Fracture Mechanics PDF
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Mechanical Engineering Series Fredrick F. Ling Series Editor Springer Science+Business Media, LLC Mechanical Engineering Series Introductory Attitude Dynamics F.P. Rimrott Balancing ofHigh-Speed Machinery M.S. Darlow Theory ofWire Rope, 2nd ed. G.A. Costello Theory ofVibration: An Introduction, 2nd ed. A.A. Shabana Theory ofVibration: Discrete and Continuous Systems, 2nd ed. A.A. Shabana Laser Machining: Theory and Practice G. Chryssolouris Underconstrained Structural Systems E.N. Kuznetsov Principles ofHeat Transfer in Porous Media, 2nd ed. M. Kaviany Mechatronics: Electromechanics and Contromechanics D.K. Miu Structural Analysis ofPrinted Circuit Board Systems P.A. Engel Kinematic and Dynamic Simulation ofMultibody Systems: The Real-Time Challenge J. Garcia de Jal6n and E. Bayo High Sensitivity Moire: Experimental Analysis for Mechanics and Materials D. Post, B. Han, and P. Ifju Principles ofConvective Heat Transfer M. Kaviany (continuedafterimlex) Dominique P. Miannay Fracture Mechanics With 543 Figures t Springer Dominique P. Miannay Department d'Evaluation de Surete NucIeaire Institut de Protection et de Surete Nucleaire Fontenay aux Roses F-92265, France Series Editor Fredrick F. Ling Emest F. Gloyna Regents Chair in Engineering Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712-1063, USA and William Howard Hart Professor Emeritus Department of Mechanica1 Engineering, Aeronautical Engineering and Mechanics Rensse1aer Polytechnic Institute Troy, NY 12180-3590, USA Library of Congress Cataloging-in-Publication Data Miannay, D.P. (Dominique P.) Fracture mechanics I D.P. Miannay. p. cm.--{Mechanical engineering series) Includes bibliographical references and index. ISBN 978-1-4612-7259-5 ISBN 978-1-4612-1740-4 (eBook) DOI 10.1007/978-1-4612-1740-4 1. Fracture mechanics 1. Title. II. Series: Mechanical engineering series (Berlin, Germany) TA409.M53 1997 620.1'126--dc21 97-10651 Printed on acid-free paper. © 1998 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1998 Softcover reprint ofthe hardcover Ist edition 1998 AlI rights reserved. This work may not be translated or copied in whole or in part without the wrltten permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly ana1ysis. U se in connection with any fonn of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the fonner are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Anthony Battle; manufacturing supervised by Johanna Tschebull. Photocomposed copy prepared from the author's files by the Bartlett Press, Inc., Marietta, GA. 9 8 7 6 5 432 I ISBN 978-1-4612-7259-5 SPIN 10576809 To my family Mechanical Engineering Series FredrickF. Ling SeriesEditor AdvisoryBoard AppliedMechanics F.A.Leckie UniversityofCalifornia, SantaBarbara Biomechanics V.C. Mow ColumbiaUniversity ComputationalMechanics H.T. Yang UniversityofCalifornia SantaBarbara DynamicSystemsand Control K.M. Marshek UniversityofTexas,Austin Energetics l.R. Welty UniversityofOregon,Eugene MechanicsofMaterials I. Finnie UniversityofCalifornia,Berkeley Processing K.K. Wang CornellUniversity Production System G.A. Klutke TexasA&M University ThermalScience A.E. Bergles RensselaerPolytechnicInstitute Tribology W.O. Winer GeorgiaInstituteofTechnology Series Preface Mechanical engineering, an engineering discipline borne ofthe needs ofthe in dustrial revolution, is once againasked to do its substantial share in the call for industrialrenewal.Thegeneralcallisurgentaswefaceprofoundissuesofproduc tivityand competitivenessthat require engineering solutions, among others. The Mechanical Engineering Series features graduatetextsandresearchmonographs intendedtoaddresstheneedforinformationincontemporaryareasofmechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re search. We are fortunate to have a distinguished roster ofconsulting editors on the advisory board, each an expert inone the areas ofconcentration. The names ofthe consulting editors are listed onthe facing page ofthis volume. The areas ofconcentration are: applied mechanics; biomechanics; computational mechan ics;dynamicsystemsandcontrol;energetics;mechanicsofmaterials;processing; thermalscience; andtribology. I am pleased to present this volume in the Series: Fracture Mechanics, by DominiqueMiannay.Theselectionofthisvolumeunderscoresagaintheinterestof theMechanicalEngineeringseriestoprovideourreaderswithtopicalmonographs aswellasgraduatetexts inawidevarietyoffields. Austin,Texas FrederickF. Ling VlI Preface This book has been written for engineers from three disciplines: the structural engineerresponsible for the design ofastructure resistant to fracture, the mate rials engineerwho has toproviderelevant mechanicalpropertiesandto improve the properties ofmaterials, and the non-destructive control engineer who must insure that no potentially noxious defect exists after the fracture or will appear duringservice. Thisbookisalsoofinteresttotheengineerassessingthesafetyof structures.Theresearcheralsowillfind someinterestingelementsforguidinghis investigation. Finally, this book isaimed to be aneducational aidforthe teacher andforthestudent. This bookhas the purpose to bea reference withthe state ofthe art is kept as simple as possible, andshould be followed withease. Thusonly basic ideas are givenandthoroughofdebatabledevelopmentshavebeenskipped.Thismonograph fillsalackinFrenchpublicationsonthesubjectduringthelast10years.Notmany referencesaregiven,buttheyarethemostrelevantonesandsometimesarereviews andthuswill befruitful forcomplementarydevelopments. The basic ideas are stated in the form ofsteps from simple to complicated and thus coherently follow the chronological evolution ofthis matter. In order, the microscopic scale is considered before the macroscopic scale since physical understandingofexperimentallyobservedphenomenaprecededunderstandingof the macroscopic behaviour ofstructures. In this last field, the relatively recent contributionoffinite elementanalyses, verysimilarto experimentalobservation, isdetermining. Thereareexercisesattheendofeachchapter. Someoftheseareexplanations; someincludeextensionofthetextmaterial.Answerstoapproximatelyonehalfof theproblemsare givenattherearofthebook. This book is restricted to fracture mechanics in homogeneous and isotropic continuum. Onlymonotoneandstaticloadingisconsidered. Chapter I treatstheprocessoffracture attheatomicscaleandgivestherelated elasticfracture criterionintermsofstress. Chapter 2 is concerned with the application by Griffith ofthis criterion and the nonequivalent energetic criterion in the case ofnotches in a purely elastic continuum. Then, in the case ofcracks, the elastic analysis proposed by Irwin ix x Preface for describing the stress and strain fields in tenns ofthe two equivalent loading parameters,thestressintensityfactor K, andthecrackextensionform Garepre sented.TheloadingparameterT,thetransversestress,isalsogiven.Thisbehaviour correspondstotheelasticrange describedinthe following figure. InChapter3,theapproximateplasticcorrectionunderitsvariousforms, which istobeappliedinorderthattheelasticsolutionsderivedintheprecedingchapter remainsphysicallymeaningful,isdescribed. Thisisthedomainofthesmallscale yieldingregimeshownintheabovefigure. ResultsfromChapters2and3leadto the procedure for measuring and determining the toughness, which is a material constant. Chapter4 exhibits the practical application for a structure with an elastic be haviour as a whole. The material scientist copes with a toughness that may be geometrydependentandscatteredoveramoreorlessextendedrange. The crack propagationisalsoconsidered. The non-destructivecontrol persontakes intoac count an existing initial flaw density with various sizesand defines aprobability ofdetection. Thedesignergathersall these previousdata fordevisingastructure withthe lowestprobabilityoffailureduringthespecifiedlife-timeunderaknown loading. The safteypersonwill verify thatthe state ofthe art has beenrespected ateachstep. In Chapter 5 the mechanisms offailure by cleavage or by tearing related to the microscopic heterogeneousdeformationarepresentedandthe corresponding fracture criteria allow the description ofthe ductile-brittle transition as observed withplainspecimens. Continuumdamagemechanicsisthentreated. InChapter6, where the treatmentofthe generalizedplasticitythat spreads all over the structure is given, the plastic instability related to the limit loading is describedand quantified. In the case ofHollomon material, the stress and strain fields, as determined analytically by Hutchinson, Rice, and Rosengren, are for mulated in terms ofthe J-integral. In the case ofa material with a non-analytic flow behaviour, the approach with reference stressas suggestedbyAinsworth is presented. In Chapter 7 the elastoplastic treatment developed by Shih in the contained yieldingandfullyplasticyieldingranges(seeFig. I)foraRamberg-Osgoodma terial is described and the loading parameters J and Qare brought in. Fortear rapture, thestationaryandthemovingcracksareconsideredsuccessivelyandthe proceduresformeasuringtherelatedtoughness are described. InChapter8,thelinkbetweenmicroscopicandmacroscopicaspectsisdisclosed with the help ofthe results ofChapters 5, 6, and 7. Toughness appears as very dependentonthegeometryandonthemodeofloading.Finally, instabilityduring crackpropagationis treated. This bookcomes from acourse taughtatthe InstitutSuperieurdes Materiaux et de la Construction Mecanique. It also represents the accomplishment of25 a years of experience in the field of fracture mechanics at the Commissariat I'EnergieAtomique.ThepresenteditionistheEnglishtranslationofaFrenchbook with corrections, expansions, and completions on the basis ofrecent additional developmentsanddemands. Preface XI Elasticity SmallScaleYielding LargeScaleYielding ContainedPlasticity FUllyPlasticYielding PIt\ r,.......---l-------l------+---...,.> ""tv pLJ §J ~ J, Q J. Q Elasticite Plasticiteconfinee Plasticiteconfinee Plasticitegimeralisee Iimitee etendue I Chapter2 Chapter3 Chapter7 Chapter6 FIGURE 1. Domains ofdeformation ofa finite cracked body, as defined along the load displacementcurveandbythesizeoftheplasticzonecomparedwiththedimensionsofthe body.Theparametersofinterestfordescribingthe loadingandthestressandstrainfields areindicatedforeachdomain.Thechapterwherethisdomain istreatedisindicated.
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