High temperature strain of metals and alloys: physical fundamentals

173 Pages·2006·2.44 MB·English

by  Valim Levitin

ValimLevitin
HighTemperatureStrain
ofMetalsandAlloys
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Valim Levitin
High Temperature Strain
of Metals and Alloys
PhysicalFundamentals
TheAuthor AllbookspublishedbyWiley-VCHarecarefully
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(cid:1)c 2006WILEY-VCHVerlagGmbH&CoKGaA,
Weinheim
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V
Contents
Introduction 1
1 MacroscopicCharacteristicsofStrainofMetallicMaterials
atHighTemperatures 5
2 InsituX-rayInvestigationTechnique 13
2.1 ExperimentalInstallation 13
2.2 MeasurementProcedure 15
2.3 MeasurementsofStructuralParameters 17
2.4 DiffractionElectronMicroscopy 20
2.5 AmplitudeofAtomicVibrations 21
2.6 MaterialsunderInvestigation 23
2.7 Summary 24
3 StructuralParametersinHigh-TemperatureDeformedMetals 25
3.1 EvolutionofStructuralParameters 25
3.2 DislocationStructure 30
3.3 DistancesbetweenDislocationsinSub-boundaries 34
3.4 Sub-boundariesasDislocationSourcesandObstacles 34
3.5 DislocationsinsideSubgrains 35
3.6 VacancyLoopsandHelicoids 39
3.7 TotalCombinationofStructuralPeculiarities
ofHigh-temperatureDeformation 40
3.8 Summary 41
4 PhysicalMechanismofStrainatHighTemperatures 43
4.1 PhysicalModelandTheory 43
4.2 VelocityofDislocations 45
4.3 DislocationDensity 49
4.4 RateoftheSteady-StateCreep 51
HighTemperatureStrainofMetalsandAlloys,ValimLevitin(Author)
Copyright(cid:1)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:3-527-313389-9
VI Contents
4.5 EffectofAlloying:RelationshipbetweenCreepRate
andMean-SquareAtomicAmplitudes 54
4.6 FormationofJogs 55
4.7 SignificanceoftheStackingFaultsEnergy 57
4.8 StabilityofDislocationSub-boundaries 58
4.9 ScopeoftheTheory 62
4.10 Summary 64
5 SimulationoftheParametersEvolution 67
5.1 ParametersofthePhysicalModel 67
5.2 Equations 68
5.2.1 StrainRate 68
5.2.2 ChangeintheDislocationDensity 68
5.2.3 TheDislocationSlipVelocity 69
5.2.4 TheDislocationClimbVelocity 69
5.2.5 TheDislocationSpacinginSub-boundaries 70
5.2.6 VariationoftheSubgrainSize 71
5.2.7 SystemofDifferentialEquations 71
5.3 ResultsofSimulation 71
5.4 DensityofDislocationsduringStationaryCreep 77
5.5 Summary 80
6 High-temperatureDeformationofSuperalloys 83
6.1 γ(cid:2)PhaseinSuperalloys 83
6.2 ChangesintheMatrixofAlloysduringStrain 88
6.3 InteractionofDislocationsandParticles 89
6.4 CreepRate.LengthofDislocationSegments 95
6.5 MechanismofStrainandtheCreepRateEquation 96
6.6 Compositionoftheγ(cid:2)PhaseandAtomicVibrations 102
6.7 InfluenceoftheParticleSizeandConcentration 104
6.8 ThePredictionofProperties 106
6.9 Summary 109
7 SingleCrystalsofSuperalloys 111
7.1 EffectofOrientationonProperties 111
7.2 DeformationatLowerTemperatures 116
7.3 DeformationatHigherTemperatures 124
7.4 OntheCompositionofSuperalloys 129
7.5 Rafting 130
7.6 EffectofCompositionandTemperatureonγ/γ(cid:2)Misfit 136
7.7 OtherCreepEquations 137
7.8 Summary 141
VII
8 DeformationofSomeRefractoryMetals 143
8.1 TheCreepBehavior 143
8.2 AlloysofRefractoryMetals 149
8.3 Summary 155
Supplements 157
Supplement1:OnDislocationsintheCrystalLattice 157
Supplement2:OnScrewComponentsinSub-boundary
DislocationNetworks 161
Supplement3:CompositionofSuperalloys 163
References 164
Acknowledgements 168
Index 169
1
Introduction
Whoevercontrolsthematerials,
controlsthescienceandthetechnology
E.Plummer
Moderncivilizationisbasedonfourfoundations:materials,energy,tech-
nology,andinformation.
Metalsandalloysarematerials,whichhavebeenwidelyusedbymankind
for thousands of years, and this is no mere chance: metals have many re-
markableproperties.One–theirstrengthathightemperatures–isofgreat
scientificandpracticalimportance.
Thedurabilityofgasturbineengines,steampipelines,reactors,aeroplanes,
andaerospacevehiclesdependsdirectlyontheabilityoftheirpartsandunits
towithstandchangesinshape.Ontheotherhand,asignificantmobilityof
crystal lattice defects and of atoms plays an important role in the behavior
ofmaterialsunderappliedstressesathightemperaturesandisalsoofgreat
interestformaterialsscienceresearchandpracticalapplications.
Mechanical tests were historically the first method of investigating the
high-temperaturedeformationphenomenon.Thetechniqueoriginatedfrom
practicalneedstousemetallicmaterialsforvariousmachines.Adeepinves-
tigationofmaterialstructurewasimpossibleinearlystudiesbecauseofthe
lackofsuitableequipmentandappropriatetechniques.Evennowmechanical
testsareasourceofindirectinformationaboutphysicalprocessesthattake
placeintheatomiccrystallatticeofmetalsandalloys.However,ifwewant
to understand the nature of these processes and to be able to use them in
practiceweshouldtrytoinvestigatethemdirectly.
Thephenomenaofhigh-temperaturestrainandcreephavebeenstudied
for many years. Numerous theories have been developed, based on the de-
pendences of the strain rate upon stress and temperature. The structure of
tested metals was also studied. The obtained results are of great value and
havebeendescribedinbooksandreviewsandimportantdataarealsoscat-
teredinnumerousarticles.Previousinvestigationsimprovedourknowledge
HighTemperatureStrainofMetalsandAlloys,ValimLevitin(Author)
Copyright(cid:1)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:3-527-313389-9
2 Introduction
oftheproblemandstimulatedfurtherexperimentalapproaches.Itisessen-
tial,however,toemphasizethatthephysicalnatureofthehigh-temperature
straininmetals,especiallyindustrialsuperalloys,isnotyetunderstoodsuffi-
ciently.Bythiswemeanthephysicalbackgroundofthedeformationonthe
atomicmicroscopicscale.
Theproblemofthehigh-temperaturepropertiesofmetallicmaterialshas
a number of experimental, theoretical and applied aspects. Naturally, it is
necessarytoidentifythescopeoftheproblemconsideredinthisbook.
Myideaisasfollows.Thehigh-temperaturediffusionmobilityofatomsand
theeffectofappliedforcesaretheconditionsunderwhichspecialprocesses
occur in the crystal lattice of metallic materials. Thus, external conditions
resultinadistinctivestructuralresponseofthematerial.Intheirturnthese
specificstructuralchangesleadtoadefinitemacroscopicbehaviorofthemate-
rial,especially,toadefinitestrainrateandtoastressresistance.Consequently,
structureevolutionistheprimarystageofresponse;mechanicalbehavioris
thesecondaryresult.Theresponseinthecrystallatticeisacause,whilethe
plasticstrainofametaloranalloyisaconsequence.Thestructuralevolution
isthereforeakeyfactor,whichdeterminesthemechanicalpropertiesofthe
metallicmaterialsathightemperatures.
Thisbooktreatsdatafromexperimentalmeasurementsofimportantstruc-
tural and kinetic characteristics which are related to physical fundamentals
ofthehigh-temperaturestrainofmetallicmaterials.Anumberofspecificpa-
rametersofsubstructure,whichhavebeendirectlymeasured,arepresented.
Theories that have been worked out on the basis of these experiments are
quantitative and contain values which have a definite physical meaning. A
methodofcalculationofthesteady-statestrainratefromthematerial,struc-
turalandexternalparametersisdevelopedforthefirsttime.
Thebookconsistsofeightchapters.
Asummaryoftheproblemispresentedinthefirstchapter.Thepeculiar-
ities of the strain of metallic materials at high temperatures are described.
The reader’s attention is drawn to the shortcomings of existing views and
theauthor’sapproachtotheproblemissubstantiated.Itisadvisableforthe
readertoremindhimselfofthemainprinciplesofdislocationtheorybyfirst
readingSupplement1.
The second chapter is devoted to experimental techniques. The unique
equipmentdevelopedbytheauthorisintendedfortheinsituX-rayinvesti-
gationofvariousmetals,i.e.fordirectstructuralmeasurementsduringthe
high-temperaturetests.Themethodoftransmissiondiffractionmicroscopy
isbrieflyconsidered.Thestudiedmetalsandalloysaredescribed.
Dataonmeasurementsofstructuralparametersarepresentedinthenext
chapter. Dependences on time of the size and misorientations of the sub-
grains are obtained for various metals. Attention is given to the dislocation
Introduction 3
structureofsub-boundariesthatareformedduringstrain.Theexperimental
dataconcerningdislocationswithinsubgrainsarepresentedanddiscussedin
moredetail.Thetotalitiesofthestructuralpeculiaritiesofthemetals,which
havebeendeformedathigh-temperatures,areformulated.
In the fourth chapter the physical mechanisms of the high-temperature
deformationofpuremetalsandsolidsolutionsareworkedoutonthebasisof
theobtaineddata.Thequantitativemodelofcreepisconsideredandvalidated.
Equations are presented for the dislocation velocity and for the dislocation
density.Thephysicallybasedforecastoftheminimumstrainrateisgiven.
The subject of the fifth chapter is a computer simulation of the high-
temperaturedeformationprocesses.Asystemofordinarydifferentialequa-
tionsmodelsthephenomenonunderstudy.Evolutionofstructuralparame-
tersandtheeffectofexternalconditionsontheparametersareanalyzed.
High-temperaturedeformationofthecreep-resistantsuperalloysisthesub-
jectofthesixthchapter.Structurechangesinmodernmaterialsandtheinter-
actionbetweendeformingdislocationsandparticlesofthehardeningphase
areanalyzed.Aphysicalmechanismofdeformationandastrainrateequa-
tion are considered. Data are presented on the connection between mean-
squareamplitudesofatomicvibrationsinthehardeningphaseandthecreep
strength.
Theseventhchapterisdevotedtothesingle-crystalsuperalloys.Theeffect
of orientation, temperature and stress on the properties of single crystals
isconsidered.Thephysicalmechanismsofthedislocationdeformationare
described.Attentionisgiventothephenomenonofraftingandtotheroleof
misfitbetweenthecrystallatticeparametersofthematrixandofthehardening
phase.
Thesubjectofthelastchapteristhepeculiaritiesofthestrainbehaviorof
refractorymetals.
Adetailedreviewofallaspectsoftheproblemunderconsiderationforpure
metalsgoesbeyondthescopeofthisbook.Thereforeknownprinciplesand
establishedfactsarementionedonlybriefly.
The reader can find reviews concerning the creep of metals in different
booksandarticles,forexample[1–8].