Stress intensity factor and limit load handbook - …

1 EPD/GEN/REP/0316/98 ISSUE 2 1999 Published in the United Kingdom by British Energy Generation LtdAll rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means,including photocopying and recording, without the written permission of the copyright holder, application for whichshould be addressed to the publisher. Such written permission must also be obtained before any part of thispublication is stored in a retrieval system of any for copies of this document should be referred to the Barnwood Document Centre, Location 12, BritishEnergy Generation Ltd, Barnett Way, Barnwood, Gloucester GL4 3RS (Tel: 777-2791)LIMITATION OF LIABILITY - Whilst British Energy Generation Ltd believe that the information given in thisdocument is correct at the date of publication it does not guarantee that this is so, nor that the information is suitablefor any particular purpose.

2 Users must therefore satisfy themselves as to the suitability of the information for thepurpose for which they require it and must make all checks they deem necessary to verify the accuracy Energy Generation Ltd shall not be liable for any loss or damage (except for death or personal injury causedby negligence) arising from any use to which the information is 002 Issue 1 Task No:SINTAP/Task Energy Generation LtdStress intensity factor and limit LoadHandbookIssue 2, April 1998By:S Al LahamStructural Integrity BranchAuthorised By:R A AinsworthTitle:Group Head, Assessment Technology GroupENGINEERING DIVISIONEPD/GEN/REP/0316/98 ISSUE 2iStress intensity factor and limit Load Dr S Al Laham, Structural Integrity BranchIssue 2 Date: 15 April 1999I confirm this document has been subject to verification and validation by internal reviewwithin Nuclear Electric Ltd. Dr R A Ainsworth, Group Head, Structural Integrity BranchDr M J H Fox, Team Leader, Structural Integrity BranchDate:Approved for Issue:Date:Dr R A Ainsworth, Group Head, Structural Integrity BranchSUMMARYThis report provides a collation of Stress intensity factor and limit load solutions for defective includes the Stress intensity factor (SIFs) in the R6 Code software and in other computer programs,which have not previously been contained in a single source reference.

3 This document has been producedas part of the BRITE-EURAM project SINTAP which aims to develop a defect assessment approach forthe European Community. Most of the solutions presented in this document were collated from industryand establishments in the UK (Nuclear Electric Ltd, Magnox Electric Plc and HSE), Sweden (SAQK ontroll AB) and Germany (Fraunhofer IWM, and GKSS). The solutions are compared to standardsolutions published elsewhere and to those in the American Petroleum Institute document API 579. In thissecond issue, the quality of the figures has been improved, minor typographical errors found in theprevious issue have been corrected, and comments from partners in SINTAP have been DIVISIONEPD/GEN/REP/0316/98 ISSUE 2iiREVISION/REVIEW ofRevisionApprovedIssue 2 Revision 115/4/1999 Summary (i) , , 44, 46,47, 49, 50, 52& & , 26 & to widthchanged in figureto 2W.

4 Equationfor K edited byremoving (2) fromthe widthchanged to 2W ofapplicabilitymodified toremove wordCompressionchanged OF CONTENTSPAGEENGINEERING DIVISIONEPD/GEN/REP/0316/98 ISSUE 2iiiSummaryiReview RegisteriiList of Contentsiii1. LOADING AND STRESSES ANALYSIS AND ASSESSMENT OF THE INTEGRITY OF METHODOLOGY USED IN COLLATING COMPUTER ListENGINEERING DIVISIONEPD/GEN/REP/0316/98 ISSUE wide range of structural configurations, loading conditions and crack geometries, together with thematerial and geometric non-linearities which characterise response under loads, has made the analyticalprediction of both the strength and Stress intensity factors (SIFs) fatigue cracks initiate at several locations, mostly around the weld region in joints and areas ofdiscontinuities, due to the high bending, welding residual stresses and weld notch stresses.

5 These crackseventually coalesce to form a single crack which grows in both the length and depth directions and which mayfinally becomes a through thickness crack. In order to assess the integrity of structures containing defects, it isnecessary to be able to estimate both plastic collapse and fracture strengths of the critical members intensity factors (SIFs) can be calculated in the Nuclear Electric s R6 Code software(1) and othercomputer programs. Further, a number of methods are now available for evaluating Stress intensityfactors(2 to 8) and limit loads(9 to 15) of structures containing order to provide a single source reference for use in a procedure being developed under the Brite-Euramproject SINTAP, this report collates solutions for Stress intensity factors and limit loads for differentcracked geometries and structures. In this document only one solution is presented for each crackedgeometry/loading combination.

6 This is the result of detailed evaluations and comparisons of availablesolutions. It should not be inferred that the solution selected is the only satisfactory one. Solutions otherthan those given here may be used in the analysis provided they are of the work presented in this document has been collated from industry and establishments in the UK(Nuclear Electric Ltd, Magnox Electric Plc and HSE), Sweden (SAQ Kontroll AB) and Germany(Fraunhofer IWM, and GKSS). In developing this source reference, care has been taken to ensure that,wherever possible, the solutions recommended have been validated. The recommended compendia of SIFand limit load solutions are given in four separate appendices. Appendix I gives the recommendedsolutions for SIFs, while guidance on calculating the limit loads is given in Appendix II. The assessmentof tubular joints used in the offshore industry also requires specialist guidance due to the complexity of thejoint geometry and the applied loading, and the current guidance for offshore structures is contained inAppendix III.

7 limit load solutions with the presence of material mismatch are given in Appendix IV ofthis report. Finally, the results of the comparison of the Stress intensity factors from different sources aregiven in Appendix V. It should be noted that the scope of Appendix III is limited to the assessment ofknown or assumed weld toe flaws, including fatigue cracks found in service, in brace or chord members ofT, Y, K or KT joints between circular section tubes under axial and/or bending five appendices form the bulk of this report. In the main text, brief sections deal with the loading,behaviour, failure of structures and a description of the methodology used in this study. It should be notedthat it is intended to update this document as and when knowledge and techniques DIVISIONEPD/GEN/REP/0316/98 ISSUE and Stresses ConsideredLoading of a structure includes all forces and other effects which cause an increase of thestrain on the part of the structure under assessment.

8 The stresses to be considered in theassessment of the integrity of structures containing defects may be treated directly, or afterresolution into the following four components(16):a) Membrane Stresses:The component of uniformly distributed Stress which is equal tothe average value of Stress across the section thickness and is necessary to satisfy thesimple laws of equilibrium of internal and external ) Bending Stresses:The component of Stress due to imposed loading which varies acrossthe section ) Secondary Stresses:The secondary stresses are self equilibrating stresses necessaryto satisfy compatibility in the structure. Thermal and residual stresses are usuallyconsidered ) Peak Stresses:The peak Stress is the increment of Stress that is added to the primarymembrane and bending stresses and secondary stresses due to concentration at DIVISIONEPD/GEN/REP/0316/98 ISSUE and Assessment of the Integrity of StructuresThe integrity of a structure containing defects may be evaluated by reference to two criteria(1 and 17), fractureand plastic collapse.

9 This may be carried out by obtaining the fracture and the collapse parameters Kr andLr respectively. The Lr parameter is a measure of plasticity effects which gauges the closeness to plasticyielding of the structure, and is defined as the ratio of the loading condition being assessed to that requiredto cause plastic yielding of the structure. The fracture parameter Kr is a measure of the proximity to linearelastic fracture mechanics (LEFM) failure of the structure. Kr is simply the ratio of the linear elastic stressintensity factor to the fracture toughness of the material used. Structural integrity relative to the limitingcondition may be evaluated by means of a Failure Assessment Diagram (FAD) using the proceduresoutlined in R6. These procedures require assessment points to be plotted on the FAD, the location of eachassessment point depending upon the applied load, flaw size, material properties, etc.

10 A necessarycriterion of acceptance is that the assessment point of interest should lie within the area bounded by theaxes of the failure assessment diagram and the assessment diagram are various Stress intensity factor solutions, particularly for flat plates and pressure vessels withvarious cracked geometries. Some of these solutions are based on the use of thin-shell theory(18), whichdoes not take into account the three dimensional nature of the highly localised stresses in the vicinity of thecrack front. Further, thin-shell theory does not take into account the effect of transverse shear acting alongthe crack front. In recent years three-dimensional finite element analyses have been performed by anumber of analysts(19 to 21). One advantage of the use of 3-D finite elements is that it is possible to take intoaccount the effect of the 3-D nature of the Stress state in the vicinity of the crack front.