Table Of ContentMechanical 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.
