,—

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

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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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