NASA NACA-TN-2924-1953 Combined-stress fatigue strength of 76S-T61 aluminum alloy with superimposed mean stresses and corrections for yielding《带有叠加平均应力和可缩性更正的76S-T61铝合金的联合应力疲劳强度》.pdf

1、mO=gIFmEmNATIONALADVISORYCOMMITTEEFORAERONAUTICS -e=90 fortwistingonly)shearstressatpointofhigheststressoctahedralshearstressjoiningpointofspecimen;seeforbendinginspecimensfatiguefatigueappliedbendinglimitstrengthinbendingstrengthintorsionbendingmomentmomentwhenmaximumstrainisatproportionalslopeofdi

2、mensionlessstress-straincurveaboveproportionallimitformattheresultingbendingortwistingstressescausedbyanisotropywillbelinearflmctionsofthenominalbendingortwistingstresses,respectively;andtheresultingbendingandtwistingstresseswillbethesamefunctionsofthenominalstressesregardlessofthecombinationofbendi

3、ngandtwistingemployed.Undertheseconditionsonecanthenreexaminealloftherationaltheoriesofinelasticaction(whichrequirespecificvaluesoftheratiob/t)bymultiplyingthenominaltwistingstressT byacorrec-tionconstantforeachmaterialsuchthattheresultingequationsatisfiestheconditionsforpurebendingandpuretwisting.A

4、 correc-tionconstantcouldhavebeenappliedtothebendingstressinsteadoftothetwistingstressortobothstresses;theresultwouldhavebeenthesame.Forexample,thetheoryofalimitingprincipalshearingstressmaybewrittenforcombinedbendingandtorsionasfollows:Thisequationrequiresthatb/t=2, asisshownbytionforthecasesofpure

5、bendingandpuretorsion.accordancewiththeabovesuggestionsonecancorrectmultiplyingeveryvaluewherebl and tl areof T introducedinequation.(5)solvingtheequa-Thereforeinforanisotropyby- “- -(5)by bl/2tlthemeasuredvalues of thefatiguestrengthin .Provided by IHSNot for ResaleNo reproduction or networking per

6、mitted without license from IHS-,-,-:Q NACATN2924 25. bendingandintorsion,respectively.Thenuniberofcyclesforwhichhland tl aredeterminedarethesameasthenuniberwhichereexpectedtoproducefailureunderthegivenvaluesof u and T. Iftheadjusted. valueT1=b17/2t1issubstitutedinequationresults:(5)thefollowingequa

7、tion()b12T2=t (6)Thisequationmayberationalizedandrewrittenas(7)theellipse-quadrantequation(seetableIII)bqwhichisidenticalwith. sinceforpuretwistinga71fromwhich._Thustheellipsequadrantmaybeconsideredtobearationalizedequationforthelimitingprincipalshesringstresswithacorrectionforanisotropyapplicablefo

8、rthesyecialtypeoftestingandorienta-tionofspecimensconsidered.Ofcourse,proofoftheeffectofsni-sotropymustbesoughtbeforethevalidityofthea%oveexplanationmaybedemonstrated.Inasimilarwaythiscorrectionmaybeappliedtotheotherrationaltheoriesoffailure.Thevaluesof b/t requiredbythesetheoriesandtheresultingequa

9、tionsaregivenintableIII.Itissignificanttonotethattheequationsforsixofthesetheories,whenrationalized,sreidenticaltotheempiricalequationproposedbyGough-theellipse-quadrantequation.Thesixtheoriesare:.(1)Principalshearstress(2)Principalshearstrain(3) tiergyofdistortion(4)OctahedralshearstressProvided by

10、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26 NACATN2924(5)Totalenergyofdeformation.:(6)Magnitudeofstate-of-stressvectorThetheorieswhoserationalizedequations(withcorrectionforanisotropy)differfromtheellipsequadrantare:(1)Principalstress(2)PrincipalstrainEF

11、FECTOFMEANSTRESSANDSTATEOFSTISSCONSIDERINGANISOTROPYMeanStressSincesixofthetheoriesareidenticalinform(withinthestatesofstresscoveredbycombinedbendingandfbrsion)whencorrectedforanisotropythecurvesforonlyoneofthesixneedtobeplotted.Thetheoryofalimitingprincipalshearstresswasselectedbecauseofitspossibil

12、itiesasshownbythereviewoftheliteratureandbecauseoftheconsiderationsdiscussedinthenextsection.Theeffectofmeanstressisshowninfigures32to34fortheprincipal-shear-stresstheorywithcorrectionforanisotropy.Thevaluesof b and t usedincorrectingforbothalternatingandmeanstresseswerethevaluesofthebendingandtwist

13、ingfatiguestrehgths,respectively,atzeromeanstressandthegivennumberof-cycles.Thereisnoreasontothinkthatthevaluesof b and t areanymoreaccuratethanthefatiguestrengthatanycombinationofbendingandtwisting.Thusacertainlatitudecommensuratewiththescatterofthedatamightbeallowedinthevalueof b/t usedincorrectin

14、gforanisotropyifindicatedbythetrendofdataforcombinedbendingandtorsion. -.Thedisagreementwhichexistsinfigures32and34betweentheeldstrengthandthemaximumstressbeyondwhichthefatiguestrength - decreasesmarkedlymaybetheresultofcorrectingboththefatigue-strengthandmean-stressvaluesforanisotropy.Anexcellentco

15、rrelationwasobservedbetweentheyieldstrengthsfromstatictestsandresultspredictedbytheprincipal-sheartheoryasmentionedearlier.Thissuggeststhattheoriginalmaterialmayhavebeennemlyisotropicasfarasgeneralyieldingisconcernedandthatthematerialmayhavebeenaaisotropiconlyatthelevelofthelocalizedactionwhichiniti

16、atesfatiguefailure.Ifthisisthecasethenthecorrectionforanisotropyshouldhavebeenappliedonlytothealternatingcomponentsofthestress.Thisrevisiondoesnotaffectthediagramforbending,figure32,butdoesaffectfigures33and34. ThereviseddiagrsmfortorsionisshowninProvided by IHSNot for ResaleNo reproduction or netwo

17、rking permitted without license from IHS-,-,-NACATN2924 27. figure35. Theapparenteffectofyieldingonthefatiguestrengthresultingfromahighmeanstressisinbetteragreementwithstaticyieldinginfigure35.ThesamereasoningwhenappliedtotheGuesttheoryhadasimilarresultalthoughtheagreementwasnotsofavorable.Themagnit

18、udeofthecorrectionforyieldinganditseffectonthediagramofsmplitudeofstressagainstmeanstressareillustratedinfigures32snd34 in whichbothcorrectedanduncorrectedvaluesareplotted.StateofStressatDifferentMeanStressesFromordinatesatfourvaluesofmeanstressindiagramssuchasfigure35andfromthedataatotherstatesofst

19、ressforzeromeanstress,diagramsshowingtheeffectofstateofstresswereconstructedasshowninfigure36forthetheoryofa limitingvalueofprincipalshearstress(withacorrectionforanisotrophyappliedtothealter-natingstress).Anexaminationoffigure36r”Tedthatthistheoryisacloserrepresentationofthetestdatathan therconside

20、red,withthepossibleexceptionofGuesttslaw.Itshouldberecalled,however,thatthealternatingvaluesarethesame,exceptforaconstantfactor,forsixofthetheories-notjusttheshear-stresstheory.Thedia-gramsformeanstressesabovezeroare,however,dependentontheshear-stresstheory(orshear-straintheory,whichisidentical)sinc

21、ethemeanstressdoesnotcontainacorrectionforanisotropy.Theprincipal-stresstheoryandprincipal-straintheorywithcorrec-tionforanisotropywerealsoconsideredforzeromeanstress.Theagreementwiththetestdatawasnotnearlysogoodasfortheprincipal-shesr-stresstheorycorrectedforanisotropy.Theeffectofthecorrectionforyi

22、eldingisindicatedinfigure36byshowingtheordinatestoboththecorrectedanduncorrectedcurvesofalternatingagainstmeanstress.Whenthecorrectionsforanisotrophyandthedataforallstatesofconibinedstress,allvaluesofmeanstress,andallcyclestofailurewereconsidered,thetheoriesoffatiguefailurewerefoundtohavethefol-lowi

23、ngorderofmerit(wherethefirsttheoryrepresentsthetestdatatheclosest):(1)(2)(3)(4)(5)Principalshearstress(principalshearstrain,etc.)correctedforanisotrophyCompleteGuestlawPrincipalstraincorrectedforanisotrophyMagnitudeofstate-of-stressvectorTotalstrainenergyProvided by IHSNot for ResaleNo reproduction

24、or networking permitted without license from IHS-,-,-28 NACATN2924ENERGYANDOTHERCONSIDERATIONS sOfthesixtheorieswhoseequations_orendg.andtorsionbecome widenticalwhencorrectedforisotropytwoarebasedonanenergycon-cept.Also,evenwithoutcorrectionforenisotropy,energytheoriesrankhighintheorderoftherational

25、theories(seesectionentitled .-“EffectofStateofStress”).EnergyasaScalarThereareanumberofobservationswhichseemincompatiblewithenergyconcepts.Energyisascalarqusmt”itysothatthecharacteristicsofstrainenergyareindependentoforientationoftheprincipalstressesrelativetothematerial.Thusanisotropyinthematerials

26、houldnotaffecttheresultsoffatiguetestsofspecimenshavingdifferentorien-tationsifenergyisthecriterionoffatiguefailure.However,datareferredtointhesectionentitled“Data-onIsotropyinFatigueofMetals”indicatethatorientationprobablyaffectstheresultsoffatiguetests.Microscopicstudieshaveindicatedthatslipbandsa

27、representinthevicinityoffatiguecracksandthattheyprobablyprecedeactual .-.-fatiguecracks.Thisbeingthecase,theorientationofstress(orforces)wouldseemtobeanimportantfactorintheoriginoffatigue wcracking.Thusonemightquestionwhetherascalarquantitysuchasenergycouldbeacontrollingfactor.IthasbeensuggestedbyFo

28、wler(inaprivatediscussion)thatenergytheoriesmightbetestedifonecoulddeviseameansofmaintainingthestateandintensityofstressconstant-inaspecimen(nofluctuationinstress)sndfluctuatetheorientationoftheprincipalstressaxeswithrespecttothespecimen.Fatiguefracturemightormightnotoccurathighstresses,accordingtow

29、hetherorientakio-io-fs-tressingisorisnotafactorinthefatiguephenomena.It.seemstothewriterthatfatiguewouldveryprobablyoccur.Suchatestmightbeaccomplishedbyusingadiskasaspecimen.Thediskshouldhaveaheavyrimandbedishedonbothsidessothatwhenloadeddiametrallytherewouldbeasectionofuniformhighstressinthecenterw

30、hosestateofstresswasbiaxial(anunequaltensionandcompression).Ifthediskisloadedthroughrollerssndrotatedunderloadthestrainenergyinthehigh-stressportionofthediskwouldremainconstantbuttheprincipalstressdirectionswouldrotatewithrespecttothedisk.Insuchatestifeitherthestateofstressorthematerialis .isotropic

31、nothingshouldhappen,butifbothereanisotropicitshouldbepossibletoproducefatiguefracture.Thisshouldbetrueeven .thoughthematerialis statisticallyisotropicsincefatiguefractureoriginatesfromphenomenaoccurring in individualgrains,whoseproper-tiesme knowntobeanisotropic.Provided by IHSNot for ResaleNo repro

32、duction or networking permitted without license from IHS-,-,-NACATN292 29. Inviewoftheaboveitwouldseemthat correctionofanisotropictheorysuchasanenergytheoryforanisotropyismeaningless.This. leadsonetosuspectthatenergytheoriesarenotapplicabletothisproblem,orthattheconceptofenergyasascalarmustbemodifie

33、d.StrainEnerandMeanStressAnotherdifficultyarisesintryingtoapplytheenergytheorytotheproblemwhenthemeanstressisnotzero.Thevariationofstrainenergywithtimewhencalculatdfromstressesmustbebasedonthevariationofthetotalstress,notonthevariationofcomponentssuchasalternatingandmeanstress.Residualstressesmustal

34、sobeaddedtotheappliedstressesbeforecalculatingtheenergy.Ifthisisnotdonelsrgeerrorsinenergywillresultsincestressesaresquaredincomputingthestrainenergy.Thusdiagramssuchasfigures26to28inwhichthealternatingandmeantotalenergiesarecomputeddirectlyfromthealternatingandmeanstresses,respectively,donotpresent

35、thecor-rectrelationbetweenthecomponentsofenergy.Anattempttopresentamoreaccuratepictureoftheenergyrelation. distlosesthefollowingdifficulties:(1) Whentheminimumstressofthecycleisofthesamesignasthemaximumstressthereisnodifficultyotherthanthattheenergycycleisnotsinusoidalasthestresscyclewas.Themaximume

36、nergyiscalcu-latedfromthemaximumstressandtheminimumenergyfromtheminimumstress.Thealternatingandmeanenergiesarecalculatedashalfthedifferenceandhalfthesumofthesemaximumsandminimums.(2)Sinceenergyisascalsxandalwayspositiveacompletelyreversedsinusoidalcycleofstresswillproducenotacompletelyreversedcycleo

37、fstrainenergybutacycleofenergyvaryingfromzero(atzerostress)toamaximum(atbothmaximumandminimumstress)whichisnotsinusoidalandhasafrequencytwicethefrequencyofthestresscycle.Thusthetotalnumberofenergycyclessustainedbeforefractureistwicethetotalnuniberofstresscyclessustained.Thesefactshavenotbeendiscusse

38、d(asfarasislmown)inpreviousstudiesofenergytheoriesoffailureappliedtofatigue.(3)men thestressduringthecycleispartlyofonesignbutnmstlyoftheoppositesign,theenergycycleconsistsoftwoalternatepulsesofthesamesignbutdifferentmagnitude.Thefrequencyofthelargerpulseisthesameasthatofthestresscycle.Whentheabovef

39、actorsaretakenintoaccountanewdiagramrepre- ._sentingtheactualalternatingenergyagainstactualmeanenergymaybeconstructedasshowninfigure37.Thisisaccomplishedby(a)computingthealternatingandmeanenergiesasdescribedinitem(1)above,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-