally welded pipes. It is important to note that as far as tests on spiral pipes are concerned, the maximum steel grade was X70, and the maximum wall thickness was 17mm; the tests were carried out mainly in the 1970s, and the tested pipes exhibited CharpyV energy in the range 70J to 220J with most of the pipes exhibiting separations on the fracture surface. As already mentioned, in some tests the fracture followed a helical path along the strip direction and not along the pipe axis; this is believed to be a consequence of the anisotropy of toughnesses between the pipe’s axial direction and the strip’s direction. The consequence of taking a longer helical path is a lower axial crack velocity, which results in a higher pressure drop at the crack tip reducing the driving force for the fracture propagation that always resulted in an arrest within the pipe. The practical problem is then whether the CharpyV toughness should be measured with a specimen transverse to the pipe or transverse to the coil. Another peculiar point of spirally welded pipes produced from coils is the lack of cold expansion and the consequent higher anticipated value of residual stresses. The presence of unrelieved residual stress should be of minor importance to fracture propagation owing to the very high elasto-plastic field that precedes the crack tip during the ductile fracture propagation. The desk study in Ref.39, by comparing similar tests carried out on longitudinal and spiral pipes, concluded that spirally welded linepipe in terms of fracture arrest predictability

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Fig.8. Separations on a CharpyV specimen: schematic (left), and the fracture surface of an X80 pipe (CSM full-scale burst test, right).

Fig.9. Rising shelf vs conventional steel [40].

behaves at least as consistently as does longitudinal-seam pipe (Fig.7, right).

Separations

During ductile-fracture propagation, high plastic deformations take place in the vicinity of the crack tip, and crack surfaces are affected by tearing and three-dimensional stress fields in the pipe wall (triaxiality). A chevron-like pattern oriented in the direction of the fracture propagation is sometimes exhibited, especially in heavily rolled steels, and the presence of separations on the fracture surface is also found. The term ‘separations’ is used to indicate through-thickness fractures that occur on planes parallel to the lamination plane, i.e. perpendicular with respect to the primary fracture plane. The separations occur within the plastic zone directly ahead of the oncoming fracture, and the result is the sharing of the fracture surface in a group of thinner sub-specimens. They may occur on the fracture surfaces of tensile, DWTT, and Charpy specimens (Fig.8, left) as well as on the pipe’s fracture surface (Fig.8, right). Tensile specimens show separations in the centre of the fractured area, while pipe, DWTT, and Charpy fracture surfaces show a system of parallel separations. Often ‘arrowheads’ are present due to the through-thickness stress. The separations occur at temperature in the vicinity of the transition temperature, and often disappear when the temperature increases. The presence of separations on fracture surfaces is typical

for high-toughness, controlled-rolled steels, and is generally associated with material production routes involving extensive rolling at temperatures around or below the transformation temperature. Steels that exhibit separations often show a ‘rising shelf’ behaviour, with a detrimental effect on the absorbed impact energy (Fig.9). The main effects of separations on the material transition curve are a decrease of the transition temperature and a decrease of the impact absorbed energy. To take into account of the presence of the separations on the CharpyV transition curve, three different parameters were introduced: • CV100 = CharpyV energy at a lower temperature corresponding to 100% shear area on the fracture surface; • CVP = CharpyV energy at the upper plateau; • CVT = CharpyV energy at the full-scale test temperature. Rising-shelf steels do not often fit the CharpyV-based correlations (Battelle, AISI, etc.) established on the conventionally rolled steels, and as a consequence the predictions made by using such relations may be unsafe. In the past, two main alternatives were proposed: • use CV100 or CVT instead of CVP; • use CVN calculated from DWTT energy correlation.

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The first alternative did not give good results: CV100 gave too-conservative results, and CVT did not give a significant improvement in the prediction ability. The second alternative follows the Wilkowski approach explained above.

Crack arrestors When linepipe toughness properties are not enough to guarantee against ductile-fracture propagation, the use of external mechanical devices or crack arrestors becomes mandatory. Various types of crack arrestor are available, the most representative being steel sleeves, welded or clamped rings, wire rope, threaded steel rings, and composite arrestors such as Clock Spring [41] or E-glass fibre reinforced pipe (Fig.1, right).

Conclusions Ductile-fracture controls for X80 linepipes have been presented showing the available predictive methods, Standards’ provisions, and published full-scale burst tests. In addition, specific topics which are noteworthy when considering the application of X80 pipe to future long-distance gas pipelines have been discussed, such as the influence of separations on the fracture surface and the difference between the behaviours of spirally and longitudinally welded pipes. Finally an alternative to the linepipe material’s self-arrestability, the crack arrestor, has been presented.

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Current guidelines for crack arrestor design are based on recommendations issued by PRCI [42] following small-scale tests conducted in the 1970s and 1980s on pipes ranging from small-diameter (150-325mm) X65 to 1020-mm DOM (drawn over mandrel). PRCI examined a range of arrestor types with varying geometry (axial length and radial clearance) and compared the results with the available full-scale data to develop guidelines for arrestor design. Using these guidelines for high-grade steel pipe can result in failure to arrest [43] or in overly conservative configurations, depending on the arrestor type selected.

effect on the running fracture, it is possible to calculate changes in crack speed and determine whether deceleration / acceleration and even arrest occurs due to the presence of the arrestor. The model has been successfully used to perform numerical predictions of the results of full-scale crack-arrestor tests performed on X100 and X120 largediameter pipes, such as the BP [46] and ExxonMobil tests [47]. The agreements between the numerical predictions and the experimental results were excellent, demonstrating the capability of the CSM code to correctly simulate the fracture event.

A new technical basis for crack arrestor design for highstrength steel pipelines has been proposed by Leis et al. [44]; this approach, although promising, is at the moment limited to integral crack arrestors with the same characteristics as those of the main pipe because it does not consider the flap-opening constraint provided by an encircling arrestor.

Looking at the available results of full-scale crack arrestor tests it can be seen that the majority were carried out on pipes up to X70 in grade. Only one test was carried out on X80 pipe: a CSM test [45] on 48-in OD x 17-mm wall thickness longitudinally welded Q&T pipes. One wire-rope-wrap arrestor was installed on a pipe nominally X70 in grade but actually X80; the fracture entered at high speed into the arrestor which was ineffective in arresting the running crack. Once more it could be noted that greater research efforts were spent on the subject for higher-grade pipes, and about ten full-scale crack-arrestor tests have been carried out on X100 and X120 pipes in recent years. Since current crack-arrestor design criteria failed when high-grade pipes are considered, CSM has developed a methodology for arrestor design based on the PICPRO finiteelement model; this model has been successfully applied to simulate full-scale burst tests carried out on X100 and X120 steel pipes with crack arrestors, both in a posteriori and in predictive modes [46, 47]. The basis of the procedure is that different crack speed entering values represent different material fracture propagation resistances. Through PICPRO’s algorithms, which reproduce the crack-arrestor constraint

In summary, the following main conclusions can be drawn: • The range of applicability of fracture-arrest criteria given in the ISO 3183 / API 5L Standard is often outside modern high-pressure, high-grade, pipeline project conditions; the designer hence has the responsibility for the choice of the most appropriate method and the consequent level of safety factor to be adopted. • The published X80 full-scale burst tests are few, and for the most part were carried out 20-30 years ago on pipes that could not be fully representative of modern X80 pipe production. • Among all the available conventional CharpyV-based predictive methods, the Battelle two-curve method still remains the most reliable, providing that an adequate correction factor of 1.43 is applied. • In terms of more representative fracture parameters, DWTT and CTOA-based methods are the most interesting: Wilkowski 2000’s DWTT equation follows the data trend well, but an adequate correction factor has to be applied. The CSM PICPRO method proved satisfactorily to describe X80 full-scale behaviour but specific input material data (CTOAc) and finite-element calculations are needed. • Past desk studies demonstrate that spirally welded pipe, in terms of fracture-arrest predictability, behaves at least as consistently as does longitudinal-seam pipe; but no full-scale burst-test data exist on X80 spirally welded pipes. In addition, spiral pipes tested in past full-scale burst tests were fairly thin (wall thickness ≤ 17mm).

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• The presence of separations on the fracture surface, typical of heavy control-rolled steels, complicates the scenario since it is more difficult to correlate smallscale to full-scale behaviour. Testing on a full-thickness specimen, the DWTT specimen, is recommended to better assess the material’s behaviour. • Full-scale burst tests results have clearly demonstrated that X80 pipes are able to arrest a propagating running fracture; however it cannot be ignored that, for particular conditions (high pressure, rich gas, low temperature), fracture-arrest toughness requirement exceed material toughness properties, and in this case a crack arrestor must be used. Conventional crack arrestor design guidelines proved to be ineffective when high-grade pipe is considered. An alternative method, based on advanced finite-element calculation, has been developed and gave good results when compared to full-scale burst-test results.

References

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1. K. T. Corbett, R. R. Bowen, and C. W. Petersen, 2003. High strength steel pipeline economics. Proc. 13th Int. Offshore and Polar Engineering Conf., Honolulu, Hawaii, USA, May 25–30. 2. D. Brkic, 2005. The international scenario for gas production and large transmission lines. 1st Int. Conf. on Super High Strength Steels, Rome, Italy, 2-4 November. 3. G.Wilkowski, D.Rudland, and H.Xu, 2006. Effect of grade on ductile fracture arrest criteria for gas pipelines. Int. Pipeline Conf. IPC 06, September 25-29, Calgary, Alberta, Canada. 4. A.Fonzo, A.Meleddu, G.Demofonti, M.Tavassi, and B.Rothwell, 2006. Ductile fracture control for high strength steel pipelines. Ibid. 5. W.A.Maxey, 1974. Fracture initiation, propagation and arrest. 5th Symposium on Line Pipe Research, Houston, Texas, November, paper J. 6. AISI, 1974. Technical report: Running shear fractures in line pipe. Subcommittee of Large Diameter Line Pipe Producers, September. 7. G.D.Fearnehough and D.G.Jones, 1980. Toughness specification for shear fracture arrest in pipelines. Int.Conf. on Analytical and Experimental Fracture Mechanics, Rome, Italy, June. 8. F.Bonomo et al., 1980. A survey and tentative revision of ductile arrest criteria in pipelines for gas transmission. Ibid. 9. R.J.Eiber and T.A.Bubenik, 1993. Fracture propagation control plan methodology. 9th PRCI/EPRG Joint Technical Meeting, Houston, Texas, May, paper 20. 10. T.K.Groves, P.R.Bishnoi, and J.M.E.Wallbridge, 1978. Can J. Chem. Eng., 56, pp664. 11. W.A.Maxey, 1983. Gas expansion studies. American Gas Association, Catalogue No. L51435. 12. R.J.Eiber, T.A.Bubenik, and W.A.Maxey, 1993. Fracture control technology for gas pipelines. American Gas Association, Catalogue No. L51691.

13. G.Demofonti and R.D’Anna, 1992. Criteri per la valutazione della tenacità d’arresto necessaria per l’arresto della frattura duttile su di un gasdotto in presenza di un gas bifasico in condizioni on-shore ed offshore. Internal CSM Report No. 7624R, Rome, October. 14. PRCI, 2002. Gas decompression behavior following the rupture of high pressure pipelines – Phase 1. Advantica Technologies Report for Materials Technical Committee of Pipeline Research Council International (PRCI), Catalog No. L51979, November. 15. ISO, 2007. Standard 3183: Petroleum and natural gas industries – steel pipe for pipeline transportation systems. 2nd Edition, 15 March. 16. A.Cosham and R.J.Eiber, 2008. Fracture control in carbon dioxide pipelines – the effect of impurities. Proc. IPC2008, 7th Int.Pipeline Conf., September 29 – October 3, Calgary, Alberta, Canada. 17. P.N.Seevam, J.M.Race, M.J.Downie, and P.Hopkins, 2008. Transporting the next generation of CO2 for carbon capture and storage: the impact of impurities on supercritical CO2 pipelines. Ibid. 18. G.Wilkowski, 1979. Fracture propagation toughness measurements. Paper K, 6th Symposium on Line Pipe Research, American Gas Association, Arlington, VA, Catalogue No. L30175. 19. G.Wilkowski, D.Rudland, and H.Xu, 2006. Effect of grade on ductile fracture arrest criteria for gas pipelines. Int.Pipeline Conf. IPC 06, September 25-29, Calgary, Alberta, Canada. 20. H.Makino, T.Inoue, S.Endo, T.Kubo, and T.Matsumoto, 2002. Simulation method for crack propagation and arrest of shear fracture in natural gas transmission pipelines. Proc. Pipe Dreamer’s conference, Yokohama, Japan, November 7-8, pp501-pp524. 21. H. Makino and I.Takeuchi, 2005. Fracture propagation and arrest of gas transmission pipelines by X100 and X120. Proc. Seminar Forum of X100/X120Grade High Performance Pipe Steels, Beijing, China, July 28-29. 22. B.N.Leis, 2000. Predicting fracture arrest based on a relationship between Charpy V-notch toughness and dynamic crack-propagation resistance. 3rd Int.Pipeline Technology Conference, Bruges, Belgium, May. 23. M.F.Kanninen, C.P.Leung, P.E.O’Donoghue, T.B.Morrow, C.F.Popelar, G.Buzzichelli, G.Demofonti, L.Rizzi, S.Venzi, and S.Cinquetti, 1991. The development of a ductile pipe fracture model. Joint Final Report by SwRI, CSM and Snam to the Pipeline Research Committee, American Gas Association, August. 24. G.Berardo, P.Salvini, G.Mannucci, and G.Demofonti, 2000. On longitudinal propagation of a ductile fracture in a gas line pipe: numerical and experimental analysis. Int.Pipeline Conf. IPC2000, Calgary, October. 25. G.Buzzichelli, G.Demofonti, S.Venzi, and M.F.Kanninen, 1995. Step by step procedure for the two specimen CTOA test. Proc. 2nd Int. Conf. on Pipeline Technology, Vol. II, Ostend. 26. G.Mannucci, G.Demofonti, and E.Mecozzi, 2002. Mill test techniques for predicting crack arrest arrestability in high toughness steels. PRCI Project PR-182-9903, March.

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40. G.D.Fearnehough and D.G.Jones, 1980. Toughness specification for shear fracture arrest in pipelines. Int.Conf. on Analytical and Experimental Fracture Mechanics, Rome, Italy, June. 41. N.C.Fawley, 1994. Development of fiberglass composite systems for natural gas pipeline service. Final Report for Gas Research Institute, GRI-94/0072. 42. G.M.Wilkowski, P.M.Scott, and W.A.Maxey, 1983. Design and optimization of mechanical crack arrestor for pipelines. NG-18 Report No. 134 to Gas Research Institute, Catalogue No. NR198308E, July. 43. S.D.Papka et al., 2003. Full-size testing and analysis of X120 linepipe. Proc. 13th ISOPE Conf., Honolulu, IV, p50, May. 44. B.N.Leis, X.K.Zhu, T.P.Forte, and B.C.Glenn, 2004. Design basis for fracture arrestors in gas transmission pipelines. 4th Int. Conf. on Pipeline Technology, Ostend, Belgium. 45. M.Bramante and M.Spedaletti, 1978. Prove di propagazione della frattura duttile nei gasdotti - Risultati della 5a prova su tubi bonificati di diametro 48”. Internal CSM Report No. 3084R, Rome, November. 46. G.Mannucci, M.Di Biagio, G.Demofonti, A.Fonzo, P.Salvini, and A.Edwards, 2004. Crack arrestor design by finite element analysis for X100 gas transportation pipeline. Proc. 4th Int.Conf. on Pipeline Technology, Ostend, Belgium. 47. A.Fonzo, A.Meleddu, M.Di Biagio, G.Mannucci, G.Demofonti, C.W.Petersen, and N.E.Biery, 2006. Crack propagation modelling and crack arrestor design for X120. Int.Pipeline Conf. IPC 06, September 25-29, Calgary, Alberta, Canada. 48. S.Kawaguchi, N.Hagiwara, T.Masuda, C.Christensen, H.P.Nielsen, P.B.Ludwigsen, T.Inoue, D.L.Rudland, and G.Wilkowski, 2004. Application of X80 in Japan: fracture control. Proc. 4th Int.Conf. on Pipeline Technology, Ostend, Belgium.

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27. A.Fonzo, A.Meleddu, G.Demofonti, M.Tavassi, and B.Rothwell, 2006. Ductile fracture control for high strength steel pipelines. Int.Pipeline Conf. IPC 06, September 25-29, Calgary, Alberta, Canada. 28. ASME, 2004. Code For pressure piping, B31: gas transmission and distribution piping system. ASME B31.8 – 2003 Edn, American Society of Mechanical Engineers, New York, NY, USA. 29. IGE, 2001. TD/1 Edn 4: Steel pipelines for high pressure gas transmission – recommendations on transmission and distribution practice. Institute of Gas Engineers. 30. Standards Australia, 1997. AS2885.1 – 1997 Pipelines – gas and liquid petroleum. May. 31. CSA, 2003. Standard Z662-03 Oil and gas pipeline systems. Canadian Standards Association. 32. Det Norske Veritas, 2007. Offshore standard DNVOS-F101 Submarine pipeline systems. October. 33. Vogt, Bramante, Jones, Koch, Hugler, Pero, and Re, 1983. EPRG report on toughness for crack arrest in gas transmission pipelines. 3R International, 22. 34. G.Re, V.Pistone, G.Demofonti, and D.G.Jones, 1995. EPRG recommendations for crack arrest toughness for high strength line pipe steels. Ibid, 34. 35. API, 2007. 5L Specification for line pipe, 44th Edn / October 1, 2007. Effective Date: October 1, 2008. 36. S.J.Dawson and D.G.Jones, 1995. Assessment of the risk of length of fracture propagation for any pipe supply in terms of the EPRG recommendations for shear fracture arrest toughness. BG Report F10001 for EPRG, 24 May. 37. S.J.Dawson and V.Pistone, 1998. Probabilistic evaluation of the safety embodied in the EPRG recommendations for shear fracture arrest toughness. 3R International, 10-11. 38. Jones and Gray, 1993. Properties and characteristics of helical seam (spirally welded) and straight seam linepipe: a comparative assessment. Microalloying International Inc., August. 39. V.Pistone and G.Mannucci, 2000. Fracture arrest criteria for spiral welded pipes. 3rd Int.Pipeline Technology Conf., Brugge, Belgium, May.

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Assessment of a gouge, a dent, or a dent plus a gouge, in a pipe using limit analysis or notch fracture mechanics by Prof. Guy Pluvinage*1, Dr Mustapha Allouti2, Dr Christian Schmitt2, and Dr Julien Capelle2 1 Fiabilité Mécanique, Conseils, Silly sur Nied, France 2 Laboratoire de Mécanique Biomécanique Polymère et Structures (LaBPS), ENIM, Metz, France

M

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ETHODS FOR PIPE defect assessment are described, particularly for gouges, dents, and combined gouge and dent defects. Due to the fact that these defects induce elastoplastic failure, the assessment methods are based on limit analysis or notch fracture mechanics, and both provide close safety factors. In this paper the following methods are described: for gouges – limit analysis and notch fracture mechanics; for dents – a ductility criterion; for combined gouges and dents – a method based on notch fracture mechanics taking into account stress triaxiality.

O

VER THE LAST 50 years, gas transmission pipelines have become significant networks for transmission of large quantities of energy over long distances from gas deposits to consumption areas. Considering European transmission pipelines alone, the onshore network mileage multiplied by more than three times between 1970 and 2007. Despite the growth of the gas transmission pipeline mileage, the failure frequencies by leak or rupture have been reduced by five in Europe at the same time. According to the European Gas Pipeline Incident Data Group report (EGIG report [1]) which has collected incident data since 1970, the primary failure frequency over the entire period (1970-2007) was equal to 0.37 per 1,000km.year, and over the five years up to 2007 was equal to 0.14 per 1,000km.year. The safe operation and high reliability of pipelines depend on various factors including mechanical damage or external interference, fatigue cracks, material defects, weld cracks, improper welding, internal or external corrosion and, most of all, on the ageing of the physical state of the pipeline material and the welded joints during their prolonged use. Damage caused by human error or vandalism is also not infrequent. Author’s contact details: tel: +33 3 8731 5277 email: [email protected]

Fig.1. A typical plain dent in a pipe. Six different causes of incident have been identified and are summarized in Table 1 with their percentages of occurrence. It can be seen that mechanical damage (external interference) is the major cause of service failures in Europe and in transmission pipelines, and this type of damage can be classified into gouges and dents. Defect assessment in pipelines is undertaken using different tools according to the defect type and the fracture mode. A dent in a pipeline is a permanent plastic deformation of the circular cross-section of the pipe (Fig.1) which causes local stress and strain concentrations and a local reduction in the pipe diameter. The dent depth is defined as the maximum reduction in the diameter of the pipe compared to the original diameter. There are several types of dent, as follows: smooth

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External Interference

Construction defect/ material failure

Corrosion

Ground Movement

Hot-Tap made by Error

Other and Unknown

49.6%

16.5%

15.3%

7.3 %

4.6%

6.7%

Table 1. Causes and percentage of incidents on gas pipes [1]. dent, kinked dent, plain dent, unconstrained dent, and constrained dent. In this paper, we only consider plain dents. Plain dents are defined here as damage to a pipe which causes a smooth change in the curvature of the pipe wall without reduction of pipe thickness. The dent depth (H) is defined as the distance between the undamaged and damaged cross sections (see Fig.2). In other words, plain dents are defined as dents having no injurious defects – such as a gouge – and which possess a smooth profile (they are often classified as smooth dents).

Fig.2. Definition of dent depth, H.

The critical variables relating to plain dents are:

Sa no m t f ple or c di op st y rib ut io n

• dent depth • pipe geometry (ratio of diameter to wall thickness) • profile curvature of the dent

The depth is the most significant factor affecting the burst strength and the fatigue life of a plain dent. The acceptability limit of dent depth is given generally by the following empirical rule: if the dent depth is more than one tenth of the pipe diameter, repair is then mandatory. It has been seen that plain smooth dents with a depth up to 8% of pipe diameter [2], and possibility 24% [3], do not significantly reduce the burst strength of a pipe, and the API 579 code [4] treats plain dents. Dents are dangerous if they occur on longitudinal weld seams because then cracks can develop; several sources report that dented seam welds can have very low burst pressures [5]. A later study was made by the European Pipeline Research Group (EPRG) [6], which discovered that for plain smooth dents located away from pipe weld seams, dent depths up to 10% of the pipe outside diameter will not fail at membrane stress levels less than 72% of the SMYS: H ≤ 10% (1) De where • H = dent depth in the non pressurized condition (mm) • De = pipe outside diameter (mm)

The pipeline’s internal pressure tends to push out the dent, thus reducing the dent depth (known as the spring-back phenomenon). The measured depth on the operational pipeline must be corrected before this criterion can be applied. EPRG found the correlation between the dent depth on a non-pressurized pipe and on a pressurized pipe to be as follows [5, 6]: H = 1.43 H0

(2)

Fig.3 (left).Typical gouges. Fig.4. (right) A gouge-dent defect.

where H0 (mm) is the depth of the dent in the pressurized condition. Therefore, the EPRG limit for plain dents on a pressurized pipe is [5, 6]: H0 (3) ≤ 7% De A gouge in a pipe is characterized by material removed from the pipe’s surface. The removed volume is characterized by a high length-to-width ratio and a sharp notch profile. The gouge is inclined from an angle to the pipe longitudinal direction: an example of a series of parallel gouges is given in Fig.3. The following geometric parameters describe the gouge: • • • • •

length depth radius width gouge angle

2c a ρ W ψ

Gouges and dents can be combined to make a gouge-dent defect, see Fig.4; this kind of defect is very complex and implies geometrical and material non-linearities. Pipes are generally made of ductile material. The current trend is to use steel with higher yield stress with the risk of elastoplastic failure, particularly if defect like a gouge induces

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high stress constraint. Defect assessment of gouges and dents can be made using two major tools: limit analysis or notch fracture mechanics. The limit of using the former or the latter tool is not very easy to determine, and this point can be clarified using a notch-failure assessment diagram (NFAD) [7]. In a NFAD, a gouge or a dent on a pipe submitted to service pressure is characterized by an assessment point of coordinates [l*r,k*r]; Kr represents the non-dimensional fracture driving force (FDF) and Lr the non-dimensional applied load. Kr = FDF/FDFc

(4)

where FDFc is the material fracture resistance. The fracturedriving force can be defined as Jρ integral, or the notchstress intensity factor Kc indicates the critical value. The non-dimensional applied force for a pipe can be defined as the ratio of service pressure over limit pressure: Lr = ps/pL

Fig.5. Notch-failure-assessment diagram indicating the domain of limit analysis and notch fracture mechanics for gouges and dents as pipe defects.

(5)

Sa no m t f ple or c di op st y rib ut io n

An example of such NFAD is given in Fig.5 where A represents the defect assessment point of coordinates [l*r,k*r]. This NFAD is limited by the failure assessment curve that gives the limit of a safe and an unsafe pipe. The safe area is divided conventionally into three zones: • Zone I: if the assessment point lies in this zone, increasing the applied pressure leads to brittle fracture; • Zone II: where increasing the applied pressure leads to elastoplastic fracture; • Zone III: where plastic collapse occurs by increasing service pressure. Based on Federsen diagram [8] the limit of these three zones is defined conventionally as follows: • Zone I: 0 < Lr < 0.62 Lr,y • Zone II: 0.62 Lr,y < Lr < 0.95 Lr,L • Zone III: 0.95 Lr, max < Lr < Lr,max

where Lr,y is associated with the yield pressure and Lr,max is the maximum value of Lr. Figure 5 also indicates the area of practical interest for gouges and dents in the NFAD. Gouges and combined gouges and dents generally fail by elastoplastic fracture but the use of limit analysis is also possible. Dents are generally assessed by limit analysis.

Gouge assessment using limit analysis

Fig.6. Defect-assessment tools for gouge, dent, and combined gouge and dent, according to failure mode.

•

•

•

• •

yield, a plastic region starts to spread through the solid. As an increasing area of the solid reaches yield, the displacements in the structure progressively increase. Under a critical load, the plastic region becomes large enough to allow unconstrained plastic flow in the solid. The load cannot be increased beyond this point. If the material is strain hardening, the stress-strain behaviour is replaced by a rigid-plastic behaviour using the concept of flow stress. The following conditions are also included in limit analysis: Stress-strain behaviour follows the maximum dissipation principle. This implies that the plasticity criterion is convex and derives from a potential function of strain rate. The normality rule is followed by this principle. Boundary conditions are compatible with free structure deformation. Strain rate is relatively small.

Limit analysis provides two limit-load boundaries: The limit load for a perfectly rigid-plastic material is obtained from limit analysis which is based on the following mechanisms: • An inelastic solid will reach yield at some critical value of some applied load. If the load exceeds

• Lower boundary if the stress and strain fields are compatible with equilibrium. • Upper boundaries if the stress and strain fields follow the principle of maximum dissipation.

⎡ 1− (2/3) × (d/t) ⎤ ⎢1− (2/3) × (d/t)/M ⎥, ⎣ ⎦

2

⎛ L ⎞ ⎛ D⎞ , M = 1 + 0.8 ⎝ D⎠ ⎝ t ⎠

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2

⎛ L ⎞ ⎛ D⎞ 0.8 ≤4 ⎝ D⎠ ⎝ t ⎠

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⎡ 1− (2/3) × (d/t) ⎤ ⎢1− (2/3) × (d/t)/M ⎥, ⎣ ⎦ Index Hoop stress σθθ

2

2

⎛ L ⎞ ⎛ D⎞ ⎛ L ⎞ ⎛ D⎞ , 0.8 2 ≤4 M = 1 + 0.8 L ⎝D ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ⎠ ⎛⎝Dt ⎞⎠ D t Local ultimate (d /t) , Code1− or method 0.8 >4 2 strength σ*ul ⎝D ⎠⎞ 2⎝⎛ tD⎠⎞ ⎡ 1− (2/3) × (d/t) ⎤ L L ⎞ ⎛ Table D⎞ 2. Hoop stress and ⎛ ⎛ , , 0.8 2local ≤4 Mσ*= =1,1 1 + σ0.8 2 ⎢⎡1− ASME B31 A(d/t) ⎤⎥⎦ σθθ = pD/2t (2/3)× ×(d/t)/M ul y⎛ L (2/3) Lin D⎝⎞2ultimate ⎠ ⎞⎝ 2t ⎠ ⎝ ⎠ ⎠ strength used different ⎛ ⎞⎝ D ⎞ ⎛ ⎛D D t ⎣⎡ G1− , 2 , 0.8 ≤ 4 M = 1 + 0.8 ⎤ 1− (2/3) × (d/t) ⎢ (2/3) × (d/t)/M ⎥ L ⎛ D⎞ and methods.⎝ D ⎠⎛ L ⎝0.8 ⎝⎛⎞tL⎠⎛⎞D⎛⎞ D>⎞4 ≤ 4 D⎠⎛2 ⎝ t⎞ ⎠codes 2 0.8 Modify ASME⎣⎢1− B31 G B[1−×(d σ*M +69 ⎦/t)⎥,]σ⎤,θθ = pD/2t ,Di, σ , and⎛ σL ⎞0.8 = 1σy+ ul =1,1 ⎡ 1− (2/3) (d/t) L ⎞⎝ ⎛ D⎠⎞D, D ⎛ ⎛ ⎞⎝⎠D⎝⎠ t ⎝⎠ t ⎠ De, are mean 1− (2/3) × (d/t)/M ul 0.8 y ⎝2D D ,⎝ t ⎠4 ⎦ ⎥, ≤4 ⎡ 1− 0.85⎣× (d/t) ⎤ × (d/t)/M ⎢1− (2/3) 2M = 1 + 0.8 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎛ D diameter, external diameter, internal DNV RP-F101 C σ = p(De-t)2t σ* =σ D D t t 2 2 ⎣ ⎦ L θθ ul ul L L D D ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎡ 1− (2/3) ⎤ ⎢1− 0.85 × (d/t)/M ⎥ × (d/t) L ⎞ ⎛ Dand ⎛ L ⎞ ⎛ D⎞diameter, ultimate ⎛strength ⎞2 ⎞ yield − 0.003375 M = 1 + 0.6275 , , 0.8 4≤⎞ 50 M = 1 + 0.8 ⎣ Choi’s method ⎦ 2 2 L⎝t ⎞⎠t ≤⎛⎠D ⎛ ⎝ ⎠ ⎡⎢⎣1− ⎤ ⎥⎦σθθ= pc(Di-t)2t ⎝ D⎠ ⎝σ*tul⎛ ⎠L=0.9 1− (2/3) (2/3) ××D (d/t) ⎝ ⎠ ⎝ ⎠ σ D (d/t)/M L D D ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎛ ⎞ ⎞ ⎛ ⎞ ⎛ ⎞ D t D D t ul 2 stress, respectively. (d /t)]0.85 [1− >4 , 0.8 ≤ 224 ⎛0.8 M = 1 + 0.8 , ⎥,⎤× (d/t) ⎤ ⎡ ×1− L2 ⎞ ⎛2D 4 2 2 2⎞ ⎝ D⎛ ⎠L⎛2⎝⎞L2t ⎛⎞⎠2D ⎝D ⎠ ⎡⎢⎣⎡1− 1− (2/3) ⎡(2/3) ⎡×(d/t)/M ⎦⎤ × ⎤(d/t) ⎤ 1− (2/3) 1− ×(2/3) (d/t) L⎞ ⎞0.8 LD⎞2⎞⎛ ⎛L⎝⎛D⎞D L⎞⎞⎠⎛ D L⎞D⎞⎞ ⎛⎛DL⎞⎞ ⎛ D⎝⎞⎛⎛DLL⎠⎞⎞2⎝⎛ t⎛D⎠D 1− (d /t) ⎛ ⎛ ⎞ 1− (2/3) × (d/t) (d/t) [ ] ⎛ ⎛ ⎛ > 2t⎞ 4 L D , ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ , , ≤ ≤504 ,2 0.8 , 0.8 0.8≤⎛ 4L⎝⎞0.8 ≤ =+ 0.8 M 1 +=0.81 ,+ 0.8 − ,0.003375 2 ⎠4 ⎛ ⎢1− 1− 0.85 ×⎥⎥,(d/t)/M ⎠≤⎝D⎠L4⎝⎞⎛⎠⎠⎝tL =+=0.6275 1M + 10.8 ⎢1− ⎥(d/t) ⎥, M = M1M ⎛⎝D ⎢1−(2/3) ⎣(2/3) 1− (2/3) ⎠⎝0.8 1− ×(2/3) (d/t)/M ⎠t ⎠⎞ D ⎞ > 4 ⎠D L⎠⎠⎞ ⎝⎛ D (2/3) ×⎡⎣×(d/t)/M (d/t)/M D ⎝ ⎝DD ⎠⎝⎠D ⎝ t⎝⎠ ⎠2⎝t⎝D ⎠Dt⎠⎠ ⎝⎝⎛ tD Geometrical t ⎠⎞⎝ D ⎛ tD⎞> ⎝⎛t4⎞D (d /t) ⎦ ⎦ ⎤⎦, [×1− ]⎦⎤⎦,××(d/t)/M D⎠⎠ ⎝ ⎛⎝t0.8 t⎠ ⎞⎠ 2⎝⎛⎝DDt0.8 (d /t) [⎢⎣1− ] ⎡⎣ ⎣1− (2/3) (d/t) , L L ⎛ ⎞ ⎛ ⎞ ⎞ , ≤4 M = 1 + 0.8 Index Geometrical correction Bulging factor M ⎠ ⎝2conditions ⎢1− (2/3),× (d/t)/M ⎥ ≤⎝tD 4⎠⎝⎠D⎝⎠ ⎠⎝ t ⎠ M = 1 + 0.8 L 2 D , ⎝2D⎠ ⎝ t ⎠ 0.8 L ⎝2 DD ⎢⎡1−1−(2/3) ⎦ (2/3) (d/t) ⎥⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 2D ⎞2 t ×⎣×(d/t)/M ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 2 L D D t t ⎦ ⎣ ⎛ ⎞ ⎛ 2 , ⎛D ≤ 4L ⎛>⎞D4⎞ ⎡ 1− 0.85⎡×⎢1− L⎛ ⎞L40.8 (d/t) ⎛ L⎞⎞ ⎛ D ⎛2 DD⎞⎞0.8 ⎥⎡⎤,×1− ⎛L ⎡(d/t) ⎤ × (d/t) ⎤, M = 1 + 0.8 1− ](2/3) (d/t)(2/3) 0.85 [1−(d⎤××(d 2 ⎝⎛ LM ⎞t1⎠⎞ (d/t)/M 1− ⎝ D>≤2⎠ 424⎝⎝⎛ tL ⎠⎠2L⎞2 ⎝⎛⎞ ⎛t2 ⎛⎞⎠D [0.85 ]/t) ,⎞ ⎛D 0.8 4 D⎞⎞⎠ 2⎛=⎝DD ⎦⎤⎢1− , ⎡ ×,1− ⎥M = M 2 0.8 2 ⎞ >≤50 , +2 0.8⎝ 0.8 = L1+ + 0.032 0.8 3.3 ⎢1− ⎥,(d/t) L D ⎛ ⎡⎣1− ⎤ 1−(2/3) (2/3) (d/t) 1− ××/t) (d/t) ⎛ ⎞ ⎛ ⎛ ⎞ ⎛ ⎞ (2/3) × (d/t)/M ⎡ 1− ⎤ (2/3) (d/t) 2 4 2 ⎤ ⎠ ⎝ ⎠ ⎝⎛ D (2/3) × 2 L L D ⎝ ⎠ (2/3) × (d/t)/M D t t ⎠⎞≤ 50 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 2 D t ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ L L D ⎢A1− 0.85 ×⎢⎡1− ⎥ L L2⎞⎞⎠2D D ⎥, (d/t)M D −⎝⎛t0.003375 2 L ⎛⎝ ⎞ 2⎞⎛⎠≤⎛⎝DD ⎞⎠, ⎛ ⎝⎛ ⎞⎛tL⎞L ⎛⎞ ⎛D ⎞LD ⎣ ⎦ = 1,+ 0.6275L Dt L ⎠ ⎞ ⎛ ⎞ D D ⎛ , ⎝ ⎠ × (d/t)/M 0.8 4 M = 1 + 0.8 ⎡ ⎤ D 1− 0.85 × ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ L D , M = 1 + 0.8 0.8 ≤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ D t D 1− 0.85 × (d/t) ≤ 4 M = 1 + 0.8 , 0.8 ⎢1−0.85 ⎥ 2 L L D D ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎣⎢(d/t)/M ⎦ 2 4 2 ⎢ ⎥ ⎥ ⎣ ⎦ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ /t)(d [1− > 4⎝ D ⎠t ⎠> >5044 (2/3) ×1− (d/t)/M ≤⎝450 ⎝+⎝ D ⎠⎠ ⎝ ⎝t⎛D⎠L⎠ 0.8 ⎠⎠D> ⎝⎛ LD⎞⎠M⎛⎝D ⎠ ⎞0.8 1− −⎠⎠0.003375 1− (2/3) (d/t)/M ⎠D /t) =⎝tD 3.3 0.85 ×[(d (d/t)/M D t0.032 t⎝D [⎢1− ]] ,,⎣×[/t) ⎣ 1− 1− ⎞⎝⎠4Dt⎠⎝⎠> ]⎦(2/3) ⎞⎝⎝⎠⎝D ⎛t⎝⎝D ⎣0.85 22t ⎣⎡1− ⎦(d , ⎤ /t) ,(d/t)/M ⎠ ⎝⎠⎝4⎝⎝tt 0.8 ⎠⎠⎛ ⎠⎠L⎝⎞⎝⎝D ×0.85 (d/t) ⎢(d ⎥=M =1 ⎦+10.6275 ⎥×]⎦M 2⎠⎞ − 0.003375 2 ⎛0.8 ⎠ ⎝ ⎝ ⎠ ⎝ ⎝ ⎠ ⎝ ⎠ t ≤ 50 ⎠ ⎝ ⎠ ⎝ ⎠ 2 + 0.6275 D D t t ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ 1− × (d/t)/M D t L D D t 1− 0.85 × (d/t)/M D ⎛ tD⎞ ⎛t t ⎠⎞ ⎣ ⎣ ⎦] ⎦ ⎛ ⎠L ⎝⎞ t ⎛⎠ D⎞ ⎝⎞D⎞⎠⎛DD⎝0.8 ⎝D ⎝ D⎠ ⎝⎛ 2tL⎠⎞2 ⎛⎛LD 1− (d⎥ /t) ⎞t ⎛⎠ L ⎞ ⎛ D⎞> ≤4 50 [ ⎢1− , ⎡ ⎤ 1− 0.85 × (d/t) 2 − 0.003375 M = 1 + 0.6275 2 4 2 1− (d /t) [ ] 0.85 × (d/t)/M 0.8 > 4 ⎠ 2⎝ t ⎠ ⎡ ⎤ 2 ⎝D , 2 4 ⎞⎛ ⎛ LD ⎣ ⎢ 1− 0.85 × (d/t) ⎦] ⎞⎠ ⎞2⎛⎝⎛D ⎛ L ⎞ ⎛ D⎛ ⎞L⎝⎞D ⎛⎠ L ⎞ ⎛ D⎞ ⎛ L⎛⎞L ⎞⎛ D ⎝>⎛D L ⎠ ⎛⎝Dt⎞ ⎠ ⎠⎛>⎞⎠L ⎠D⎝⎞M= ⎝⎛⎝D ⎝≤DL⎞⎠50 [1−⎥ (d /t) 0.8 4⎝⎛ ⎞D t ⎠0.8 t t ⎞ ,[1− ⎛ ⎞ 1− (d /t) − 0.003375 M = 1 + 0.6275 [ ] 0.85 × (d/t)/M 0.8 4 ≤⎞ 50 (d /t) ⎥ ] >4 A ∞ ⎠ ⎝ , ⎣⎢⎡1− ⎦ ⎤ ⎦ 1−0.85 0.85 × (d/t) − ⎝0.003375 M = ,1 + 0.6275 ⎝ t ⎠ ⎝t D⎠ 2 ⎝ t ⎠ 2 ⎝ D 1− (d/t)/M ⎝ D⎠ 2⎝ t ⎠ ⎠ 4⎝ t ⎠ 2 2 ⎝ DL⎠ 2D 2 t ⎠ D ⎣ D 2 ⎞⎠ ⎝⎛ D ⎝ ⎠ ⎝ ⎠ L L D D ⎛ ⎞ ⎛ ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ t L ⎡ ⎤ 1− 0.85 × (d/t) 2 ⎞ 2D D D t t ⎛ ⎞ ⎡ ⎡ ⎤ ⎤ 1− 0.85 1− × 0.85 (d/t) × (d/t) L 2 2 D 2 4 2 ⎢ ⎥ 2 2 4 2 4 ⎛ ⎛ ⎞ 2 L D 2 ⎡⎡ 1− (d/t) L ⎛LD ≤⎛⎛50 −⎞⎞0.003375 M ⎛ D⎞ ⎞⎞⎛tL⎠⎛⎞D 0.85(d×× (d/t)/M (d=/t)]1,+ 0.6275 ⎛ L ⎞ ⎛⎛LD ⎞4l⎞⎛⎛⎞DD 4 LD⎞⎛⎞2 ⎛⎞⎛0.8 L⎛>⎞⎛⎞D 1− /t) ⎣1−0.85 ⎦⎥⎤⎤][1− ⎞⎞t4⎠>>50 [⎢⎡0.85 ](d ⎛⎞DL 1− /t) 1− × (d/t) L⎛⎛L ⎛⎛DL⎞+⎞ 0.032 ⎛⎝DD⎞⎛⎛⎠ L ⎞L [⎢⎡(d/t)/M ,×−0.85 > ⎞t2⎞⎛⎠2⎛⎞⎛DD ⎢1− ⎠ +⎝ M 1−0.85 (d/t) D1 t =⎠ =3.3 3.3 ⎡ 1 − (d/t) ⎤0.85 ⎝⎞⎞50 ⎞⎞⎝⎞⎞D2⎛⎛⎠DL⎝0.8 50 ⎛0.8 ⎛≤⎠D ⎞⎝⎝ D ≤2t ⎠⎠l50 ≤ 50 −++ 0.003375 M= 1− (d/t) ⎠ ⎛2⎞⎝⎝L ×0.85 1−⎝⎝⎞0.003375 −2 ⎛0.003375 M⎥⎤⎦1=+ 0.6275 M 1 +=⎝0.6275 0.6275 ⎡1− ⎤⎥⎦⎤(d/t) 1− ×10.85 (d/t)/M ××, ×(d/t) (d/t)/M 4⎝D t ⎠ ⎢⎢1− ⎥ ⎞ M 0.032 1 ⎣ 1− ⎦ D > ⎣ ⎣ ⎛ ⎡ ⎤ 1− 0.85 2 M = 3.3 0.032 2 4 2 ⎝ ⎠ ⎠ > 50 ⎝ ⎠ ⎝ ⎠ ⎡ ⎤ 0.85 × (d/t) ⎥ ⎝ D⎛⎠=L2⎝⎝⎞Dt⎛1 L⎠⎞⎠⎠ ⎠⎝⎛⎝D D⎝ D2⎝⎠⎞D⎝t⎠⎠D⎝⎝⎠⎜⎝⎛⎝ tD ××0.85 (d/t)/M < 66 ⎠⎠ + ⎝⎝⎛ tM L⎠⎛⎠⎞DL L⎠⎠⎞2= ⎝⎛ D t t⎠⎞⎟⎟⎠ < D D ⎣⎣1−0.85 ⎦ 1− ⎠D ⎝4⎝t⎞⎛⎝D L⎝ ⎞⎠L 1t ⎠⎞+⎝⎝⎛ D 0.31 ⎛⎞⎠⎝D ⎢⎢1− ⎥ (d/t) 0.85 (d/t)/M D t⎠Dt⎠⎠2⎞⎠⎠t⎛2⎝L⎝⎛2t⎞D ⎥⎥⎦, 0.85 ⎥,⎢⎣0.85 1− ×−0.85 (d/t)/M L+⎞0.6275 ⎛ ⎞⎛⎞4≤t⎝250 ⎛DD2⎞ t ⎝⎜⎠ tRt ≤ 50 ⎛1M ⎛ DD ⎞ ⎞⎛−0.31 ⎛ 0.003375 2Rt2 − M 0.003375 1⎤+=0.6275 1(d/t) (d/t)/M 1− 0.85 B ⎢⎣1 − (d/t)/M ⎤⎥⎤×⎦⎡×(d/t)/M L 1− 0.85× ×× D⎞⎞2⎠⎝⎛Dt ⎣×⎣⎢⎣(d/t) ⎦M =⎥⎦ ×⎦1M 1− 0.85 (d/t) ⎞⎠ ⎛⎛⎝⎝ 2 ⎠ ⎝ t ⎠− 4⎠ Dt ⎛L ⎛⎞⎛D ⎡⎢⎣⎡⎡1− ⎤(d/t)/M 1− D ⎦0.85 ⎝ ⎠ ≤ 50 L D ⎝2⎞D ⎠D ⎝⎠Lt⎞L ⎠⎝ t⎛ D L D 0.003375 ⎞ +=0.6275 ⎝ ⎠ ⎝ ⎠ ⎛ ⎝+D ⎠⎞⎠⎛ ⎝⎝tL L D ⎛ ⎞ ⎛ ⎞ (d/t)/M ⎝ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎠ ⎝ ⎞ ⎞ D D t D t ⎦ 2 ⎢ ⎥ M = 3.3 0.032 >⎠⎞ 50 L D L=⎠⎞ ⎝M ⎛1D ⎞0.6275 ⎞ ⎠ 2⎝ ⎝⎛D ⎝⎛ D ≤ 50> 50 ⎥ ⎥⎣1− ⎝⎛ D ⎝⎛ D t ⎠⎞⎞ 2≤⎛⎝50 × (d/t)/M D t+⎠= ⎢⎢⎣1− ⎡⎡1−1− ⎤ 0.85 2⎝ t0.032 1− 0.85 ×(d/t) (d/t) ⎦ ⎝⎛M ⎝3.3 ⎠+ ⎠ ⎛⎝L D ⎞⎠ ⎝−⎠⎞⎛0.003375 ⎞t⎝ ⎠D D0.003375 0.85 ××(d/t)/M ⎞ tD⎠⎠4 ⎝ ⎛t ⎠L ⎢1− ⎥ − M = 1 + 0.6275 ⎠ ⎝ ⎠ 0.85 (d/t)/M ⎦ ⎝ ⎠ ⎝ D t ⎡ ⎤ 1− 0.85 × (d/t) D t 2 ⎤ ⎣ ⎦ 0.85 × L D 2 2 ⎠ ⎝ ⎠ L ⎛ ⎞ ⎛ ⎞ ⎝ ⎠ ⎝ ⎛ ⎞ ⎛ ⎞ 0.85 ××0.85 (d/t)/M ⎝⎞D ⎠ 2 ⎝⎞ t ⎠ 2 ⎛ L D ⎤ ⎦⎥ ⎤ 0.85 (d/t)× (d/t) ⎠ 2+⎝=0.032 ⎠ 2 +⎛0.032 4 ⎝ t ⎠ 24 t⎛ L ⎡ 1− ⎣ ⎡ ⎢⎢1− D2⎠⎝D DM t3.3 L ⎞ ⎛ ⎝D ⎞⎠2 > ⎛ D50 ⎞ t⎠ =⎛⎝ 3.3 ⎞⎛⎝ ⎠L 2 D ⎢1−⎥⎤⎥0.85 ⎥ M ⎠L⎝⎞2⎞D⎠⎛ D L2⎠ ⎞⎛>2D50 D 2 ⎛ ⎝ ⎝ ⎠ L D D 1−⎡0.85 0.85 ×(d/t)/M (d/t)/M ⎛ t ⎛ ⎞ L D ⎞ ⎛ ⎞ ⎞ ⎛ t L D ⎛ ⎞ ⎞ ≤ 50 ⎝ ⎠ ⎝ ⎠ − 0.003375 M = 1 + 0.6275 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎣⎣1− ⎦ × (d/t)/M ⎝ × D t ⎡⎢1− 0.85 × (d/t) L D t 2 ⎡ ⎤ ⎤ 1− 0.85 1− × 0.85 (d/t) × (d/t) L L D D ⎢ ⎥ L D 2 ⎛ L⎠ ⎞0.003375 ⎛⎠⎞ ⎞⎞ ⎛⎛ ⎞⎞ ⎛L ⎝⎞D⎛D⎠ ⎞⎝ ⎛t⎛L⎠ ⎞⎞ ⎛≤⎛D ⎦⎦ × (d/t) L 50 ⎞⎞⎠ ⎛≤⎝D50 − 0.003375 M 1 +=⎦0.6275 0.85 (d/t)/M 1 + 0.6275 ⎝⎞+⎛⎛t0.032 ⎡2 1− ⎤ M D D t ⎞⎠ > 50 ×⎣0.85 (d/t)/M ⎛− D ⎞ ⎠ ⎝⎛⎝ t ⎠⎠ >⎝⎝50 M =M⎠M 3.3 +⎠3.3 0.032 ⎣1−×0.85 ⎦ = =D +=t⎝0.032 M 3.3 2⎠⎛ ⎝⎞ ⎛⎝⎠D 22⎝⎝ D ⎞t ⎠>2 ⎞50 ⎝ ⎝ ⎝ ⎠ ⎠ = 3.3 + 0.032 ⎢⎣1− ⎥ B 2 D D t t > 50 ⎝ ⎠ ⎝ ⎠ ⎢ ⎢ ⎥ ⎥ ⎛ ⎞ D t 1 − (d/t) l ⎛ ⎤ ⎡ ⎢ ⎥ a a ⎝ ⎠ ⎝ ⎠ ⎞⎣1− ⎛ ⎦ ⎞ ⎦⎤ 1⎠1t⎠ ⎞1⎝⎝⎛ tD 1− 0.85 ×(d/t)/M (d/t) L⎠⎠⎞ ⎝⎝⎛DD × ⎣⎡(d/t)/M D⎠ ⎛⎛⎝2⎝tD 1⎣11− −− ⎛(d/t) L 0.85 ×− (d/t)/M ⎝D ⎞⎝⎝ tD⎠ ⎠ 2⎝⎝Dt⎠⎠ ⎝⎛⎝ tD l⎠⎞⎠ ⎛⎝l D t ⎞⎠ 0.85 2t⎠ ⎠ ⎤0.85 ⎡ 0.85 2 ⎤⎦⎥×⎡,×(d/t)/M 0.85 ×1− (d/t) 1 C 0 ⎡⎣= ⎡1− 0.06 0.1035 ⎛+0.31 ⎞+20.032 ⎛⎛D ⎞⎞ ⎞ ⎛ L M =M1=+3.3 ⎤ 1−⎦ 0.85 ×+ ⎛ ⎞L ⎞ 2⎛⎜D⎜⎞ ⎛⎜⎟L 50 ⎝ ⎠ ⎝ ⎠ = 3.3 + 0.032 ⎢ t ⎦ ⎝ ⎠ ⎝ ⎛ ⎞ Dt × (d/t)/M D t D t⎠ ⎝ ⎠ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎡1− ⎤ 1− 0.85 × (d/t) L D < 6 , 1 − (d/t)/M 1 − (d/t)/M L D ⎛ ⎞ ⎛ ⎞ Rt Rt ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎣ ⎦ M = 1 + 0.31 ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ 0.85 × (d/t)/M D t ⎝ ⎠ ⎝ Dt Dt + 1 C 0 = 0.06 − 0.1035 1− 0.85 × (d/t)/M D t D t ⎝ > ⎝50 D 2⎠ t ⎠ ⎣⎢ ⎢⎣1 − (d/t)/M ⎥⎦ 2 ⎦⎥⎣ ⎦ M = 3.3 + 0.032 ⎝ Dt ⎠ 2 ⎛22 Rtl ⎠⎞ ⎛ ⎞ ⎡⎡1⎝1− ⎝ t⎠ 0.85 × (d/t) ⎡ 0.85 ⎛ 1 ⎝⎞ D⎠ 2 ⎝ 1t ⎛⎠ 221⎛ L⎞⎝⎞ ⎛ D ×⎠(d/t) (d/t)/M 2 ⎤⎞⎝ D ⎠⎝⎛50 C ⎣⎢ ⎦ ⎥ ⎥0.85,× (d/t)/M Dt M = 3.3 D tRt M =⎢=1C0.032 3.3 +C⎛0.31 0.032 ⎞ ⎠⎟ lRt ⎞⎠⎞⎠ 2 >⎝ 50 ⎝− t(d/t) M +00.31 ⎢1−⎢⎣⎡10.85 −⎡(d/t) (d/t)/M −1−(d/t)/M l⎝⎝ ⎝t ⎠⎠l⎛Rt 1 ⎝D ⎤⎡⎢⎣⎠×⎣⎥⎦11− ⎠⎛ ⎝2Dt 1(d/t)/M −⎤(d/t)⎥⎦ ⎥⎤ ⎝ t ⎠ ⎦ ⎝ ⎠ ⎦−1(d/t)/M 2× ⎝ ⎝ ⎝ ⎠ Dt 1 ⎠⎠⎝⎛Rt ⎝ ⎠ (d/t)/M 1 1 t Rt ⎝ ⎠ ⎠ ⎛ ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ D l ⎝ ⎠ ⎞ ⎞ 0.85 D t Dt 2 Rt a ⎣ 2⎛⎣1⎢⎣a1− ⎦ D t ⎝ ⎠ ⎛ a⎞ ⎛ ⎞ 6 ⎟⎞⎞ < 6 ⎞⎢ ⎛ a ⎞ ⎦⎥, M = M1⎣+L ⎡ ⎤ 2 2 ⎦ ⎜ ⎜ ⎟ Rt