Post on 19-Jan-2019
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I/-
FORAERONAUTICS
OF
By
TECHNICALNOTE
STRESSRUPTURE
AircraftEngineResearchLaboratoryCleveland,Ohio
I
HEAT-RESISTINGALLOYSASA RATE
E. S.MachlinandA. S.Nowick
PROCESS
H’\DO ~TECtUWCALL:BRARy
AF-1834-LO ~
=qJRJJ7
WashingtonSeptember1946 AFMDcT~~}??~!pai.etiAL L%WWY
-.—
https://ntrs.nasa.gov/search.jsp?R=19930081820 2019-02-04T06:46:22+00:00Z
TECHLIBRARYKAFB,NM
d-.
NATIONALADVISORYCOMMITTEEFORAERCNAUTICS.
TZCENICALNOTENO.1126
S!lXISSRTE’TOREOFHEAT-?3EXISTINGALLOYSAS A RATEI?ROCIES
By E.S.MwM.inandA. S.X’?owick
SUMMARY
Theequationsofthetheoryofrateprocessesareappliedtostressruytureandpredicttheexperimentalstressandtemperaturedependenceofthethe forruptureforthreeheat-resistingalloys.It isconcludedthat,althoughthissuccessfulpredictionforthreealloysdidnotconclusivelyprovethatstressrupturewasa rateprocess,itdidprovidea basisforrecommendingthattherate-processstress-ruptureequationsobtainedshouldbe usedto inter-polateandextrapolatedatafordifferenttengmraturesandtoreducethenumberof stress-rupturetests.
It is indicatedthatstressmayhavean affectonthecrystalstructureby causinga phasechange.Alsoitappearsthatthesamerate-processmechanismisresponsibleforbothtranscrystallineandintercrystallinefailureandthata correlationmayexistbetweenstressruptureandcreep.
Therecommendationistie that‘&emethodof presentingstress-ruptmredataona semflogplot(logaritkuofrupturetimeagainststress),whichhasa basisintheory,be investigatedforuseinylaceof thepresentempiricalmethodofpresentingstress-rupturedataon log-logplotsof timeforruptureagainststress.
INTRODUCTION
Oneofthemaincriteriausedtoratetheheat-resistingprop-ertiesofalloysis stressrupture(referencel),.Durihgai3tresa-rupturetesta tensilespecimenisheldundera constantloadat aconstanttemperatureunttlthespecimenfractures.Thechiefmeas-urementmadeduringthistestIsthetimerequtiedforruptureatthesyecificteststressandtenpra%ure.Itwasempiricallyfoundfroma aoriesof stress-ruytumtestsata constanttemperaturethatwhenthelogarithmofthetimoforruptureisplottodagainstthologarithmof stress,a straightlineisobtainodwithinexpertientalerror(references2 ati3). Thismethodof showingstress-rupture
data-hasbeenadoptedbytherepoi’tsof theiZKM
NACATN~0.1126
manyinvest~atorsproject(reference
‘!●
andispresentlyusedin1)andMe I?A.CA(refer-
ence4). By interpolationandextrapolationfrc?ntheseplots,valuesofthe”eiressesre~uiredtorupture;hespecimens(therupturestrengths)in10,100,and10GOhoursareobtainedforsyecifictem-peratures.Alloysarethenratedfora IWJ%iculauapplicationontheba~isoftheirrupturestrengtiasat thenrpturelifethatmostnearlyrepresentstheap@hation.
Inasmuchas stressrup%ureisan importantcriterioninratingheat-resistingalloys,itwouldbe advan+~eousto knowthequanti-tativedependenceof thetimeforruptureOD stress,teayerature,composition,andstructure.Inordertoobtainthisim”ormation,an investigationwasmadea% theNACAClevelandlaboratoryduringthespringof1945usingthetheoryofrateprocesses.Thistheorywasused%ecauseithas%eenfoundto”applyto certainprocessessuchas chemicaireactions,viscousflow,andcreepthatoccura%adefiniterateforgivenconditions.-Itwasthot~htthatstressrupturewassucha process.An equationwasderivedthatgives,fora givencompositionandstructure,thedependenceofthettmeforruptureon stref3sandtempeaaturegTheinvestigationispartofageneralprogramto provideirfmmationthatwillultimatelyleadtothedevelopmentofletteralloysinorderthattheefficiencyandpowerout~utofgasturbinesumd inaircraftpropulsioncanbeincreased.
ThereaderwhoiB solelyinterestedinthepracticalapplicationofthefundamentalequations,whichgivethedependenceofthetimeforruptureon stress,temperature,compositionandstructure,mayproceeddirectlytoHLW’IICMLAPTLIOATIOFOFS’TRE3S-RU1’TC~EQUATIONS.
SYM1301S
Thefol.lowi~sydolsareusedinthereport:
c proportionalityconstant
AFa freeenergyofactivationpermolecule
AFa‘ a~~~entfreeenergyof activationpermolecule
h. PMncklscomtant,
A% heatofactivation
6.62X 10-27ergseconds
permolecule
2
●
%0
k
r
rf
ASa
Asa!
tr
T
P
0
T
NACA
heatOractivationperzero
TNNo. 1126‘.-.
moleculeat temperatureofabsolute
E&tzmann’sconstant,1.38X 10-16ergs
rateofreactionyerunitconcentrat~on
rateofoccurrenceoftheunitprocess
entropyofactivationpermolecule
permoleculepe~*‘K
of reactantO
apparententrcyyofactivationpermolecule
tiresforrupture
alsolutetemperature
~ro-fmrtionalityconstant
externallyappliedtensilestress
shearstress
TIIEORY
Thetheoryofrateyrocesse8willfirstbe discussedas a gen-eraltheo~~.Itwillthenbeshownthatif stressruptureofheat-resistingalloyscanbe treatedas a rateprocess,certainequationsmustbe satisfied.Latersectionswillthenshowthattheseequa-tionsaresatisfied.
GeneralTheoryofRateProcesses
ThetheoryOFrateprocesses(reference5)developedly 5yringandothershasbeene,pplledto chemicalreactionsaswellas otherprocessessuchasviscosityof liquidsandd~=fusion.In everycasetowhichrate-processtheoqycanbe applied,thereisa small sub-divisionsuchthatthemacroscopicprocessistheneteffectofallthesmallprocesses.TMs smallestsubdivisionis calledtheunitprocess.Forexam~le,ina chemicalreacttontheunitprocessisthereactfonbetweentheatcmsreactinginnunibersgivenby thestoichiometriccheruicalequation.Rate-processtheorycanbe appliedtoanyprocessprovidedthatthecorres~ndingunitprocessinvolvesa moloculeorgroupofmcleculesthat,inpassingfrbmtheiniti~l
3
XACATNNo.1126
tothefinalstate,mustfirstattaina certainmini.mumthermalmer&y. Thisenergyisoftenconsiderablygreaterthanthoordinarythermalenergyofmolecules;thereforethemoleculeorgroupofmoleculesparticipatingintheunitprocessis saidtobe ‘1.activated”ortohaveformodan “activatedcomplex”whentheminimumenergyisattained.Theunitprocessisbestillustratedby thepotontial-enor~ycurveforthoroactton,illustratedinfigure1. Theheightof&e barrier,whichistheminimumener~ requi.rodforpassageintothefinalstate,is calledtheheatofactivationA%. !l%isenergybearsno relationtotheheatofthereactionAH, theenergydifferencebetweentheinitialandfinalstatesalsoshown.By tho“reacticmcoordinate”ismeantthemostfavorablereactionpathonthepolydimensionalpotontial-energysurface.
!Che-basicassumptionofra.to.procosstkooryis thatthoinitialreactantsandactivatedcomploxesarealwaysin equilibrium.statist-ical mechanicalconsiderationsthengivo(reference5)fortherateof theprocess(numberofunitprocesstakingplace/unittime)theequation
4?JkTr = (kT/h)e . (1)Theterm kT/incan%e~ogudedas theeffectivofrequencyat
whichactivatedcomplexescrossovorthebarrier.W thecalculationof Al?ajthecontributiondueto thetranslationaldegreeoffreedomalongthereactioncoordinatehasbeendisregardedbecauseitisinoludcdinthefactorkT/h. ThofactorAFa Is interpretedasanordinaryfree-energytermandcsmbe e~ressedas
AFa= A% - TASa (2)
Thoentropyofactivationhastheusualphysicalsignificance.Itisrolatodtotherelativoprobabilityoftheinitialandactlvatodstatesexcludingtheenergydifferenceorwhatmayho calledtherelativefreedomsofthotwostates.A nogativoVCLIUOof ASa moansthereforethattheactivatedstateinvolvesgreaterrestrictionsonthedegreescffreedomof themoleculesthantheinitialstateinadditionto theenergydifferencebetweenthetwostates.
A processwillbe termeda “rateprocess”if equations(1)and(2)canbe apyliedto it;thatis,iftheunitprocesscanbetreatedas involvingthepassingofactivatedcomplexesovera potential-energyIarrier.
4
?JACATNMo.1126
Stress-lkpendentRateProcesses
In somerateprccessesthe-heightofthepotential-energyWrri.erisa functionof theappliedshearstress.Theunitproc-essesinthesecasesmaygenerallytakeplacein eitherof twooppo-sitedirectionsinvolvlngthesameenergybarrieras shownby thesolidcurveoffigure2,thusthenetrateis zero. Iftheshearst~essT isapplied,itmaylowerthebarrier in onedirectionandraiseitintheoppositedirectionas shownby thedashedcurve(fig.2). Theactivationenergiesforthetwodirectionsarenolongerequalandtheprocesstakesplacewitha definitenetrate.Thedirectionto therightinfigure2 Isdesignatedpositive.
Xxamplesof sucha processaretheflowofviscousliquids(reYerence5)wheretheunitprocessisthejumyof onemoleculepastanotherandthecreepof&tals (reference6)wherethegener-ationofa dislocationistheunitprocess.Inboththeseprocesses,theener~bywhichthebarrierisluweredinthepositiveandraisedinthenegativedirectionwasshowntobe approximatelyproportionalto theshearstress.Theheatofactivationforthestress-dependentprocessintheyositivedirection(theheightoftheharrierinthepositivedirection)is thereforeA% - 13T’andinthenegativedirectionAHa+ 13T.Thefreeenergyofactivationinthepositivedirectionis A% - p? - TASa andinthenegativedireotionA% + ~T - TASa. IIEEMIUCIIas AFa= A% - TASa therateof occur-renceof unitprocessesinthe~ositivedirectionistherefore
andinthenegativedirection
Thenetrateinthepositivedirectionistherefore
Thefactorp is,ingeneral,a function
ApplicationofRate-ProcessTheory
of
to
temperature.
StressRupture
(3)
Thesupyo=ttionismadethatstressruptureofheat-resistingalloysisa rateprocessinthesenseof thedefinitionpresentedin tiiS report.Whentheunitprocess3.sconsideredinanabstractsense,it ispossibleto detemnineonlythetemperatureandstress
5
NACATN No. 1126
dependenceof therate r. A definitephysicalunitprocesssuchasthegenerationofa dislocation(reference6)wouldenablethepredictionofthedependenceoftherate r onthephysicalstruc-tureandpropertiesofmaterials.Thisreport,however,considerstheunitprocessonlyinthea“ostractsenseandthereforethecon-tributionthatwillbe e~ectedisa knowledgeof thetemperatureandstressdependenceofthetimeforrupturefora constantcom-positionandstructure.
If stressru@ureisa rateprocess,thetimeforrupturetristobe expectedtobe inverselyproportionalto a rate rf or
tr = c/rf (4)
Theunitprocessisexpectedtobe stressdependent.If theeffectof stressis similartootherstress-dependentrateprocesses,thatis,iftheamountbywhichtheharrierisloweredorraisedby shearstressisapproximatelyproportionalto theshearstress,then rfwouldbe givenby equation(3). If,as inthetheoryof creep(reference6),thegrainsaretakento‘beorientedsuchthattheunitprocessoccursundermaximumshearstress,where T . 0/2, thisequationbecomesinlogarithmicform
logerf = 1088 (2kT/h)- (AFa/kT)+ logeSinh(pG/2kT) (5)
Thefactorp mayincludea stressconcentrationfactoriftheunitprocesstakesplaceat stressraisers.
ex - e-xInasmuchas sinhx = ~ , when x becomeslarge,e-x
rapidlyapproacheszeroand shh x thenisgiventoa gooda_pprox-1~im-ationby ~ e . Thusforsufficientlyhighvaluesofapplied
stress
(6)
Ifequation(6)is substitutedinequation(5)andcombinedwithequation(4),theresultingequationforthetimeforruptureis
logetr = @e (h/W)+ (ma’/kT)_-(Po/2kT) (7).
.
where
AFa‘ = AFa--CT =A~ - T (ASa+ C)
c = -klo$eC
6
(8)
NACATN ~0. 1126
Theterm ASa+ C is thereforetheayparententropyofactivation.
Forthepurposeof checkingthevalidityof equation(7),comnon10@X’ithDISaremostconvenient.Equation(7)canbe written
10$tr = log(h/kT)+ (AFa’/2.3W)- (~(y/4.6kT) (9)
A @Ot Of 108 tr againstG fora fixedtemperatureshouldthenbe a straightlineofnegativeslopej3/4.6kTandintercept
logt~ = log(I@?)+ (A~a’/2.3k@ (lo)
Fromequation(10),AFa~ canbe obtainedforeachtemperature.TheheatofactivationyermoleculeAHa isusuallyeitherconstantorexpressibletoa gcodapproximationasa linearfunctionof Taccordingto
Thusa
where
h% = A~O +A~l T (11)
linearplotof KFaY againstT shouldbe a straightline
AFa‘ = A~o - TASa’ (12)
ASa‘ isgivenby
ASa‘= ASa- A%’ + C (13)
E stressruptureisgivenby equation(9),practicalueeofthisequationfordesigncanbemadeby lettinglog(h/k’T)equala constant.Theapproximationthat logT is constantrelativetothetermin T willinvolveno detectableerrorovera largersngeoftemperature.Thisapproximationwasmadefortheequationgiveninthesectionentitled“I?RACTICALAPHJXJITIONOFSZRISS-RUF’TUREEQUATIONS.”
SOURCESANDPIU3CISIOEOFDATA
Stress-m@uredatawereobtainedfronreference4,fromtheAlleghenyLudlumSteelCorporation,andfromtheUniversityofMichiganforthreedifferentalloys:S816cast,S816forged,andlowcarlmnN155hotworked.Thesealloyswerechosen%ecauseenoughstress-rupturedatawereavailableforthemintheliter.atureat differenttemperaturesandstresses.
7
NACATNNO.1126
An examinationofthedata,ingeneral,showedthata particularruptureliffemightvaryby asmuchas 100percent.Appro-teexperimentalerrorsforthefactorsP, AHaO, and ASai are
350percent,&5 X 10-13ergs,andM x 10-16ergsper‘K,respec-tively,i)uttheerrorsin A~O and ASa* willgenerallybe inoppositedirectionsandthereforetendto compensate.Reference7givesanapproximatevalueofthereproducibilityof stress-rupturedataobtainedfromdupllcatetestson specimensfromthesameheat.Thisvalueis=5 percentfortwo-thirdsofthetestsconducted.Forone-thirdoftheteststhevariationwasmuchlargerthan*25percent
RESULTSA~DISCUSSION
StressDependenceof logtr
Equation(9)statesthatat constanttemperaturea plotoflogtr againststressathighstresfieswillyielda straightlinehayingthenegativeslope13/4.6LdJ!.h examinationoftheprimarydataforS816cast,S816forged,endlowcarbonN155hotworkedshowedthatthe@ots of log-tragainststressforthesealloyswerestraightlineswhoseslopesvariedwiththetemperature.(Seefigs.3,4,and5.) Theliterature,however,showsstraight-lineplotsof logtr againstlogG forthesesamealloys.fiasmuchasbothplotsarenotmathematicallyconsistent,onlyoneplotiscorrect.Itwillbe shownthatstressruptureisa rateprocessandthereforethesem~logplotshouldbe used.Themagnttudeoftheexperimentalerrorexplainswhybothplotscanbe simultaneouslyobtained.PrevioushL~est@ators havealsonoticedthatstraight-lineplotsmuld be obtainedby plottinglog~ againsto (disc-ussionofreference3). Wasmuchasnobasisforchoosingbetweentheplotshadbeenavailable,stress-rupturedatawerestandardizedOnplOtaOf 10gtr against10g0.
Thechangein slopethatoccursbecauseof oxidationon thelog-logplotsofrupturetimeagainststress(reference3) alsooccursonthesemi.logplotatapproximatelythesamerupturetimeendstress.At thesauetemperature,transcrystalline-iypefailUrf3S
. willoccurat higherstressesthanintercrystalline-typefailures.No correlationexists,however,betweenthechangein slopeandthetransitionbetweentransc~stallineandintercrystallineregionsoffatlure.A nmnberof thelinesshownInfigures3 and4 showchangesin slopethatcannotbe explainedby eitherintercrystallineoxida-tionorthehyperbolicsinedependenceof stress.Thechangein
8
NACATNNO.1126
slopeisoppositein signtothatexpected~orintercrystallineoxidationandalsoismuchsharperthanthateqectedfora hyper-bolicsinedependencecf stress.It isleltevedthatthechangeinslopeis duetoa changeof structureasa resultof theeffectofstress.Reference8,forexample,hasshownthatstressathighte~yerat-urescaninduceanage-har~eningreacticn.
TemperatureI@endenceof
Inreference6 itwasempiricallydependenceofthe !3factor~orcreepfollowingrelation:
= 20Pa
Sloye
foundcould
Factorj3
thatthetemperaturebe descri%ed_by”the
Thedataforstressrupturewereinvestigatedto showwhethera similarrelationexistedfm stressrupture.A p~oljOf Mg pagainstT, whichgivesstraightlineswithine.~erimsntale=orforthethreealloysstudied,is showninfigure6. The ~ values
# offigure6 areofthesameorderofmagnitudeas thoseobtainedforcreeyof iron(reference6).
TemperatureDependenceofApparentFree
EnergyofActi-rationAl?a’
~uation(12)predictsthattheqr@ntityAFa’} theapparentfreeenergyofactivation,willbe linearlydependentontemperature.
Valuesof AFa’ werecamputedfraadatasubstitutedinequa-tton(10)andwereplottedagairisttemperatureforS816cast,S816forged,andlowcarbonK155hotworked.Theresultsareshown“inffgure7,whichsubstantiatesthepredictionmadeby thetheoryofrateprocessesthat AFa’ wouldbe linearlydependentontemperature.
,Valuesof AHao -d ASa’ forstressrupture,theintercepts
andslopes,respectively,ofthelinesinfigure7,aregiveninthefollowingtable.Thevaluesof similarparametersforcreeyo%tainedfromreference6 aregivenforcomparison.TheparametersA~O andASa’ forthecreepprocessareapproximatelytheenergyofactiva-tionendtheentropyofactivation,respectively,involvedinthegenerationofa d%locationandareA andB, respectively,inthenotationofreference6.
9
NACATNNO.1126
!&pe of test ~Jf~erial %30 Asa 1
(a) (ergs) (ergs/%)
StressruytureS916cast 1.71x lo-~z 5.7x 10-15StressruptureS816forged 2.98 4,2!StressruptureN155lowcarbon4.19 2.75
hotworkedCreep Iron 2.10 4.0Creep Nickel 2.67 4.0
%Jocreepdataworeavailableforcobaltbutthevalue.of itsconstantswouldbe expectedtoapproximatec~og~ly ~~o~e fog iron and nickel.
Thetableshowsthat A~O and ASa’ areof thesameorderofma@itudofor the stress-ruyturerateyrocessas forthecreeprateprocess,respectively.ItthereforGay~oarsthattheentropyof act%yationASa forthestress-rupturerateprocossisprobablya largenegativevalueof thecameorderofma~itudeas theentropyof activationforthegenerationofa dislocationandthattheparameterC is mall comparedwith AS=.(Seeequation(13).)
EVALUATIOiiOFRESULTS
Thetheoryof rateprocosseshaspredictedtheternporaturodepcmdonceofthetiresforruptlmeandthispredictionhasleonsubstantiatedby thodataforthreeheat-resistingalloys.Thissuccessful~redicttonisthojustificationforayplyingthetheoryofrateprocessesto strf3ssrqhuro. Becauseit is indicatedthatstressruptureIsa rateprocess,plotsoftk.elogtimeforrup-tureagainststressshouldbe investigatedforuseinplacecf’tholog-logplotsnuwused.Hoton~yisthosamilogplotbasedontheorybutit isalsotheonlyplotfromwhichdatacanlm obtainedtopredictstroem-rupturedataatadditionaltempcn?atures.Anexampleof theaccuracywithwhichdataat difforonttemporatumscanbe predictedisgiveninthesectioncntitlod“PRACTICALJWPLI-CATIONOFSTK!33S-RUPITJRZEQUATIONS.”
Thodatahaverevealedthata givenmaterialmayhavothrocdifferentsetsof constantsdependentonthestressandtemperaturetowhichthespecimenis subjected.Twosetsof theseparametersholdfortheunchangedmaterial(stablestructure)andforthematerialinthersngeof intercrys’allineoxidation,respectively.Thethiz’dset,whichdescribestkeregionofhigheststress,isbestexplainedonthebasisofa changeinducedintheoriginalstructure
10
. NACATNNO.1126
.
by shearstress.Whetherthise~lanationiscomectcouldbe deter-minedbymeansofanX-rayanalysisofthecrystalstructuresintwodifferentregionshavingdifferentsetsofmaterialparameters.
Ona log-logplotofrupturetimeagainststress,thelinethatrepresentstheregicncf interci~stallinefailureinth-eabsenceofoxidationisa extensicnofthelineoftheregionof iranscmystal-Iinefailure(refexence3). In theplotof logrupturethe againststressforthesamedata,thelineobtainedisalscunbroken,Internsofthetheoreticalequation(9),the &Fa’ and p valuesfortremscrystallinefailureareexactlyequalto the AFa~ =d ~valuesforintercrystallinefailurointheabsenceof oxidation.Itthereforeappearsthattherate-~ocessmechanismres~neibleforthetranscrystallinefailureisthesamerate-processmechanismresponsiblefortheinteucrystallinefailure.Thisfactleadstothebeliefthata correlationmayexistbetweencreepandstressrupture.Fromreference9 itcanbe impliedthatduringthetrans-crystallinemodeoffailure,a relativelylargeamountof creeptakesplace.IftranscrystalltneI’ailurefinallyresultsfromashearingof theindividualgrafms,thencreepmaybe thecontrollingfactor.Furtherevidenceofa cmi~elationbetweencreepandstressrupturewastheagreementofVaeorderofmagnitudesandtemperaturedependenceof similar terms intheequatiom-forcreepandstressrupture.Furthertests,however,arenecess&.ryin ordertoprovewhethersucha co~ellationexists.
Thepracti=lapplicationGfthest~ess-rupturetheorytoengineeringprobl~ isextensivelydescribedinthenextsection.On thebasisof’We theorygiveninthisreport,thepresentengi-neeringmethodofpresentingstress-rupturodatashouldbe revisedtopreventinaccuzzateapplicationoftheresultstothedesignofpartsforhigh-temperatureuse andtofaciliktethemethodofratingthestress-ruptureresistanceofheat-reststingalloys.
PRACTICALAPPLICATIONCB’STRESS—RUPNJREEQUATIONS
Theequation
(14)
where
tr timeforruptuzze,hours
11
NACATNNo.1126
T absolutetemyeratme,‘%
0 appliedtensilestress,youndspersquareinch
A, B constantsof structureand
and
logD =
where
E,F constantsof structureand
wasderivedinthetheorysection
composition
E+FT (15)
composition
of thisreyortfromthetheoryofrateprocessesas developedby EglWngandothers(reference5).Equation(15)WS foundem~irically.Thepredictionsof equa-tion(14),especiallyinregardtothetemperaturedependenceofstressrupture, wereinvestigatedandverifiedfora numberofheat-resistingalloys.Equation(14)isthereforevalidandcouldbeueedto obtainthedependenceoftimeforruptureon stressendtemperaturefora givenstructureandcomposition.
In orderto obtainan evaluationoftheconstantsA,B, E,andF, it isnecessarytodetermineat eachofthreeorfourtem-peraturesthetimeforruptureforat leastfourdifferentstresses.TheconstantsE and F areevaluatedby plottinglog~ against0 at a constauttemperature.Theslopeofthestraightlineobtainedisequalto -~. Whenvaluesof logD soobtainedareplotteda~ains%tem~erature,a straightlineisobtained.Theslopeofthestraightlineis equalto F andtheintercept(atT.= O) isequalto E.
TheconstantsA and B areevaluatedby obtainingvaluesoftheintercept(a= O)of theplotof logtr againststress.Fromequation(14)thisintercept,logti: willsattsfytherelation
Tlogti=A+BT (16)
Whenvaluesof T logti areplottedagainstT, a straightlineisobtained.Theslopeofthislineis equalto B andtheinter-cept(’l!= O) isequalto A.
It shouldbe understoodthattheparametersA, B,E, andFwillbe constantonlyfora givencompositionandstructureendintheabsenceof intercrystallineoxidation.Ifa heat-resistingalloyshouldhavedifferentstructures,as is sometimesthecase,thenthe
12
NACATNNO.1126
valuesoftheparametersToronestructurewouldnotapplytopre-dictingstsess-mq$mreda+xafortheotherstructure.Forexample,thebreakinthestress-rupturecurveat 1350°F infigure4 indi-catesthatthestructureinthehigh-stressrangediffersfromthatinthelow-stressrangebecausethevaluesofthestructureparam-etersA,B, X, andF forbothrangesarenotthesame.In theeventthatintercrystallineoxidationtakesplace,thesetofparam-eterswillno longerbe valid.Theselimitations,however,arenotsevereforthedatapresentedinthisreport.
Enordertoillustratetheuseoftheequationsfnpredictingdata,theprimarydataforforgedS816giveninfigure4 for1350,1500,1600,and1700°F willye usedto computevaluesof A,B, E,andF. Thenthesevalueswillbe usedto obtaina stress-rupturecurvefor1800°F,whichwillthenbe comparedto theexperimentalstress-rupturecurvefor1800°l?.
Theabsoluteslopeofthe1350°F stress-rupturecurveis
D logtrl- logtr~ 3.00 - 2,00-=T ‘1 - 02 = 30,000 - 41,200 = ‘“oooogm
whichthengives
D1350=
Similarly,
T X 0.0000900= ~810X 00(3~0900= (3.163
Thethe
Tne
%500 = 0.264
%600= “350
D1700= .435
plotof logD againstT isgivenstraightlineinfigure9 is
F ~Og0.%81- 1o$0.1.69_= —2;30 - 1810
interceptofthisstraightlineis
infi~ure8. Theslopeof
1.218X 10-3
E = log 0.381 - 1.218 X 10-3 x2100 = -2.977
Squation(15)thengivesfor D at 1800°F
logD=Z+lKC= -2.977 + 1.218 x2260 X10-3 = -0.220
13 :: -:,WJ
p MWiL Litlfih?yAF-1834-L()
NACATNNO.1126
D= 0.600
The interceptcf the13!50° F stress-ru@uretune infigure4 is
logt~= D10gtr+~O
0.163= log1000+ =X 30,GO0
10~ ti = 5.70
Then
Shnilarly,
T 10S t-j,(1500)= 102580
(1600) = 9320
(1700) = 8650
Theplotof”T’logti againstT Isofthestra~Zghtlineobtainedis
Theintercept
Equation(14)valueaof A
B= 10,420 - 90501900 - 21O(I
is
giveninfigure9. Theslope
= -6.950”
A= 10,420 - (-6.95x 1900)
was used,withthevalueof
= 23,630
D at 1800° F andtheand B ~ustdetermined,toobtainthestress-rupture
curvefor1800°F that-isshownpI.ott&dinfigure4 asa dotte~line.Theexperimentalpointsaregivenby thesymbolo andgivea measureof theaccuracythatcanbeo%tainedusingequations(14)and(15)topredictstress-rupturedata. It shouldbe notedthatthepredictedvaluesfallwithinthereproducibilityof*25percentfour!!by reference7. Thisreproducibilityfigurewasobtainedfroma duplioateseriesof stress-rupturetestsof specimenstakenfromtheseineheat.
Thenumberof stress-ruptureteststhatarerequiredatpresentcanbemateriallyreduoed%y usingthemethodjustdescribedtopre-dictdataatnewtemperatures.Specifically,ifit isdesiredtoextendthestress-rupturedatatohighertemperatures,it isneces-saryaccordingtopresentmethodsto obtainvaluesof ~ forat
14
PW2ATNNO. 1126
leastfourdifferentstressesat thehighertemperatureinorderto‘keabletoplota curveof lo~tr againstlog0. IfvaluesofA, B,E, andF werecomputedforthisalloyfromtheavailabledata,thenonlyonetestat thehighertemperaturewouldbe requiredto checkwhetherthealloystructurewasstableat thishighertem-perature.IXthealloystructurewasfoundtobe stable,thatis,tk.eeqerimental.valueof tr at thehighertemperaturecheckedwithinexperimentalerrorwiththevaluepredicted3Y equations(14)and(15),the~-theequationscouldbe usedforpredictingthestressdependenceoftheruptt:retimeat thishighertemperature.Thus,abouttlu?ee-fourthsoftheadditionalstress-rupturetestswouldbeeliminated.
Themetallurgistwhoprformsstress-rupturetestsimordertoratetheheat-resistingpropertiesofalloyscannowmakeuseof thefourparametersA,B, E, andF as a meansofratingthealloys.~ ordertohavelongrupturelives(hi@ tr)at co~tantstressandtemperature,it isnecessarythat Aand Bbelargeand E andFsmall.(Seeequations(14)and(15).) Wen A and B arelargerand E and F aresmallersimultaneouslyforonealloythanforaiiother,thefirstalloywillhavelongerrupturelifeovertherangeof stressandtemperaturewherethevaluesof A,B, E, andF apply.Wherethefourparametersdonotcompareinthissi?nylefashion,thestress-mptureratingsofvariousalloyswillgenerallynothethesamefordifferentranges& stressandtemperature.Thesoallayscanthereforebe ratedonlywithrespectto their~roposeduse. For~~ple, alloysforgas-turbinebucketscanberatedonthebasisof thedesigntemperatureandstress.Valuesoftheabruc-tmreparameterscanthenbe usedtoobtaineasilyan orderofmeritrattngat thesetof CGnditiOnSthatcorrespondto theproposeduse.
RECOMMENWTION
It isreconmsndedthatthemethodofpresentingstress-rupturedataona smilogplot(logaritbmofrupturetimeagainststress),whichhasa basisintheory,be investigatedforuseinpiacoofthepresentempiricalmethodofpresentingstress-rupturedataonlog-logplotsoftimeforruptureagainststress.Inaddition,theuseofthestress-ruptureequationspresortedinthisreportarereconmmndodtopermittenperaturointerpolationandextrapolationandtorGducothenumberof stress-rupturetestsrequired.
AircraftEngineResearchLaboratoW,NationalAdvisoryCo?mnittcmforAeronautics,
Cleveland,OhiojFoln?uary8, 1946.15
NACATN ~~0. 1126
REFERmm
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1.Cross,HowardC.,smdSimnons,WardI’.:ProgressReportonHeat-ResistingMetalsforGas-Turb*ineParts(N-102).OSRDNo.4717,Ser.No.M-477,NDRC,(EID,WarMetallurgyComm5ttee,Feb.20,1945●
2.White,A.E.,ClarkjC.L.,andWilson,R. L.: TheRuptueStrengthofSteelsatXlevatedTemperatures.Am.Sot.MeklsTrans.,VO~. 26,M5Q’oh1939,PP.52-69;discussion,PP+69-!30.
3.White,A.E.,Clark,C.L.,andWilson,R.L.: ‘llneFractureofCarbonSteelsat ElevatedTemperatures.Am.SOC.Mstils.Trans.)vol.25,Sept.,1937,pp.863-884;discussionPP.~85-888.
4.Freeman,J.W.,Rote,F. E.,andWhitebA.X.: Hi@ TemperatureCharacteristicsof 17AlloFsat i200 and1350°F. NACAACE?No.4C22,1.944.
5.Glasstone,Samuel,Laidler,KeithJ.,andEyring,Henry:TheTheoryofRateProcesses.Chs.1,IV,VII. McGraw-HillBookCo.,Inc.,1$?41>pp.1-27,153.-201,477-551.
6.Nowick,A. S.,andMadilin,ii.S,: QuantitativeTreatmentof theCreep05MetalsbyDislocationandRate-ProcessTheories.NACATNNo. 1C39,1946.
7S Anono:StatisticalAnalysism?Effectof ChemicalCompositiononStress-RuptureProperties ofa GYoupofAlloysTestedatM.1.T’.AMPRep.122.lR,SRGRep.485,Colu?ibiaUniv.,Statis-ticalRes.Group,Aypl.l.hth.Panel,NDRC,May1945.
8.Harrin$ton,R. H.: TheRoleof StraininPreclpftationReactimsInAlloys.AgeHarden@ ~~Metals,SymposiumonprecipitationHard5ning,Twenty-FirstAnnualConvention,Am.Sec.Metals(Chicago), Ott.23-27,1S39,pp.314-340;discussion,p. 341.
9.‘TMelemmn,R. H.,andParkeu,33.R.: FractureofSteelsatElevatedTemperaturesafterProlcngedLoading.Tech.Pub.1034,Trans.Am.Inst.MiningandMetallurgicalEng.,IronandSteell?iv.,VO1. 135,1939,gp.559-575;discussion,pP.576-582.
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