PrefacetotheThirdEdition
Thisthirdeditionhewscloselytoitspredecessorswithsignificantadditionsincertainareas wheresubstantialadvanceshaveaccumulated.Inallareas,thetexthasbeenreviewedand, whereappropriate,re-writtentoaccountforrecentadditionstotheliterature.Concerning theauthorship,MaxHatherlyisnolongerwithus,sadly;JohnHumphreyshasretiredandis nottobeblamedforanyerrorsormistakesthatwemayhaveintroducedinthisnew edition.Intermsofcontent,computermodelingofgrainboundarieshasresultedinnew insightsabouttheirproperties,especiallyenergyandmobility.Thecombinationof automatedserialsectioningandsynchrotron-basedcharacterizationhasprovided3-Dmaps ofmicrostructureandadditionalnewinsights.Thedescriptionsofworkhardeningand texturehavebeenstrengthened.
AnthonyRollett
GregoryRohrer
August2017
fromMichaelFerryandRobertMoonoftheUniversityofNewSouthWaleshavebeen extremelyvaluable.
ThethirdeditionowesmuchtotheresearchconductedatCarnegieMellonUniversityon interfaces,largelyunderthesupportfromtheUSNationalScienceFoundationofthe MaterialsResearchScienceandEngineeringCenter.ADRandGSRaregratefultothe manyindividualswhohelpedwithdiscussion,data,figures,etc.
Symbols
Thefollowingnotationisgenerallyusedinthetext.Thesubscripts i or n indicatetheuseof lettersornumbersforparticularsymbols.Onrareoccasionswherethelettersorsymbolsare usedforotherpurposes,thisisspecificallystated.
b Burgersvectorofadislocation
c,cn,C,Cn,Kn Thesedenote“local”constantswhicharedefinedinthetext
d Diameterofsecond-phaseparticle
D Grainorsubgraindiameter
Di Diffusivity(s ¼ bulkdiffusion,b ¼ boundarydiffusion,c ¼ core diffusion)
Ei Energy,e.g.,storedenergyofdeformationED
Fv Volumefractionofsecond-phaseparticles
G Shearmodulus
k Boltzmannconstant
M Boundarymobility
n Exponent,e.g.,intheJMAKequation
Nv Numberofgrainsorsecond-phaseparticlesperunitvolume
Ns Numberofparticlesperunitarea
PorPi Pressureonaboundary
QorQi Activationenergy,(fordiffusion:s ¼ bulk,b ¼ boundary,c ¼ core)
R Grainorsubgrainradius
s Shearstrain
t Time
T,Tm Temperature,meltingtemperature(K)
v Velocityofdislocationorboundary
V Volume
X Fractionrecrystallized
a, b Constants
g Energyofaninterfaceorboundary
gSFE, gRSFE Stackingfaultenergy,reducedstackingfaultenergy
gb Energyofahigh-angleboundary
gs Energyofalow-angleboundary
ε Truestrain
_
ε Truestrainrate
q Misorientationacrossaboundary;also,workhardeningrate
l Interparticlespacing(definedinEq.A2.13)
n Poissonratio
n0 Atomicvibrationalfrequency
r Dislocationdensity
Sn Coincidencesitelattice(CSL)grainboundaries.1/nisthefraction ofsitescommontobothgrains
s Truestress
s Shearstress
41, F, 42 Eulerangles,Bungeconvention(definedinAppendix1)
U Orientationgradient
Abbreviations
ARB Accumulativerollbonding
CA Cellularautomata
CLS Cahn,Lu¨cke,Stu¨we(theoryofsolutedrag)
CPFEM Crystalplasticityfiniteelementmodeling
CSL Coincidencesitelattice
DDW Densedislocationwall
DRX Dynamicrecrystallization
EBSD Electronbackscatterdiffraction
ECAE Equalchannelangularextrusion
ECD Equivalentcirclediameter
FE Finiteelement(modeling)
FEGSEM Fieldemissiongunscanningelectronmicroscope
GBCD Grainboundarycharacterdistribution
GBE Grainboundaryengineering
GNB Geometricallynecessaryboundary
HAGB High-anglegrainboundary
HSLA High-strengthlow-alloy(steel)
HVEM High-voltagetransmissionelectronmicroscope
IDB Incidentaldislocationboundary
IF Interstitialfree(steel)
JMAK Johnson Mehl Avrami Kolmogorovkineticmodel
LAGB Low-anglegrainboundary
MD Moleculardynamics
MLI Meanlinearintercept
ND,RD,TD Normal,rollingandtransversedirectionsinarolledproduct
ODF Orientationdistributionfunction
PSN Particle-stimulatednucleationofrecrystallization
SEM Scanningelectronmicroscope
SFE Stackingfaultenergy
SIBM Strain-inducedboundarymigration
SMG Submicron-grained(alloy)
SPF Superplasticforming
TEM Transmissionelectronmicroscope
Table1.1: Examplesofstaticannealingphenomena.
RecoveryRecrystallizationGrainGrowth ContinuousSubgraingrowthContinuousrecrystallizationNormalgraingrowth DiscontinuousDiscontinuoussubgraingrowthPrimaryrecrystallizationAbnormalgraingrowth
growth,inwhichthesmallergrainsareeliminated,thelargergrainsgrow,andthegrain boundariesassumealowerenergyconfiguration(Fig.1.1e).Incertaincircumstancesthis normalgraingrowth maygivewaytotheselectivegrowthofafewlargegrains (Fig.1.1f),aprocessknownas abnormalgraingrowthorsecondaryrecrystallization.
Recentresearchhasshownthatborderlinesbetweenthevariousannealingphenomenaare oftenunclear,anditisknownthatrecovery,recrystallization,andgraingrowthmayoccur intwoways.Theyoccurheterogeneouslythroughoutthematerial,suchthattheymaybe formallydescribedintermsof nucleation and growth stages,andinthiscase,theyare describedas discontinuous processes.Alternatively,theymayoccuruniformly,suchthat themicrostructuresevolvegraduallywithnoidentifiablenucleationandgrowthstages.In thiscase,theprefix continuous isusedtocategorizethephenomena.Itshouldbe emphasizedthatthisisaphenomenologicalcategorizationthatdoesnotimplythe operationofanyparticularmicromechanism.The“continuous”phenomenainclude recoverybysubgraingrowth,continuousrecrystallizationandnormalgraingrowthand the“discontinuous”phenomenaincludediscontinuoussubgraingrowth,primary recrystallization,andabnormalgraingrowth.Therefore,asshownin Table1.1,thereare atleast six staticannealingphenomenathatneedtobeconsidered.Notethemodern approachtophasetransformationsdistinguishesbetweenfirst-orderwithlatentheat,i.e., discontinuitiesinthefirstderivativeoffreeenergy(withlatentheat)versussecond-order withdiscontinuitiesinthesecondderivative.Again,primaryrecrystallization,forexample, certainlyreleasesheat(asmeasuredbycalorimetry)likeafirst-ordertransitionbutthere clearlyisnosenseinwhichonecandefineathermodynamicequilibrium.Therefore,all annealingprocessesare,strictlyspeaking,second-ordertransitions.
Althoughtheseprocessesareanalyzedseparatelyinlaterchapters,therearecircumstances whentheycanbeconsideredwithinaunifiedframework,asdiscussedinChapter10.This hasthemeritofnotonlyemphasizingthecommonfeaturesofthevariousprocesses,but, inbreakingdowntheconventionaldistinctionsbetweenthevariousannealingphenomena, allowsalsofortheemergenceofnewphenomenawhichmaynotconvenientlyfitintothe traditionalcategories.
1.1.2ImportanceofAnnealing
Manymetallicmaterialsareproducedinitiallyaslargecastings,whicharethenfurther processedinthesolidstatebyforging,rolling,extrusion,etc.,toanintermediateorfinal
In1898,Steadproposedthatgraingrowthoccurredbygrainrotationandcoalescence,and althoughEwingandRosenhainpresentedconvincingevidencethatthemechanismwas oneofboundarymigration,Stead’sideawasperiodicallyreviveduntiltheworkof CarpenterandElamfinallysettledthematterinfavorofboundarymigration.
1.2.1.3ParametersAffectingRecrystallization
By1920,manyoftheparametersthataffecttherecrystallizationprocessandtheresultant microstructurehadbeenidentified.
Kinetics:Therelationshipoftherecrystallizationtemperaturetothemeltingtemperature wasnotedbyEwingandRosenhain(1900)andHumfrey(1902)showedthattherateof recrystallizationincreasedwithanincreaseinannealingtemperature.
Strain:Sauveur(1912)foundthattherewasacriticalstrainforrecrystallization,anda relationshipbetweengrainsizeandpriorstrainwasreportedbyCharpy(1910).Carpenter andElam(1920)laterquantifiedbothoftheseeffects.
Graingrowth:Inaveryearlypaperonthecontrolofmicrostructureduringannealing, Jeffries(1916)showedthat abnormalgraingrowth inthoriatedtungstenwaspromoted inspecimensinwhichnormalgraingrowthhadbeeninhibited.
Furtherdevelopmentsintheunderstandingofrecrystallizationwerenotpossiblewithouta moredetailedknowledgeofthedeformedstate.Thiswasprovidedbythedevelopmentof thedislocationtheoryin1934,andanotableearlyreviewofthesubjectfollowingthe adventofthedislocationtheoryisthatofBurgers(1941).
Fromaboutthisperioditbecomesdifficulttodistinguishthepapersofhistoricalinterest fromtheearlykeypapersthatarestillrelevanttocurrentthinking.Thelatterarecitedas appropriatewithinthevariouschaptersofthisbook.However,itmaybehelpfultothe readertohaveasourcelistofbooks,reviews,andconferencesonthesubjectfromthe past50years,whichisgivenbelow.
1.2.2SelectedKeyLiterature(1952 2003)
MonographsonRecrystallization
Byrne,J.G.(1965), Recovery,RecrystallizationandGrainGrowth.McMillan, NewYork.
Cotterill,P.andMold,P.R.(1976), RecrystallizationandGrainGrowthinMetals. SurreyUniv.Press,London. Novikov,V.(1997), GrainGrowthandControlofMicrostructureandTexturein PolycrystallineMaterials.CRCPress,BocaRaton.
Multiauthor, EditedCompilationsonRecrystallization
Himmel,L.(ed.),(1963), RecoveryandRecrystallizationofMetals.Interscience, NewYork.
Margolin,H.(ed.),(1966), Recrystallization,GraingrowthandTextures.ASM, Ohio,USA.
Haessner,F.(ed.),(1978), RecrystallizationofMetallicMaterials.Dr.RiedererVerlag,G.m.b.HStuttgart.
ReviewArticlesandBooksContainingChaptersonRecrystallization
Burke,J.E.andTurnbull,D.(1952), RecrystallizationandGrainGrowth.Progressin MetalPhys., 3,220.
Beck,P.A.(1954), AnnealingofCold-workedMetals.Adv.Phys., 3,245.
Leslie,W.C.,Michalak,J.T.andAul,F.W.(1963), Theannealingofcold-workediron In: IronanditsDiluteSolidSolutions.(eds.)SpencerandWerner.Interscience. NewYork.119.
Christian,J.W.(2002), TheTheoryofTransformationsinMetalsandAlloys.Second edition,Pergamon,Oxford.
Jonas,J.J.,Sellars,C.M.andTegart,W.J.McG.(1969), StrengthandStructureUnder HotWorkingconditions.Met.Revs., 130,1.
Martin,J.W.andDoherty,R.D.(1976), TheStabilityofMicrostructureinMetals. CambridgeUniversityPress. Cahn,R.W.(1996),in PhysicalMetallurgy.(eds.)CahnandHaasen.Fourthedition. North Holland,Amsterdam. Hutchinson,W.B.(1984), DevelopmentandControlofAnnealingTexturesinLowCarbonSteels.Int.Met.Rev., 29,25. Honeycombe,R.W.K.(1985), ThePlasticDeformationofMetals.EdwardArnold. Humphreys,F.J.(1991), RecrystallizationandRecovery.In: ProcessingofMetals andAlloys.(ed.)R.W.Cahn.VCH.Germany.371. Doherty,R.D.,Hughes,D.A.,Humphreys,F.J.,Jonas,J.J.,JuulJensen,D.,Kassner, M.E.,King,W.E.,McNelly,T.R.,McQueen,H.J.andRollett,A.D.(1997), Current issuesinrecrystallization:areview.Mats.Sci.&Eng., A238,219. Verlinden,B.,Driver,J.,Samajdar,I.,andDoherty,R.D.(2007), Thermomechanical ProcessingofMetallicMaterials,Elsevier.
ProceedingsofInternationalConferences
InternationalRecrystallizationConferenceSeries(1990 1999)
Chandra,T.(ed.),(1991), Recrystallization’90.TMS,Warrendale,USA. Fuentes,M.andGilSevillano,J.(eds.),(1992), Recrystallization’92.Trans.Tech. Pubs.Switzerland.
The force, F,ontheboundaryisgivenby dG/dx,andthe pressure, P,ontheboundary,is givenby F/a,andthus
If DGin Eq.(1.2) isgiveninunitsofJ/m3,thenthepressureontheboundary(P)isin N/m2.Thereissomeconfusionintheliteratureregardingterminology,andtheterms force onaboundary and pressureonaboundary arebothusedfortheparameterthatis definedaboveby P.Since P hasunitsofN/m2,whicharethoseofpressure,thereissome logicinusingtheterm pressure,andthereforeweadoptthisterminology.
1.3.2UnitsandtheMagnitudeoftheDrivingPressure
Althoughwewillbediscussingtheforcesandpressuresactingonboundariesinsome detailinlaterchapters,itisusefulatthisstagetoexamine,withexamples,someofthe forcesinvolvedinannealing.Thiswillservetodemonstratethe units usedinthebookand alsotogivesomeideaoftherelativemagnitudesoftheforcesinvolvedinannealing.A gooddiscussionofforcesarisingfromavarietyofsourcesisgivenbyStu ¨ we(1978).
1.3.2.1Recrystallization:DrivingPressureDuetoStoredDislocations
Thedrivingforceforrecrystallizationarisesfromtheeliminationofthedislocations introducedduringdeformation.Thiscanbeestimatedbyformingtheproductofthe energyperunitlengthofadislocation(i.e.,thelinetension)andthedislocationdensityas linelengthperunitvolume.Accordingly,thestoredenergyduetoadislocationdensity r is w0.5 rGb2,where G istheshearmodulusand b theBurgersvectorofthe dislocations.Adislocationdensityof1015 1016 m 2,whichistypicalofthecold-worked stateincopper(G ¼ 4.2 1010 N/m2, b ¼ 0.26nm)thereforerepresentsastoredenergy of w2 106 2 107 J/m3 (w10 100J/mol)andgivesrisetoadrivingpressurefor primaryrecrystallizationof w2 20MPa.
1.3.2.2RecoveryandGrainGrowth:DrivingPressureDuetoBoundaryEnergy
Recoverybysubgraincoarseningandgraingrowthfollowingrecrystallizationareboth drivenbytheeliminationofboundaryarea.Iftheboundaryenergyis g perunitarea and theboundariesformathree-dimensionalnetworkofspacingD,thenthedrivingpressure forgrowthisgivenapproximatelyas3g/D.Iftheenergyofalowanglegrainboundary (gs)is0.2J/m2,andthatforahighangleboundary(gb)is0.5J/m2,wefindthat
P w0.6MPa forthegrowthof1 mmsubgrainsduringrecovery,andthat P w10 2 MPa forthegrowthof100 mmgrains.
