FrettingWearandFrettingFatigue
FundamentalPrinciplesandApplications
Editedby TomaszLiskiewicz DanieleDini
Elsevier
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Contributors
MagdAbdelWahab LaboratorySoete,FacultyofEngineeringandArchitecture, GhentUniversity,Ghent,Belgium
JoseAlexanderArau ´ jo DepartmentofMechanicalEngineering—ENM,Facultyof Technology—FT,UniversityofBrası´lia—UnB,Brası´lia,Brazil
M.HelmiAttia AerospaceManufacturingTechnologyCenter,Institutefor AerospaceResearch,NationalResearchCouncilofCanada,Ottawa,ON;Mechanical EngineeringDepartment,McGillUniversity,Montreal,QC,Canada
AndrewR.Beadling InstituteofFunctionalSurfaces,SchoolofMechanical Engineering,UniversityofLeeds,Leeds,UnitedKingdom
BenD.Beake ApplicationsDevelopment,MicroMaterialsLtd,Wrexham,Wales, UnitedKingdom
AliBeheshti DepartmentofMechanicalEngineering,GeorgeMasonUniversity, Fairfax,VA,UnitedStates
NadeemAliBhatti LaboratorySoete,FacultyofEngineeringandArchitecture, GhentUniversity,Ghent,Belgium
MichaelG.Bryant InstituteofFunctionalSurfaces,SchoolofMechanical Engineering,UniversityofLeeds,Leeds,UnitedKingdom
Fa ´ bioComesCastro DepartmentofMechanicalEngineering—ENM,Facultyof Technology—FT,UniversityofBrası´lia—UnB,Brası´lia,Brazil
AdrianConnaire Woodplc,Parkmore,Galway,Ireland
PascaleCorne MinesSaint-Etienne,Saint-Etienne,France
IandeMedeirosMatos DepartmentofMechanicalEngineering—ENM,Facultyof Technology—FT,UniversityofBrası´lia—UnB,Brası´lia,Brazil
DanieleDini ImperialCollegeLondon,FacultyofEngineering,Departmentof MechanicalEngineering,London,UnitedKingdom
JaimeDomı ´ nguez UniversidaddeSevilla,Sevilla,Spain
JorgeLuizDeAlmeidaFerreira DepartmentofMechanicalEngineering—ENM, FacultyofTechnology—FT,UniversityofBrası´lia—UnB,Brası´lia,Brazil
SiegfriedFouvry LTDS,EcoleCentraledeLyon,Ecully,France
JeanGeringer MinesSaint-Etienne,Saint-Etienne,France
AntoniosE.Giannakopoulos MechanicsDivision,NationalTechnicalUniversityof Athens,Athens,Greece
AnnetteM.Harte RyanInstituteforMarine,EnergyandEnvironment; CivilEngineering,SchoolofEngineering,NUIGalway,H91HX31,Ireland
ToshioHattori GifuUniversity,Gifu-City,Japan
DavidA.Hills DepartmentofEngineeringScience,UniversityofOxford,Oxford, UnitedKingdom
IlkwangJang SchoolofMechanicalEngineering,YonseiUniversity,Seoul, RepublicofKorea
YongHoonJang SchoolofMechanicalEngineering,YonseiUniversity,Seoul, RepublicofKorea
RachelJanuszewski DepartmentofMechanicalEngineering,ImperialCollege London,London,UnitedKingdom
MurugesanJayaprakash DepartmentofMetallurgyandMaterialsEngineering, IndianInstituteofTechnologyIndore,Indore,India
HyeonggeunJo SchoolofMechanicalEngineering,YonseiUniversity,Seoul, RepublicofKorea
AmirKadiric DepartmentofMechanicalEngineering,ImperialCollegeLondon, London,UnitedKingdom
RemyBadibangaKalombo DepartmentofMechanicalEngineering—ENM,Faculty ofTechnology—FT,UniversityofBrası´lia—UnB,Brası´lia,Brazil
ChaosuanKanchanomai DepartmentofMechanicalEngineering,Facultyof Engineering,ThammasatUniversity,Pathumthani,Thailand
ThawhidKhan ManchesterMetropolitanUniversity,FacultyofScienceand Engineering,DepartmentofEngineering,Manchester,UnitedKingdom
MichaelM.Khonsari DepartmentofMechanicalandIndustrialEngineering, LouisianaStateUniversity,BatonRouge,LA,UnitedStates
KrzysztofJ.Kubiak SchoolofMechanicalEngineering,UniversityofLeeds,Leeds, UnitedKingdom
Sea ´ nB.Leen MechanicalEngineering,SchoolofEngineering;RyanInstitutefor Marine,EnergyandEnvironment,NUIGalway,H91HX31;I-FormCentrefor AdvancedManufacturing,Ireland
TomaszLiskiewicz ManchesterMetropolitanUniversity,FacultyofScienceand Engineering,DepartmentofEngineering,Manchester,UnitedKingdom
YanfeiLiu BeijingInstituteofTechnology,SchoolofMechanicalEngineering, Beijing,China
TaisukeMaruyama CoreTechnologyR&DCenter,NSKLtd.,Tokyo,Japan
ThomasG.Mathia LTDS,EcoleCentraledeLyon,Ecully,France
AllanMatthews UniversityofManchester,Manchester,UnitedKingdom
MatthewR.Moore DepartmentofPhysics&Mathematics,UniversityofHull, Kingston-Upon-Hull;MathematicalInstitute,UniversityofOxford,Radcliffe ObservatoryQuarter,Oxford,UnitedKingdom
YoshiharuMutoh DepartmentofSystemSafety,NagaokaUniversityofTechnology, Nagaoka,Niigata,Japan
CarlosNavarro UniversidaddeSevilla,Sevilla,Spain
DavidNowell DepartmentofMechanicalEngineering,ImperialCollegeLondon, SouthKensingtonCampus,London,UnitedKingdom
SineadM.O’Halloran RyanInstituteforMarine,EnergyandEnvironment,NUI Galway,H91HX31;SEAMResearchCentre,SchoolofEngineering,Waterford InstituteofTechnology,Waterford,X91TX03,Ireland
AbimbolaOladukon InstituteofFunctionalSurfaces,SchoolofMechanical Engineering,UniversityofLeeds,Leeds,UnitedKingdom
xvi Contributors
YoungwooPark LGElectronicsVehicleComponentsUSA,Troy,MI,UnitedStates
KyviaPereira LaboratorySoete,FacultyofEngineeringandArchitecture,Ghent University,Ghent,Belgium
JohnSchofield ConsultantinStructuralIntegrity,Derby,UnitedKingdom
PhilipHowardShipway FacultyofEngineering,UniversityofNottingham, Nottingham,UnitedKingdom
Jesu ´ sVa ´ zquez UniversidaddeSevilla,Sevilla,Spain
AndreyVoevodin UniversityofNorthTexas,Denton,TX,UnitedStates
AlekseyYerokhin UniversityofManchester,Manchester,UnitedKingdom
ThanasisZisis MechanicsDivision,NationalTechnicalUniversityofAthens, Athens,Greece
Preface
Appliedresearchinfrettingwearandfrettingfatiguehasgainedsignificantmomentuminrecentyears;however,thereisnosinglereferencebookcurrentlyavailablethat caneducateresearchersinacomprehensivewayonbothwearandfatigueaspectsof thefrettingphenomenon.Hence,thisbooktakesacombinedmechanicsandmaterials approach,providingreaderswithfundamentalunderstandingoffretting,related modelingandexperimentationtechniques,methodsfordesignandmitigationagainst fretting,androbustexamplesofpracticalapplicationsacrossanarrayofengineering disciplines.
Theaimofthebookwastobringtogether,systematicallyinasinglevolume,the state-of-the-artknowledgeonfretting.Thiswasachievedthroughacollaborative approachbetweentwoeditorsspecializingindifferentaspectsoffretting.Oftenrecognizedastwodistinctareasofresearch,frettingwearandfrettingfatigueare addressedinonevolumeforthefirsttime.Thiscreatesauniquesynergyandopportunitytoexpandhorizonsandlearn.
Weassembledthebestexpertsinthefieldtocontributetothisproject,manyof whomaremembersoftheInternationalSymposiumonFrettingFatigue(ISFF)community.Webelievethatthisbookcanbeakeyreferenceforstudentsandscholars fromdiversescienceandengineeringbackgroundssuchasthosefrommechanical engineering,materialsscience,structuraldesign,andmanymore.Wehopethebook willalsobeofusetopractitionersandengineerswhofrequentlyencounterfrettingrelatedproblems,andwhorequiretimely,butadequatesolutions.
Wetriedtopresentthecontentsinalogical,easilyassimilatedmanner.Thisbook containsfivesectionswrittencarefullytocoverthefundamentalaspectsaswellasthe keytheoreticaldevelopmentsandexperimentalmethodologiesassociatedwithfrettingwearandfrettingfatigue.Thefirstsectionofthisbookintroducesthereader tothehistoricalaspectsoffretting,providingausefulstartingpointandbackground totherestofthebook.Thesecondsectiondiscussestheunderpinningbasictheories, providingagoodintroductiontothesubjecttoanylearnernewtofretting.Thethird andfourthsectionsofthebookpresentcontributionsthatcoverdifferentfacetsand provideacompletein-depthunderstandingoffrettingwearandfrettingfatigue, respectively.Thesubsequentsevenchaptersinsectionfiveofthebookarededicated tothestudiesofsomeofthemainapplicationswhereunderstandingoffrettingphenomenacontributestoimprovedengineeringdesignandpractice.
Thisbookismeanttobeanactivesourceofreference,whichareadercanflip throughtofindusefulguidanceonspecifictopicswhenthereisaneedforsome perspectiveoradvice.Thefundamentalsoffrettingarecoveredinsectiontwo;however,whenitisimportantforthecontext,somebasictheoriesarealsodiscussedinthe subsequentchapters.Therewillbesomedegreeofrepetitionbetweenthechapters,
whichresultsfromthefactthateverychapterisastand-alonecontributionmeantto provideafullunderstandingofagiventopic.Thereaderisalsoadvisedtopayattentiontothenomenclatureusedbythecontributors,asthismightdifferbetweenthe chapters.Weacceptedthisfact,asitspansfromcommonpracticeinafield approachedbyscientistsfromdifferentbackgrounds,anddidnottrytomanipulate thenomenclature,asanyattempttocreateafrettingunifiedglossaryandlistofsymbolswouldbeuntruetothefieldandcouldcauseadegreeofconfusion.
Theeditorsarethankfultoallcontributingauthorsforagreeingtobeapartofthis project.ThisisespeciallyappreciatedasthebookwaseditedduringtheCOVID-19 globalpandemic,whenallofuswerepresentedwithunprecedentedcircumstances andchallenges.Wealsothankcolleaguesandassociatesworldwidewhohaveoffered helpfulcommentsandsuggestionsforimprovementofthetext.Inparticular,we acknowledgesupportandencouragementfromourfamiliesintheprocessofcompletingthisbook.
DanieleDini
ManchesterandLondon
June2022
TomaszLiskiewicz
1.2Initialmilestonesintheunderstanding ofthemechanicsoffretting
Althoughitwasnotalwaysrecognizedinthesetermsatthetime,manyofusnow thinkofthefrettingproblemasbeingsplitintothreeparts,eachcapableofindependentstudy.Firstly,thefrettingprocessitselfinvolvesthereciprocatingmotionofone contactingsurface(orpartofonesurface)overanother.Thishasbeenthesubjectof muchmathematicalanalysissincethepioneeringworkofCattaneointhe1930s (Cattaneo,1938),rediscoveredbyMindlininthe1940s(Mindlin,1949).Secondly, thepresenceofdifferentialmotionmodifiesthesurfaces,causingwear,andmay beinstrumentalincontrollingtheconditionsunderwhichcracksnucleate.Lastly, thepresenceofcontactstresseswillhaveanimportanteffectontheearlypropagation ofcracks,untilthetipgrowsoutoftheinfluenceofthecontactstressfield.Itiseasy,in hindsight,toseethingsinthisway,butwemustrememberthatfracturemechanics itselfwasstillfarfromfullydevelopedinthe1950s,sothateventhepropagation aspectoftheproblemwasstillasubjectofstudy.The1950sarethereforethefirst goldenageforfrettingresearch,whichcoincidedwiththeboomingofthestudies inallthreekeyaspectsthatcharacterizefretting: BowdenandTabor(1950) published PartIoftheirclassicworkonfrictionandlubricationofsolids,thefieldsoffatigueand fracturemechanicssawaplethoraofdevelopments(Irwin,1948; Orowan,1949; Bishop,1955; Gordon,1978)andArchardformulateditswearlaw(Archard,1953; ArchardandHirst,1956).
In1952,FengandRightmireproposedatheoryonfrettingmechanisms(Fengand Rightmire,1952).Aswell,Wrightandcoworkers(Wright,1952a,b; Fenneretal., 1956)performedextensivestudiesontheroleofoxidationinfrettingandrecognized thatferricoxidewasseparatingthetwooriginalsurfaces.Theyobservedthattheformationofoxidesacceleratedthedevelopmentoffrettingdamage.Withmostofthe studiesfocusedontheimportanceofoxidationandcorrosioninfretting,by1952 enoughprogresshadbeenmadetoorganizeanASTMsymposiumonfrettingcorrosion(ASTM,1952),consistingoftheeffectoftheinteractionbetweenfrettingand corrosioninreducingthefatiguelifeofmechanicalcomponents.Thiswasalandmark eventbecauseitbroughttogetherinvestigatorsinthefieldandprovidedfocusanda stimulusforadditionalactivity.Fivepaperswerepresentedatthissymposium.Itis interestingtonotethattermsthatwereusedtodescribefrettingatthismeetingwere: (i)frictionoxidation,(ii)wearoxidation,(iii)falsebrinelling,(iv)bleeding,and (v)cocoa.Subsequently, Horger(1953), Uhligetal.(1953a,b), Uhlig(1954), Waterhouse(1955),and Corten(1955) alsomadeimportantcontributionsinthisarea.
Studiesby McDowell(1953) pointedoutthatthecombinedeffectsoffrettingwear andfatigueweresevere,withaquantificationoftheeffecttentativelyprovidedthat showedareductioninstrengthbyafactorvaryingfrom2to5orevenmore.The absenceofdistinctfrettingfatiguelimitssuchasthosefoundinplainfatiguetests (OrdingandIvanova,1956)inducedsomeresearcherstostatethatitwaspossible tofindsomeanalogiesbetweenfrettingfatigueandcorrosionfatigue(Horger, 1956).SeveralpapersonfrettingfatiguewerepresentedattheInternationalConferenceonFatigue—reportedin1956(OrdingandIvanova,1956). HallidayandHirst (1956) and Liuetal.(1957) alsomadeimportantcontributions.Inthelate1950s, FennerandField(1958,1960) carriedoutabasicinvestigationoffrettingdamage. Theirworkshowedaseriesofinnovationsandconceptsthatstillconstitutethebackgroundofmostoftheresearchcarriedoutinthisfield.Notonlyweretheythefirstto demonstratethatfrettingacceleratedcrackinitiation,buttheywerealsoamongthe firsttousea“bridge”typeoffrettingpadwithtwoflatsurfaces,whichwastobecome popularwithseveralresearchers(e.g., Doeser,1981; Edwards,1981a).However,it hastobenotedthatuptothemid-to-late1960sverylittleunderstandingoftheimportanceoffrettingandknowledgeofthecharacteristicparametersgoverningthephenomenonhadbeenachieved.Inparticular,furtherexaminationsoftheinfluenceof parameterssuchascontactpressure,contactsize,relativeslipdisplacementamplitude,environmentalcondition,frettingwear,andstressconcentrationonfretting strengthwereneeded.
By1963,thefieldoffrettingcorrosionhadreachedsuchconcernthattheUSArmy issuedamajorliteraturereview(ComynandFurlani,1963).Shortlythereafter, BowdenandTabor(1964) publishedPartIIoftheFrictionandLubricationofSolids. PartsIandIIofthisclassichavehadagreatinfluenceontheevolutionofknowledge onfrettingwearandfrettingfatigue.Oneofthepioneersofexperimentalworkinthe fieldwasRobertWaterhouse,whostartedtomakehismarkintheearly1960s (Waterhouse,1961; Waterhouseetal.,1962).Onlyin1965,when Waterhouseand Allery(1965) testedthedependenceofmaterialstrengthonfrettingcorrosion,was itshownthattherewasnocorrelationbetweentherateofoccurrenceofcorrosion andthereductionoffatiguestrength.Theseresearcherschangedtherateoffretting corrosionbytestingthesamematerialunderfrettingconditionsinatmosphereand ininertgas,butthereductionofcorrosiondidnotgiverisetoafatiguestrength increase.
1.3Crucialstepstowardabetterunderstanding
offrettingwearandfrettingfatigue
Aturningpointintheresearchfieldcanbeidentifiedinthecomprehensiveseriesof testsandstudiesundertakeninthelate1960sby Nishiokaetal.(1968) and Nishioka andHirakawa(1969a,b,c,d,1972) usingcylindricalsteelpadsandsteelspecimens. Theyexaminedtheinfluenceofmanyofthefactorsreportedaboveindependently.
Themostimportantconclusionoftheirfirstpaperwasthesmallinfluenceofthefrequencyofcyclicloadingonthelifeoffrettedspecimens.Inthefollowingseriesof papers,theyreportedtheexistenceofnonpropagatingfrettingfatiguecracks[asalso observedin WaterhouseandAllery(1965) and FennerandField(1958)],suggesting that,althoughfrettingmayassisttheinitiationandinitialgrowthofcracks,theremay becombinationsofotherparametersunderwhichthesecracksself-arrest.Another conclusionreachedwasthattheamountofrelativeslipbetweenthesurfacesinfluencesfatiguelife.Below5 μmofslipdisplacement,thereappearedtobelittlereductioninlifeinthepresenceoffretting.Between5and50 μm,thefatiguestrengthwas reducedtoaslittleas1/8ofthevalueintheabsenceoffretting.Above50 μmofslip displacement,significantweartookplaceandfatiguecrackswerenotobserved,probablybecausetheywerewornawaybeforetheycouldstarttopropagate.Anotherinterestingfindingwastheincreaseofthecoefficientoffrictionduringthefirstfewcycles oftheexperiments.Thiswasconfirmedbyotherstudies(MilestoneandJaneczko, 1981; Endoetal.,1974)andhighlightedasoneoftheessentialfeaturesofthefretting fatiguemechanisminconjunctionwithanincreaseoftherealcontactarea,as suggestedin WrightandO’Connor(1972) and Bramhall(1973).Furtherinvestigationsby NishiokaandHirakawa(1969c),highlightedtheinitiationsiteanddirection ofinitialpropagation.Crackswerefoundtostartinaregionofhighstressneartothe edgeofthecontactandtopropagateobliquelyunderthecontactduringtheinitial phaseofgrowth.Furthermore,theyfoundthatthemeancyclicstressappliedtothe specimenhadalittleeffectonthefrettingfatiguelife.Therefore,thefrettingcontributiontothetotalfatiguelifeofthecomponentsseemstoassisttheformationof embryocrackswhereastheremotebulktensionplaysthemainroleinthelaterstages ofpropagation.Intheirlastpaperoftheseriesofsix,thetworesearchersinvestigated theinfluenceofthecontactpressureanddiscoveredthesmalldependenceoffretting fatiguelifeonmaterialhardness.
In1970,thefirstpartofaNATO/AGARDmanualby Barrois(1970) emerged. Thissetthestageforhistreatiseonfrettingcorrosion( Barrois,1975 ),whichwas trulyasignificantcontributiontotheliterature.In1970, Hurricks(1970) provided anextensivereviewofthemechanismsoffrettingandnotedthatfrettingwearmechanismsinvolvedthefollowingthreestages:(i)initialadhesionandmetaltransfer, (ii)productionofdebrisinanormallyoxi dizedstate,and(iii)steady-statewear condition.
Additionalresearchby Waterhouseetal.(1971), WaterhouseandTaylor(1971), and Hurricks(1972) providedadditionalinsightintotheknowledgerelatedtothe effectoftheenvironmentonfretting.In1971,thefirstinternationalconferenceon corrosionfatiguewasheld(Devereauxetal.,1972)andnumerouspapersonfretting werepresented.Majorfrettingmechanismsofthedayandtheconceptofafretting fatiguedamagethresholdwerepresented.Ataboutthesametimethattheconference proceedingswerepublished,thefirstbookofWaterhouseemerged(Waterhouse, 1972).Thisseminalbookhasbecomeaclassicinthefieldandhasbeenusedextensivelyinthepastdecades.
Duringthe1970s,thenumberofinvestigationsinfrettingwearandfrettingfatigue increasedmarkedly.NoticeableworkscontinuedtoemergefromWaterhouseandcolleagues(see,e.g., WaterhouseandTaylor,1972; TaylorandWaterhouse,1972; WaterhouseandDutta,1973; Whartonetal.,1973a,b).Taylor’sworkwithWaterhouse(TaylorandWaterhouse,1972)onsurfacetreatmentsandthestudiesconducted atthemicroscopicscaleclearlyshowedthattheoriginoffrettingcrackswasinthe boundarybetweentheslipandnonslipregionsofthecontactarea.Intheearly 1970s,significanteffortswereagainfocusedonfrettingcorrosionandfrettingwear. Thenewconceptoffrettingthresholdswasproposedby HoeppnerandGoss(1972), whonotedthatacertainamountoffrettingdamagewasnecessarytogiverisetoany changeinthefatiguestrengthofthematerial.Byanalyzingsometestsconductedon Ti6Al4Vand7075-T6aluminum,theyshowedthatremovalofthefrettingsource afterfrettingdamagehadoccurredabovetheproposedthresholddidnotaffectthe fatiguelifeofthetestedspecimens.Lateron, EndoandGoto(1976) confirmedthe possibilityofusingfrettingthresholdsinordertopredictthedecreaseoffatiguelife duetofretting.
Atthisstage,attemptsweremadebymanyresearcherstofindguidelinesfor designingmechanicalcomponentsagainstfretting.Themicrodisplacement-based approach[firstlyproposedby Tomlinson(1927) andlateronusedasathreshold by NishiokaandHirakawa(1969b,c)]wasthemostconvenienttoolinorientating engineersfacingthiscomplexphenomenon.Predictionofthereductionoffatigue strengthbasedonfrettingmicrodisplacementsissimplebutitshouldonlybeused forqualitativerankingofmaterialcombinationsduetothedifficultiesinapplying resultsfromsimplespecimengeometriestocomplexcomponents(Lindley, 1997).Anumberofdifferentapproachesweredevelopedinthe1970sandsomeof themstillconstitutethebasisofmorerecentstudies.Anumberoffrettingmodelsproposedduringthatdecadehavebeendevelopedinthelast50years,duringwhichmany investigatorshaveaddressedtheproblemoffretting.Afewresearchershavefocused onstressconcentrationeffects(e.g., WrightandO’Connor,1972).However,the objectivedifficultyofobtaininganaccuratevaluefortheelasticstressconcentration factor, Kt,forfrictionalcontactproblems,andthefactthattheverysteepgradientsof thestressfieldandtheothercomplexaspectsofthephenomenonrequiremorecomplexmodelingthanthe Kt-basedapproach,probablydiscouragedtheearly researchers.Anotherwaytoapproachtheproblemwassuggestedby Collinsand Tovey(1972).Theyproposedamicrocrack-initiationmechanismbasedonfatigue stressconcentrationattheasperity-contactlevel.Similarmethodshavealsobeen attemptedmorerecentlyby Ballardetal.(1995) and Moobola(1998).Thesekinds ofapproacharebasedontheassumptionthateventhoughmacroscopicstresses remainelastic,microscopicstressesontheasperitylevelcanlocallyexceedyield. Inparticular, Ballardetal.(1995) analyzedthecyclicplasticresponseandpredicted crackinitiationwhentheelasticshakedownlimitwasexceeded.However,this asperity-basedmethod,asisgenerallythecasewiththeroughcontacttheories,still leavesunresolvedthequestionoftheresolutionatwhichtheroughnessismeasured.
8FrettingWearandFrettingFatigue
Whatoneseesasanasperityatonescalecanbeseenasacomplexpatternofasperities atascalejustbelow.
AdditionalresearchbegantoemergefromJapanduringthisperiodandprovidedsignificantcontributionstothefield.Theresearchof EndoandGoto(1976) isextremely importantasit,inconjunctionwiththeworkof Edwardsetal.(1977) and Hoeppner (1977),suppliedthebasisfortheapplicationoffracturemechanicstofretting.They investigatedcrackgrowthinmildsteelcylindricalfrettingpadsunderfullslipconditions.Theywereabletoseparatethreemainphasesinthecrackingprocess: (i)initiation:afirststageofcrackinitiationonshearplanes,followedveryshortly byasecondstageinwhichthecrackpropagatedinadirectionnormaltothesurface, (ii)earlypropagation:crackgrowthstronglydependentonthefrictionalforcearising inthecontact;and(iii)propagation:crackpropagationataratewellreproducedbyParis lawtakingintoaccountonlythealternateremotestressesappliedtothespecimen.These resultsshowedhowfrettingcanberesponsiblenotonlyfortheinitiationphase(asproposedby HoeppnerandGoss,1974)butalsofortheearlystageofcrackpropagation. Thisledtotheconclusionthatthefrettingtangentialforceshouldhavebeenincludedin thecalculationoftherangeofstressintensityfactorsusedintheParislaw.Another important“pieceofthepuzzle”wasaddedin1973byBramhall,whoinvestigatedvariationinthecontactsizewhilekeepingconstantthemagnitudeofthepeakcontactpressure.Analysisofsomeseriesoftheseexperimentsshowedthatfrettingsubstantially reducedfatiguelifeforcontactsizelengthaboveacertaincriticalvalue.Infact,shorter lifewasfoundforcontactdimensionslargerthanthecriticalonewhileinfinitelife (>107)wasfoundforsmallercontactsizes.Therefore,hepostulatedthatthiswas duetothehighgradientofstressesinducedinthecaseofsmallcontactlengthsthat resultsinastressfieldinsufficientlyextendedthroughoutthespecimentocauseacrack topropagatetoastagewhereitcangrowundertheinfluenceoftheremotebulkstress. Edwards(1981b) publishedanimportant,andextensive,paperontheapplicationof fracturemechanicstofretting.Thisresearch,alongwithEndoandGoto’searlierpaper andtheworkof Hoeppner(1981) andotherresearchers,hasformedthebasisforextensiveapplicationoffracturemechanicsuptothepresenttime.Morerecently, Nowell (1988) confirmedtheexistenceofacriticalcontactsizebytestingthesamematerial (4%CuAluminumalloy)recordingsomeimportantparameters,whichwerenotfully takenintoaccountbyBramhall.SimilarresultswereobtainedwithTi6Al4Valloyina furtherinvestigationby Arau ´ jo(2000).ThesamegroupatOxford,whichhasextensivelycontributedtotheliteratureinthisfieldinthelast40years(e.g., Nowelland Dini,2003;NowellandHills,1987,1990; Hillsetal.,1988; Nowell,1988; Hills, 1994; HillsandNowell,1994; HillsandFellows,1999; Mugadu,2002; Mugaduand Hills,2002; Sackfieldetal.,2002; Navarroetal.,2003; Nowelletal.,2006; Hills andAndresen,2021),hasdevelopedinthelate1980sandearly1990sadistributeddislocationmethodtocalculatethestressintensityfactorforcracksgrowingwithdifferent orientationswithrespecttothefreesurface(HillsandNowell,1994; Hillsetal.,1996), allowingtheinvestigationofthefirststageofcrackgrowth(obliqueinitialpropagation hadbeenshownby NishiokaandHirakawa(1969c) and EndoandGoto(1976) as describedabove).
Inthelate1970sandearly1980s,therewas asignificantincreaseofactivitiesand researcherspublishednumerousworksonfretting(Hoeppner,1977,1981; Reeves andHoeppner,1977,1978a,b ; HoeppnerandSalivar,1977; Waterhouse,1977, 1978,1981 ; SprolesandDuquette,1978; Czichos,1978; PoonandHoeppner, 1979; WhartonandWaterhouse,1979; Alicetal.,1979 ; AlicandHawley,1979; Barrois,1975; WaterhouseandSaunders,1979 ; Satoetal.,1980 ; Hoeppnerand Gates,1981; NATO-AGARD,1981; Edwards,1981b ).Duringthisperiod,these researchersconcludedthatfrettingispre dominantlyinfluencedbymechanicalsurfacedamage.Theconceptofthefrettingdamageenvelopeanddamagethreshold wereintroduced.Extensiveresearchwasdoneonaluminumandtitaniumalloysduringthisperiod.Also,principlesandconceptsthatcouldbeusedinengineering designthatcouldeitherpreventoralleviatefrettingwerepresented(Hoeppner, 1981; HoeppnerandGates,1981).Therelativeroleoftheenvironmentonfretting alsowasstudiedinagreatdeal.Thesystemsviewoffrettingbegantoemergeduring thisperiod,whichisextremelyhelpful inapproachingbothresearchinfretting fatigueandengineeringdesignchallengesinfretting.Thebookby Czichos (1978) isanextensivetreatiseonthesystemsapproachtothescienceandtechnologicalchallengesoftribology.
Additionalinvestigationsinthesetwoveryimportantdecadesforfrettingwere conductedbynumerousinvestigatorsandby1981amajorbookonfrettingemerged Waterhouse(1981) andanotherASTMsymposiumwasheldthatwaspublishedin 1982(ASTM,1982).Variouspapersofimportanceonenvironmentaleffectsinfrettingfatigueemergedduringthisperiod(Bill,1981a,b; Leadbeateretal.,1981; Brown andMerritt,1981; SAE,1982).In1981,Billpublishedanoteworthypaperonacomparisonbetweenfrettingwearandfrettingfatigue(Bill,1981b).Inthisperiod,significantdevelopmentsonresearchonfrettingbegantoemerge(Mann,1982; ASTM, 1982; Kusneretal.,1982; Bill,1982; Cooketal.,1983; Waterhouse,1984; Colombieetal.,1984; Johnson,1985; LindleyandNix,1985; NixandLindley, 1985a,b; Harrisetal.,1985; Hoeppner,1985; Tanakaetal.,1985; Iwabuchi,1985; WaterhouseandIwabuchi,1985; AttiaandD’Silva,1985; Sato,1985; Satoetal., 1985; BrownandMerritt,1985).Someoftheseweremoreextensivestudiesrelated toorthopedicimplants(Brownetal.,1988; MerrittandBrown,1988).Eventhough frettingwearandfrettingfatigueoforthopedicimplantswasrecognizedby1980,the concernwasacceleratedaroundthistimesinceorthopedicsurgeonsandimplantcompanieswereinterestedinmodularimplants.Becausetheseimplantspossessedmore mechanicaljoints,theconcernforfrettingdamageincreasedmarkedly—especiallyin certaintitaniumalloymaterials.Thisisduetotheconcernforinfectioninthebody thatmayresultfromthedebris.
Turningourattentiontowear,earlywearmodelsoriginatedfromempiricalequationsdevelopeddirectlyfromtribologicalexperiments.Inthe1970sand1980s,wear modelsstartedbeingelaboratedonthebasisofmechanicalcontact.Manyofthem consideredtherealcontactareaandmechanicalpropertiesofthematerialssuchas Young’sModulusandhardness.Themostrecognizedwearmodelfromthatperiod wasintroducedby Archard(1953).Thismodelwasproposedwellinadvancetoother
lawsofcontactmechanicsandwasderivedbyArchardfromanequationpreviously givenby Holm(1946),inwhichadimensionlesscoefficient K wasintroducedtoprovidetheconformityoftheformulawithexperimentalresults.The K coefficientwas interpretedbyArchardasaprobabilitytoformawearparticlebytheasperitiesofthe interactingsolidbodies;however,otherauthorsproposedifferentinterpretationsof thiscoefficient(Shaw,1977; Hutchings,1992; Johansson,1993).
Amajorbookoncontactmechanics( Johnson,1985)appearedandtheconceptsof athirdbodywasreinforced(Colombieetal.,1984; Berthieretal.,1988a,b,c).This concept,andtheanalysis,wasasignificantcontributionrelatedtoimprovingour understandingoffretting.Aroundthesametime,NixandLindley(Lindleyand Nix,1985; NixandLindley,1985a,b)performedextensivestudiesonfrettingdamage formationandfracturemechanicsappliedtofrettingfatiguecrackpropagation.Bythe mid-1980s,AttiaandcolleagueswereperformingextensiveresearchatOntarioHydro inCanada(AttiaandKo,1986; Attia,1989).Theywereattemptingtoapplythermal evaluationandmodelingtechniquestothechallengeoffretting.Attiaalsocontinued theworkofmanyinASTM(Horger,Grover,Hyler,Hoeppner,Niefert,Marbleetal.) onfrettingfatigue.ThisculminatedintheASTMsymposiumheldin1990and plannedbyAttiaandWaterhouse(ASTM,1992).Satoandcoworkersalsostudied frettingdamageformationandcrackpropagationduringthisperiod(Satoetal., 1986a,b,c,d).Hattorialsobeganhisextensivestudiesonapplyingfracturemechanics tofrettingfatigue(Hattorietal.,1988).
Theconceptoffrettingmapsemergedduringthisperiodaswell(Vingsboand Soderberg,1987,1988; Berthieretal.,1988b). VingsboandSoderberg(1988) introducedthebi-dimensionaldiagrams(namedfrettingmaps)inwhichthefretting regimes,i.e.,stick,partialslip,andfullslip,wereplottedasafunctionofdifferent combinationsofnormalloadandtangentialdisplacement.Theyalsostudiedtheeffect ofslipamplitudeonfrettinglifeconfirmingtheexistenceofacriticalamplitude(about 30 μm)correspondingtotheminimumfrettinglife.Theirworkhasbecomeoneofthe majorcornerstonesinthefield,andstilltodayprovidesthebasisfortheidentification offrettingregimesexperiencedbydifferentcomponents.
The1980shavealsobeentheyearsinwhichresearchonfrettingwearbenefitted withinterestinstudyingdifferentmechanismtestsofdifferentmaterials.Forexample, experimentsonsteel/steelandchalk/glasswerecarriedoutby Colombieetal.(1984). Resultsrevealedthatthewearofthematrixmaterialwasgovernedbythecompetition ofgenerationandmaintenanceofthedebrislayerwithabrasionofthedebrislayer. Variousstudies(Blau,1981; Quinn,1984; Sakaetal.,1984; Beard,1988)demonstratedthatwearmechanismscanbedifferentaccordingtodifferenttypesoffretting couples,withexperimentalresultsshowingthattheabrasivemechanismwasprevailinginthepairofsteel/steelwithacceleratingthedamagebydebris,whileforthe combinationofsteel/bronze,theadhesivewearmechanismwaspredominant,and thedebrisactedasakindoflubricantreducingthedamageoffrettingwear.Hardness offrettingcouplesmayaffectwearmechanisms.Duringthe1980sotherbookson wearandsurfacesbegantoemerge(Budinski,1988; Meguid,1990).Morerecently,
ASMpublishedanewvolumeofthehandbookwhichincludesanimportant,and extensive,contributionby Waterhouse(1992).
In1994, Klaffke(1994) usedavariantofArchardwearcoefficienttocomparedifferentsurfacetreatmentsasafunctionofrelativehumidityunderfrettingwear.AsimilarapproachwasusedbyCelisetal.,whorelatedthewearresistanceofseveralhard coatingstotheslidingdistance,forcenormal,andnumberoffrettingcycles(Blanpain etal.,1993).Consideringthatunderfrettingthewearvolumeresultsfromthetangentialeffortinducedbyfrictionforce,thedissipatedenergyapproachwasproposed (Mohrbacheretal.,1995; Fouvryetal.,1996;FouvryandKapsa,2001; 2003).Here, thewearvolumecorrelateswiththequantityofcumulateddissipatedenergyinthe contactarea.Thisapproachconsidersthenormalload,evolutionofthecoefficient offriction,displacementamplitude,andthefrettingtestduration.Itispossibleto determinetheenergywearcoefficientstocomparethewearresistanceofdifferent bulkmaterialsandcoatings.Morerecently,Farris’groupproposedquantifyingfrettingwearbylocalformulationoftheArchardlaw Goryachevaetal.(1999,2001).The evolutionofwearwascorrelatedwiththedynamicmodificationofthecontactgeometryduringfretting.Thistakesintoaccounttheevolutionofcontactgeometryandthe resultingredistributionofcontactpressure.Thoseglobalanalysespermitustodeterminethescalarwearcoefficientsindependentlyfromthetestconditions.However,the wearvolumeisexpressedbytheenergydissipatedwithinthecontactarea,whichdoes notconsiderthelocalaspectsofdegradation.Hence,alocalenergyapproachwas developedasamorereliableformulationtorelatethelocalweartotheamountof energydissipated(Fouvryetal.,1997).
Anotherattempttocharacterizethefrettingdamagewasmadeby Ruizetal.(1984) and RuizandChen(1986).Theywereamongthefirsttoexaminethedesignofdovetailjointsofaturbineengineagainstfretting.Followingthefirstattempts,usingthe slipamplitude δmax tocharacterizefretting(itwasshownby Nishiokaetal.(1968) that themostdetrimentaleffectonlifewastheoneobtainedfor δmax ofapproximately 15 μm),theyproposedasecondparameterviz.,thefrictionalenergydissipation, D ¼ (τδ)max,which,beinganenergydissipation,maywellbecorrelatedtothedamage mechanismsonthefrettedsurface,andindeedhasthemeritofbeingsignificantalsoin thegrossslipregime.Ithasalsobeenshowntogiveameasureoftheaccumulated shearstrainaccordingtotheBower-Johnson’sratchettingmechanism(see Hills andNowell,1994).Furthermore,Ruizetal.suggestedacompositesurfacedamage parameter, R ¼ (στδ)max,whichtakesintoaccountempiricalevidencethatcracks aremorelikelytodevelopinaregionoftensionratherthancompression,therefore accountingalsofortheearlystagesofpropagation.However,thelastdefinitionof damageparameter, R,althoughapparentlydealingmorecompletelywithsalientvariables,doesnothaveapurephysicalinterpretation.Also,itdependsstronglyonthe surfacestress,whichinturnisthesumofthreeseparatecontributions(bulkstress, stressinducedbytangentialtractions,andstressduetothenormalpressure).FEM andanalyticalandexperimentalresultsondovetailjointsindicatedaqualitativegood predictivecapabilityoftheRuizparameter, R,buttheincreasedcomplexityofthe
parameterdoesnotnecessarilycorrespondtoanincreasedpredictivecapabilityasdiscussedin HillsandNowell(1994).
1.4Stateoftheartatthebeginningofthenew millennium
Intheearly1990s,somesignificantworkwasproducedbytheOxfordUniversity group.In1992,HillsandNowelldiscussedtheequipmentandtechniquesneeded toobtainasatisfactorystandardizationoffrettingfatiguetests.Inparticular,they statedthattheHertziangeometry,i.e.,cylindricalfrettingpadspressedagainstaflat tensilespecimen,wasthemostreliableinthatitallowsnotonlyvariationofthenormalforce/geometryratioinordertopreservethepeakcontactpressurebutalsocontrol oftheexternalforcesonthepadsindependently.
Theyalsostudiedthevariationofthecoefficientoffrictionwithinthecontactarea (Hillsetal.,1988)andmuchoftheworkundertakenwaspublishedinabook(Hills andNowell,1994)thatisonlythesecondcompletelydedicatedtofrettingfatigue(the firstwaswrittenbyWaterhousein1981).Theirsubsequentworkthenfocusedonthe improvementofanalyticaltechniquesandtheextensionofanalyticalsolutionstodifferentcombinationsofloadingcyclesandgeometries.In1995, Fellowsetal.(1995) analyzedthedifferencesbetweenthestressescomputedwiththeanalyticalhalf-plane solutionandthoseinducedinthespecimen’sgeometry.Itwasclearlypointedoutthat thestresscomponentparalleltothesurfaceinatypicalspecimenislesscompressive thaninahalfplane,highlightingthecarerequiredinsimulatingtherealstressesby analyticalclassicalsolutions.Later, NowellandDai(1998) developedaquadratic programming-basedroutineabletodescribethevariationofthesheartractionsalong thecontactinterfaceforageneralloadingcycle(forexampleinLCF/HCFinteraction).Thisisausefultechniqueasitallowsanalysisofthecaseinwhichthebulkload hasameanvaluegreaterthanzero(unsymmetrical)orisoutofphasewiththetangentialload;inthiscase,theanalytical“semistatic”solutioncannotbeused.Furthermore,ananalyticalsolutionforflatpadswithroundededgesagainstaflathalf-plane contactwasfoundin1998(Ciavarella,1998; J€ ager,1998).Suchsolutionsfacilitated theuseofthisspecimen/padgeometryintheexperimentalandanalyticalworkin ordertoachieveamorerefinedapproximationofthedovetailjointgeometry.Analyticalandnumericalsolutionsforpartialslip,i.e.,whenlocalizedslipoccursat thecontactinterfacebutthereisnorigidbodymotionbetweenthecontactingbodies, havebeenalsoderived(see Navarroetal.,2003a).Arau ´ jofocusedhisD.Phil.work (2000)onshortcrackarrestmethodologies(Arau ´ joandNowell,1999)andmultiaxial fatiguetheoriesappliedtofrettingfatigue.Manytestswereanalyzedandanumberof parametersappliedinordertofindapracticalpredictioncriterion(moredetailswillbe providedlater).Someofthealternativeslookpromisingbutfurtherexperimental workandinvestigationsareneededtoapplythemtorealcomponentdesign.Atthe sametime,asymptoticsolutionsforcompletecontactshavebeenappliedinorder tostudyfrettingfatigueinturbineenginesplines(Mugaduetal.,2002b).Amore refinedasymptoticanalysesofflatandroundedcontacts(ingrosssliding,
Sackfieldetal.,2003)hasbeenalsocarriedoutbuttheapplicationofsuchmethodology,althoughpromising,needsfurtherdevelopments.
Withtheapproachofthenewmillennium,alargenumberofresearchgroupsand researchers,joinedbyanincreasedinterestofaerospacecompanies,triedtopredict frettinglifewithdifferenttechniques,mostofwhichhavebeenbasedonmultiaxial fatiguemodelsandfracturemechanics.In1996, SzolwinskiandFarris(1996) were thefirsttousethe Smith,Watson,andTopper(SWT)(1970) multiaxialfatigueparametertoassesscrackinitiationlife,themaincracksitelocation,andthedirectionofthe firststageofpropagation.Theirfirstanalysesshowedsomeoverconservative predictedvaluesandtheinabilityofSWTtoincorporatethesizeeffect. Neuetal. (2000) usedanumberofcriticalplaneapproachesinordertocorrelatethelocation andtheearlycrackgrowthwiththeonesresultingfromtestsonPH13-8Mostainless steel.Theyshowedthatthe FatemiandSocie(1988) criterionwasabletopredictquite accuratelyboththelocationandtheearly-stagecrackorientationwhiletheSWTcriterionwasnotabletopredictthecrackorientation.Atthesametime, Fouvryetal. (2000) carriedoutaseriesofanalysespredictingfrettingcrackinitiation(onTi6Al4V) applyingthemacro/micromechanicsapproachdevelopedby DangVanetal.(1989). Thismayalsobeconsideredasacriticalplaneparameterasitpredictsthatcrackinitiationtakesplaceonspecificcrystallographicplanesbutitassumesthattheformation ofcracksisamicroscopic-dominatedphenomenon.Elasticmicroscopicshakedown canbeseen,then,asthecauseofcrackpropagationbecauseforamacroscopicelastic stressfieldonlylocalizedplasticitycanbeobserved.Theyalsoobtainedanoverconservativelifepredictionavoidableonlybyaveragingtheparameteroveracritical volumethatwasnotclearlyidentifiedasamaterialconstant.Furtherworkby Arau ´ jo (2000) and Arau ´ joandNowell(2001,2002) appliedalltheseparameterstofretting fatigueexperimentswithbothAl-4CuandTi6Al4V,findingthatallofthemneeded tobeaveraged(alongaline,overacertainareaorvolume)totakeinaccountthe“size effect”andthattheaveragingdistance(areaorvolume)wassimilartothegrainsizeof thematerialeventhoughitwasimpossibletodefineauniquedimensionforthetwo materials.Astheaveragingofsuchparametersiscomputationallyquiteexpensive, anothertechniquewasproposedby Murthyetal.(2001),whoelaboratedastressinvariantmultiaxial-fatigueapproachconsistingofthereductionofthemultiaxial cyclicstressstatetoasingleequivalentstress(seetheWalkermethod, Doner etal.,1981)followedbytheuseofthisequivalentstresshistoryinconjunctionwith themodifiedManson-McKnightmultiaxialmodel(Slaviketal.,2001).Inthiscase, thecorrectionduetothehighstressregimeisbasedonaWeibullstatisticapproach anditinvolvesonlyaveragingonthesurface.Inparalleltotheseinvestigations, Giannakopoulosetal.(1998,2000a,b) alsosuggestedtheexistenceofastronganalogy betweenthecontactmechanicsproblemandfracturemechanics,wherebythecontact edgecouldbetreatedasacrackfrontinordertoassessthelikelihoodofcrackinitiationundervariouscontactconditions.
Theearly2000salsosawasignificantincreaseineffortstostudytheeffectofformationandaccumulationofweardebrisinthefrettingprocessandtheidentificationand classificationofwearprocesses,aswellastheadventofnumericalsimulationsusedto modelwear. ElleuchandFouvry(2002) studiedtheeffectsofdifferentdisplacement amplitudesonthefrettingbehaviorofaluminumalloy(A357)/52100steel.Theyfound
thatadisplacementamplitudethresholdexistedrelatingtotheformandcompositionof thedebris,whichwasindependentoftheslidingvelocityandtemperature.
TheworkcarriedoutbyFouvryandhisgroupinLyon(Fouvryetal.,2003)showed limitationsoftheArchardlawforquantifyingwearunderfretting.Theinterfacial shearworkwascorrelatedwithwear,andtheapproachwasappliedtostudyavariety ofmaterialsincludingdifferentsteelsandhardcoatingsunderreciprocatingsliding conditions.Byidentifyingwearenergycoefficientsforthosematerials,thewearresistancecanbeestablished.Shipwayandcoworkerslookedatdifferentaspectsoffrettingweardebrisformation,includingthedevelopmentofpredictivemethods(Everitt etal.,2009),integratingamacrowearsimulationtoolandamicroasperitymodelina multiscalemodeling(Dingetal.,2009),andtheroleofsurfacemicrotexturinginthe accelerationofinitialrunning-induringlubricatedfretting( Jibikietal.,2010).Bythe mid-2000s,afewmainapproachestofrettingstrengthpredictionhadbeenidentified. Therecentresearchcarriedoutbythe“frettingcommunity”wasbasedonthefollowingtechniques:(i)linearelasticfracturemechanics(LEFM)-basedapproaches(see Arau ´ joandNowell,1999; Nicholasetal.,2003; Conneretal.,2004);(ii)multiaxial initiationparameters(see Arau ´ joandNowell,2001; SzolwinskiandFarris,1998; Neu etal.,2000);(iii)macro-micromechanics(see Fouvryetal.,2000; Arau ´ joandNowell, 2002);(iv)crystallographicplasticity(see Gohetal.,2003);and(v)asymptotics(see Mugaduetal.,2002a;Sackfieldetal.,2003)Abetterunderstandingandimprovement oftheLEFM-basedmethods(i)(withparticularapplicationtotheexperimentaldata obtainedduringtheresearchproject)andthedevelopmentofanasymptoticmethodology(v)bothtobeappliedtocracknucleationpredictioninfrettingfatiguehavebeen pursuedatthebeginningofthemillenniumbyDiniandcoworkers(Dini,2004; Dini andNowell,2004; DiniandHills,2004; Dinietal.,2005,2006; HillsandDini,2006, 2016; Nowelletal.,2006; Hillsetal.,2012,2013; Fliceketal.,2013,2015).
Whiletheabovebriefoverviewoftheearlydevelopmentsinthefieldoffretting providesimportanthistoricalinformationaboutthisthrivingresearcharea,aplethora ofdevelopmentshavealsobeenmadeinthepasttwodecades,manyofwhichwillbe reviewedinthefollowingchaptersandsubchaptersofthebook.
Acknowledgments
Wegratefullyacknowledgeinputtothischapterandpayourgratitudeandourrespectstoour colleagueDavidW.Hoeppner,whopassedawayonFebruary18,2022.Davidwasalong-time facultymemberandformerchairoftheUniversityofUtah’sDepartmentofMechanicalEngineering.Davidworkedonandmadesubstantialcontributionstoexperimentalandanalytical modelingofthebehaviorofstructuralmaterialsinfatigue,corrosion,andcorrosionfatigue, andwasoneofthekeycontributorstoresearchonfrettingfatigue.HefoundedFASIDE (FatigueandStructuralIntegrityDesignEngineering),theHOLSIP(HolisticStructural IntegrityProcess)Conference,andtheQualityandIntegrityDesignEngineeringCenterat theUniversityofUtah.Davidwasalsooneofthemaincontributorsandorganizerofseveral NATO-AGARDandASTMsymposiaonfretting.Asuccessfulscientist,whoseacademic endeavorsledtotheenhancementofindustrialpractice,hesupervisedhundredsofundergraduate,130masters,and48PhDstudents.DavidwillbegreatlymissedasacolleaguewhocontributedgenerouslytotheInternationalSymposiumonFrettingFatigue(ISFF)community. 14FrettingWearandFrettingFatigue
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