fcn m ul a 2-=— g < a c NATIONALADVISORYCOMMITTEE a z FORAERONAUTICS
TECHNICAL NOTE 4225
INTERNAL-FRICTION STUDY OF ALUMINUM ALLOY
CONTAINING 4 WEIGHT PERCENT COPPER
By B. S. BerryandA. S. Nowick YaleUniversiw
Washington August1958
? {“.,-.- . . TECHLIBRAKYKAFB,NM Illllllllllllllllslllll’ iL NATIONALADVISORYCCMMIT!E3EIK)RAERONAUTICS 0DLLi5Cl u TECHNICALNOTE4225 ‘-d INTERNAL-FRICTIONSTUDYOF KWMINUMALLOY CONTAINING4 lJl?JGHTPERCENTCOPPER By B. S. BerryandA. S. Nowtck
SLJM4ARY
A studyhasbeenmade,by meansof low-frequencyinternal-friction measurementsin bothtorsionalandflexuralvibration,of aluminum(Al) alloycontaining4 weightpercentcopper(Cu)duringaging.Both polycrystallineandsingle-crystalspecks exhibitan initialinternal- frictionpeakat 173°C (fora frequericyof 1 cps) aftersolutiontreat- mentandquenching.Thispeakshowsallthecharacteristicsof a Zener relaxation,includingstrongsdsotropy.It fallson agingin a msnner simplyrelatedto thedecreasein thecopperconcentrationof thematrix. Thepeakis alsosensitiveto thereversionof Guinier-l?reston(G.P.) [1] zones. Theprecipitationof thephase e’ ismarkedby theappearanceof a b secondpeakat 135°C (fora frequencyof 1 cps)andby a risein thehigh- --. temperaturebackgroundinternalfriction.Boththesecontributionsgrow withkineticsshilarto thosefortheprecipitationof (3‘. Thesecond u peakis associatedspecificallywiththepresenceof thenonequilibriwn phase e’;it is reducedby thetransformationfrom El’to ~ andis absentin specimenscontainingonlythe e phase.Thehigh-tem~”rature background,however,is increasedfurtherby thistransformation.Possible causesof thesecondpeakandthebackgrcxmdchangesarediscussed.
INTRODUCTION
InternalFrictionandInelasticity Internalfrictionis oftenlooselydescribedas theabilityof a solidto dampoutvibrations.Morestrictly,it is a measureof the vibrationalener~ dissipatedby theoperationof s~cificmechanisms withinthesolid.Internalfrictionarisesevenat thesmalleststress levelsifHooke’slawdoesnotproperlydescribethestaticstress-strain curveof thematerial.ThenonelasticbehatiorwhichZener(ref.1) has 4! calledinelasticityariseswhenthestrainin thematerialis dependenton variablesotherthanstress.Amaterialshowingthesimplestkindof 2 lUICATN 4225
M inelasticityrespondsto a suddenly~lied stresswithan elasticstrain -. followedby an anelasticstrainwhich”increasesexponentiallywithtime b to a limitingvalueproportionalto theappliedstress.Therateat which“ theanel.asticstrainincreaseswithtime(aprocesscalleda relaxation) ismeasuredconvenientlyby thetime T requiredforthecompletionof thefraction1 - e‘1 (about63percent)of”thetotalanelasticstrain. Themagnitudeof theanelastlcbehaviorismeasuredby a quantitycalled therelaxationstrengthA whichi< definedas theratioof thetotal anelasticstrainto theelasticstrain. Importantrelaxationsareproducedinmanyalloysby atcramovements — whichareinducedby an appliedstress,a processknownas stress-induced ordering.Heretherelaxationthe T is relatedintimatelyto themean Jumptimeof theaffectedatoms,andthus T followsan equationof the L - form
T = To exP(@@ (1) where To and H areconstantsand R and T are,respectively,thegas constantandtheabsolutetemperature.In somecasestheenthalpy(heat) of activationH canbe fden~ifl.eddirectlywith= activationener~ for diffusion,andtheconstantTo canbe relatedto thepreexponential constantDo in theArrheniusexpressionforthediffusioncoefficientD. _&4
Fora givenfrequencyof vibrationf thetemperaturedependenceof F theinternalfrictionof a materialshowingsimpleinelasticity may be predictedfromforml theory(ref.1) in termsof theparametersA and T
b/fi=A ‘ (2) 1+ (U# where 5 is thelogarithmicdecrement,definedsubsequently,and u = l%f. Whentheinternalfriction(mehsured,e.g.,by therateof decayof free vibrations)isplottedagainstl/T as abscissa,a sytmnetrlcalbell-shaped c~e is obtainedwhichis referredto as an internal-frictionpeak. Inspectionof equation(2)showsthatihepeakoccursat thetempera- ture Tp,forwhich UJT(TP)is unity.Experimentalmeasurementof the peakat onefrequencyenablesnumericalvaluestobe obtainedfor A and T at thetemperatureof thepeak. If,in addition,a seconddifferent frequencyis used, H and To may also be‘obtainedby calculation.
*
F mm TN4225 3 9 Twoexemplesof inelasticityarisingfromstress-inducedorderingare nowpresented.Thefirst,whichmaybe calledtheSnoekrelaxation,is 2’ foundinbody-centeredcubicmetalscontaininginterstitialsoluteatoms. The-bestknownexsrupleIs thatofa-ironcontainingcarbon.Thecarbon(C) atomslieat themidpointsof thecubeedgesof theiron(Fe)latticeand cause,alocaldistortionwhichismostseverealongthecubeedgeJoining thetwonearestironatoms.E thecubeedgesaretakenas a setof axesX, Y, sndZ, a givensitefora carbonatombelongsto oneof threegroups,the x-,Y-,or Z-sites,accordingto whichdirectionisthatof greatestdistor- tionwhenthatsiteis occupied.Becauseof theverysmll solidvolubility of carbonina-iron,veryfewof thetotalpossiblesitescanbe occupied. Underzerostressthecarbonatomsarerandomlydistributedandthetotal distortionalongeachof,theX-,Y-,andZ-directionsis thesame. However, if,forexsmple,theX-siteswereoccupiedpreferentially,an elongation wouldoccurin theX-direction.Hence,fromthetherm-c reciprocity relations,applicationof a stressin theX-directionwillcausethe X-sitesto becomepreferentiallyoccupiedthroughstress-inducedmovement of saneof thecarbonatoms.A detailedtheoryof thisrelaxationhas beenworkedoutin reference2. There~ation timeisrelatedsimplyto themeanatomic’jmp timeof csrbonatoms,theactivationenergyof the relaxationis thatforthediffusionof carbonina-iron,andtherel=a- tionstrengthis directlyproportionalto thenmiberof cartinatomsin solution,as shownexperimentallyby Dijkstra(ref.3). Theunique relationshipbetweentheconcentrationof interstitialatomsin solution andtherelaxationstrengthmadepossiblean importantstudyofprecipita- tionwhichwillbe mentionedlater. Thesecondexsmpleof inelasticitycausedby stress-inducedordering is foundin severalface-centeredcubicsubstitutionalsolidsolutionsand isknownoftenas theZenerrelaxation.Theatomicrearrangementwhichis responsibleforthisrelaxationis notknownfully.IeClaireandLomer (ref.4) havetreatedtherelaxationin termsof a stress-inducedchange of short-rangeorderin differentnearestneighbordirections;thistreat- mentappesrsto be an advanceovertheoriginalhypothesisof Zener (ref.5) inwhichtheprocesswasregardedas a stress-inducedreorienta- tionofnearestneighborpairsof solute atoms. The experimentalevidence concerningtherelaxationis summarizedas follows: (a)Thereis at presentnomethodforpredictingdefinitel.ywhich alloysshouldshowtheZenerrelaxation.An earliersuggestionof a correlationbetweentherelaxationstrengthandthesizedifferenceof thesolventandsoluteatomshasnotbeensubstantiated. (b)Therelaxationstrengthis stronglydependenton thecomposition of thealloy.Theexperimentsof ~lds andLeClaire(ref.6) on a-brassesindicatedthattherelaxationstrengthisproportionalto the squareof theconcentrationof zinc,whileworkon silver-zinc(Ag-Zn) alloys(ref.7) ledto thesameconclusion. 4 NACATN 4225
b (c)As a resultof thestrongconcentrationdependence,measurements havebeenmademainlyon alloyscontaininginexcessof 10 atomicpercent .k, solute. (d)Thehalf-peakwidthis generallyonlya littlegreater(3to 20percent)thanthatpredictedfora relaxationhavinga singlerelaxa- tiontime(eqs.(1)and (2)). (e)In thesingleinstancewhereaccuratemeasurementsexist(ref.8) theactivationenergyof therelaxationis closebutnotequalto thatfor latticediffusionof eitherthesolventor soluteatoms.Nowick’sSJldySiS (ref.7) showsthatdifferencesaretobe expectedbutdoesnotexplainthe directionof thedeviationobserved. (f)Followingtheproceduresuggestedby WertandMarx(ref.9) it is foundfora standardfrequency,usuallychosenas 1 cps,thattheabsolute temperatureof a Zenerpeakis directlyproportionalto theactivation ener~ fortherelaxation.Theimplicationof thisrelationshipis that thevalueof To isverynearlythesameforallZenerrelaxations. Experimentallydeterminedvaluesof logTo rangefrom-14.0to -15.2 (To in seconds),withmostvaluesbetween-14.5 and-15.0.In the absenceof a specificmodelfromtherelaxation,a relationshipbetween 70 andtheappropriateDo fordiffusioncannotbe,calculated.However, accuratediffusionmeasurementsin face-centeredcubicsubstitutional solidsolutionsindicatea fairlyconstantvalueof Do of about d 0.3 cm2/sec. Thisvalueof Do,combinedwiththevaluesof To given above,indicatesthattheZenerrelaxationisaccomplishedby relatively P fewatcmicjumps,withoneto threeatcmicjumpsas a reasonableestimate. (g)NowickandSladek(ref.10)observedthattherelaxationtime fora silver-zincalloyis decreasedgreatilyby quenchingfromelevated temperatures.Thesamebehaviorwasfoundalso~ Li (ref.11)in a copper-aluminumalloy.An explanation.hasbeenadvanced(ref.10)in termsof thefreezing-inof an.,excessof latticedefects(mostlikely singlevacancies)whichincreasethemea atomicjmp rateandhence causetherelaxationto occurmorerapidly.Duringa low-temperature annealtherelaxationtimeof a quenchedspecimenincreases,andmeasure- mentsof thiskindhavebeenusedto studythedecayof theexcessof latticedefects(ref.12). Thedecaytakesplacein twostages,thefirst beingmuchmorerapidandhavinga slightlydifferentactivationenergy thanthesecondstage.Possibleexplanationsof thisbehaviorhavebeen advancedin references12 and13. NACATN 4225 5
< helasticityofPrecipitationAlloys 7 IhthDijkstra(ref.14)andWert(refs.15 and16)havemade internal-frictionstudiesof theprecipitationof carbonandnitrogen fromsupersaturatedsolidsolutionina-iron.Usingtheheightof the Snoekinternal-frictionpeakas a directmeasureof theconcentration of interstitialatomsin solution,quenchedspecimenswerestep annealedat oneof a seriesof temperatures,andtheheightof the peakaftereachannealwasusedto obtaintheconcentrationremaining in solution.Dijkstra’swork,dealingprincipallywiththeprecipitation of nitrogen(N),revealedthatcertainagingtemperaturesanddegreesof supersaturationledto theprecipitationof twophases,oneofwhichwas Fe4N. Theother,calledN phase1,wasnotidentified.Thekineticsof theprecipitationwereexplainedqualitativelyby thetheoryof nucleation andgrowth.Wertextendedfurtherthestudyof theprecipitationof nitrogenandalsomadea moredetailedstudyof theprecipitationof carbon.No indicationwasobtainedin thiscaseof a precipitateother thanFe5C. Theactivationenergiesobtainedby plottingthetimefora givenfractionaldecreasein initialconcentrationagainstl/T gavefor bothcarbonandnitrogenvaluesmarkedlylowerthanthepreciselyknown activationenergiesfordiffusion.Wertpredictedandshowedexperimen- tallythatthedifferencearosebecausethenumberof growingparticles isnotthesameat differenttemperatures.HardyandEeal(ref.17) have emphasizedthedangerof ignoringthisfactin calculatingactivation energies.Werta&yzed fisres~tson thekineticsofprecipitation * withthesemiempiricalequation
- eQ(-t’/A)m (3)
where u is thefractionaldecreasein supersaturation,c is the concentrationof soluteremainingin solutionaftera growthtime t’, and Co and Cm are, respectively,theinitialandequilibriumsolute concentrations.Both A and m areconstants.Itmaybe notedthat when tt = A theprecipitationis 63 percentcompleteregardlessof the valueof m. When t’/X<<1 (therangeinwhichtheequationismost strictlyf’ollowedbecauseof theabsenceof interferencebetweenneigh- boringparticles),equation(3)becomes
u= (t’/h)m (t’< Zener(ref.18) has shownforthediffusioncontrolledgrowthof a pre- cipitateparticleinan infinitematrixthattheexponentm is related .* 6 NACATN 4225 to theshapeof theparticle.Thisanalysiscanbe appliedalsoto a collectionofwidelydispersed(noninterfering)particleswhichare nucleatedat thesameinstant.Forprecipitatesin theformof flat disks,cylinders,andspheres,thevalueof thegrowthexponentm is, respectively,5/2,2,and3/2. It shouldbe noted,however,thatif nucleationandgrowthareoccurringsimultaneouslythevalueof m is increasedby unity.Thus,forexemple,thesimultaneousnucleationand growthof spherescouldbe confusedwiththesimplegrowthof flatdisks. Microscopicobservationsareclearlydesirableto avoidpossible confusion. TheresultofWert’sanalysiswasthat m = 3/2 fortheprecipi- tationofFe3Cand5/2forNphase1. No inmibationperiodwasdetected in theseexperiments,so thegrowthtime t’ wassetequalto theaging time,andtheshapesof theparticleswerethereforetakenas spheresfor Fe3Cand,in egreementwiththemicroscopicobservationsof Dijkstra, (ref.14)as disksforN phase1. !Fhedepletionofbothcarbonandnitrogenfromcold-workeda-ironhas beeninvestigatedby Harper(ref.19)whofoundthatforbothelementsthe growthexponentm waschangedto 2/3. ‘Thisprovidedstrikingsupport fora theoryof Cottrell(ref.20)andBilby(ref.21.)whichpredicted thisexponenton thebasisthatdepletionwouldoccurby theformationof atmospheresof interstitialatcmsarounddislocations.Dijkstra(ref.14) hadnotedearlierthata ssmpleof cold-workeda-ironcontainingnitrogen showednomicroscopicallyobservableprecipitateevenwhenthenitrogen 4 internal-frictionpeakhadfallento theequilibriumvalue. P Otherinvestigationsofprecipitationby anelasticmethodshavebeen confinedso farto aluminum-basedalloys,withtheexceptionof thework of &g, Sivertsen,andWert(ref.22)on gold-nickel(Au-Ni)alloys.The equilibriumdiagremof thissystemshowscompletesolidvolubilityat high temperatures.At lowertemperaturesa miscibilitygapexistsacross virtuallythewholeof thediagramanda high-temperatureface-centered cubicsolidsolutionbreaksdownon SIUWcoolingintotwootherface- centeredcubicsolidsolutionsof differentlatticeparameters,onerich in gold,theotherrichinnickel.T’WOunstableInternal-frictionpeaks wereobservedin solution-treatedandquenchedalloysof severaldifferent compositions.FortheAu alloycontaining30 atomicpercentofNi the peaksoccurredat 250°C and400°C at a frequencyof approximately1 cps. Thepeakat 4~0 C wasidentifiedtentativelyas a Zenerpeskandwas foundto decreaseon agingwiththekineticsof thedecompositionof the quenchedphase.In contrastto thehigh-zeraturepeak,theheightand positionof thelow-temperaturepeakwerefoundtobe dependenton the quenchingtemperature,andthepeakwasnotfoundin specimensquenched fromjustInsidethemiscibilitygap. Further,thispeaksmnealedout muchmorerapidlythanthe400°C peakanddisappearedcompletelybefore NACATN 4225 7 ● resistivitymeasurementsormicroscopicexaminationrevealedthestartof 4 precipitation.Whileno explanationfortheoriginof thispeakwas advanced,itprovidesanotherillustrationof thesensitivityof internal frictionto theconditionof an agingalloy. In thefieldof aluminum-basedalloys,an investigation(ref.23) wascarriedouton Al alloycontaining39weightpercentofZn. No internal-frictionpeakwasobservedin thisalloy.Precipitationoccurs in a discontinuousmanner,andtheanelasticbehatiorwasexplainedin termsof coupledrelaxations(ref.2) acrossthenewinterfacesproduced by precipitation.IkmaskandNowick(ref.24)didfinda peakin the Al alloycontaining20weightpercentof Ag. Duringagingfollowing solutiontreatmentandquenchingthepeakumderwentfoursuccessive changesas follows: Stsgel.-Therelaxationtime T increasedrapidlywithouta detectablechangein thepeakheight.A significantchangein T was detectedafter1.5hoursagingat 26°C. Thisstagewas attributedto theemnealingoutof quenched-invacancies. Stage2.-Stage2 followedthecompletionof stage1 andpersisted up to about2 hoursat 165oC. king thisstageno changeoccurredin thepeak,andthestructureof thealloyconsistsof clustersof silver atomsin a considerablydepletedmatr~. Stage3.- Stage3 appesmto be associatedwiththereversionof thesilverclusters.Thepeakincreasedin heightby about50percent as thepeakmigratedto slightlyhighertemperatures,anda hysteresis % wasobservedbetweenmeasurementsafterheatingandcooling.!Jhis stageis completeafterabout2 hoursat 20~ C. Stage4.- Stage4 commencesat aboutthesametimeas theinter- mediateprecipitate7’ is detectedby X-raysandconsistsof a fall in thepeakheightanda slightdecreasein thepeaktemperature. AfterrejectingtheZenerrelaxationas theoriginof thepeak,a newmechanismwasproposed,basedon theinteractionof an appliedstress withthelocalinternalstressesarounda precipitateparticle.A dis- cussionof thismechanismwill.be givensubsequently,butinpassingit maybe remarkedthatsanedifficultiesareencounteredin describingthe behaviorofAl alloycontaining20weightpercentofAg in termsof this mechanism. Entwistle(ref.25)hasstudiedtheearlystagesof agingin a varietyof sluminumallo~,usingapparatuswitha verylowlevelof externalenergyloss. Twosmallrelaxationsweredetectedafterlow- -& temperature(200to 600C) agingin,thecmmnercialalloyDuralumin,but 8 ~cA ~ k225 8 thesewerenotfoundin thepurebinaryAl alloycontaining4 weight percentof Cu norin severalotherbinaryalloysexsmined.Thesimplest b alloyshowinga re~tion akinto thema$oronefoundin Duraluminwasa quaternaryalloyof aluminum,copper,magnesium,and.silicon.Whilea calculationshowsthat log‘rOhasa valueassociatedwitha relaxation by singleatomicJwnps(logTo = -15.0),theactivationener~ hasthe strikinglylowvalueof 13kcal/mole,whichis fartoolowfornomal atamjumpsin thesubstitutionalsolidsolution,andis evenlowerthan tightbe reasonablyexpectedfordiffusiondowndislocations.No satis- factoryinterpretationof thisvaluehasyetbeenoffered. A preliminarystudyhasbeenmadeby @ on thealloysAl containing 0.5weightpercentof Cu (ref.26) endAl containing4 weightpercentof Cu (ref.27)usinga torsionpendulmn.A strongly&mplitude-dependent “anomalous”peakwasclatiedto existnearroomtemperaturein cold-worked Al alloycontaining0.5weightpercentof Cu aftercoolingfra a recovery annealof 1 hourat 3000C. (Thevolubilityof copperin aluminumat 300°C is 0.45percentweight.)It hasbeenshown(ref.2),however,that theeffectis difficultto reproduceandtkt priorcold-workingdoesnot seemnecessary. In solution-treatedandquenchedAl alloycontaining4 weightpercent of Cu,I@ obtainedevidencefortheexistenceof a peakat 2~0 C. This peakwasnotpresentafterthespecimen”hadbeenfurnacecooledfrom 525°C. K8 concludedthatthepeakarosefromviscousslipalonggrain boundaries,a phenomenonwhichhe hadpreviouslystudiedextensively 4 (refs.28 to 30). Thedisappearanceof thepeakcausedby precipitation duringfurnacecoolingseemedreadilyexplicableon thegroundsthat precipitationat theboundarypreventsslipfromoccurring,a phenomenon ? againsuggestedfrom@’s earlierwork(ref.30). Inhislastknown publicationon thesubject(ref.31)@ claimedthatuponisothermal agingat 2@0 C thepeakfirstdecreased,thenincreased,andfinally (afterabout10 days)fellagain.An attemptwasmadeto correlatethis behaviorwiththemicroscopicallyobservedconditionof thegrain bouudmies.Thepresentworkshowsthatthepeakdoesnotoriginate fromgrain-boundaryslipandhenceinvalidatestheinterpretationgiven to theseresultsbyK8 andlaterby G&.sler(ref.3Z). MorerecentlyMaringer,Marsh,endManning(ref.33)havereportid resultson theinternalfrictionofld.alloycontaining4.82weight percentof Cu. Twomaximumswerefoundbelow2000C in theinternal.- frictioncurveobtainedon heatingthesolution-treatedandquenched alloy,andbothwereinterpretedas anelasticpeaksarisingfromthe stress-induceddiffusionof copperatomsin solidsolution.Maringer, Marsh,andMsmningreportedfurtherthatafteraginga relativelyfine- grainedspecimenofAl alloycontaining4.82weightpercentof Cu at 300°C for17 hoursthecurveon heatingshowedamsdmznat 400°C. Thismaximumwasinterpretedas thegrain-boundarypeak. NACATN 4223 9 Thepresentworkis concernedwithan investigationof theanelastic 7 behaviorof theAl alloycontaining4 weightpercentof Cu. Sincethis workis farmoreextensivethanthatofpretiousworkers>it iSpossible to.obtaina clearerpictureof thevariousphenomenathattakeplaceand to establishtheirorigins.Inparticular,singlecrystalsaswellas polycrystallinespecimenswereusedin orderto showwhich,if any,of the effectsobservedweredueto grainboundaries. StructuralChangesEuringAgingof Al-Alloy Containing4 WeightPercentof Cu Thepurposeof thissectionis to bringtogetherthosefindingsof otherworkerson thestructuralchangesduringagingofAl alloycon- taining4 weightpercentof Cuwhichareof importancein theinterpre- tationof thepresentresults. Thephasein equilibriumwiththeterminalaluminum-richsolid solutionis theintermetalliccompoundCuA12(f3phase).Thestructure of CUA12wasfo~d by ~ia~ (ref.34) tobe of tetragonalsymnetrywith theparametersa = 6.04A and c = 4.86A andwithfourcopperandeight aluminumatomsperunitcell. BradleyandJones(ref.35)confirmed theseconclusionsandgavemoreprecisevaluesof thelatticeparam- etersforCuA12containing47weightpercentof Al. WhenAl alloy containing4 weightpercentof Cu is agedat temperaturesbelow300°C simpleprecipitationof the e phasedoesnotoccur.Instead,oneor moreof threeotherstructuresmaybe produced,dependingon theaging temperature.lCurrentknowledgeof thesestructures(ref.17)is sunmmrizedas follows: (I-) T!&G.P.[I.]zones:Itwasdiscoveredindependentlyby Guinier andPrestonin 1938thatroan-temperatureagingof singlecrystalscauses theappesraaceof scatteringstreaks(non-Braggianreflections)on Laue transmissionphotographs.Thecauseof thestreskswasgivenas the modulationin interplanarspacingandscatteringpowerarisi froma localenrichmentin copperof“smallaxeasdistributedon the7)100 planes of thematrix.TheseareasarenowcalledG.P.[I]zones.At roomtem- peraturethezonesaredetectedafter7 hoursofagingandreacha constant conditionina fewdays,afterwhichn6 furtherchangehasbeendetected. Thethicknessof thezoneswasestimatedto be about2 atomdistances(8A) andthedismeterafterroom-temperatureagingtobe somewhatlessthan50A %he viewspresentedhereareprincipallythoseof Guinier,Preston, SilcockHeal,andHarm. Howe=r,Geisler’sopinion(ref.36)iS that G.P.[1~zonesarestructurallyperfecte’ plateswhicharetoothinto 4. causenormaldiffraction. 4 10 NACATN 4225 & (ref.37), althoughthezonesattainlargerdiametersat higheraging temperatures.Usingthesefiguresandthefurtherestimatethat10per- V; centof thetotalavailablecoppersegregatesin zoneshavingonecopper atcmto fouraluminumatoms,Preston(ref.~) concludedthatthefully forehedzoneswerescatteredabout2~A apartin thematrix.The insensitivityof thelatticeparameterto theformationof G.P.[1]zones is thebasisforthesuggestionthatthefrag~ionof thetotalavailable copperatomswhichsegregateto thezonesis fairlysmall. Useof themorerecentX-raytechniqueof small-anglescatteringhas supportedthegeneralpicturegivenabove.Gerold(ref.39)hasmade quantitativecomparisonsof themeasuredintensityof small-angle scatteringwiththatpredictedfroma varietyofpossiblemodels.He -. concludedthatthemostsatisfactoryagreementwasobtainedwitha model .— containinga singleplaneof exclusivelycopperatomswithneighboring close~~spacedplanesof aluminumatcvnsandin successiveplanesa decree,singdisturbanceof thenormalinterplanarspacingextendingto the 16thplaneon eithersideof theplane.of copperatoms. (2)TheG.P.[2]or e” structure:Thisstructurewasfirstdis- coveredby Guinier(ref.40)in spec-ns whichhadbeenagedat room tempefk”.ureandthenheatedforseveralC@ysat 100°C or forsomehours at 150°C. GuinierfoundthattheG.P.[1]streaksdevelopedintensity maximmmalongtheirlengthandresolvedultimatelyintofourdiffuse spots. Thestructureresponsibleforthesespotswastermede“ by Guinie,randlaterG.P.[2]by Hardy.Theappearance”ofthespotssuggests .c that‘tiheG.P.[2]structureformsin thin.platesparallelto the {100] plane~of’thematrix.GuiniersuggestedthattheG.P.[z]structure consistsof copper-ehrichedregionswhereorderinghasoccurred,in the F sensethatcopper-enrichedplanesalternatedwithimpoverishedplanesin a regul~or orderlysequence~the-repetitionoccurringaftereveryfourth plane. Thespacingsbetweensuccessive100 planesinthe c directionof theG.P.[2]unitcellhavebeengivenly{} Gerold(ref.39)as 1.82A,2.02A, 2.02A,and1.82A,thesmallerof thetwospacingsbeingthedistancebetween a copper-richplaneanda neighboringplane.Thesumof thesespacings . givesthe c parsmeterof G.PL[2 as 7.68A,in agreementwiththat foundby Silcock,Heal,andHa&dy1ref.41)foragingat 165oor 1900C, whereG.P.[2]wasthefirststructuredetected.On agingat 1300C Silcock,Heal,andHardynoticed,however,thatthe c parameterchanged progressivelyonaging,from8.08Ato 7.68A,a resultwhich.ledthemto obser-rethatsinceG.P.Fl]precededG.P.12]in theagingsequence, G.P.[lomayserveas a nucleusforG.P.[2j~ Thequestionofwhe%~r-the G.P.[2]structureis siqplya morestableorderedarrayof G.P.[1]zones has apparentlynotbeendiscussed.Silcock,Heal,andHardyarguethat G.P.[1]is essentiallydifferentfromG.P.[2]on thegroundsof the * behaviorof the c parametermentionedaboveandalsobecauseof the —..— NACATN 4225 u markeddifferencein thegrowthcharacteristicsof thetwostructures (ref.41). (3) The 6’ phase: TheStrUCtUreof thisphasewassubjectto structureanalysisby Preston(ref.42)afteritsdiscoveryin 1935by WassermannandWeerts(ref.43). Prestonconcludedthatthestructure is slightlytetragonalbutotherwiseof thecalciumfluoride(CSY2)type, containingalwninumandcopperin theproportion2 to 1. Theplanes [lm}e, matchtheplanes {}100~ with (lOO}.lparallelto (l-lO)=; theboundaryacrosstheseplanesis thereforecoherent.Sanelossof coherencymu”stoccuralongthe c axisof the El’structurebecauseof a differencein theinterplanarspacingof 0’ and*healuminummatrix in thisdirection.Theprecipitationof 8’ phasein theformof plate- letson the {lCO}~trix planesis shownwellin thephotographsof Calvet, Jacquet,andGuinier(ref.37). Prestoncheckedhisproposedstructureby comparisonof thecalcu- latedandobservedintensitiesof thediffractionspotsandfoundgood thoughnotperfectagreement.Silcock,Heal,andHardy(ref.41)pointed outthattheintensitydiscrepancieswhichdo exist,togetherwiththe frequentappearanceof an unexplaineddiffractionspot,reducePreston’s proposalto “averygoodapproximation”of the El’structureonwhich theywereunableto improve. Theworkof Silcock,Heal,ad Hardy(ref.41)hasestablishedthe generalsequenceof structuresduringagingas G.P.[1],G.P.[2],0’, and e. No morethsntwoneighborsin thissequenceareknownto coexist, andas thetemperatureof agingis increasedprogressivelyfewerof the structuresaredetected.IHOW roughly165°C, G.P.[13is thefirst structuredetected,between165oand220°C it is G.P.E2j,andabove 220°C, thephase 0’. Thetemperatureabovewhich (3 precipitates directlyisprobablyin therange3500to 400°C. Ithasbeenmentioned earlierthatpresentetidenceindicatesthatG.P.[2]isnucleated directlyat temperaturesabove165°C. At lowertemperatures,where G.P.[1]is formedfirst,nucleationof G.P.[2]fromG.P.[1]appears probable. Withregardto thepossibilityof thetransformationof G.P.[2]to e’,Silcock,Heal,andHardyhaveshownthat e’ platelets,whenformed subsequentlyto G.P.~2],havean initialthicknessgrea~rthanthatof G.P.[2],a factsuggestingthat (3’canbe fotiedby transformationof G.P.[2]. Guinier(ref.~) haspublishedresultswhichbearon this point.Forthethreeagingtemperatureslx”, 180°,and190°C he has givencurvesshowingthevsriatio~in thesmountof G.P.[2]and Q’ as. a functionof agingtime. Thecurvesshowthatthesmountof G.P.[2] firstincreases,reachinga maximumwiththedetectionof 0’,andthen fallssteadilyas theamountof e’ increases.If theG.P.[21structure 12 NACATN 4225 is notitselftransformingto e!,theseresultsrequirea gradual re-solutionof G.P.[2]anda diffusionof comer atansto otherregions wherethe 0’ phaseisnucleated.Possiblycalorimetricmeasurements wouldbe of’helpin settlingthisquestion. Thekineticsof theprecipitationof the 0’ phaseareknownat varioustemperaturesfrom(a)theX-rayworkof Guinier(ref.M) and.of Silcock,Heal,sndHardy(ref.41)whomeasuredquantitativelytheinten- sitiesof G‘ spotsduringagingand(b)fromthedllatometricstudies of LankesandWassermann(ref.45). A smallcontractionisassociated withthedevelopmentof theG.P.[I.]and G.P.[2]structures,whilea muchgreaterexpansionaccompaniestheprecipitationof 0’.2 (An expansionoccursbecausethepredominanteffectis theincreasein latticeparsmeterof thematrixas copperis removedfromsolution.) WherecomparisonwaspossiblebetweentheX-rayanddilatometricmethods, goodagreementwasobtained(ref.W). Guinierhasproducedconvincingevidencethatthe e’ phasetrans- formsallotropicallyto the 0 phase(ref.40). Whenprecipitated directlyat hightemperatures,thecrystallographicorientationsof the 13particlesarerandom.However,the 0 particlesproducedby high- temperatureannealingof the 01 phaseshow-definiteorientationrela- tionshipsto thematrix,whichGuinierhasshownto be thoseexpected froman allotropictransformationof theorientedet phase.Thereis littleinformationon thekineticsof thistransformation.Foran aging temperatureof 3000C, C!alvet,Jacquet,andGuinier(ref.37)detected . 0’ phaseafter30 seconds,andlaterthespotsbecamemoreintense.‘The 0 phasewasdetectedafter1 hour. On furtheragingtheintensityof the 0’ spotsdecreased,beingjustvisibleafter8 daysandundetectable P after16 days,bywhichtimethe 8 spotswerewelldefined. Theonlyothertopicrequiringmentionhereis thephenmnenonof reversion.As an exsmpleof reversion,a specimenagedto an increased hardnessat roomtemperaturerevertsto theas-quenchedhardnessif it is annealedfora fewminutesat 200°C. TheX-rayphotographsof Preston (ref.46)showclearlythat,aftertheanneal,theG.P.[1]zonesformed duringroom-temperatureaginghavedisappeared.Theenergyrequiredto dispersetheG.P.[11zoneshasbeenobtainedfromspecific-heatmeasure- ments,by Suzuki,forexsmple(ref.47). Reversionisexpectedwhenthe temperatureis raisedeitherto a valueabovethatatwhichparticles thathaveformedbecomeof subcriticalsizeforstabilityor above thatat whichthestructureisno longerevenmetastable(ref.17). !I!hisinvestigationwasconductedatYaleUniversityunderthespon- sorshipandwiththefinancialassistanceof theNationalAdvisory CommitteeforAeronautics. 21tis difficultto reconciletheseresultswithGeisler’sopinion thatG.P.zonesaresmallplateletsof e’. NACATN 4225 13 ● SYMBOLS ✜ A,B constsnts An smplitudeof oscillationafter n cycles A. initialamplitudeof oscillation c (loo) [010] shearmodulus M! relaxationstrengthof the C modulus c’ (11.o)[ilo]sheermodulus AC’ relaxationstrengthof the C’ modulus c concentrationof copperin solution D diffusioncoefficient Do preexponentialconstantfor D E Young’smodulus L m relaxationstrengthofYoungismodulus f frequencyof vibration x G shearmodulusof thespecimen AG shearrelaxationstrength E enthalpyof activation K bulkmodulus AK bulkrelaxationstrength m growthexponent n numberof cycles R gasconstant 14 NACATN4225 9 S11N129S44 elasticconstantsof a cubiccrystal absolutetemperature -w tw gruwthtime strainenergy totalenergy potentialener~ of a weight fractionaldecreasein su~rsaturation snglesbetweenaxisof a single-crystalspecimenandthe threecubeaxes relaxationstrength logarithmicdecrement constant Poisson’sratio relaxationtime preexponentialconstantfor T orientationfunction circularfrequencyofvibration Subscripts: f final o initial P peak R relexed s specimen f NACATN 4225 15 k t afteragingtime t 3 u unrelsxed w equilibria APPARATUS TorsionPendulum Withtheexceptionof a fewexperimentsconductedintransverse (flexUral)vibration,alltheinternal-frictionresultshavebeen obtainedwiththetorsionpendulum.Thisa~aratuscameintoprominence throughtheresearchesof @ andis thesimplestandyetthemostuse- fulinternal-frictionapparatuswhichhasbeendetised.ThoughV=iOUS designmodificationshavebeenpublished(refs.48 and49),thepresent pendulumfollowscloselythedescriptionof @ (refs.28 and50),with theadditionalfeatureof permittingtestsin a vacuum. Thetorsionpendulumrequiresspecimensin thefom ofwires,USUllY 8 to 12 incheslongandof approximatelyO.0>-inchdismeter.Thetopend of thewireis clampedby a pinvisefastenedrigidlyto thetopcapof a verticaltubefurnace.A steelextensionrodprojectingfromthebottom endof thefurnaceis fastenedto thelowerendof thewireby a second pinvise. Thespecimen,pinvises,andextensionrodarelocatedcen- trallydowntheverticalfurnace tube. A steelcrossbaranda concave G mirrorareattachedto theprojectingendof theextensionrod. The momentof inertiaof thecrossbar(whichmsybe variedby theadditionof suitableweights)is chosen.togivenaturalfreetorsionaloscillations in theeasilyobsenablefrequencyrange(i.e.,0.2to 2.5CPS). Oscil- lationsareexcitedor stoppedby manualoperationof a tappingkeywhich makesandbreaksthecurrentenergizinga pairof electromagnets appropriatelyplacedto attracttheendsof themagneticallysoftcross- bar. Theamplitudeof oscillationis observedon a galvanometersscale placedseveralmetersfromthespechnenbymeu of a be- of light reflectedfromtheconcavemirror. Themeasureof internalfrictionusedIn thisreportis theloga- rithmicdecrementb“ definedas (4) 16 NACATN4225 & where ~ is theamplitudeof oscillationobservedon thescale n .= cyclesaftertheamplitudeA.. A strainamplitudeof 10-5in the -. b specimencorrespondsto the & valueof 4 centimetersusuallyused. Thefrequencyof oscillationf wasdeterminedwitheachinternal- frictionmeasurementby timingtheperiodrequiredfortheexecutionof the n cycles. To reducetheair-dampingener~ lossin theapparatus,testswere conductedin an atmosphereof heliumat 10millimeterspressure.The pressuredependenceof internalfriction,bothin airandhelium,iS shownin figure1 fora specimenofAl alloycontaining4 weightpercent Cuvibratingat 1.95cpsat roomtemperat~e.Theinternalfrictionin heliumis appreciablylowerthanthatin airforpressuresabove1 milli- — meter. Theuseof a highvacuumwasfoundto be undesirablebecauseof thelargelagin thethermalresponseof thespecimenuponchangingthe temperatureof thefurnacewall. Theuseof a 10-millimeterpressure of heliumprovedmosteffectivein eliminatingthislagwhilereducing theinternaLfrictionto one-thirdthat”observedat atmosphericpressure in air. Becausespeedof operationis essentialin studiesof an aging alloy,thefurnacewasbuiltwiththemininnnnthermalcapacityconsistent witha maximumoperatingtemperatureof,>20°C (i.e.,a temperaturein the a phasefieldofAl alloycontaining4 weight.percentCu). Heating ratesof 300C perminutewerereadilyobtainable,andthecoolingrate * of thefurnacewascomparablyhighaboveroughly1200C. Despitethe fastheatingratesused,troubleduetoovershootingthetemperature desiredwasavoidedby theexcellentperformanceof an electronictem- P peraturecontrollerof theproportioningtypeworkingfroma control thermocoupleplacedverycloseto thenoninductivefurnacewinding. Thetemperatureof thespecimenwasmeasuredby a secondthermocouple placedwithinthefurnacetubeandclose”to thespecimen.Duringthe majorityofmeasurements,thetotaltemperaturevariationof thespeci- mendidnotexceed0.50C. Thetemperaturedistributionwithinthefurnacewasinvestigatedat at a seriesof temperatures,withtheresultsshownin thefollowing table: Maximumtemperaturedifference,‘C,for- Temperature,~ Oc Specimen8 in.long Specimen12 in.long 150 1 2 205 2 3 265 2.5 367 3.5 ::; ● NACATN 4225 17 FlexurePendulum In thecourseof thisworkitbecamedesirableto testsomeof the torsion-pendulumspecimensinflexuralvibrationandat approximately thessmestrainamplitudeandfrequencywhichwereusedin torsion.A searchof theliteraturerevealednothingsuitedto thispurpose,so a newappsratus,calledtheflexurependulum,wasdesignedandbuilt. Thisappsratuswasproducedby s~le modificationof thestandard torsionpendulum. Theimportantfactorswhichmustbe consideredin thedesignof a flexurependulumwillnowbe discussed.Observationof thetipof a transverselyvibratingwirerevealsthatthevibrationis nonplanar. Thewirevibratesin an ellipsewhichundergoesan alternatingchangein eccentricityas themajoraxisof theellipsealternatesbetweentwtY perpendicularplanes.Thiscomplicatedbehaviorarisesevenin an elasticallyisotropicwireif thespecimenhasa nearlybutnotexactly symmetricalcrosssection.Thepracticalresultofpresentimportanceis thata nonplanartibrationmakesan internal-frictionmeasurement extremelydifficult.Theeasiestmethodof avoidingthisbehavioris by theuseof a spectienwhichhasconsiderableasynmetryof crosssection, forexsruple,a reedwitha largewidth-to-thicknessratio.However,this solutionwasof no usein thepresentcasewheretheobjectwasto test in flexurethewirespec~ns usedin thetorsionpendulum. Themostsuitablechoiceof themodeof transversevibration appearedtobe thatinwhichthespecimenis clsmpedat oneendas a cantilever.‘Thefundamentalfrequencyof vibrationin thismedeis the lowestnaturalfrequencyattainablein anytransversemode. Evenso, thewirespecimensto be testedhadfrequenciestoohighto be measured tisually,anditwasthereforenecessarytoweighttheendof thespeci- mento lowerthefrequencyto thedesiredvalue.Withthewireheld horizontally,theadditionof thisweightcausedan slarmingl.ylargesag in thewire. Holdingthewireverticallywould,of course,removethe sta~icbendingstrainsimposedby theweight,butat thesametime anotherveryseriousfactoris introduced.For,whenvibratingabout a verticalaxis,thetotalener~ UT in a positionofmaximumdeflec- tionis thesumof thestrainenergyus storedin thedeflected specimenandthepotentialenergygainedby weight~ (assumea specimenof negligiblemass). If AUS istheenergylostduringthe nextcycleof vibration,theobserveddecrementbobs is givenby (5) , 18 NACATN 42= b However,thedecrementof thespecimenitself5S (aswouldbemeasured if gravitywerezero)is b (6) Hence, (7) Calculationshowsthat ~>> Us,andhencevibrationabouta vertical axisleadsto an observeddecrementmuchlowerthanthatof thespectien itself.Measurementof thecorrectdecrementcanbe obtainedif the specimenisheldhorizontally. Thewayinwhicha planarvibrationsnda restrictedstaticsag wereobtainedinhorizontallymountedspechms is shown@ thediagram of theflexurependulm(fig.2). Followingthenotationof figure2, twoidenticalspecimensH areused. Theseareparallelandmountedin horizontalpinvisesF, oneabovetheotherandseparatedby about 0.75inch. TheloadingweightJ is constructedof almninwnin two equalparts,andeachparthasa grippingflangeof 2 millbeterswidth projectingfromtheinnerside. TheweightJ is securedto thespeci- mensby sandwichingtheendsof thespectienqbetweentheflangesand tighteningup thesteelscrewsjoiningthetwohalvestogether.When viewedendon,thereis a slitdownthemiddleof J thewidthofwhich isequalto thedismeterof thespecimens.Thestaticsagof this arrangementis acceptablysmalJ.becauseof themuchgreatervertical bendingstiffnessof thissystemcomparedwiththatof a singlespeci- men. A planarvibrationis obtainedin thedirectionshownbecausethe bendingstiffnessin thehorizontalplaneis appreciablylowerthan thatin theverticalplane. Thegeneralfomnof theappsratusis showninthelowerdrawing of figure2. ThetorsionpendulumfurnaceG ismountedhorizontally andthe2invisesF joina hollowsteeltubeE whichmaybe secured rigidlyto theendof thefurnace.Thefurnaceistidevacuumti~htby thecoverD. Theshadedareasareflatrubbergaskets.Windowsit C andK permitlightfromthelap A to shinethr&@ thetubeE, theslit in theloadingweightJ, andthelenEL. Thelow-powermicroscopeN, fittedwitha graduatedeyepiece,is focusedon therealimageof the slitformedatM by thelensL. A greenfilterB reducesthelight intensityto a comfortablelevelandremoveschromaticaberrationfrom . Y NACATN 4225 19 . theimage.Transversevibrationsareexcitedby meansof an electro- magnetactingon thesteelscrewsin theloadingweightJ. Thismagnet d (notshownin fig.2)wasIocatedinsidethefurnaceandwaswoundwith glass-coveredsilverwiretowithstandelevatedtemperatures.Thehot junctionof themeasurementthermocouplewaslocatedbetweenthetwo specimens. Iagarithmicdecre~ntmeasurementsweremadein thesanemsmneras thatdescribedforthetorsionpendulumby observingoneedgeof the imageof theslitvibratingacrossthescaleof thegraduatedeyepiece. Tominimizethesagin thespecimens,theweightJ wasreducedto theminimumvalueconsistentwithvisualdeterminationof thefrequency. Theparticularconditionsusedme sunmarizedin thefollowingtable: Lengthofspecimens,in...... 8.o Approximatediameterof specimens,in...... 0.035 Loadingweight,g...... 3.00 Approximatefrequency,CAP S ...... Maximumstrainemplitudeat startofmeasurement...... 1::5 Atmosphere Heliumatpressure,mu,of ...... 10 Ccanparedwiththetorsionpendulum,theflexurependulumhasseveral disadvantages.Twinspecimensarerequiredinsteadof a singlespecimsn, andtheerrorofmeasurementis larger(*5percentforthemea of five * readings).Eyefatiguebecsmeconsiderablewhenmanymeasurementswere taken,aswasdoneto ccmpnsatepartiallyforthepoorerprecisionof a singlemeasurement.Theroom-temperaturedampingof solution-treatedand % quenchedAl aUoy containing4 weightpercentof Cu (ameasureessentially of externalenergylosses)wasconsiderablyhigherin theflexurependu- lwn 51 = 1.8x 10-3)thsnin thetorsionpendulum52 = 0.4x 10-3). ( ( HoweverjaE testsshowedthatthevalueof 51 wasreproducible,the resultsobtainedfromtheflexurependulumwereconsideredto be ready forcomparisonwiththosefromthe-torsionpendulumaftersubtraction- of 82, 51 - 52= 1.4X 10-3. Heat-Treatment(Quenching)Furnace A well-insulatedelectrictubefurnacewitha 36-inchwindingwas builtfortheheattreatmentof specimens.Thefurnacewasmounted verticallyanddirectlyabovea quenchingbath,so thatuponreleasea specimendroppedfreelyfrcmthefurnaceintothebath. 20 NACATN 4227 . A desiredtemperaturecouldbe maintainedtowithin1° C overi3eVer81. weeksby an electroniccontrollerof theproportioningtype. Themaximum u temperaturedifferenceovera 12-inchzonein thefurnacewas30 C t’$”‘)O VacuumFurnaceforAlloyPreparation To insurefreedomfromgasporosityin theingotsandtohelpin maintainingthepurityof thestartingmaterials,a smallfurnacewas builtformelting,alloying,stirring,andcastingaluminumalloysin a vacuwn. A steelchannel,carryinganAlundummeltingcrucibleanda split steelmoldwithitstopnormallydownwardfacingthemouthof the < crucible,wasmountedverticallyinsidea stainless-steelfurnacetube. Thepartof thistubecontainingthecruciblewascoveredon theoutside . by a &mountableelectricfurnacecapableoflraisingthecrucibleto 8500C maximumtemperature.Thecoolendof thetubertiotefromthe furnace,carrieda simplerotaryvacum sealthroughwhichpasseda steel shaftterminatingin a graphitebladewhichcouldbe loweredintothe crucibleandrevolvedto stirthemelt. A deliveryrod,extendingfrom thecoolendof thefurnacetubeto themouthof thecrucible,enabled a coldadditionto bemadeto themelt. Uponreleasinga catchfromthe outsideof thefurnace,theadditionsliddownthedeliveryrodintothe crucible. b Castingwasperformedby invertingthefurnacetube,whichwas pivotedin a frsme.,Thiscausedthealloytopourfromthecrucibleover R a graphite-linedrunnerintothepreheatedmold. Aftercasting,the furnacewasremovedfromthe‘tubeto allowmorerapidcooling. Thefurnacetubewasevacuatedby a rotaryoilPUMP,andthepres- sureattainedwiththefurnacein operationwti0.02-millimeterof- mercury. FREPARATIONOF SPECIMENS Materials Thepurityof thestartingmaterialsis shownin thefollowingtable: NACATN 4225 21 Metal Puxity, Source percent Al 99.99+ AluminumCo.of Am. (Analysis,percent:Cu,0.002;Fe,0.001 Si,0.032;Mg,0.000 Na,0.000;Ca,0.000) Cu Am.Smelting& RefiningCo. 99.999 - PreparationandCm-positionof Pol.ycrystallineWire TheAl alloycontaining4 weightpercentCuwasmadein thevacuum furnacedescribedpreviously.Themetalsweremeltedtogetherin a new Alundumcrucibleat a pressureof 0.02millimeterofmercury,andafter thorough.stirringthemeltwascastintoa steelmoldyieldingan ingot 5 incheslongand5/16inchin diameter.Ingotsweremachinedto 0.25-inchWmeter andthenhanogenizedat 450°C foroneday. ‘I’his treatmentandlaterrecrystallizationannealswerecarriedoutwiththe alloywrappedin alminumfoil. Theingotswerecold-rolledandcold-dxawntowireof 0.062-inch and0.033-inchdiameter.An annealof 1 hourat 400°C!wasgiveneach G timethecold-workingamountedto roughly50-percentreductionin area. The0.033-inch-diameterwirewascutinto12-inchlengthsforuse in thetorsionpendulan.The&.ainsizeof thiswireafterthefinal drawingwasapproximately0.1millimeter,butrapidandconsiderable graingrowthoccurredafterrecrystallizationduringthefirstsolution treatmentof severalhoursat 525°C. Afterthissolutiontreatmsnt thegrainswerelargerthanthewiredimneter(i.e.,about1 milltietir), ad theboundariesextendednormallyacrossthewireto forma bamboo structure. A randomssmpleofwirewassubmittedforchemicalanalysis,and thereportgave the coppr contentof thewireas 4.08 weightpercent. Preparationof SingleCrystals Afterseveral.failures,attemptswereabandonedto growlongsingle- crystal wiresby thestr”ain-annealtechn.ique.Thefirstattemptsto grow singlecrystalsfrmnthemeltwerealsounsatisfactorybecauseof the \ 22 NACATN 4225 porositycausedby gaspickupthroughthewallof thegraphitenmld. Themorerefinedtechniquedescribedbeloweliminatedthistrouble andseveralsoundsinglecrystalswereobtained. Themoldsusedconsistedof a 0.5-inch-dismeterbakedgraphiterod 13 incheslongwitha centralholeO.~ inchin diameterdrilledto a depthof 12.5inchesfromoneend. A lengthof 0.062-inch-dismeter pol.ycrystallinewireofAl containing4 percentCuwaspusheddownthis hole,sadthenioldinsertedintoa longPyrextubeclosedat oneend. The lowerportionof thistube(containingthemold)wasplacedin a furnace at 750°C, andtheupperopenend,projectingfromthefurnace,wascon- nectedto a vacuumpump. In thecourseof a fewminutestheglassflowed to forma tenaciousskinoverthemoldwhicheffectivelyexcludedthe atmosphereduringthelatergrowthof thecrystal.Beforeremovalfrom thefurnace,thebottomof themoldwastappedvigorouslyagainstthe furnacefloorto insurethatthemoltenalloyformeda continuouscolumn insidethemold. Themoldwasthenremovedfromthefurnaceandthe superfluouslengthof glasstubingremovedwitha flsme. Singlecrystalswereobtainedby remeltingthealloyIn a vertical furnaceat 750°C andthenloweringthemoldoutof thefurnaceat a rate of 1.5ixL./hrthrougha steeptemperature~adient. Specimenswere extractedfromthemoldby firstbreakingawaytheglasscoveringand thencuttingandfilingawaythegraphite.A l-inchlengthwascutfrcm eachendof thespecimensto removetheregionsofworstsegregation,and afteretchingandvisualexsninationthespecimenswereelectropolishedto [email protected] onepart w by volumeofperchloricacidto fivepartsby volum ofmethylalcohol. Polishingwasconductedbelow300C andwitha potentialof 8 volts 3 betweenthespecimenanda graphitecathode. Theanglesa, j3,and 7,betweenthecrystallographicaxes(i.e., thecubeedges)andthespecimenaxiswereobtainedfromstereographic projectionsofX-reyback-reflectionphotographs.At leastbothendsof each,specimenwereX-rayedto verifythesingle-crystalconditionof the specimenwhenthiswasindicatedby etching.Dataon thespecimens grownfromthemeltaregivenin tableI. It willbe notedthat,in allcaseswherea singlecrystalwas obtained,a [1.w]directionis closelyparallelto thespecimenaxis. Thissuggestsstronglythat[1oo]is a preferredgrowthdirectionduring freezing. NACATN 4223 23 ExPEmMENmLPROCEDURE Exceptwherenotedlater,specimensweresolution-treatedat a temperatureof 525°C. Thefirstsolutiontreatmentof specimensgrown fromthemeltwasprolongedas longas convenientlypossibleto reduce microsegregation.Thetimevariedfroma weekto a monthfordifferent specimens.Theperiodof firstsolutiontreatmentofpolycrystalline specimenswas1 dayor longer,a timesufficientto stabilizethegrain size. Subsequentsolutiontreatmentsof allspecimenswereof overnight duration. Solutiontreatmentswerecarriedoutin thefurnacedescribedpre- viously. Forsupportinsidethefurnaceandduringq~-nching,specimens wereplacedalonga flatsurfacefileddownthelengthof an l/8-inch- diametersteelrodandheldinpositiontherewitha fewturnsof fine Nichromewire. Specimenswerequenchedinwaterat roomtemperature, removedfromthesupport,driedin acetone,andmountedin thetorsion pendulumwhichwasthenevacuatedto about0.03millimeterofmercury. Duringthisperiodadjustmentsweremadeto theopticalsystemto sec~e theoptimumimageon thegalvanometersscale.Priorto thestartof measurementsthepumpwas stoppedanda 10-millimeterpressureof helimn admitted.No subsequentpressureadjustmentswererequiredduringmost runs,butforprolongedtreatmentsthependulumwaspumpedoutbriefly andtheheliumrenewedoncea day. - Runswerestarted1/2to 1 hourafterquenching,andallaging treatmentsweregivento specimenswhiletheyweremountedin thetorsion . pendulun.Forprolongedagingtreatmentsabove2500C thetensilestress on thewirewasreducedbetweenrunsby removalof theinertiaweights. CrystalsgrownfrcmthemeltwereX-rayedfora secondtimeat the endof theinvestigation,withtheresultsalwsysthesameas thosegiven previously(table1). ExPERzlmNTKLRESULTS Internal-frictionBehaviorWithoutIntentional Aging- fiitialPeak As briefintroduction,a summaryis givenbelowof scmeresultsfor solution-treatedandquenchedspecimenswhichwerenotagedexceptforthe periodat roomtemperaturebetweenquenchingandtestingandthatunavoid- ablyproducedduringmeasurement: 24 NACATN 4225 (a)~ internal-frictionpeakexistsat 1850C fora frequencyof 2 Cps● Thiswillbe calledthe“initialpeak.” (b)Theinitialpeakis unstableanddecreaseson agingbutnot rapidlyenoughtopreventuseful.measurements.Whenmeasurementsare madeon coolingfromtherangeof 200°to 230°Cx thesymmetryof the peakindicatesa virtuallystableconditionduringtherun. (c)Fromabout240°C to at least330°C thedecrementrisessharply as thetemperatureis raised.Theinternal-frictioncontribution responsibleforthisbehaviorwillbe calledthe“hightemperature background.” Thefeatureofparticularinterestin theseresultsis theinitial peak. Inasmuchas temperaturesaboveapproximately210°C arenot requiredto traceoutthepeak,theminimumagingtreatmentwhichwas unavoidablein determiningthepeakwhiledecreasingthetemperature thereforeconsistedof thedelayat robintemperature,theheatingof the specimento 210°C,whichrequiredabout5 minutes,anda stayat this temperatureof a further5 minutesto obtainthefirstreading.Thepeak obtainedon subsequentcoolingto rocmtemperaturewillbe called‘%he initialpeakon firstcooling.” Thetimerequiredto coolfrom210°C to thepeaktemperature,taking measurementsat fivetemperatureson theway,wasabout 35minutes,and some2$ hourswererequiredto completemeasurementsdownto roomtempera- - ture. Inviewof themuchlongertimerequiredto traceoutthepeak comparedwiththatof thepreviousagingtreatment(heatingto 210°C with ~ a stayof 5 minutes),it appearedunlikelythata completelystablecondi- tionwouldprevailduringthe”run. Accordingly,sometestswereconducted to assessthestabilityof theinitialpeakduringtheperiodof first cooling. Specimen3 (tableI)wasused,andtheresultsareshownin figure3. CurveA is theinitialpeakon firstcoolingfrom2110C. Aftercompletionof thisrunthespecimenwasrapidlyreheatedbackto 211°C,pausingonlyformeasurementsroundthetopof thepeak(curveB). CurveC is thepeakon secondcoolingfrom211°C. Allmeasmementswere madeat a room-temperaturefrequencyof 1.71cps.3 The3-percentdiffer- enceinpeakheightbetweencurvesA andB wastakenas sm indicationof thestabilityof thepeskduringmeasurementof curveA belowthepeak temperature(183°C). The7-percentdifferenceinpeakheightbetween curvesA andC wastakenas an indicationof theoverallsta%ilityof curveA. Thisdifferenceis in linewiththeestimatethatduring 3Throughoutthisreport,thefrequenciesquotedsrethoseat room temperature(25°C) unlessotherwisestated.Frequenciesat anyother temperaturet below2C0°C maybe obtainedfromtherelationship ft = ‘25P-- o.00027(t- 25)]. L NACATN 4225 25 . measurementof thatpartof curveA abovethemaximum,thepeakheight doesnotfallby morethan10percent,an estimatemadefroman inspec- tionof thenesrsymnetryof curVeA (ona plotof logarithmicdecrement againstT-l)andtheassumptionof a stableconditionduringmeasure- mentof thelow-temperaturesideof thepeak. Itwillbe shownlater thattheheightof theinitialpeakvariesdirectlyas thesq.usreof the free-copperconcentration;4 thus,duringmeasurementof thepeakon first coolingthefree-copperconcentrationdoesnotdecreaseby morethan 5 percent.Thisresulthasa mostimportantimplicationwhichit is con- venientto discussinunediately. Duringtheperiodof 1/2to 1 hourat roomtemperaturebetween quenchingandthebeginningof a run,a spechnendoesnotretaintheas- quenchedcondition.IYomtheresultsofCalvet,Jacquet,andGuinier, reference37,forexsmple,theBrinellhardnessnumberrisesfrom56 immediatelyafterquenchi~to72 after10minutesat 25°C, to 82 after 1 hour,andto 96 after4 days. Thestructuralchangesassociatedwith thishardeningaretheproductionof G.P.[1.(ref.41)anda reduction of thefree-copperconcentration.However,thisstructureis notretained on heatingthespecimento 200°C!fora fewminutes,as shown,for exsmplejby theresultsof Preston(ref.k6). TheG.P.[1]zonesdis- solveandthefree-copperconcentrationrevertsto thetotalconcentration of copperin thealloy.As thisis thestageatwhichinternal-friction measurementssrestarted,theheightof theinitialpeekon firstcooling relatesto a conditioninwhichabout~ percentof thetotalavailable copperis randomlydispersedin thematrix.Thisconclusionis basedon theassumptionthatat 210°C reversionis complete.Ifhardnessis taken as a criterion,theobservedreturnto theas-quenchedvalueindicates reversionis trulycompleteevenafterthealloyhasbeenfullyagedat roomtemperature(ref.~); it is to be recalledthatinternal-friction specimenswereagedforonly1/2to 1 hourpriorto test. Further, Guinierwasunableto detectG.P.[1]at roomtemperaturedirectlyafter a reversiontreatment(ref.44). Finally,internal-frictionmeasurements alsoconfirmthecompletenessof reversionafterroom-tmeratureaging, forno detectabledependenceof theheightof thepeakon firstcooling uponthesgingtimeat roomtemperaturewasfound(upto 2monthsof *W). Thestabilityof theinitialpeekis of considerableimportancewhen considerationis givento thedeterminationof theactivationenergyof thepeakfromtworunsat differentfrequencies.Althoughthesecondrun yieldsa somewhatsmallerpeakthanthefirst,it is to be expectedthat by normalizingtheheightof thesecondcurveto thatof thefirsta constantshiftshouldbe obtainedon a l/T plotif indeedthepeakis %hat is,theconcentrationof copperin thematrixat points,remote . fromanyG.P.[I],G.P.[2], e’,or e structureswh.ichmaybe present. w 26 NACATN 4225 . simplyactivated.Sucha resultwasobtained,as showninfigure4, for a solution-treatedandquenchedpolycrystallinespecimen.Theactivation c’ energyof thepeakis 28.2t 1.5 kcal/mole,and log TO = -14.6+ I (whenTa is in seconds).Thewidthof thepeakat halfmaximumis ~0perce%greateron thelow-temperaturesld~thanthatpredictedfrom equations(1)and(2)fora singlerelaxationtime. Comparison.offigures3 and4 revealsthattheinitialpeakheight of thepolycrystallinespecimensis significantlygreaterthanthatof specimen3. Measurementof theinitialpeaksonfirstcoolingfora varietyofpolycrystallinespecimensandW.the specimensshownin — tableI yieldedtheresultsshowngraphicallyin figures5 and6. It ~ be seenthatthelargestinitialpeakswerefoundinpolycrystalline wires,thatspectiens1 and3 showedpeaksof intermediatesize,andthat thesimilarlyorientedsinglecrystalspecimens2, 4, and5 havemutually similarbutmuchsmallerpeaks.Thepeakheightsfoundfrcmtheseexperi- mentsaregivenin tableII. Theextremevaluesdifferby fullorderof magnitude,a moststrikingvariation. Sequenceof Internal-FrictionChangesDuringAging Initial.instability.-Theinitialp@ obtainedon firstcoolingis notclaimedas theinternal-frictionbehaviorof theas-quenchedcondition. It is,however,thebehaviorof thealloyin a conditionwhere95percent ormoreof thetotalavailablecopperis freelydispersedin solidsolu- * tion. Evidencethatthecurveon firstcoolingdoesnotin factrepresent theas-quenchedconditionis obtainedby cmparisonof theportionof this curvebelow150°C withmeasurementsmadeon firstheatingthequenched r spectienup to thistemperature.Themeasurementson firstheatingfell considerablyabovethecurveon firstcooling,andsuccessivemeasurements at constanttemperatureshowedthattheinternalfrictionwasdecreasing rapidly.Thisbehavior,observedon firstheatinga quenchedspecimen aboveroomtemperature,willbe called“theinitialinstability.”In figure7 thesolidcurveis theinitialpeakobtainedon firstcooling. Foreachpointon thebrokencurvethespecimenwasre-solution-treated andquenched,andheatedin thecourseof 2 to 4 minutesto thedesired temperatureandtheinternalfrictionmeasuredimmediately.Thepoints on thebrokencurverepresentthereforetheinternal-frictionmeasurements madeaftertheleastpossibleaging.Becauseof therapidchanges occurringin theinternalfriction,eventhebrokencurveis no indication of thebehaviorin theas-quenchedcondition.A ~-minuteannealat 2000C followedbyair-coolingis sufficienttowipeoutalltraceof theinitial instability.Afterthistreatmentthecurveobtainedon heatingthe specimento 150°C duplicatesexactlythatobtainedin theusualman- neron cooling. NACATN 4225 27 . Thesmountof theinitialinstabilityat 70°C (i.e.,thediffer- L enceat 70°C betweenthebrokenandfullcurvesof fig.7)wasfound to be muchgreaterforthepolycrystallinespecimenthanforsingle- crystalspecimen5. Specifically,— theamountof theinitialinstability detectedat 70°C was1.3x 10-3forthepolycrystallinespechnenand only0.084x 10-3forspecimen5,a differenceof a factorof 15. b theratioof thepeakheightsis a factor10,a correlationis suggested betweentheheightof theinitialpeakandtheamountof initial instability. Agingbelow185°C.-Overperiodsof severaldaystheonlychange otherthantherapiddecayof theinitialinstabilitywasa progressive decreasein theheightof theinitialpeak. By loweringthefrequency of vibrationthepeakis shiftedto lowertemperatures(fig.4), andfogthelowestconvenientfrequency(0.~cps)thepeaktemperature iS 164 C. Foragingtemperatureabove164 C it is thereforepossible to takemeasurementsat thepeaktemperaturewithoutintroduc~ngany changeas a resultof themeasurementsthemselves.&l-ow164 c changes in thepeakheightmustbe inferredmainlyfromtheportionof thelow- temperaturesideof thepeakexistingbelowtheagingtemperature becauseit is notpossibleto makeprolongedexcursionsabovetheaging temperaturewithouttherealdangerof changingtheconditionof the specimen.However,itwasusuallypossibleto tie a briefexcursion to about30°C abovetheagingtemperaturewithouta detectablechange in theinternalfrictionon returningto theagingtemperature.As one * exsmple,duringagingat 164°C theinternalfrictionof a pol.ycrystalline specimenvibratingat o.k cpsfellfrom0.0060at thestartof measure- * mentsto 0.0021after70.5hoursof aging.At theendof thisperiodthe temperaturedependencewasmeasuredon coolingfrom164°C. Thiscurve wasretracedaftera 5-minuteannealat 200°C, andalltheresultsfell nearlyon thesamesnmothcurve,indicatinga stableconditionduring allof themeasurements.After70.5hoursat 164°C theinitialpeak. had”decreasedto a sizewhereitwasno longerclearlyresolvedfrom thebackgnmnd;theestimatedheightwas0.001,comparedwiththestarting peakheightof 0.0355.Usingthesquare-lawrelationshipthefree-copper concentrationwasreducedto 0.44of itsoriginalvalue. Forspecimensagedat 130°C, evenforseveraldays,an excursion to a temperatureabove1600C causedan increasein theinternalfric- tionwithtimeat thehighertemperature.Thisis a manifeswtionof a strikingphenomenonwhichwillbe calledrestorationof theinitialpeak, a phenomenonpredictedandexplainedby thetheorythattheheightof theinitialpeakis relatedto thefree-copperconcentration.Restora- tionof theinitialpeak.isillustratedgraphicallyin figure8. CurveA is theinitialpeakobservedon firstcooling,andthesolidpartof curveB is thereproducibleinternal-frictionbehaviorafter hoursof % 28 NACATN 4225 . agingat 132°C. Above1600C theinternalfrictionbecomesunstable withtimeandthebrokenpartof curveB cannotbe takentooseriously. Aftera periodof 9 minutesat 200°C thespecimenwascooledbackto roomtemperaturewiththeresultsshownby curveC. Thisshortanneal at 200°C hasrestoredthepeakalmostto theoriginalvalue.Thesub- sequentbehaviorof therestoredpeakis completelynormal;further agingcausesit to decreasein themsmnerexpected.Thealmostcomplete restorationobsenedafter 1 hoursat 130°C maybe contrastedwiththe % completeabsenceof restorationat 2000 C after70.5hoursof agingat 164°C andwiththeverylimitedrestorationobservedafter15 hoursof agingat 170°C. Restorationof theinitialpeakis attributedsimplyto reversion, thatis,there-solutionof structureswhichareno longerevenmetastable at thereversiontemperatureeitherbecauseof theirsizeor structure (ref.17). Theresultsshownin figure8 willnowbe consideredinmore detail.Theworkof Silcock,Heal,andHardy(ref.41)hasshownthat, forperiodsup to 3 daysat 130°C, G.P.[1]istheonlystructurepro- duced.Hence,thefallin theinitialpeakduring~ hoursof agingat 132°C is dueto thedecreaseinthefree-copperconcentrationresulting fromtheproductionof G.P.”[I].Usingthesquare-lawre~tionshipit appearsthatroughlyone-quarterof thetotalavailablecopperhasin thistimesegregatedto theG.P.[1]zones.Afterreversion,therestored - peakis somewhatlowerthanthestartingvalue,butin termsof thefree- copperconcentrationthereversionis 95percentcomplete. ● Theabsenceof reversionafter70.5hoursat 164°C is tobe expected, sincetheG.P.[2]structureformedat 164°C is alsometastableat 200°C. Presumably,theagingtreatmentwaslongenoughat 1.64°C forgrowthof G.P.[2]to a pointwherereversiondueto theexistenceofparticlesof a subcriticalsizeisunlikely. Agingat 203°c.-Thetemperaturedependenceof internalfrictionof spechen3 duringa sequenceof agingtreatmentsat 203°C is shownin figure9.5 Theinitialpeakobtainedon firstcoolingis omittedfrom thisfigure;it is showninfigure3. After30minutesat 203°C the %he curvesshownin fig.9 andsimilaronesshownelsewhere(e.g., figs.14 and17) were obtainedon coolingfromtheagingtemperature. Theassumptionof a stablespecimenconditionduringsuchrunswas _. — justifiedby thecloseagkeementbetweentheresultson coolingand thoseon subsequentreheatingbackto theagingtemperaturewhenever sucha comparisonwasmade. ● 3 NACATN4225 29 ● initialpeakheighthasdecreasedfrom0.~311to 0.cQ264,andafter u 4.6hours,to 0.00146.At theendof thistimethefree-coppercon- centrationhasfallen(intermsof thesquarelaw)to 0.69of itsini- tialvalue. l%esemeasurements,andothersmadein furthertests, . showedthatduringthisperiodthepeaktemperaturereminedconstant (fora giventitrationfrequency).Mter 4.6hoursat 203°C theacti- vationenergyof thereducedpeakwasstillthesane,withinexperimental error,as thatfoundoriginally(28.2kcal/mole);thusthevalueof To alsoremainsconstant.Thereductionin thefree-copperconcentration forup to 4.6hoursof agingat 203°C isbelievedto be causedexclusively bythe productionof G.P.[2]. TheG.P. [1]structureisnotformedat thistemperature,andthe e’ phasehasnotyetprecipitated,as indi- catedby theabsenceof otherinternal-frictioneffectsto be discussed later.PreviousX-rayworkhasplacedtheupperlimitof thetemperature rangeof G.P.[12 formationat between1900and220°C (ref.41);the presentresultsindicatethatG.P.[2]isdefinitelyformedat 203°C. AfterI.1.lhoursat 203°C, theinternal-frictioncurveshowsa changeof chsracter.Thepresenceof a reducedinitialpeakis seen fromthehumpinthecurve,butothetisethepeakis obscuredby other newcontributionsto theinternalfriction.Theriseon thehigh-tem- peraturesideof thepeakwasfoundfromotherexperimentsto be the resultof an increasedhigh-temperaturebackgroundcontribution;itwas notpossible,however,to analyzethecurveintoa reducedinitialpeak * anda smoothlyrisingincreasedbackground.Subtractingfromthecurve for11.1-houraginganyreasonableestimateof theremaininginitial peakgivesa curvewhichis clearlya combinationof a backgroundsnmothly * risingto highertemperaturesanda broadpeakcenteredat about120°C. Thisnewinternal-frictionpeakwillbe calledthe“secondpeak.’!Oneself- consistentanalysisof thectie for11.1-houragingis shownin figure10. Forlongeragingtimesat 203°C thenewinternal-frictioncontribu- tionsdetectedafter11.1hoursincreaseconsiderably,andafter22hours thereisno directindicationof theexistenceof a remaininginitial peak. Thecurvesfor40.6and59hoursshowa kneeat abut 120°C which marksthecommencementof a plateauextendingto 180°C. W plateauis replacedby a maximumin thecurveafter144hours,by whichtimethe internal-frictionchamgeshavebecomeveryslow. Thecurvesfrom 11.1hoursonwardarereadilyexplained-bythecontinuedgrotihof the high-temperaturebackgroundandsecondpeak. Althoughthesecondpeak isneververywellresolved,theplateaus.onthelatercurvesandpar- ticularlythemaximumfhallydevelopedafter144hoursarestrongevi- denceforitsexistenceandgrowth.In formulatingthisinterpretation ithasbeensupposedthaitheinitialpeakdecreasescontinuallyon aging,untilit isnotsignificantin theinterpretationof thelater . curves.‘Ibisis consistentwiththetheorythattheinitialpeak 30 NACATN 4225 . decreasesas thefree-copperconcentrationis reduced.On makingthe reasonableassumptionthatthelatercurvesinfigure9 arecomposed w onlyof a symmetricalsecondpeakanda smoothlyrisingbackground,an approxtiteseparationof thesecondpeakfromtheobservedcurvecan be madeon a trial-and-errorbasis.Usingthisproceduretheestimated secondpeakafter144hoursof agingat 203°C is shownin curveB of fig. ureIl. CurveA isthesecondpeakredrawnfromfigure10 forcompari- son,andcurveC willbe discussedlater.Thesecondpeakismuch broaderthantheinitialpeak,andduringitsgrowthat 203°C appar- entlyretainsem approximatelyconstantshapeandpeaktemperature. Analysisof observedcurvesintotheirvariouscontributions,as shownin figures10 and11,cannotbe claimedto be correctexceptin broadoutline.Eowever,suchan smalysisis reliableenoughto permit oneto arriveat thefollowingconclusions: (a)On agingat 203°C, therisein thedecrementat temperatures below120°C is dueprincipallyto thegrowthof thesecondpeak. (b)On agingat 2Q3°C, theriseinthedecrementat temperatures above200°C isdueprincipallyto a riseinthehigh-temperature background. It followsfrom(a)thattheactivationenergyof thesecondpeakmaybe obtainedfromthetemperatureshiftwithchangein frequencyof thepor- tionof thecurvebelow120°C. Tb thisendthecurvefor144-houraging wasdeterminedat twofrequencies,andtheresultsshownin figure12 yieldan activationenergyforthesecondpeakof 21..9* 1 kcal/mole,a valuesignificantlylowerthanthatfortheinitialpeak. Usingthis activationenergythewidthof thesecondpeakwasfoundto be about threetimesbroaderthanthat“fora singlerelaxationtime. Thevalue logTo = -12.5A 0.8 isobtainedby takingthetemperatureof thefully formedpeakas 132A 7°C (curveB, fig.n). As thepeakretainsapproximatelythesameshapeandpeakteqera- tureduringgrowth,a secondconsequenceof conclusion(a)aboveisthat on agingtheriseindecrementat some temperaturebelow120°C maybe usedas a relativemeasureof theheightof thesecondpeak,andhence a plotof thesevalues against aging time at 203°C givesthekinetics ,ofgrowthof thesecondpeak(c&e-B, fig.13). Sfiilarly,fromcon- elusion(b),therisein decrementat 203°C maybe takenas.ameasure of thegrowthof thehigh-temperaturebackground(curveA, fig.13). It maybe seenthatthekineticsof growthof boththesecondpeakandthe high-temperaturebackgroundarestrikinglysimilarsmdthatlittlechange occursin eitheroneafter100hours.* NACA‘lN4225 31 Agingat 203°C wasfoundto increase6thesheartiulusby about 2 percent(asevidencedby sm increaseinfrequencyof approx-tely w 1 percent),andthecourseof thechangeon agingisplottedin fig- ure13 (curveC) forcomparisonwfthcurvesA andB. Itmayappearthat themoduluschangeis completedbeforecompletionof theinternal-friction chsmges,butit shouldbe notedthatwithinexperimentalerrorthemodulus curvecouldhavebeendrawnto paralleltheinternal-frictionbehavior. Agingat ~“ C andabove,followingagingat 203° c.-Theleveling offin thegrowthof thesecondpeakandbackgroundafter100hoursat 203°C (fig.13)wastakenas an indicationthata metastablecondition hasbeenattainedwhichwouldbe affectedonlyslightlyby furthertreat- mentsofpracticabledurationat 203°C. To acceleratefurtherchanges theagingtemperaturewasraised(after1~ hoursat 203°C) to 298°C in thefirstinstanceandlaterto 330°C,withtheresultsshownin fig- ure14. Thecurvefor144hoursat 203°C is drawnagainin figure14 forcomparisonpurposes.BearinginmindthatthedecrementbelowI@ C is essentiallya measureof thesizeof thesecondpeak,itwillbe seen thatthesecondpeakdecreasesprogressivelyuponagingat thesehigher temperatures.Thehigh-temperaturebackgroundundergoesa furtherappre- ciableriseduringthefirsttreatmentbutthenremainspractically constant. Theextensionof theagingtemperatureto 330° C allowsa more extensiveexaminationof thehigh-temperaturebackgroundthanwaspre- * viouslypossible.Figure15 givesthecompleteinternal-frictioncurve aftertheannealof 15.1hoursat 330°C (thelowerpartof thiscurve is shownalsoin fig.14). Thehigh-temperaturebackgroundfalJscon- I1 tinuouslyandrapidlyas thetemperatureis lowered,so thatit decreasesby an orderofmagnitudebetween330°and200°C. Theshape of thebackgroundcurvesuggestedthatthetemperaturedependencemight be expressedby an empiricalequationof thetype b =A ~(-B/T) (8) where A and B areconstants.Thisformulawassubstantiatedby the straightlineobtainedon repottingtheresultsas log5 (internal friction)againstl/T,as shownin figure16. Thevaluesof thecon- stantsA and B werethusdeterminedto be: A = 280 and B = 5,100. Eoth A and B werefoundto be affectedby aging.Thedeparturefrom %rdinarily a decreasein shearmadulusaccomp~iesa risein inter- nalfrictionbecauseof an elasticrelaxation.In thepresentcase, however,therelaxationeffectsaretoos-U. to be detectedby fre- s quencymeasurements. -. 32 NACATN4225 linearityin figure16 is causedby thesecondpeak. Apartfroma possi- bletheoreticalsignificance,equation(8) isof’practicalimportance becauseit canbe usedwithsomeconfidenceto obtainby extrapolation‘ = the,backgroundinternalfrictionat temperaturesbelow220°C. Subtrac- tionof theextrapolatedbackgroundfromtheexperimentalcurveenables thesecondpeakto be separatedoutmorepreciselythanwaspreviously possible.Theshapeof thepeakobtainedby performingthisseparation (curveC, fig.11)comparesfavorablywiththeearlier,andof necessity lessquantitative,estimatesof thesecondpeak. Despitetheuncertainty in theestimationof peaks A and B in figure11,theapparentmigra- tionof thepeakto slightlyhighertemperaturesas agingprogressescan probablybe takenseriously. Theactivationenergyforthehigh-temperaturebackgroundwas obtainedasusualfromthetemperatureshiftresultingfroma changein frequency.Thevalueobtainedwasapproximately33 kcal/mole. ARingat 230°C.-Thesequenceof”internal-frictionchangesduring theagingof specimen2 at 230°C (fig.17) differsfromthatof speci- men3 at 203°C in onerespectonly. At 203°C theinitialpeekdeclined considerablyin strengthbeforeothercontributionsto theinternalfric- tionweredetected,whileat 230°C thesmalldecreasedetectedin the initialpeakafter0.8hotiwasaccompaniedby thedetectionof theother contributions.Laterremarksjustifytheconclusionthatat 230°C the phase f3’andnottheG.P.[2]structureisthefirststructureformed, as is indeedto be expectedfromtheworkof Silcock,Heal,andHhrdy (ref.41). Comparisonof figures9 and17 indicatesthatat Mth 203° and230°C thelatergrowthof thesecondpeakandthehigh-temperature backgroundareverystiilarexceptfora differencein rate. lb empha- sizethissimilarity,theu~ermostcurvesof figures9 and17havebeen plottedin figure18 togetherwiththecurveobtainedfroma polycrys- tallinespecimenwhichhadbeenagedfor1.10hoursat 2CX1°C to develop fullythesecondpeak. Allthreecurvesexhibita kneeof roughlythe sameheight,whichis a reasonableindicationthattheheightof the fullyformedsecondpeakisaboutthesamein thethreespecimens.This behavioris in strikingcontrastto thelargedifferencesintheinitial- peakheightsof thesespeci=ns(tableII). Thekineticsof growthof thesecondpeakandbackgroundareshown in figure19foragingat 230°c. Againthecurvesfollowa similar coursewhichisparalleledalsoby therelativechangein shearmodulus. Comparisonof figures13and19 showsthattheimportantgrowthoccurs in theinterval10 to 100hoursat 203°C andin 1 to 10hoursat 230°C. AginRat 185°C.-Thechangesof internalfrictionandrelative shearmodulusduringisothermalagingat 185°C of a polycrystal.line specimenareshowninfigure20. Thedecreasein theinternalfriction NACATN 4225 33 firstobservedis dueto a fallin thestrengthof theinitialpeak. Othere~erimentsmentionedpreviouslyshowthatduringagingthepeak . temperatureremainsconstant,andhencethefirstpartof curveA in figure20 gives~ indicationof thekineticsof thefallof thepeak at 1850C. Somecareis requiredin thedetailedinterpretationof measurementsmadeonlyat onetemperature,forwithouta knowledgeof thetemperaturedependenceof internalfrictionaftervariousaging timesit is notpossibleto estimatehowmuchof theobservedinternal frictionat theagingtemperaturearisesfromtheinitialpeak. This isparticulmlyimportamtwhentheinternalfrictionhasfallento values neartheminimum.Experiencehasshown,however,thatforagingtemper- aturesbelow200°C!thepeskmayfallto one-halfof thestartingvalue andstillbe welJresolvedfromthehigh-temperaturebackground.This correspondsto a fallof 25percentin thefree-copperconcentration. Neartheminimumof curveA, theinitialpeakheightis estimatedto havefallenby a factorof 4, andthefree-copperconcentration,by a fac- torof 2,whichis in agreementwithGuinier’sresultsfortheamountof G. P. [2]formedon agingat 180°and190°C (ref.44). Afteragingfor1~ hoursat 1850C theinternalfrictionshowsa sharprise,andthetemperaturedependencebelow1850C wasthenobserved to be typicalof thatcausedby thegrowthof thesecondpeakandback- ground.Theactivationener~ obtainedfromtheshiftin thecurveof decrementplottedagainstl/T withfrequencyafter1,000hoursaging agreedwiththatpreviouslygiven(21.9kcal/mole)forthesecondpeak. Therisein curveA isthereforeinterpretedas dueto theincreasing contributionsat 1850C fromthegrowthof boththesecondpeakandthe background. s Theformof curveA (fig.20)is in qualitativeagreementwiththe curvegivenby @ (ref.31)foragiggat 200°C,whichis reproduced infigure21. As mentionedin theIntroduction,KG’sinterpretation of thesephenomenawasin termsof a grain-boundaryrelaxation,which is clearlyruledoutby thepresentwork. He alsoassumedthattherise in fiternalfrictionaftertheminimumin figure21.is causedby a regrowthof theinitialpeak. Thefactthatthislatterassumptionis incorrecthasalsobeendemonstrated. Effectof QuenchingTemperatureon ~itialPeak Because of therelatively small sizeof theinitialpeaksshownby single-crystalspecimens,measurementswereconfinedmainlyto poly- crystallinespecimenson accountof thegreatersensitivityattainable. I!bwever,no differencewasdetectedin thebehaviorof thetwotypesof specimen. . 34 NACATN4225 Quenchingfromabovephaseboundsry.-Forthisseriesof measure- ments,a polycrystallinespecimenwasfirstsolution-treatedat the d highestof thethreequenchingtemperaturesusedto insurethatno graingrowthwouldoccurduringlaterre-solutiontreatments.Thethree quenchingtemperatureschosen(5700,536°,and501°C) spannedthephase fieldfromjustbelowthesolidusto justabovethephaseboundary.The sanefrequencywasusedthroughout(0.396cps),andaftereachquenching thespecimenwasheatedat thesamerateto lgo”C. Eachheatingwas interruptedat 100°C fortheminimumtimerequiredto makean internal- frictionmeasurement.Theinitialpeaksmeasuredon firstcoolingare shownin figure22,fromwhichitwasconcludedthatthequenchingtem- peraturehasno observableeffecton theinitialpeakas determinedby theprocedureused. Themeasurementsmadeon firstheatingto 100°C gavetheamountof theinitialinstabilityat 100°C (definedas in sec- tionentitled“Sequenceof Internal-FrictionChangesDuringAging”).The fo~owingvalueswereobtained:0.00125,0.ool.15,and0.00073,for quenchingtemperaturesof 570°,536°,and501°C, respective~.It appearsthatthelowerthequenchingtemperature,thesmallertheamount of initialinstability. Quenchingfrombelowphaseboundsry.-Thepolycrystallinespecimen usedforthisseriesof measurementswasalwws solution-treatedat the standardtemperatureof 527 C. It is not th~specimenmentionedin the precedingsection.Aftera solutiontreatmentthespecimenwaslowered to a desiredtemperaturebelowthephaseboundaryandlefttherefora periodconsideredlongenoughto establishtheequilibriumproportion of e(CuA12)(seetableIII). Thespecimenwasthenquenchedandthe initialpeakmeasuredon firstcoolingin-theusualmanner.Thispro- cedurewasrepeatedforeachof fourdifferenttemperaturesbelowthe phaseboundary,and,inaddition,theinitialpeakon quenchingdirectly from5250C wasdetermined.Theresultsgivengraphicallyin figure23 areswmnarizedbelow: (a)Theinitialpeakremainsat thesanetemperaturebutdecreases progressivelyin strengthas thequenchingtemperatureis lowered. (b)Thehigh-temperaturebackgroundrisesprogressivelyas the quenchingtemperatureis loweredandisparticularlyprominentafter quenchingfrom4270C. Mer %.bistreatment,thecombinedeffectof thedecreasein thepeakandtheriseinthebackgroundis sufficient to obscurethepeak,whichis detectableonlyas an inflectionin the curve. (c)Thesecondpeakisnotevidentintheseresults. (d)A correlationexistsbetweentheheightof theinitialpeak andtheamountof copperremainingin solution.IhtableIIIthepeak heightsaretabulatedtogetherwiththeamountof copperremainingin NACATN 4225 35 solutionas calculatedfromthevolubilitydatagivenin the‘*Metals Handbook”(ref.51). Thepeakheightmaybe seento varymorerapidly w thanthefirstpowerof thecopperconcentrationand,as shownin fig- ure24,a squarelawfitsthebehaviorwithinexperimentalerror.The empiricalstatementof thislawis ~ = 0.00167c2 (9) where ~ is thepeakheightand c is theatomicpercentageof copper in solution.Thisrelationshiphasbeenusedseveraltimespreviously in thisreportto calculatethefree-copperconcentrationremaining aftervariousagingtreatments. Measurementsin Flexure fiitial peak.- A considerationof thepretiousresultssuggestedthe particulardesirabilityof determiningin flexuralvibrationtheinitial peakof a singlecrystalorientedwith{1~} parallelto thespecimen axis. Theflexurependulumspecialdydevelopedforthispurposehas beendescribedpreviously.Therequirementof twinspecimenswasno disadvantagein thepresentcaseas threesinglecrystalsof virtually thedesiredorientationhadbeengrown(specimens2, 4, and5,tableI). w Of these,specimens4 and5 werechosenforthepresentinvestigation. Thespecimensweresolution-treatedandquenchedtogetherfromthe standardtemperatureof 52P C andtested-oncoolingby thesamepro- . cedureas thatusedfortorsionalvibration.Theresultsshownby curveA in figure25maybe compareddirectlywiththeindividualtests in torsion(fig.6), of whichcurveB is typical.Theinitialpeak heightsof thesespecimensin torsionandflexurearegivenin tableII. Thepeakin flexureis 13 timeslargerthanthemeanpeakheightin tor- sionandis thelargestof anyfoundin thiswork. Measurementsin flexurewerealsomadeof theinitialpeakin a pairof polycrystal.linespecimens.Theapproximateidenti~of these specimenswasindicatedby theseparatedeterminationof theinitial peakintorsionforeachspecimen.Theresults(table11)forthetwo specimensin torsiondifferedby 7 percent,theaveragepeakheight being0.00448.On theotherhand,thepeakheightin flexureis 0.0065. Polycrystallinespecimensthereforedo notexhibitthespectaculardif- ferencefoundfor<100}orientedsinglecrystals. Secondpeak.-In torsion,thefullyformedsecondpeaksin single- crystalspecimens2 and3 andin a polycrystallinewirearebelievedto . 36 NACATN 4225 . be m- equal(fig.18). Measurenmrbswerenowmadein flexureusing specimens4 and5 afteran agingtreatmentof 22.5hoursat 230°C, a * treatmentresultingvirtuallyin completegrowthof thesecondpeak (cf.fig.19)0 Theresultsof themeasurementsin flexureareshownin figure26 togetherwiththosefromspecimen2 testedin torsionaftera ,_ similaragingtreatment.Usingas beforetheheightof thekneein the curveas a gageof theheightof thesecondpeak,it ispossibleto con- cludethattheheightof thesecondpeakisabout50percentlargerin flexurethanin torsion. InternalFrictionat ELghTemperatures Above300°C,thevolubilityof copperin aluminumstartsto increase at a significantrate. Forexample,at 300°,33!)0,and400°C thevolu- bilityis,respectively,0.45,0-.85;and1.5”weightpercentcopper.If appreciablere-solutionof precipitates.occursduringan internal-friction runon heatingabove300°C!,theapparentinternal-frictionbehavior observedwillbe modifiedby thechangingvolubility.To investigate this,specimen5 (asinglecrystal)wassolution-treated,quenched,and agedfor35.5hoursat 300°C. Afterthistreatmmtrunsweremadeon coolingfromandheatingbackto 300°C. Thebehaviorobsenedis shown by theportionof curveA, figure27,below300°C. Above200°C the high-temperaturebackgro~dcontributionwaspredominant(cf.fig.15). Uponreaching300°C therunon reheatingwascontinuedto 5Q5°C, a temperaturejustabovethephaseboundary,withtheresultsshownin ● theremainderof curveA. Thecurvecontinuedto increaseup to about 370°C,whereupodthecurvepassedthrou&a maximumbeforecontinuing a riseto highertemperatures.Intheregionof themaximum,successive ‘ measurementsat a constanttemperatureshowedtheinternalfrictionto be fallingwithtime,andthe’pointsshownaremeanvaluesobtainedby ignoringthetimedependenceof successive~asurements.Themaximumin thecurveisnotinterpretedthereforeas a peakof anelasticoriginbut ‘“- ratheras a manifestationof thedecreasingbackgroundcontribution resultingfromrapidre-solutionofprecipitateson reachingtemperatures aroundthatof themaximum.Thisconclusionis supportedby theresults shownin curveB, figure27,whichwereobtainedon coolingafterthe specimenhadbeenheldat 505°C for1.5hoursto insurecomplete re-solutionof anyremainingprecipitates.In contrastwithcurveA, this curvefallsrapidlyandwithno signof-amaximumat 380°C. Theinter- nalfrictionbelow400°C ismuchlowerthanthatobservedon heating andis so lowbelow300°C thatit appearsdoubtfulthatanyappreciable precipitationcouldhaveoccurredon cooling,a conclusionsupportedby thedetectionof theinitialpeak(thisisnotapparentin curveB because of thescaleof thefi@e). Above430°C theresultson coolingarehigherthanthoseon heating. Thisisa reflectionof therisein internalfrictionfrom0.140to 0.221 * w NACATN 4225 37 duringthesolutiontreatmentat 5050C. ~ andBrook(ref.52)have u reportedincreasesin thehigh-temperatureinternalfrictionofpure aluminumresultingfromcreep.A s~lar explanationis offeredin the presentcasebecauseafterthecompletionofmeasurementsthespecimen wasfoundto haveelongatedby 2 percent. INTEWRETATIONANDDISCUSSIONOF RESUL!ES iaitial Peak A summaryof theresultsto be explained~ a theoryof thetiitial peskis givenbelow. On firstcooling: (a)A widevariationexistsin theheightof theinitialpeak exhibitedby differentspecimenstestedintorsionalvibration. (b)Theinitialpeakheightof (100)orientedsinglecrystalsis muchgreaterin flexurethanin torsion. (c)Theinitialpeakheightis insensitiveto thequenchingtempera- tureabovethephaseboundary. (d)Theheightof theinitialpeakvariesas thesquareof thecop-- perconcentrationin thematrti. (e)Theactivationenergyof thepeakis 28~ 1.5kcal/mde,the log To valueis -14.6 t 1, smdtheexcesshalf-peakwidthis 15-to 30percent. On aging: (f)Theinitialpeakdecreasesinheightbutretainstheseinepeak temperatureW activationenergy.!bLStheValUeOf To mUStalso remainconstxmt. (g)APartfromtheMtial-tistabil-imeffect,thedecreasein the peakheightis thefirstindicationof a structuralchangein thealloy on agingat temperaturesbelow200°C. At 230°C thedecreasein the peakis accompaniedby otherchangesintheinternalfriction. (h)Thedeclinein theheightof thepeakcausedby agingat low temperaturescanbe resturedal.nmstcompletelyby a shortannealat 2000c. 38 NAC!ATN 4225 Considerationmy be givenfirstto @’s opinionthatthepeakwas dueto grain-beundaryslip. Thisideais clearlyincorrect,sincethe peakispresentin singlecrystals.Inspectionof theresultssuggested ratherthatthepeakoriginatesfromthepresenceof copperatomsin solidsolution;thissuggestionis consistentwiththefactsthatthe peekhasnotbeendetectedinpurealuminumandthat&tdecreasesin Al alloycontaining4 weightpercentCuwheneverspecimensaretreated in a mannerthatreducesthefree-copperconcentrationin thenwtrti. Theobservedrestorationof theinitialpeakby a treatmentknownto restorethefree-copperconcentrationis strikingevidenceforthecor- rectnessof a theoryrelatingtheexistenceof thepeakto thepresence of copperfreelydispersedin solidsolution.Froma closerinspection of theresultsit ispossibleto be morespecific;alltheavailable evidencepotitsto theZenerrelaxationas theoriginof theinitial peak. Thisconclusionis reachedin viewof thefollowingconsiderations: (a)Themagnitudeof theactivationenergyof theinftialpeaksug- geststhatrelaxationoccursby atommovementsin thebulkof thematrix. It is closeto themeasuredandcalculatedvaluesof thediffusionacti- vationener~ of copperin aluminum(28 to 33kcal/mole)andishigher thanmightreasonablybe eqectedforatommigrationin dislocated regions.Eecauseof theverysmallcoppercontent(1.7 atomicpercent) of thepresentalloy,themovementof,copperatomsin thematrixshould be thefactorcontrollingtherateof therelaxation(ref.7),anda comparisonof theactivationenergyreportedherewiththatforthedif- fusionof radioactivecopperinthealloywouldbe significant.Impor- tunatelysuchdiffusiondatadonotexist. ● (b)Thevalueof To is of thecorrectmagnitudefora Zenerrelax- , ation.Thesignificanceof thisvalueof To istheinferencethatthe relaxationis causedby a rearrangementwhichdoesnotrequireatomsto jumpmorethana fewatomicdistances. (c)Thewidthof thepeakathalfmaximumrelativeto thatcalcu- latedfromequations(1)and(2)is calledthe“relatinpeakwidth.” If therelmoationprocessis identicaleverywhere,therelativepeak widthisequalto unity.Localvariationsin structureor in composi- tionwillresultina distributionof activationenergiesandtherefore in a spectrumof relaxationtimes,whichismanifestas a broadenhgof thepeak. Usuallytheobservedwidthistakenfromthelow-temperature sideof thepeakonlyto minimizethecomplicationof apparentpeak broadeningdueto thepresenceofa high-temperaturebackground.Some of thevaluessoobtatiedforvariousinitialpeaksinAl alloycontaining 4 weightpercentCu on firstcoolingaregivenas follows: NACATN4225 39 . Specjmenandmodeof tibration Relatinpeakwidth & Polycrystallinewiresin torsion 1.3 (100}orientedsingle-c~stal specimens4 and5 in flexure 1.3 Spec~n 1 h torsion 1.15 Thesevaluesaretypicalof otherso~d solutionswhichdisplaythe Zenerrelaxation. (d)Thesqmre-kw dependenceof theinitialpeakheighton thecon- centrationof copperinthematrixisthesameas thatfob forthecon- centrationdependenceof theZenerpeakin copper-zincandin silver-zinc alloys. Forsmsllconcentrationsof solutea squarelawispredicted bothfromthetheoriesof Zener(ref.5)smdof LeClaireandIcnner (ref.4). In termsof Zener’s“pairreorientation”theorythesquare lawhasa sfmpleinterpretation,namely,thattheheightof thepeakis proportionalto thenumberof pairsof soluteatomswhichin turnis proportionalto thesquareof thesoluteconcentration. (e)A simplee~lanationof theinitial@stabilityin solution- treatedandquenchedAl alloycontaining4 weightpercentof Cu canbe advancedby identifyingtheinitialpeakwiththeZenerrelaxation.It iswellknownthatquenchingfromthesolution-treatmenttemperature d willtrapan excessof latticedefectswiththeresultthattherelaxa- tiontimeisgreatlydecreased(refs.10 and~). Theinitialpeak, observedin a hypotheticale~erimentwherethequenchedconditionis . presemed,wouldthereforeoccurat a muchlowertemperature.According to thisexplanationtheinitialinstabilityisdueto a migrationof the initialpeakto Ix@hertemperaturesduringheating,becauseof thedec~ of latticedefects.~s interpretationis supportedby threeobservations: (1)Themagnitudeof theinitial instabilitydecreasestiththequenching temperatureeventhoughtheinitialpeakheighton firstcoolingisthe same(seesectionentitled“Quenchingfromabovephaseboundary”).This is e@ained by thedecreaseintheequilibriumnuniberof defectspresent as thesolution-treatmenttemperatureis lowered.(2)Themagnitudeof theinitialinstabili~fordifferencespecimensis roughlyproportional to theheightof theinitialpeak(seesectionentitled“Initialinsta- bil.i@”),aswouldbe expectedif theinitialinstabili~is causedby themigrationof thispeak. (3)A closesimilarityexistsbetweenthe formof figure7 andanalogousmeasurementsobtainedfromquenched Ag alloycontaining33 atomicpercentof h (ref.12),whichis an alloy showinga ~ical Zenerpeak. Theweightof theevidencepresentedabove, togetherwiththeabsenceof anyconflictingresults,leadsto thecon- clusionthattheinitialpeakis dueto a Zenerrelaxation.A checkon * thisconclusionwouldbe possibleif itwerepracticableby theuseof higher frequencymeasurementsto ver~ theexistenceof thepeakinthe . 40 NACATN 4225 solid-solutionrangebetweenthesolidusandthephaseboundag. Unfor- tunately,thevibrationfrequencyrequiredis sohigh(106cps)thatthe experhentis notpossiblewithexistingtechniques. Theheightof a Zenerpeekisknownto be affectedby thedegreeof orderpresentinthealloy(refs.16 and53). Ibwever,theobserved insensitivityof theinitialpeakto thequenchingtemperatureabovethe phaseboundarydoesnotpermitanyconclusionsto be drawnregardingthe existenceof short-rmgeorderabovethephaseboundary.Evenif short- rangeorderdoesexistandismarkedlytemperaturedependent,itmaynot be possibleto retaintheconditionon quenching. It is of interestto comparetherelaxationstrengthof theinitial peakinpolycrystallineAl alloycontaining4 weightpercentof C!u(i.e., Al alloycontaining1.7atomicpercentof Cu)withthatfortheZener relaxationin silver-zincandcopper-zincalloys.Experimentaldatafor thelasttwoalloysexistonlyat highersoluteconcentrations,butcor- rection~ be madeto 1.7atomicpercentsolutewiththeaidof the square-lawrelationship.Theresultsobtainedshowthattherelaxation strengthin aluminum-copperalloyis,respectively,5 and30timeslarger thanthatcalculatedforthesilver-zincandcopper-zincalloys. Attentionwill.be givennowto thestrikingvariationintheheights of theinitialpeaksinvariousspecimns,asmeasuredon firstcooling fromabout200°C. As pointedoutpreciously,theinitialpeakmeasured by thisprocedurerefersto a conditioninwhichatleast95percentof thetotalavailablecopperis freelydispersedin solidsolution.The widelydifferingpeakheightsobtainedin torsionandflexurefor<100} orientedsinglecrystalsshowsthattherelaxationstrengthis strongly anisotropic. Theformaltheo~ of anisotropicinelasticity(i.e.,one whichrequiresno knowledgeof therelaxationmechemism)hasbeengiven forcubiccrystals(thefollowingconsiderationsarerestrictedto crys- talsof cubicsymmetry)by Zener(refs.1 and5). Thegeneralanelastic responseof a crystalmsybe expressedby threerelaxationstrengthsAL!, N’, snd AK,definedbelow.Theabsoluteandrelativemagnitudesof theseconstemtsareof coursere~tedto theparticularmechanismof relaxation;theirdeterminationthereforeprovidesem importantcluein a theoreticalinterpretationof therelaxationin termsof an atomistic nmdel.An outlineof theforml theoryof anisotropicinelasticityis givenbelow.Thisis followed~ an analysisof thepresentexperimental resuits. Thedeformationof an elasticallyanisotropiccrystalunderpure shearstressesmaybe describedintermsof twoshearnmduliC and Cl, definedby theequations NACATN 4225 41 c = l/s& (lo) . 1 c’ = (u) 2(SU - S12) !I!hequantities Sllj Su, snd S~ aretheelasticconstantswhich appearfora cubiccrystalin thegeneralizeddefinitionof Iboke’slaw (ref.1). ThenmdulusC representstheelasticresistanceof thecrys- tal to the shearingof (100)plsmesacrossoneanotherin the [010]direc- tionj amd C1,thatforshearingof (110)planesin a @~ direction. Further,if a stresssystemwitha hydrostatic componentis imposed, thebulkmdulus K nmstbe introducedalso,as follows: 1 (12) ‘=3pu+2su) E thecrystalbehavesinelasticallythevaluesof C, C’,and K dependon theconditionsof measurement.Measurementsmadeundercondi- tionswhererelaxationdoesnotoccurwillyieldtheunrel=ednmduli Cuj d ~’, and q~. Similarly,measurementsmadeunderconditionsof complete r&axationgivetherelaxedmoduli CRJ CR’,W KR. Thegeneralane- lasticresponseof thecrystalis accordinglydeterminedby thethree . relaxationstrengths L&= (CU- cR)/cR (13) . AC’= (Cu’- CR)/‘ (!R’ (14) (15) ~= (%- +% TheshearmodulusG of a single-crystalwiredetermined,forexsmple, fromthefrequencyof vibrationin thetorsionpendulumis given(for eithertherelaxedor unrelaxedcondition)by 42 N&2ATN 4225 (16) Theorientationfunction@ isdefinedas $ = Cos% Coszpi-Cos% COS27+ COS27COS2U where a, ~,and 7 aretheanglesbetweenthespecimenaxisandthe threecrystallographicaxes(i.e.,thecubeedges).Therelaxation strength& foundby internal-frictionmeasurementsin thetorsion pendulumisthen7 ++ 2($ - g)fl m= (17) $+ 2(+ - ~)$ where C and C’ maybe eithertherelaxedorunrelaxedquszrtities (sincetherelaxationstrengthsareassumedsmall). ThetensilemodulusE of a single-c~stalwiredetermined,for example,fromthefrequencyof vibrationintheflexurependulumis givenby (18) dndtherelaxationstrengthAE determinedfrominternal-frictionmeas- urementsin theflexurependulumis AK N!’ /2(2‘ AAA (19) 71&omequation(2),therelaxationstrength& iS 2/fltimes thelogarithmicdecrementat thepeakintorsion,while LE isthe sameforthepeakmeasuredin flexure. NACAm 4225 43 . Eromequations(17)and (19)it is apparentthattherelaxation strengthobservedinWth torsionandflexurewillbe orientation . dependent,unlessboth W snd N’ arezero(i.e.,unlessrelaxation occursunderhydrostaticpressureonly).Further)elasticisotrom (C. c‘) doesnot@l-y ,snelasticisotro~butinsteadreducesequa- tions(17) and (19) to-simplerforms,wheretherelaxationstrengthis a linearfunctionof @. Theimportantcase $ = O is obtainedwhenthespecimenaxisis parallelto a <100)direction.Equations(17)and (19)thenreduceto (20) Ac,(L+u&.) 1+* (a) Equation(21)canbe writteninthemuchsimplerform AE@oo}2 Lx! (22) * ‘ when C’/3KKK1,protidedtheassum@ionistie that AK is notmuch greaterthan N!’. No proofof thisass~tion ispossiblewithout appropriateexperimentaldataor knowledgeof thecorrectnmdelof the relaxation. TheelasticconstantsofAl alloycontaining4 weightpercentof Cu haveapparentlynotbeenmeasured.Thedataavailableforpurealuminum (ref.~) andAl alloycontaining5 weightpercentof Cu (ref.55)are givenin tableIV,togetherwiththecalculatednmduli.Differences betweenthetwomaterialsarequitesmll, sothevaluesgivenfor Al alloycontaining5 weightpercentof Cuhavebeenusedforthepresent 4-percentalloy.lheratio C/C’ showsthealloyto be nmreisotropic elasticallythanpurealuminum.ForAl alloycontaining5 weightpercent of Cu thevalueof C’/3K is 1/37,whichmaybe smallenoughcompared withunityto justi~neglectingthebulk-relaxationcontributionto flexureforthisalloy.Usingthesemoduli,sadthe~erimentalresults forsingle-crystalspechens4 and5 in torsionandflexure(tableII), thevaluesof K! and AC’ werecalculatedfromequations(17)and (19) withtheassumptionof a negligiblecontributionfromthebulkrelaxation. * Theresultsare: . 44 NACATN4225 ~ = 0.00034 AC’= o.oo~ Usimzthesevalues, andthefactthattheal.lqyis atist isotropic elastically,it is notedthat W in torsionincreasesalmostlinearly with # from & . NACATN 4225 45 SecondPeakandEigh-TemperatureBackgromd A comparisonofpresentresultswithdilatometric(ref.45)and X-raymeasurements(ref.44)showsthattheappearsaceandgrowthof thesecondpeakparallelstheprecipitationof thephase e’. Good correlationbetweenthedifferenttypesof datais obtainedby assuming thattheheightof thesecondpeakisproportionalto thesmmuntof e’ precipitated.Usingtheinternalfrictionat 120°C as a relativemeas- ureof theheightof thesecondpeak(seesectionentitled“Agingat 203°C’t)andtheassumptionofproportionalitymentionedabove,the kineticsof precipitationof ei it 203°and-23@C areobtainedfrom figures13 and19 usingtherelationship t%-e~ Percentof e’ = 100 bf - 8s (23) where ~ is thedecrementat 120°C!afteran agingtime t, and 8S and ~ are,respectively,thedecrementat 120°C beforetheappear- mce of thesecondpeakandaftercompletegrowth.me resultsfor203°C areplottedin figure28togetherwiththeresultsof IankesandWassermsmn (ref.45)andof Guinier(ref.44)for2~0 C. Theresultsforagingat 230°C areshownin figure29,togetherwiththevariationinferredfrom thedilationcurveat 230°C. Theagreementbetweentheresultsis satis- factoryconsideringthatthekineticsofprecipitationareaffected~ thetypeof specimenusedandthemethodof quenching(ref.41). If equa- tion(23)is assumedto holdexactly,thevalueof thegrowthe~onent m obtainedby analysisof thepresentdatain termsof equation(3)differs somewhatfromthevalueobtainedby othertechniques.Thedilatometric andX-rayresultsat 200°C yield m = 1.7,whiletheinternal-friction resultsgive m = 1.5. Thedilatometricmeasurementsat 230°C again yield m = 1.7,butthenoticeablylowervalueof m = 1.3 is obtained fromtheinternal-frictionresults.As e’ islmownto precipitatein theformof platelets,thediscrepancybetweenallof thesevaluesof m andthevalueof 2.5predictedfromZener’stheory(ref.18) indicates thattheassum@ionsof Zener’sanalysisarenotvalidin thepresent case,as firstpointedoutby Gutiier(ref.44). Thefallin thesecondpeakon agingat 300°to 330°C afterprior “fulldevelopmentat 203°C is to be associatedwiththetransforma- tion el+e. Therateof thistrsmsformationas indicated~figure14 is consistentwiththeobservationsof CalvetjJacquet,andGuinier (ref.37). As thereisno signof thesecondpeakin specimenscon- tainingonlythe e phase(see,e.g.,fig.23),thesecondpeakis apparentlyrelatedspecificallyto the e’ phase. 46 NACATN 4225 . Thepresentmrk hasproducedthefollowinginformationconcerning thesecondpeak: . (a)Thepeakisproducedspecificallyby precipitationof the phase f3’. Thekineticsof growthofthepeakindicatethattheheight of thepeakis roughlyproportionalto theamountof e’ precipitate~. (b)Therelaxationstrengthof thef%llyformedpeakappearsto be roughlyisotropicformeasurementsin torsion(seefig.18). If this conclusionis correct,a largerpeakin flexure(fig.26)canarise onlyfroma substantialbulkrelaxation.Fora materialshowingboth an isotropicshearrelaxationof strengthN anda bulkrelaxation of strengthAK,therelaxationstrengthinflexureAE is calculated fromequations(17) and (19) as & .;(l+U)LG+(l;%K (24) where a is Poisson’sratio.For a g 1/3, equation(24)reducesto m++% (25) 9 Thevalueof & forthefullyformedpeakis estimatedto be 0.0025, andthevalueof LE,to be 0.0037.Substitutionintoequation(25) givestheresultAK 2 0.013.ThuE,thesecondpeakmayhavea substan- tialbulk-relaxationstrength. . (C) me @Ue 10gTo = :12.5t 0.8 is calculatedfromtheactiva- tionenergyandtheestimatedpeaktemperatureof thefullyformedpesk. If theslightshiftofpeaktemperatureuponaging(fig.11)is attributed whollyto changesin To,thevaluesobtainedare logTo= -12.7and -12.0 forthenewlyformedandoveragedpesks(curvesA andC, fig.Il.), respective~.Therelativeaccuracyof thesefiguresis goodenoughto inferan increaseof halfsm orderofmagnitudein To as agingpro- gresses.If it is assumedinsteadthat To remainsconstantthroughout, theincreaseinpeaktemperatureimpliesan increaseof 5 percentIn the activationener~. Inanycase,thequotedV8,1uesof To arelarger by twoordersof magnitudethanthevalueexpectedforarel&xationwhich is completedby veryfewatomicjumps,forexample,_.the&ner rel~tion. It thereforeseemsthatabout100atomjumpsarerequiredto completethe relaxationinvolvedin thesecondpesk. * . NACATN4225 47 . (d) Theactivationenergyof thepeak(21.9~ 1.0kcal/mole)is con- . siderablylowerthanthatfornormallatticediffusion.Sucha value couldhoweverbe associatedwithatommovementsin dislocatedregions, forexample,mound theinterfaceof a e’ particle. (e)Oneof themoststrikingfeaturesof thesecondpeakis its relativepeakwidth,whichisaboutthreetimesthatfora singlerelax- ationtime. Thepeakthereforeinwlvesa spectrumof relaxationt-s. Sucha spectrum~, ingeneral,be attributedto a distributionof values forboth To and H. Themeaningof theexistenceof a range of To valuesis thatthenumberof atomicjumpsrequiredto complete therelaxationis notthesamethroughoutthespecimen. b connectionwith(d)above,thegxain-boundarypeskinmetalspro- videsanotherexampleof a broadinternal-frictionpeak. lh thiscase To ispropoti,ionalto thelinear&ain dimension,anda spectrumof To valuesarisesbecausethegrainsarenot~ of thesamesize. Thegrain- bundaryrelaxationis explainedby ascribingto theboundariesthemechan- icalpropertiesof a viscouslayer.A similarinterpretationof thesecond peak,namely,thatit arisesfromtiscousslipacross e’ interfaces, appearsunlikely.Xh termsof suchan interpretation,itwouldbe diffi- cultto explatiwhythepeakdecreasesandemtually disappearsas the boundarybecomesmoreincoherentbecauseof the e’+ E)transfo~tion. Furthermorejat leastin thelater stages of e! development,the * e! plateletformsan intersectingn&workthroughoutthematrix,as shownl& themicrographsof CalVet,Jacquet,andGuinier(ref.37). Under thesecircumstancesitwouldseemiike~ th&tcoupledrel&atio~s’would . occur(ref.2)0 Theconceptof coupledrelaxationswaspreviouslyused to explainthemonotonicallyincreasinginternalfrictionas a function of temperatureforan aluminum-zincalloy(ref.23)duringprecipitation. It isthereforeapparentthatviscousslipacrossthenewinterfacespro- ducedby precipitationprovidesa morelikelyexplanationforthehigh- temperaturebackgroundthanforthesecondpeak. On thisbasis,therise inthehigh-temperaturebackgroundwouldbe eqectedto followthecpurse of the e’ precipitation.Thatthispredictionis correctis indicated in figures13 and19 W theparallelgrowthof thesecondpeakandback- groundsndby thedirectcomparisonof theisothermalinternal-friction anddilatometriccurvesat both1850and200°C (figs.20 and21),.The risein thehigh-temperaturebackgroundduringthe t3’~13transformation is interpretedreadilyintermsof thegreaterapmuntof slippossible as progressivelymoreof theWundaryareabecomesincoherent.Therise inthehigh-temperaturebackgroundcausedby thedirectprecipitationof the e phaseis shownin figure23. Finally,theactivationenergyof thehigh-temperaturebackground(33kcal/mde)isnotinconsistentwith thatforgrain-boundaryrelaxationinpurealuminum(32to 34.5kcal/nmle)● 48 NACATN 4225 . In searchingforan explanationof thesecondpeak,speculationwas directedtowardpossiblewaysinwhicha stress-inducedatoticrearrange- . mentmightoccurinvolvingthepresenceof a precipitatedphase. This problemhasbeenexaminedpreviouslyby DsnaskandNoWick(ref.24)whose viewsformsm essentialpartof [email protected] cipitationtheloweringof thetotalfreeenerg ~ chemicaldecomposi- tionis opposedby bothsurfaceandstrain&ergy terms.Althoughfinal thermodynamicequilibriumisnotreacheduntilprecipitationof the stablephaseis complete,it seemsreasonableto applytheusualthermo- _c CriteriOn fortheoccurrenceof smelasticityto a statewhichis metastableduringtheperiodof anelasticmeasurements.It followsfrom thiscriterionthatanyprecipitationcausinginternalstrainswillgive riseto anelasticrelaxationeffects,sincean appliedstresswillthen changethestateofprecipitation.Considerforexsmplethecasewhere precipitationcausesa bulkexpansion.Applicationof hydrostaticpres- surewillcausea limitedre-solutionofprecipitateandhencean anelas- ticchsmgeinvolumefollowingtheinstantaneousvolume.change.If shearingstrainsareassociatedwithprecipitation,applicationof a pureshearstresswillalsocausea relaxation.Sincepureshearcannot producea changeinvolume,theaccompanyingrelaxationwillnotbe asso- ciatedwitha changeinthequantityofprecipitatebutwitha redistri- butionof theprecipitate(i.e.,witha changeintheshapeof thepre- cipitateparticles).Thesegeneralconsiderationsapplywhetherthe precipitateis coherentornot. b orderto explaintheabsenceof a detectablepeakwhen 0 phaseis theonlyp~cipitatepresentinAl slloy-- containing4 weightpercentof Cu,it isnecessazyto supposethat 8 coherencystrainsplaya majorrolein determiningthemagnitudeof the relaxation.Themechanismof relaxationby a stress-inducedchangein theshapeofprecipitateparticlesmaybe usedqualitativelyto explain - thelarge To valueof thesecondpeakintermsof thelargenumberof atomicjumpsrequiredto changetheshapeof a precipitateparticle. Further,thenumberof jumpsrequiredto completetherelaxationwould — be expectedto increaseas theparticlesgrowin size,whichis consist- entwiththeanslysisthatsuggestedan increasein To withaging. Theactivationenergyfor,therelaxationwouldbe thatforatomdumps acrosstheinterfaceof theprecipitateparticles,which,mayreasonably be expectedto be considerablylowerthamthatfornormallattice diffusion. In conclusion,mentionwillbe madeof the2-percentwdulus increase whichwasfoundto..accompanytheprecipitationof thephase 0’. These resultsarein goodaccordwiththemoreaccuratehigh-frequencymeasure- mentsof Tanaka,Abe,andHirsmo(ref.~). Themoduluswillbe Increased somewhatby therejectionof copperfromsolidsolution,butthepre- dominanteffectmaywellbe a stiffeningof thematrixby a morerigid precipitate,as discussedby Dudzinski(ref.57). . . NACATN 4225 kg . CONCLUDING~ . A studyhasbeenmade,by meansof low-frequencyinternal-friction measurementsinbothtorsionalandflexuralvibration,of aluminumalloy containing4 weightpercentof copperduringaging.Theresultsof this studyareas follows: An internal-frictionpeakshowingallthecharacteristicsof a Zener relaxationexistsin solution-treatedandquenchedspecimensof Al alloy containing4 weightpercentof Cu. Theheightof thepeakis strongly dependenton thedirectionsof thecrysta~ographicsxeswithrespectto thespectienaxis. Thebasicquantitiesnecessaryfora descriptionof theanisotropicbehaviorof thepeakhavebeencalctitedfromexperi- mentaldata. On aging,thepeekheightdecreasesas thesqwe of thecoppercon- centrationthatremainsfreelydispersedin solidsolution,whilethetwo parsm-etersof theZenerrelaxation,namely,To andtheactivation energyH, remainconstant.Nonewanelastic effectsattributableto thepresenceof G.P.[I]or G.P.[2]zonesaredetected,buttheZener peakis sensitiveto thereversionof G.P.[1]zones. Thegrowthof a secondbroaderpeakanda risein thebackground internalfrictionareassociatedwiththeprecipitationof thephase 0’. Theheightof thesecondpeakis at leastrouglilyproportionalto the amountof 0’ precipitated.Thekineticsof growthof thispeakandof thehigh-te~eraturebackgroundareverysimilarduringprecipitation of e’,butthedifferentoriginsof thesetwoeffectsarereflectedby thedifferencetitheiractivationenergies?Thepeakis associated specificallywiththepresenceof the 0’ phase,whereasthebackground isnot. Forexample,thesecondpeakisreducedby thetransformation e’~e, andisnotfoundin specimenscontainingonlythe e phase. ‘The high-temperaturebackground,on theotherhand,isfurtherincreasedby the Q’ to e transformation.A possiblemechanismforthesecond peakintorsionis thestress-inducedchangein shapeof thecoherent precipitateparticles.Thechangesin thehigh-temperature-background internalfrictionarediscussedin termsof thepossibilityof coupled relaxationsarisingfromviscousslipacrossthenewinterfacesproduced by precipitation. Theheightof theinitialpeakisverysensitiveto thefree-comer concentration(asquare-lawvariation)andis thereforeparticularly suitedto a studyof thedecreaseof thesupersaturationof thematrix duringtheearlystagesof aging.Thisis theonlypropertyknownto dependin a uniquemanneron thesupersaturationof copperin thematrix. . ThemethodIs onlyapplicable,however,fortemperaturesaboveabout130°C!. . 50 NACATN 4225 Evidencehasbeenobtainedforthepresenceof quenched-inlattice defects(possiblysinglewcsacies)whichgreatlydecreasethemean . atomicjumptime. Thedefectsdecayoutrapidlyonheatingthequenched specimen;specifically,theequilibriumconcentrationisobtainedin less than5 minutesat 200°C. Comparedwithotherfundamentaltechniques(e.g.,resistivity,dila- tometry,parsmagneticsusceptibilitymeasurewnts,etc.)thelnternal- frictionmethodis extremelysensitiveto theagingprocess.Forexample, a changein theinitialpeakheightby a factorof 4 on agingat l~” C maybe comparedwitha contractioninlengthof 0.005percent.Thegrowth of thesecondpeakassociatedwiththeprecipitationof 0’ causesthe internalfrictionat 120°C to increaseby a factorof 10;theassociated increasein lengthis 0.15percent. Thesuccess~ interpretationof theinternal-frictionbehavior duringaginghasbeenmadepossibleonlyby thecomparativewealthof knowledge,particularlyfromX-rayanalysis,whichisavailablefor Al alloycontaining4 weightpercentof Cu. However,continuedstudyof thisalloyin connectionwiththebehaviormentionedabovemaysupplement considerablyexistingknowledgeof theearlystagesof aging. llnternal-frictionstudiesof otherprecipitatingsystemsarealso expectedto be of considerablevalue.Forexample,preliminaryworkon thealuminum-richaluminummagnesiumalloyshasshowntheexistenceof an internal-frictionpeakinthesolution-t~atedandquenchedcondition, . as wellasmarkedchangesintheinternal-frictionbehavioron aging. An internal-frictionstudyof thesealloysmaybe particularlysignifi- cantbecausethesimilarityof theatomicscatteringpowersof alumtium andmagnesiumdecreasesconsiderablythesensitivityofX-raytechniques. YaleUniversity, NewHaven,Corm.,November27,19X. . . NACATN 4225 51 REFERENCES 1. 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K.: bvestigationof PlasticBehaviorof BinaryAluminumAlloYs.- by Internal-Fkiction Methods. NACATN 3681,1955. 34.Friauf,J. B.: TheCrystalStructureof Two Wbermetal.lic Compounds. Jour.Am.Chem.Sot.,vol.49,no.12,Dec. 1927,pp.3107-311k. 359Bradley,A. J.,andJones,P.: An X-Rayfivestigationof theCopper- Aluminiummqs . Jour.tist.Metals,Vol.~, no.1, 1933, pp.131-162. 36.Geisler,A. H.: PrecipitationFYomSolidSolutionsofMetals. m. 15. PhaseTransformationsin Solids,JohnWiley& Sons,tic., 1951,pp.387-544. 54 NACATN4225 37● Calvet,J.,Jacquet,P.,andGuinier,A.: TheAge-Hardeningof a CU-A1Alloyof VeryHighPurity.Jour.Inst.Metals(London), vol.65,no.2, 1939,pp.121-137. 38. I%eston,G. D.: Age-Hardeningof C!opper-Al.uminumAlloys.Proc. Phys.Sot.,no.289,VO1.52,pt.1, Jan.1940,pp.77-79. 39● Gerold,V.: &r dieStrukturderbeiderAush&tungeiner Aluminium-Kupfer-LeigierungAuftretendenZust&de. Zeit.f. MetalJ..,Ed.45,Heft10,1954,pp.599-607. 40. 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D.: PrecipitationintheSolidState.Jour.Sci.Inst., vol.18,no.7,July1941,pp.154-157. 47. Suzuki,T.: On theNatureof Preston-GuinierAtom-Groupsin anAge- HardenedAluminiumCopperAlloy.“Sci.Rep.of theRes.Inst., TohokuUniv.,ser.A, vol.1,no.3, Oct.1949,pp.183-188. 48. AngjC.,andWert,C.: A TorsionalPendulunofLowThermalIntertia. Jour.&pl. Phys~(I@tersto theEditor),vol.25,no.8, A“&g.1954, p. 1061. 49. Weinig,S.: High-VacuumTorsion.PendulumforAnelasticStudies. b Rev.Sci.Inst.,vol.26,no.1.,Jan.‘1955,pp.91-92. NACATN 4225 55 . ~. I@, T. S.: Anelastic Propertiesof Iron. K&ans.A.I.M.E.,vol.176, . Nov.1948,pp.448-476” 51.-, Taylor,cd.: Metalsmdbook. A.S.M.(Cleveland>Ohio)) 1948,p. IL59. 52.Brook,G. B.,andSully,A. M.: SomeObservationson themter~l FYictionof PolycrystallineAluminiumDurtigtheEarlyStagesof Creep.ActsMeta~urgicajvol.3,no.5,,Sept.1955,PP.460-469* 53. Lulay,J.,andWertC.: InternalFkictionof Cadmiun-lkgnesium Alloys. ActsMetallurgic,vol.4, no.6, NOV.1956,pp.627-631. ~. Goens,E.: ElasticConstantsofAluminiumSingleCrystals.Ann.d. physik.,vol.17,no.3,June1933,pp.233-242. 55. KSXTIOp,R.,andSachsG.: TheFlow,ofMetallic~stals UnderTor- sion. Zs.f. Physik.,vol.53,no.9,Mar.1929,pp.605-618. %. Tanaka,K.,Abe,H.jandHlrano,K.: On theMecbs.nismofAgingin Alumimun-SilmrAlloys.III- Variationof theYoung’sModulus. Jour.phys.Sot.of Japan,vol.10,no.6, June1955SPP.454-4%” 57. Dudztiski,N.: TheYoung’sMedulus,Poisson’sRatio,andRigidity Modulusof SomeAluminiumAlloys.Jour.Inst.Metals(London), vol.81,Sept.1952,pp.49-55. NACATN 4225 . . TABLEI DATAON SPECIMENSGROWNFROMMELX @nisheddiam.of specimens,O.OhOin.;finishedlength of specimens,8 to 10 in~ COS2CL+ Specimen Condition a> P) 7) deg deg deg CoSap+ 0 COS27 1 Nesxlysingle ------crystal . 2 Singlecrystal 4 86 88 1.001 0.006 . 3 Tricrystal ------“4 Singlecrystal 4 86 88 1.001 .006 5 Singlecrystal 2 88 89 1.000 .0015 3L NACATN 4225 57 . TABLEII INITIALPEAKHEIGHTSONFIRSTCOOIJNG ‘Peakheight, logarithmicdecre~nt Specimen Condition x 103 fl a In torsion In flexure 1 Nemly single 0.18* 0.02 3.56 ---- Crystal 2 Singlecrystal .ca6 .98 ---- 3 ‘lricrystal ------3.11 ---- 4 Singlecrystal .006 ● 79 8.9 5 Single crystal .0015 .56 { Polycrystalline------5.6to 4.3 ---- A Polycrystall.ine------4.32 6.5 B Polycrystalline------4.64 [ aObtainedby subtractionof theroom-temperaturedecrement fromthemaxim~decrement.Forspectiens2; 4, and5 in torsion theestimatedhigh-temperaturebackgroundcontributionwasalso subtractedfromthemaximumdecrement. . 58 NACATN 4225 . TABLEIII CONDITIONSUSEDINEXPERIMENTSON Q~CHING FROM BELOWPHASEBOUNDARY [Timeallowedforsolutiontreatmentbetweenruns>12 hxl Time CalculatedPeakheight Annealing allowed atomic (logarithmicTemperature~q~;y temperature,for percent decrement) Oc ofoy~~ temperature, equilib-copperin Cps rium, matrti (a) 525 > 24 1.78 5.30x 10-3 176 0.900 488 40 1.60 4.38 176 .gll. 477 80 1.45 3.31 174 .894 464 50 1.26 2.74 175 .897 427 35 .87 .7to 1.7 --- .897 %iven as maximumdecrementminusroom-temperaturedecrementforall resultsexceptthelast,wherea rsngeof possiblevalueswasdetermined frominspectionof curve. . * TABLEIV ELASTICCONSTANTSANDMODUIJOF PUREALUMINUMANDALUMIWM ALLOYCONTAINING5 WEIGHTPERCENTCOPPER Elasticconstants Sll, s=> S&, Source Material ~2 ~ of data /w cm2/dyne ~2/me Al 15.9x 1013 -5.8x 1013 35.2x 1013 Ref.54 Al alloy (5per- 15 -6.9 37 Ref.55 centCu) . Calculatedelasticmoduli Material c, c’, K, Anisotropy dynes/cm2 dynes/cm2 dynes/cm2 ratioC/C’ Al 0.284X 10-W 0.230x 10-12 0.77x 10-w 1.23 Al alloy (5per- .27 .228 2.78 1.18 centCu) 8 16x KY4 I I I I ● 14 - /: ● 12- t-lo - /: 6 A“ z */A E8 - / s /: a “jB 6 - ./ g ● ./’ ‘ *../.& z / :4 - ● .../AH” z o 52 - 0 I I I 1 I -2 -1 0 I 2 3 LOG,0 PRESSURE, mm Hg !!! r IHgUre 1.- The pressuredependenceoftiternelfrictionin~ (A)andhelium(B)fora spectien M of’Al alloyconlxdningA weightpercentofC’utestedat mm temperaturein torsionalvibra- 3 tion at 1.95cps. , , I , # fURFCTltlN OFVIBRATION / A II ~r’ TO PUMP Figure2.- Flexrmependulum. (A)Gal.vanometerlamp; (B)greenfilter;(C) lightinletwhl.ow; D) vacuumcovm for furnace;(E)hollowstahless-steeltube; (F)piu vises;(G) furnace; [H) rqechens; (J) losdingweight;(K)lightexitwindow;(L) &inch focal-le@h lens; (M) planeof hage of elitIn J; (IV)microscopewith graduatedeyepiece;shadedareas indi- cateflatrubbergaskets. T’hs,electrcmagnetused for excitingV1.brationsaud the measure- mentthermoccnqikare placedalongsidethe specimensand sxe omittedfromthe figurefor m Clarity. F 62 NACATN 4227 . 33,XIO-3 I I I 1 . . / / . I I I I I 100 150 200 - TEMPERATURE,‘C Figure3.- Internal-friction-behaviorof solution-treatedandquenched specimen3, tested in torsionat 1.71cps. After~0-minuteaging at roomtemperaturethespecimenwasheatedto 211°C in 6 minutes. CurveA indicatesinitialpeakon coolingafter6 minutesat 211°C; peakheight,0.00310.CurveB indicatesinitialpeakon reheating fromroomtemperatureto 211°C; peakheight,0.00X0. CurveC tidi catesinitialpeakon coolingaftera further5 minutesat 21.1°C; peakheight,0.00288.Peakheightsgivenas themaximumdecrement minustheroom-temperaturedecrement. - NACATN 4225 63 TEMPER ATURE,”C 100 150 200 I I I /bA\ ●“\ 5.0 x IO-3 2,7 2.6 2,5 2.4 2.3 2.2 2.1 2.0 1,000/T”K Figure4.-Initialpeakinpol.ycrystallineAl alloycontaining4 weight percentof Cu deterndnedat twofrequenciesby successiverunson cooling.CurveA is tiitialpeakfora frequencyof 0.360cpsat thepeaktemperature;theroom-temperaturedecrementhasbeensub- . tractedfromtheexperimentalresults.CurveB is fora frequmcy of 1.95cps at thepeaktemperature.A decrementof 0.00066was ftistsubtractedfromthe~erimentalresultsto compensatefor thelsrgerroom-temperaturedecrementfoundat thisfrequency.The e peakso obtainedwasthennormalizedto curveA by increasingsXL valuesby 4.6 percent.Theresultis curveB. . 64 NACATN 4225 eo x I0-3 I I I I I I I .—. —— ______RANGEOF INITIAL-PEAK HEIGHTSIN POLYCRYSTALLINE SPECIMENSOFAL-4% CU .—— —__ ___ I I I I I I 1 030 100 I50 200 TEMPERATURE, ‘C FigureP.-Initialpeakson firstcoolingforspecimens ofAl alloy containing4 percentCu testedIntorsion.CurveA showsspeci- men1 vibratingat 1.71 cps;curveB shotispecimen5 vibratingat 1.41cps. I& inclusionof therangeofpeakheightsfoundinpoly- crystallinespecimens(withoutsubtractionof theroom-temperature decrement)thisfigureservesalsoas a graphicalillustrationof . largedifferencesfoundinpeakheightson firstcoolhgforvsrious typesof specimens. NACATN 4225 ● 1.6XI0-3 1.4 ● I*2 1.0 a .6 .4’ .2 . 0,( I 1 I I t o 120 140 160 180 200 : TEMPERATURE,”C Figure6.- Initial”peakson firstcoolingfors~lsrly orientedsingle crystalstestedintorsion.A 6.0 XIO-s i I I r 1 I 1 . J t&---- .—— A-- )“ / o~ 50 100 150 200 TEMPERATURE,’% .. Figure7.- Initial testabilityin polycrystalddneAl alloycontaining 4 percentof C!utestedh torsionat 0.90cps. Solidcurveindi- catesinitialpeakon firstcooling.Foreachpointon thedashed curvethespecimenwasre-solution-treatedandquenched,heatedin thecourseof 2 to 4 minutesto thetemperatureshown,sndtheinter- . nalfrictionmeasuredimmediately. . NACATN 4225 67 6.0X10-3 I I I 1 I I I of 1 I I I I I 50 100 150 200 TEMPERATURE;C Figure8.- Restorationof theinitialpeskinpolycrystallineAl alloy containing4 percentof Cu,testedin torsionat O.gOcps. CurveA showsinitialpeakon firstcooling;curveB showsinitialpeakon r heatingto 200°C fromroomtemperatureafter9 ~ hourssgingat 132°C;curveC showsinitialpeakon coolingaftera stayof 9 min- utes at 2C@ c. Thedashedlineof curveB indicatestherangein whichchangesweretakingplaceso rapidlythattheinternalfriction wasunstable. 68 NACATN 4223 . . 144hr t 5.0% 10-3 ●/ .-• \ ●~. / ●/ 59hr / /’ ,0 ~o-o — ●— ● .01 ● ✍ ✏✏✏ /0- ~-oq,J”J●’ ● .“ /“ ● ●—9 E ..’” a ✎ a 5 I o~ 40 80 120 I 60 200 TEMPER ATURE, ”C Figure9.- Temperaturedependenceof internalfrictionof specimen3 aftersgingat 203°C fortimesMicated. Measurementswere made intorsionalvibrationat 0.7cpsexceptfor0.7-hourcurve,which wasobtainedat 1.3cps. . NACATN 4225 69 . 25X 10-3 I I I I 1 1 . 2a 1- A L I 1 1 0 50 100 ‘- 150 TEMPERATURE,‘C Figure10.- A possibleanalysisof contributionsto internalfriction of specimen3 after11.1hourssghg at 203°C. CurveA showstem- peraturedependenceobservedafterI.1.lhoursat 203°C intorsional vibrationat 0.5cps;curveB showsesttitedreducedtiitialpeak superimposedon a decrementof 0.00025whichis attributableto a constantexternal-energyloss;curveC showsesthatedsecondpeak; curveD showsestimatedhigh-temperaturebackground.Thesna2ysis is self-consistentinthesensethatsumof ordinatesof curvesB, C, andD at anytemperatureis equalto ordinateof curveA at that temperature. . 4 XIO-3 I I I I -10 20 50 100 150 200 250 TEMPERATURE:C ~ cl. P Figure11.- The estimatedsecondpeak in specimm 3 sftervaxiouasgingtreatments.Peaksare !=! for torsionalvibrationat a frequencyof 0.5 eps. CurveA indicatespeak afterIl.1 hours at 203°C; curveB indicatespeakafter1~ hoursat 203°C; curveC indicatespeakafter j!j ‘14-4hoursat~3° C,plus15.7hoursat2g& C,plus15.1hoursat330°C. t * * . , 71 NACATN 4225 TEMPERATURE,”C 50 79 Iqo 1* qo I 1 I 1 I I I I 50% 10-3 4.0 I . 01 I I I 1 I I I I 3.1 2.9 2.7 2s 23 l,OO~T”K Figure12.- Temperaturedependenceoftheinternalfrictionof speci- men3 after144-houragingat 203°C, fortwofrequenciesof tor- sionalvibration.CurveA is forfrequency0.5~ cps;curveB is forfrequency2.o4cps. . I m 50x IO-3 ,/-- I / / ● .#-A— */ 4.0 ✏ I /“ Al HOURS AT 203°C Figure13.- Changesin isothermalinternalfrictionand shearmcdulusof specimen3 tithaging time at 203°C. Resultsaxe for torsionalvibrationat 0.5 cps;chargeinshearmodulusG isexpre.w=dby ratioG/Go,where Go IsmoduJ-uaat startof ag5ng. CurveA indicates intemsl frictionat 203°C; curveB indicatesinternalfricticmat 120°C; curveC .iniUcates relativechangein she= mdul.us G/G.. a # . NACATN 4225. 73 . 9,0 XI0-3 ~=— . / 8,0 7.0 Id n 4,0 . ● J/ ✏✏ . t44hrat203° C ● A / A PLUS iwhr at 298° C /// ■ PLUS 15.1hr at 330” C + PLUS 56hr at 330° C I ,(I , Figure14.- Temperaturedependenceof internalfrictionof specimen3 aftercumulativetreatments.Measurementsweremadein torsion~ vibrationat 0.5cps. * 74 NACATN 4225 . cI0-3 I 1 I 1 # A . I . . / /A t .*A A’ A-A I 1 I 1 0 I c 20 I00 200 350 TEMPERATURE,‘C Figure15.- Temperaturedependenceof theinternalfrictionof speci- men3 afterthefollowingcumulativeagingtreatment:1~ hoursat 203°C, plus15.7hoursat 298°C,plus15.1hoursat 330°C. Meas- urementsweremadein torsionalvibrationat 0.5cps. NACATN 4225 TEMPERATl{RE,% a 1 280 w D 100x IO-3 y I I I I I 1 I I I I ./ ./ ./ / ./ / A ./A/ A/ . A/ A A/’ i I I I I I I I I 1 1 2.2 2.1 2.0 1.9 1.8 1,000\T°K Figure16.- A replotof figure16 to demonstratethelinearrelationship . betweenlogb and l/T “above220°c. . . 76 NACATN 4225 8.OX10-3 I I I I HOURSAT230% r 4 001 8 2.0 ● s.5 + 10.2 w 20.7 4 61.0 v 157.6 50 100 I50 200 TEMPERATURE,‘C Fee 17.- Temperaturedependenceof internalfrictionof specimen2 afteragingat 230°C forthetimesindicated.Measureme&swere madeintorsionalvibrationat O.0~ cps. NACA~.k225 77 aoxIO-3 I 1 I I . 30 2a . . LO o 50 100 [50 200 TEMPERATURE,‘C Figure18.- A comparisonof internal-frictionbehatiorshownby three ‘differentspec-tiensaftersufficientsgingto developfu31ythesec- ondpeak. Allmeasurementsweremadeintorsionalvibration. CurveA showsresultsforspecimen2 agedfor157.6hoursat 230°C, frequency= 0.81cps;curveB showsresultsfora polycrystalline specimenaged110hoursat X-O”C, frequency= 1.80Cps;curvec showsresultsforspecimen3 aged1~ hoursat 203°C, freqpency= 0.55Cps. Thepolycrystallinespecimenwastestedin airat atmos- phericpressure,smdpointsshownhavebeenobtainedby subtract~ 0.00120fromexperimentalobsexwationsto allowfordifference . betweenroom-temperaturedsmpingin airat atmosphericpressureand heliumat 10 millimeterspressure. . 03 02 G 5 *OI o , ,A ,-- ,00 J I Uu ‘HOURS AT 230”C ‘u F1 Figure19.- Changesin isothermalinternalfrictionend shearmmluluaof specimen2 with aghg x= H time at 2300c. Measurementsweremade in torsionalvibrationat 0.8 cps. Changein shear z modulus G is expressedby ratio G/G. where Go is modulusat stsrtof aging. curveA -r= hdl.catesinternalfrictionat 250°C;-curveB In&ates Internalfrictionat 3.20°C; $ curveC Indicatesrelativechangein shesxmodulus G/G.. * , r , . * 6 5 4 3 2 I o I I 1 1 I I 0.1 I 10 100 Ipoo “99 HOURS AT 18S°C Figure20.- Change6 h polycrysttie specimensof Al alloycontaining4 percentCuon ag~ at 1850c. Curves A andB are for torsionalvibrationat 1.4cm. CurveA hmlicatesiso- thexnk.internalfrictionat l~” C. pOktB shownare experime&talobservationsafter subtractionof room-temperaturedecrementpriorto s@& - CUI’W B indicatesrelative-e b shearmodulus G/Go;curveC indicatesrelativeexpansionat lo” C, takenfromthe resultsof Lsakesand Wassermann(ref.45). .- 10xIO-3 I I I I 9 - z k D 27 - E k#6 - a m u w a 5 - ;4 - - 20 ~ z x ~3 - B E 6 2 - 3, _“ o I I I I 1 .1 I 100 1,000 HOURS’OAT 200°C ~ Figure21.- Changesh polycrystalltiespecimensof Al alloy containing 4 per-t Ofm m W* . at 203° C. CurveA ~cates internalfrictionat 2C0°C fromthe resultsgivenby @ (ref.31);frequency of measurement)% not givenbut is estimatedto be 1 * 0.5 c’&;room- temperaturedecrement(sJEounlomwn estimatedto be 0.0015f O.0005;curveB indicates the relativeexpansionat 200°C, takenfromthe resultsof LankesandWaasermamn(ref.45). . , L NACA‘TN4225 81 “ : 10-a I I I I I 1 . 570”C 4.C 536°C sol ‘c . a ● a c 50 100 I50 200 TEMPERATURE, ‘C Figure22.- Initialpeakofpolycryst@MneAl alloycontaining4 per- centCu on firstcoolingfrom190°C afterquenching from solution- treatmenttemperaturesindicated.Measurementsweremadeintor- . sionalvibrationat 0.396cps. ● 82 NACATN 4223 6.0~10-3 I I I I I I 4,0L ol 1 1 a 1 I 1 50 100 I50 200 TEMPERATURE,‘C Figure23.- Initialpeaksonfirstcoolingshownbya polycrystalline specimenofAl alloycontaining4 percentofCuafterquenchingfrom 525°C sndfromfourt~eraturesbelowthephaseboundaryfollowing an annealto establishequilibrium.Measurementsweremadeintor- sionat0.90cps. NACATN 4225 83 . 6.0x 10-3, I I I I [ A 5.0 . A / . . - * . ‘8 1- C9 .0. 0 -J 0 Lo 2.0 3.0 (ATOMIC% COPPER)2 Figure24.- Initialpeakheightsoffigure23plottedagainstthesqwe of atomicpercentageof copperremainiagin solution. NACATN4225 “ :10-3 1 I I I I I . I I o~ 1 I I t t 50 100 150 200 TEMPERATURE,‘C Figure25.- Init$alpeakonfirstcoolingforsinglecrystalsofAl alloycontaining”kpercentC!uorient~with . NACATN 4225 85 8.OX10-3 1 I I I I I 1 I 50 I00 150 200 TEMPERATURE,‘C Figure26.- bternal-frictionbehaviorofnearly~O@ orientedsingle crystalsofAl alloycontaining4 percentCu aftersufficientagingat 230°C to develop-y thesecondpeak. CurveA showsresultsfor spectien2 testedin t&sionalvibr&ionat 0.81cpsafter20.7hours %- at 230°C; cum B showsresultsforspecimens4 and5 tested togetherin flexmalvibrationat 3.0cpsafter22.7hourssgingat 230°c. E% NACATN4225 . ! 160x IO-3 I I I I I t I I fT . 140 100 ea. . . 20 .A/i / 0 I 1 I I 100 200 300 400 so TEMPERATURE,“C Figure~. - Internal-frictionbehatiorofsingle-crystalspecimen~ at hightemperatures,afteragingfor’55.~hoursat3C0°C. Measure- mentsweretie intorsionalvibrationat 1.4cps. CurveA shows resultswhenspecimenis heatedto 505°C; curveB showsresultswhen spectienis cooledfrom505°C aftera stayof 1.5hours. , , . I “ IL o t -1 100 500 TIME, HR F-e 28.- Percentageof 13’phaseas a functionof agingtime. CurveA showsresultsfrom internal-frictionmeasurements,for an agingtemperatureof ?J130C; curveB show results fmm the dilatumetricmeasurementsof LsnkesandWaase~ (ref.45),for an aging-@mpera- tureof 200°C; curveC showsresultsf!rcmthe qmntitativeX-raymeasurementsof Guinier (ref.44), for an egg temperatureof 200°C. 100 60 - A IL o 60 -“ A 40 -. -20 - “3 1 10 70 TIME, HR z $ 4 mgu.re 2$1. - Fercentageof’ 9‘ phsseas a functionof ? f@W tiDIe at 250° c. (!urv’e A ShOWS resultsfrcuuinternal-frictionmmsurement6;CUX-VEB showsresultsfranthe dil.atometric measurementsof LenkesandWassermeno(ref.45). , 4 .