Marcel Dekker, Inc. New York
•
Basel
Mechanical
Properties of
Engineered
Materials
Wolé Soboyejo
Princeton University
Princeton, New Jersey
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Copyright © 2003 Marcel Dekker, Inc.
ISBN: 0-8247-8900-8
This book is printed on acid-free paper.
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Copyright © 2003 Marcel Dekker, Inc.
The book concludes with an overview of time-dependent viscoelastic/visco-
plastic behavior, creep, and creep crack growth phenomena. Wherever pos-
sible, the text is illustrated with worked examples and case studies that show
how to apply basic principles to the solution of engineering problems.
This book has been written primarily as a text for a senior under-
graduate course or first-level graduate course on mechanical properties of
materials. However, I hope that it will also be useful to practicing engineers,
researchers, and others who want to develop a working understanding of the
basic concepts that govern the mechanical properties of materials. To ensure
a wide audience, I have assumed only a basic knowledge of algebra and
calculus in the presentation of mathematical derivations. The reader is also
assumed to have a sophomore-level understanding of physics and chemistry.
Prior knowledge of basic materials science and strength of materials con-
cepts is not assumed, however. The better-prepared reader may, therefore,
skim through some of the elementary sections in which these concepts are
introduced.
Finally, I would like to acknowledge a number of people that have
supported me over the years. I am grateful to my parents, Alfred and
Anthonia, for the numerous sacrifices that they made to provide me with
a good education. I am indebted to my teachers, especially John Knott,
Anthony Smith, David Fenner, and Stan Earles, for stimulating my early
interest in materials and mechanics. I am also thankful to my colleagues in
the field of mechanical behavior who have shared their thoughts and ideas
with me over the years. In particular, I am grateful to Frank McClintock for
his critical review of the first five chapters, and his suggestions for the book
outline.
I also thank my colleagues in the mechanical behavior community for
helping me to develop my basic understanding of the subject over the past
15 years. I am particularly grateful to Anthony Evans, John Hutchinson,

tical year (1997–1998) at MIT provided me with a stimulating environment
for the development of the first few chapters of this book.
I also thank Dawn Wechsler, Janet Sachs, Elizabeth Curione, and Rita
Lazzazzaro of Marcel Dekker, Inc., for their patience and understanding.
This project would certainly not have been completed (by me) without their
vision, patience, and encouragement.
Finally, I thank my wife, Morenike, for giving me the freedom and the
time to write this book. This was time that I should have spent with her and
our young family. However, as always, she was supportive of my work, and
I know that this book could have never been completed without her fore-
bearance and support.
Wole
´
Soboyejo
Copyright © 2003 Marcel Dekker, Inc.
Contents
Preface
1OverviewofCrystal/DefectStructureandMechanicalProperties
andBehavior
1.1Introduction
1.2AtomicStructure
1.3ChemicalBonds
1.4StructureofSolids
1.5StructuralLengthScales:Nanostructure,Microstructure,
andMacrostructure
1.6Summary
Bibliography
2DefectStructureandMechanicalProperties
2.1Introduction
2.2IndicialNotationforAtomicPlanesandDirections

5.3Elastic–PlasticBehavior
5.4EmpiricalStress–StrainRelationships
5.5ConsidereCriterion
5.6YieldingUnderMultiaxialLoading
5.7IntroductiontoJ
2
DeformationTheory
5.8FlowandEvolutionaryEquations
(ConstitutiveEquationsofPlasticity)
5.9Summary
Copyright © 2003 Marcel Dekker, Inc.
Bibliography
6IntroductiontoDislocationMechanics
6.1Introduction
6.2TheoreticalShearStrengthofaCrystallineSolid
6.3TypesofDislocations
6.4MovementofDislocations
6.5ExperimentalObservationsofDislocations
6.6StressFieldsAroundDislocations
6.7StrainEnergies
6.8ForcesonDislocations
6.9ForcesBetweenDislocations
6.10ForcesBetweenDislocationsandFreeSurfaces
6.11Summary
Bibliography
7DislocationsandPlasticDeformation
7.1Introduction
7.2DislocationMotioninCrystals
7.3DislocationVelocity
7.4DislocationInteractions

9.3Rule-of-MixtureTheory
9.4DeformationBehaviorofUnidirectionalComposites
9.5MatrixversusCompositeFailureModesin
UnidirectionalComposites
9.6FailureofOff-AxisComposites
9.7EffectsofWhisker/FiberLengthonComposite
StrengthandModulus
9.8ConstituentandCompositeProperties
9.9StatisticalVariationsinCompositeStrength
9.10Summary
Bibliography
10FurtherTopicsinComposites
10.1Introduction
10.2UnidirectionalLaminates
10.3Off-AxisLaminates
10.4MultiplyLaminates
10.5CompositePlyDesign
10.6CompositeFailureCriteria
10.7ShearLagTheory
10.8TheRoleofInterfaces
10.9Summary
Copyright © 2003 Marcel Dekker, Inc.
Bibliography
11FundamentalsofFractureMechanics
11.1Introduction
11.2FundamentalsofFractureMechanics
11.3NotchConcentrationFactors
11.4GriffithFractureAnalysis
11.5EnergyReleaseRateandCompliance
11.6LinearElasticFractureMechanics

13.10MicrocrackShielding/Antishielding
13.11LinearSuperpositionConcept
13.12SynergisticTougheningConcept
13.13TougheningofPolymers
13.14SummaryandConcludingRemarks
Bibliography
14FatigueofMaterials
14.1Introduction
14.2MicromechanismsofFatigueCrackInitiation
14.3MicromechanismsofFatigueCrackPropagation
14.4ConventionalApproachtoFatigue
14.5DifferentialApproachtoFatigue
14.6FatigueCrackGrowthinDuctileSolids
14.7FatigueofPolymers
14.8FatigueofBrittleSolids
14.9CrackClosure
14.10ShortCrackProblem
14.11FatigueGrowthLawsandFatigueLifePrediction
14.12FatigueofComposites
14.13Summary
Bibliography
15IntroductiontoViscoelasticity,Creep,andCreepCrackGrowth
15.1Introduction
15.2CreepandViscoelasticityinPolymers
15.3MechanicalDumping
15.4TemperatureDependenceofTime-DependentFlow
inPolymers
15.5IntroductiontoCreepinMetallicandCeramic
Materials
15.6FunctionalFormsintheDifferentCreepRegimes

In ancient Greece, Democritus postulated that atoms are the building blocks
from which all materials are made. This was generally accepted by philoso-
phers and scientists (without proof) for centuries. However, although the
small size of the atoms was such that they could not be viewed directly with
the available instruments, Avogadro in the 16th century was able to deter-
mine that one mole of an element consists of 6:02 Â 10
23
atoms. The peri-
Copyright © 2003 Marcel Dekker, Inc.
odictableofelementswasalsodevelopedinthe19thcenturybeforethe
imagingofcrystalstructurewasmadepossibleafterthedevelopmentofx-
raytechniqueslaterthatcentury.Forthefirsttime,scientistswereableto
viewtheeffectsofatomsthathadbeenpostulatedbytheancients.
Aclearpictureofatomicstructuresoonemergedasanumberof
dedicatedscientistsstudiedtheatomicstructureofdifferenttypesofmateri-
als.First,itbecameapparentthat,inmanymaterials,theatomscanbe
groupedintounitcellsorbuildingblocksthataresomewhatakintothe
piecesinaLegoset.Thesebuildingblocksareoftencalledcrystals.
However,therearemanymaterialsinwhichnocleargroupingofatoms
intounitcellsorcrystalscanbeidentified.Atomsinsuchamorphousmate-
rialsareapparentlyrandomlydistributed,anditisdifficulttodiscernclear
groupsofatomsinsuchmaterials.Nevertheless,inamorphousandcrystal-
linematerials,mechanicalbehaviorcanonlybeunderstoodifweappreciate
thefactthattheatomswithinasolidareheldtogetherbyforcesthatare
oftenreferredtoaschemicalbonds.Thesewillbedescribedinthenext
section.
1.3CHEMICALBONDS
Twodistincttypesofchemicalbondsareknowntoexist.Strongbondsare
oftendescribedasprimarybonds,andweakerbondsaregenerallydescribed
assecondarybonds.However,bothtypesofbondsareimportant,andthey

IGURE
1.1 Schematic of the layered structure of graphite. (Adapted from
Kingery et al., 1976. Reprinted with permission from John Wiley and Sons.)
F
IGURE
1.2 Schematic of an ionic bond—in this case between a sodium atom
and a chlorine atom to form sodium chloride. (Adapted from Ashby and
Jones, 1994. Reprinted with permission from Pergamon Press.)
Copyright © 2003 Marcel Dekker, Inc.
whereaisaproportionalityconstant,whichisequalto1=ð4"
0
),"
0
isthe
permitivityofthevacuum(8:5Â10
À12
F/m),Q
1
andQ
2
aretherespective
chargesofions1and2,andristheionicseparation,asshowninFig.1.2.
Typicalionicbondstrengthsarebetween40and200kcal/mol.Also,dueto
theirrelativelyhighbondstrengths,ionicallybondedmaterialshavehigh
meltingpointssinceagreaterlevelofthermalagitationisneededtoshear
theionsfromtheionicallybondedstructures.Theionicbondsarealso
nonsaturatingandnondirectional.Suchbondsarerelativelydifficultto
breakduringslipprocessesthataftercontrolplasticbehavior(irreversible
deformation).Ionicallybondedsolidsare,therefore,relativelybrittlesince
theycanonlyundergolimitedplasticity.Examplesofionicallybonded