The friction coefficient evolution of a TiN coated contact during sliding wear

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Applied

Surface

Science

j o ur na l ho me pa g e :w w w . e l s e v i e r . c o m / l o c a t e / a p s u s c

The

friction

coefficient

evolution

of

a

TiN

coated

contact

during

sliding

wear

Guojia

Ma

a

,

Liliang

Wang

b,∗

,

Haoxiang

Gao

b

,

Jie

Zhang

b

,

Tom

Reddyhoff

b

aScienceandTechnologyonPowerBeamProcessesLaboratory,BeijingAeronauticalManufacturingTechnologyResearchInstitute,Beijing100024,China bDepartmentofMechanicalEngineering,ImperialCollegeLondon,LondonSW72AZ,UK

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received24October2014

Receivedinrevisedform23March2015 Accepted24March2015

Availableonline31March2015 Keywords:

Frictionmodel TiNcoating Slidingwear

a

b

s

t

r

a

c

t

ThispaperdiscussedthefrictioncoefficientevolutionofaTiNcoatedcontactduringslidingwear.A hardTiNcoatingwaspreparedonabearingsteel(GCr15)substratebyapplyingthecompositemethodof cathodearcandmagnetronsputtering.Themicrostructure,microhardness,microscratchandtribological behaviourofthiscoatingwerestudiedtoobtaintherelationshipbetweenfrictioncoefficientandother coatingproperties,meanwhilethefullfrictioncoefficientevolutioncurvewithdifferentstagesduringthe wearprocessofTiNcoatingwasshown.Itwasfoundthat,coatingfrictionandwear,astwointeractive responsesfromatribo-system,mutuallyaffectedeachotherandshouldbestudiedasasinglephysical phenomenon.Therefore,anovelfriction-wearinteractivefrictionmodelwasdevelopedtorepresentthe evolutionoffrictioncoefficientandtopredictcoatingbreakdown.Theresultsshowthattheevolution ofthefrictioncoefficientcurvecanreflectdifferentstagesofthewearprocessandthewearlifecanbe estimatedusingthenewfrictionmodel.

©2015ElsevierB.V.Allrightsreserved.

1. Introduction

Thehardcoatingsarebeingwidelyusedinmanyfields,because oftheirhighhardness,goodchemicalstability,wearresistanceand anti-oxidationcapability[1,2],suchasthehighspeedmachining andmetalformingindustries,inwhich,thecoatedtools experi-enceinevitablein-serviceimpactsatelevatedtemperatureswith heavycyclic dynamicloading[3–7].Tounderstandthe interac-tiveresponsesofthecoatingsareof greatimportance notonly for the tribological behaviour prediction, but also theresearch anddevelopmentofadvancedcoatings[8,9].Duetothecomplex wearmechanismsassociatedwithsuchcoatings,researchintotheir tribologicalbehaviournever ceased. Previousstudies[8,9] have focusedmainlyontheeffectsofslidingwearandhaveshownthat, forcontactsinwhicheitheroneorbothsurfaceswerecoated,four majorparameterscontrolin-contacttribologicalbehaviour[10].

Theseparametersarethecoating-to-substratehardnessratio, thethicknessofthecoating,thesurfaceroughnessandthesizeand hardnessofdebrisatthecontactinterface.Inaddition,thesestudies alsocharacterisedcertaintribologicalpropertiesofthecoatings, suchasroughness,hardness,ductility,oxidefilm,reactionlayer

∗ Correspondingauthor.Tel.:+44020758943648;fax:+4402075947017. E-mailaddresses:lemontree7678@163.com(G.Ma),

liliang.wang@imperial.ac.uk(L.Wang).

andadhesivetransfer.However,researchontheevolutionofthe frictioncoefficientofthecoatinghasbeenlacking,whichnotonly resultsinalimitedunderstandingoffrictionandwearprocesses butalsopreventstherelationshipbetweencontrolparametersand coefficientoffrictionbeingelucidated.

Thecoefficientoffrictionisnotanintrinsicmaterialproperty, butinsteaddescribesthestateofcontactbetweenbodiesandvaries duetotheoccurrenceofwear.Inthemajorityofpreviousstudies onslidingwearofTiNcoatings,researchesfocusedontheaverage valueoffrictioncoefficient[8,11–13],withtheevolutionoffriction coefficientbeinglargelyignored.Thisissurprisingsincethe evo-lutionoffrictioncoefficientindicatesdifferentwearstages[14], includingthebreakdownofthecoatings,whichisofgreat bene-fittounderstandingwearmechanisms.Afewresearchersshowed experimentalresultsontheevolutionoffrictioncoefficient[15] andtheinteractiveeffectsbetweenfrictionandwear,especially, forthetribo-systemswithhardcoatingandlubricant,the break-downofthecoatingand(or)lubricantwouldleadtothetypical dualplateaufeatureinthefrictioncoefficientevolution.However, thecoatingfrictionandwear,astwointeractiveresponsesfroma tribo-system,havenotbeenintegratedtogetherandmodelled,for instance,DenapeandLamonhavealreadyconsideredinteractive effectsbetweenfrictionandwearofavailablestructuralceramics [16],KojiKatoreviewedwearinrelationtofrictionandshowedthe effectsofsomemajorparametersduringwearprocess[9],these findingsconfirmedthattheinteractiveeffectbetweenthefriction http://dx.doi.org/10.1016/j.apsusc.2015.03.156

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andweardoesexistandshouldbestudiedandmodelledjointly andthisisthenoveltyofthepresentresearch.

Thepurposeofthisworkistofurtherunderstandthe relation-shipbetweenwearmechanismsandfrictionandisachievedby monitoringfrictioncoefficientevolutionofaTiNcoatingcontact. Basedonthesestudies,anovelfrictionmodel,theinteractive fric-tionmodel,isdevelopedtopredicttheevolutionofthefriction coefficientandthewearlifeofhardcoatings.

2. Experimentaldetails

TiN coatings were prepared on bearing steel GCr15 (C: 0.95–1.05, Mn: 0.20–0.40, Si: 0.15–0.35, S: ≤0.020, P: ≤0.027, Cr:1.30–1.65, Mo: ≤0.10, Ni: ≤0.30, Cu: ≤0.25, Ni+Cu: ≤0.50, theequivalence ofAISI52100)substratesbythecombination of cathodearcandmagnetronsputteringmethods.Aschematic dia-gramof theequipmentusedis showninFig.1.Theequipment hasfoursourcesincludingtwomid-frequencymagnetron sputter-ingtargetsand twocathodearctargets,theirdimensionsbeing 400×120mm.Arotatingworkpieceholderislocatedinthecentre ofthevacuumchamber.Toobtainionswithhighenergyandplasma withhighdensity,apulsebiaspowersupplywasemployedonthe holder.ToachieveimprovedTiNcoatingproperties,aheating sys-temispositionedinthevacuumchamber,capableofraisingthe ambienttemperaturetoapproximately450◦C.

Allsamplesweregroundandmirrorpolished,thencleanedwith acetone,driedwithhot air andfinally fixedonto thesubstrate holderin thechamber.Whentheambientpressurein the vac-uumchamberreached2×10−3Pa,argongaswasintroducedand thepressureadjustedtoproduceaplasmadischarge.Undesirable

Table1

DepositionparametersofTiNlayer.

N2gasflowrate,sccm 500

Workingpressure,Pa 0.6

Cathodearcpower,kW 2

Mid-frequencymagnetronsputteringpower,kW 4

Substratebias(pulse),V −160

Depositiontemperature,◦C 350

Depositiontime/min 75

contaminantlayerswereremovedbyArionsputter-cleaningfor 30min.Then,twocathodearctargetswereturnedon,andaTi tran-sitionlayerwasfirstdepositedonsubstratetogiveanenhanced adherentstrength.Duringthisstage,−100VDCand−500Vpulse compositebiaseswereappliedandthedepositiontimewas5min. Followingthis,twomid-frequencymagnetronsputteringtargets wereturnedonandnitrogengaswasintroducedintothechamber sothataTiNlayerwasdepositedovertheTitransitionlayer.Other experimentparametersusedinTiNcoatingprocessareshownin Table1.

Ascanningelectronmicroscope(SEM-JEM2010),wasusedboth tocharacterisethe surface morphologyof the sampleand also toobservethecross-sectionof thesamplein ordertomeasure thethicknessoftheTiNcoating.Threedimensionalmaps show-ingtheroughnesssamplepriortotestingandthetopographyof the worn surfaces after testing were measuredusing a white-lightinterferometricsurfaceprofilometer(NewViewTM7100).The

adherentstrengthofthesamplewasassessedbyamicro-scratch tester(WS-2004)withthemaximumloadof50Nandthe maxi-mumscratchdistanceof5mm.Themicro-hardnessofthesample and nano-hardness were evaluated by a micro-hardness tester

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(WoleprtWilsonInstruments–Tukon2500)withanappliedload of20Nandanano-hardnessindenter(MTS),respectively.The tri-bologicalpropertiesofthesampleswerecharacterisedusingaball ondisctribometer(UMT-2),inwhichtheevolutionoffriction coef-ficient,wearrateandwearvolumewererecorded.AWC-6% Co ball(microhardness1780HV,abrasionstrength1380N/cm,elastic modulus71GPa),6mmindiameter,wasusedasthecounterpart. Alltheweartestswereconductedinanambientenvironment,at atemperatureof25◦Candarelativehumidityof30%.Inthelinear testsoftheballondisc,therelativeslidingspeedwas5mm/sand theslidingdistancewas10mm.

3. Resultsanddiscussions

3.1. Surfacemorphology,roughnessandthicknessoftheTiN coating

ThesurfacemorphologyofTiNcoatingisshowninFig.2.Here, itcanbeseenthatthesurfaceissmoothandflat,withonlyafew visiblemicro-poresandslightspallation.Themeanroughness(Ra)

oftheTiNcoatingis0.10±0.005␮m,measuredusingthethree dimensionalopticalprofilometer,andisveryclosetoRaoftheTiN

coatingpreparedusingsinglemagnetronsputteringmethod[9]. Fig.2showsthecoatedsurfacewithultra-lowroughness,asmost ofthehardnitridecoatingswerefabricatedbyplasmaenhanced physicalvapourdeposition(PEPVD)andplasmaenhanced chem-icalvapour deposition (PECVD).Therefore, the influence ofthe surfaceroughnessonfrictionandwearpropertieswasignoredin thisstudy.Thecross-sectionoftheTiNcoatingisshowninFig.3, showingathicknessofapproximately2.1±0.05␮m.

3.2. BondingstrengthandhardnessoftheTiNcoating

Themicro-scratchcurveandscratchtrackmorphologyofthe TiNcoatingareshown inFig.4.Byrampingtheindenting load,

Fig.2.Surfacemorphologyofthesample.

Fig.3. Cross-sectionofthesample.

Fig.4.Micro-scratchcurveandscratchtrackpictureofthesample.

followedbyvisualexaminationoftheweartrack,thecriticalload which causesthefailure oftheadhesive bondingcanbe deter-mined.Thescratchingprocessisaccompaniedbyafrictionsignal (Fig.4), which exhibitssevere fluctuations when theindenting loadisgreaterthanacriticalvalue.AsshowninFig.4,thecritical loadoftheTiNcoatingisapproximately43.7±0.1N,suggesting thatthebonding strengthofTiNcoatingis sufficientfor indus-trialapplication.In addition,themicro-hardnessofthesamples weremeasuredwithanappliedloadof20Nandtheresultsshow thatthemicro-hardnessofthesubstrateandtheTiNcoatingare 500±8HVand622±10HV,respectively.ThestrengthoftheTiN coatingwasmeasuredbynano-indentation,andtheaveragevalue of5measurementswas32.45±0.43GPa.

3.3. FrictionandwearpropertiesoftheTiNcoating

ThefrictioncoefficientevolutionoftheTiNcoatingundera nor-malloadof200NisshowninFig.5.Fourinterruptionsweremade duringthetestsothattheweartrackcouldbeimagedusingan opticalmicroscope.Thisrevealeda varyingsurfacemorphology overtheentireweartrackasshownbytheimagesinFig.5and themicrostructuralchangesshowninFig.6.Fromthisdataitcan beseenthattheevolutionof friction,canbedividedintothree stages accordingtodifferentwearbehavioursand mechanisms. ThesecompriseofstageI:lowfrictionstage,stageII:ploughing frictionstageandstageIII:coatingbreakdownstage[17,18].

InstageI,thefrictioncoefficientwaslowandstable,withthe valuerangingfrom0.15to0.2.Thesurfacemorphologyofthewear

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Fig.6.Weartrackpicturesofthelocalenlargementunderdifferenttimepoints.(a)180s–point1,(b)350s–point2,(c)400s–point3,(d)450s–point4.

trackat weartime of 180sis shown in Fig.6(a).Only a small numberofmicrocracksarevisible,butnocoatingspallationcan beobserved,thusanegligibly smallvolumeofweardebriswas generatedduringthefirsthalfofthisstage.Astheweartime (slid-ingdistance)increases,furthermicrocracksdeveloped,andwear debriswasgeneratedduetolocalisedcoatingspallation,as indi-catedbyFig.6(b),inwhichtheweartrackmorphologyisshown afteraslidingdurationof350s.ThefrictioncoefficientinstageI wasprimarilygeneratedbythecontactbetweentheballandthe coatedsurface.Here,thefrictionforcestemmedfromtheploughing frictionarisingfromthemicrosurfaceasperities.Theadhesive fric-tionbetweentheballandthecoatingwasverylowandislikelyto contributeonlyslightlytotheoverallfriction.Sincetheweardebris generatedduringtheinitialstageofslidingwereloosepowder-like andsmallinsize,theploughingfrictioncausedbytheentrapped hardwearparticleswasverylowandnegligibleinterlockingeffects occurred. However, atthe end of this stage (between 300 and 350s),theaccumulationandentrapmentoflargewearparticles initiated,theincreasingquantity(density)andtheenlargedsizeof thewearparticlesresultedinfrictionduetothird-bodyhard par-ticlesploughing[19,20]andledtooscillationandrapidincreasein thefrictioncoefficient.Therefore,instageII(after350s),the fric-tioncoefficientstartedtoriserapidlyfrom0.2to0.55.These“third bodyparticles”areusuallygeneratedintheslidingcontactandplay acriticalrole indeterminingfriction[21,22],whiletheireffects dependontheirchemical composition and mechanical proper-ties.Inthecurrentstudy,thethirdbodyparticlesweregenerated fromhardTiNdebris,whichcouldincreasethefrictioncoefficient pronouncedlyand acceleratethewearofthecoating.Thewear trackmorphologyduringthisstageisshowninFig.6(c).Here,the smallspallationareashavejoinedtogetheranddevelopedintolocal delaminationinsomeareasoftheweartrack,whiletheremaining TiNcoatingwithcrackscanstillbeobservedinotherregionsof theweartrack.AttheendofstageI,looseweardebrismusthave agglomeratedtoformlargerparticles,which–possiblycombined withotherlargeparticlesgenerateddirectlyfromthedelaminated weardebris–causedthequantityandsizeofentrappedwear par-ticlestoexceedacriticalvalue.Asaresult,stageIIwasdominated

byploughingfrictionduetoroletheentrappedhighstrengthwear particles.Thewearprocessthenwentintosevereabrasivewear stage,wherethestrongdynamiccouplingbetweenfrictionand abrasiveweartookplace,i.e.thefrictioncoefficientincreased sig-nificantlybecauseoftheincreasingquantityof entrappedthird bodyparticles.Ontheotherhand,theincreasedfrictioncoefficient resultedinhighershearstresses,whichinturnacceleratedthewear andthebreakdownofthecoating.SincetheWC-6%Coballisvery hardandhasexcellentwearresistance,theWC-6%CoballandTiN hardcoatinginthisstudyofferedverylittleadhesivefriction,which wasobservedexperimentallyfromthepresentresearchand sim-ilarresultscanbefoundin[23].Sincetheoccurrenceofstick-slip phenomenondependsonthecontactmaterials,particularly,when adhesivefrictionisthepredominantcontributortotheoverall fric-tioncoefficient,thusitwasassumedthattherewasnostick-slip phenomenonduringthestagesIandIIofsliding.

InstageIII,thefrictioncoefficientreachedaplateauwithan averagevalueof0.6, which isclosetothat ofa typicalcontact betweenGCr15(substratematerial)and WC-6% Coball.In this stage,theploughingfrictionduetothethirdbodyparticleswould stillplayanimportantrole,withthequantityandsizeofthe parti-clesreachingadynamicbalance,i.e.thequantityofwearparticles entrappedin, and ejectedout from,thecontactinterfacebeing equivalent.Inthemeanwhile,theploughingfrictionbetweenthe ballandtheGCr15substratemusthavereachedamaximum,since thecoatinghasbeencompletelydelaminated.InstagesIIandIII, numerouswearparticlesweregeneratedandtheseentrappedwear particlescouldleadtotheseparationofthecontactinterface.Due tothenatureofploughingfriction,thenormalloadistakenby theentrappedhardwearparticles.Theamountofwearparticles willaffecttherealcontactareaandalsothepenetrationdepthof eachwearparticle,butwillnotaffecttheoverallploughingfriction. Fig.6(d)showsthattheTiNcoatinghasbeencompletelyremoved andanoxidelayerhasformedonthesubstratesurface.The evi-denceoftheoxidelayerformedonthesubstratesurfacecanbe alsofoundin[14,24].However,theoxidelayer,adhesivedebrisor abrasivegroovescannotbeobservedonthesurfaceoftheWC-6% Coballduetoitsexcellentwearresistanceandoxidationresistance.

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Fig.7.Weardepthandwearvolumeofdifferentwear-timepointsunderloadof 200N.

Fig.7illustratesthedepthandthevolumeofthewearscarat differentstagesduringthetest.Awhite-lightinterferometric sur-faceprofilometer wasusedtomeasurethewidth anddepthof thewearscartodeterminethevolumeofwear.Here,thewear depthandvolumeincreasesmonotonicallywithtime,howeveran increasedwearrateisobservedbetweenpoints2and4owingto hardwearparticlesinducingabrasivewear,withthesametrend beingobservedforthewearvolume.ComparedwithFig.3,itwas foundthatthedepthoftheweartrackisgreaterthanthe coat-ingthickness,whichisduetothesevereplasticdeformationof thesubstrateandthecoating,indicatingthatthebondingstrength betweenthecoatingandsubstratewasexcellent.Theenhanced bondingstrengthwasattributedtotheTisub-layer,althoughthis layeritselfisnotabrasionresistantandthewear-resistanceofthe samplewilldecreasewhentheTiNlayerisremoved,becausethe Tisub-layerpreventstheTiNcoatingfromfallingoffwheninitial crackingoccursintheTiNlayer.Inaddition,inFig.7,itwasfound thatthewidthoftheweartrackhasasmallchangeduetoalager deformationandasmallwearrateofthesampleunderthebigload. Theeffects of normalloadonthe fictioncoefficientare dis-playedinFig.8forthreeseparatetests.Here,eachplotoffriction coefficientshowsthesameevolutionagainrevealingthreedistinct stagesofwear.ThedurationofstageIdecreasedsignificantlywith increasingnormalload.Thefrictioncoefficientofthecoatingis pri-marygovernedbyfourimportantfactors;coatinghardness,coating thickness,surfaceroughnessandentrappeddebris[14].Because theexperimentswerecarriedoutonthesamesample,the differ-enceinfrictioncoefficientbetweenloadsmusttherebeattributed tovariationsindebrisbehaviour.Duringstage I,higher normal loads wouldlead tolarger cracklengths and largersized wear

Fig.8. Simulativeandexperimentalfrictioncoefficientcurvesofthesampleunder 200N,300Nand400N.

particlesbeinggenerated,whichwouldresultinafaster transi-tionfromstageItostageII.Inadditiontothis,thefaster wear ofthecoatingunderhighernormalloadscanbeexplainedbythe Archard’swearlaw[25].InFig.8,severeoscillationinthefriction coefficientwasobservedat300N–6000MPa.Theoscillationinthe frictiontestresultsisacommonlyobservedphenomenon,because thefrictioncoefficientvalueisnotamaterialproperty,whichcan beaffectedbymanyfactors.Inthepresentresearch,thiscouldbe causedbytheentrapmentoflargewearparticlesandthepartial breakdownofthecoating.

3.4. Interactivefrictionmodel

ThefrictionbetweentheWC-6%Coballandthecoatingstems fromtwoorigins(Eq.(1))correspondingtotwodifferent mecha-nisms,namelyinitialfrictioncoefficient˛andploughingfriction

coefficientpc.

=pc+˛ (1)

where˛isafrictioncoefficientrepresentingtheinitialwear

pro-cessshowinglowfriction.Itwasfoundthattheadhesivefriction didnotplayanimportantroleinthepresentresearchsincethe materialtransferbetweentheWC-6%Coballandthecoatingwas verylittleaccordingtotheexperimentalobservations.Inthe ini-tiallowfrictionstage,wearparticlesweresmallinsizecompared totheheightoftheasperities,thustheploughingfrictionmainly stemmedfromthehardasperities,whichisrepresentedby˛in

Eq.(1).ThehardnessoftheWCballisconsideredtobemuchhigher thanthatofthecoating,thusthemorphologyofthehardasperities (ontheball)didnotchangesignificantlyduringthewearprocess. Therefore,itwouldbereasonabletoassumeaconstantinitialvalue offrictioncoefficient˛≈0.17,whichcanbedeterminedby

run-ningshortslidingdistanceweartests.InstagesIIandIII,largewear particlesweregeneratedasthenumberofwearparticlesincreased andonlythewearparticlesentrappedbetweenthecontactsurfaces contributedtotheploughingfriction,pc,thefrictioninducedby theploughingofhardwearparticles,canbemodelledbyEq.(2):

pc =psexp[−(1h)2] (2)

wherepsisploughingfrictionofthesubstrate,1and2aremodel

parameters,andhistheinstantaneousthicknessofthecoating.Eq. (2)wasdevelopedconsideringthephysicalmechanismsofhard wearparticlesinducedploughingfriction.However,toimprovethe numericalintegrationefficiency,theequationshavebeen simpli-fiedconsiderably.

Theploughingfrictiongeneratedfromasinglesphericalshaped wearparticlecanbeestimatedbyusingEq.(3):

pc1= 2{sin−1(w/2r)−{(w/2r)[1−(w/2r)]}1/2} (w/2r)2 +4{1−[1−(w/2r) 2 ]1/2} (w/2r)2 s (3)

wherewisthediameteroftheindentation(determinedbythe pen-etrationdepthofawearparticle),ristheradiusofawearparticle andsistheshearfrictioncoefficientattheparticle/coating

con-tactinterface.wisdeterminedbythehardnessofthetwomaterials incontactandthecontactpressure.sisdeterminedbythenature

ofthematingmaterials.Duringthewearprocess,thenormalised wearparticledensity,entrappedatthecontactinterface,achieved adynamicbalancebetweenthenewgeneratedwearparticles(first term in Eq. (4))and the particles ejected from the weartrack

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(secondterminEq.(4)),wheren1,n2,BandCaremodelconstants,

andhistheinstantaneouscoatingthickness.

˙=B ˙hn1Cn2 (4)

Thetotalploughingfrictiongeneratedfromalltheentrapped wearparticlesisestimatedbyEq.(5),(Npcismodelparameter)i.e.

theoverallploughingfrictionisdeterminedbythenormalisedwear particledensityand theploughingfrictiongenerated fromeach singleentrappedwearparticles.However,theploughingfriction (calculatedfromEq.(5))onlycontributetotheoverallfrictionwhen thenormalisedwearparticledensityisgreaterthana critical value,representingtheentrapmentofthelargewearparticles.

pc=Npcpc1 (5)

CombiningEqs.(3)–(5)willenablethemodellingofthe inter-activephenomenonofahardcoatingtribo-system,althoughthis setofequationsrequiressignificanteffortsonmodelparameters calibrations.Therefore,Eq.(2)wasdevelopedtosimplifythe com-putationprocedures. Dueto thenatureof Eq. (2), thevalue of pc isverylow(≈0)overtheentirerangeofstageItorepresent

theneglectableploughingfrictioneffectofthewearparticles.pc

startedtoincreaseinstageII.Thishasenabledthemodellingof thecomplexnatureoffrictionandwearinacoatingtribo-system, i.e.attheveryinitialstage,thegeneratedwearparticlesare nor-mallyfewandsmallinsize,andarethereforeunlikelytobecome entrappedbetweentheasperitiesandhencecontributenegligibly totheploughingfriction.Asthewearprocesscontinues,the coat-ing’sthicknessgraduallyreducesanditsload-bearingcapability declines.Meanwhile,thenumberofcracksgraduallyincreases(as showninFig.6(b)),someofwhichjointogethertoformlocal delam-ination(asshowninFig.6(c))andhenceresultsinanincreasein thesizeandnumberofwearparticles.Ploughingfrictionchanges chieflywiththevariationofwearparticles,andthesewearparticles arerelatedtothecoatingthickness,thereforeanequationrelating ploughingfrictiontothecoatingthicknesscanbebuilt.The instan-taneousthicknessofthecoatinginEq.(2)canbeobtainedfrom h=h0− ˙hdt,whereh0istheinitialthicknessofthecoating,and ˙h

isthetimedependentwearrateofthecoatingthatcanbecalculated byEq.(6):

˙h=KP

v

Hc

(6) whereKisthecoefficientofwear,whichisadimensionless con-stant,Pisthecontactpressure,

v

istheslidingvelocity(

v

=dl/dt) andHcisthecombinedhardnessofthecoatingandthesubstrate.

ThisequationisbasedonArchard’swearequation[25],whichis awidelyusedmodeltoestimateslidingwear.Atime-dependent integrationalgorithmisintroducedinthepresentmodel,by inte-gratingtheamountofwearineachtimestep/incrementtomodel theevolutionofwearoccurredinthetribo-system.Thebenefitof thisalgorithmistotakethetimehistoryofwearintoaccount,e.g.if theslidingspeedhaschangedduringtheweartest,theinteractive frictionmodel will, uniquely, adjust thewear rate correspond-ingly.AlthoughArchard’sequationindicatesthatthevolumeof theremoved debrisdue towear isproportional to thefriction forcesandthematerialhardness[26],someimportantfactorshave notbeenconsidered[27,28].Theseinclude theevolution ofthe coatingthicknessandcombinedhardness.Duringthewear pro-cess,thecoatingthicknessdecreasesleadingtoareductionofthe combinedhardness that,in turn, accelerates thebreakdown of thecoating.Therefore,Archard’sequationshouldbemodifiedby introducingthecombinedhardnessHc.Toachievethis,thecurrent

researchappliesKorsunsky’smodel(Eq.(7))tocalculatecombined

hardnesssinceithasshowngoodagreementswithawiderangeof experimentaldata[29,30], Hc=Hs



˛2+2 ˛+hˇ2



(7) whereHsisthehardnessofthesubstrate,˛isthehardnessratio

betweenthe coating and thesubstrate, ˇ is an influence coef-ficientof thethickness,andh istheinstantaneousthicknessof thecoating.ThecombinedhardnessisVicker’shardnessvalue,a jointresponseofthecoatingandsubstrate,determinedbyusinga Tukon2500hardnesstester.AsindicatedbyEq.(7),thecombined hardnessisdeterminedbytheresidualthicknessandthe mechan-icalpropertyofthecoating.Therefore,astheweartestproceeds, thecombinedhardnessreducescorrespondingly.Whenthe coat-ingwaswornoffcompletely,thecombinedhardnessvaluewas equivalenttothehardnessofthesubstratematerial.Inthepresent research,wecalibratedthemodelbyinterruptingtests,to deter-minethemodelparametersinEq.(6),theArchard’swearlaw,and toensurethatthepredictedresidualcoatingthicknesstofollow theexperimentalresults.Inaddition,thewearmodelintegratedin theinteractivefrictionmodelofferssufficientflexibilitytodescribe differenttrendsofwear,e.g.aparabolaorlineartrendetc.

Theoverallinteractive,mechanism-based,modelusedinthis studycombinesEqs.(1),(2),(6)and(7).P,

v

,Hs,and˛ are

ini-tialconditionsoffrictionmodelforTiNsample.Throughoutthe numericalanalysis,ps,˛,2andˇareloadindependent

param-eters,while1andKareloaddependentparameters.Thoseload

dependentparameterscanberepresentedbythefollowingPower Lawequations(Eqs.(8)and(9)):

1=k1P

N1 (8)

K=kKPNK (9)

where P is the pressure load applied, and k1, kK, N1, and NK are material constants. ps and ˛ are determined by the friction coefficient at the initial and final stage of testing. Nk,N1,k1,2,˛andkKvaluescanbedeterminedfromthe fric-tionevolutioncurves.

Thefrictionmodelwascalibratedusingtheexperimentaldata fromthetestscarried outunderthree differentloads shownin Fig.8.Inordertooptimisetheinteractivefrictionmodel,the mate-rialconstantsweredeterminedbetweenthenumericalsimulation andexperimentaldata.Theresultingmaterialconstantsalongwith certainmodelparametersusedintheinteractivefrictionmodel arelistedinTable2.Oncetheparametersandconstantshavebeen determinedinthisway,themodelcanbeusedtopredictthe evo-lutionoffrictioncoefficientunderdifferentloads.Thisapproach hasbeenverifiedandtheresultsshowninFig.9,where simula-tiveandexperimentalfictioncoefficientcurvesarecomparedfrom twonewtests(withoutrecalibrationofthemodel)presented, indi-catingthattheinteractivefrictionmodeldevelopedinthepresent researchenablesthepredictionoffrictioncoefficientevolutions withintheboundariesforcalibration,i.e.between200and400Nin thepresentresearch.Itisevidentthatthesimulationcurvesagree closelywiththeexperimentalresults.Furthermore,thesimulation curveincludesthreestages;alowfrictionstage,adebrisfriction stageandacoatingfailurestage.Theevolutionoffrictioncoefficient featuredbythethree-stagepattern(orthedoubleplateaupattern),

Table2

MaterialconstantsandmodelparametersofinteractivefrictionmodelforTiNlayer.

2 ps N1 Nk

2 0.311 −3.84 4.095

˛ k1 kK ␮˛

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Fig.9.Simulativeandexperimentalfictioncoefficientcurvesofthesampleunder 250Nand350N.

duetothebreakdownofthecoating,isverywidelyobservedin thehard-coatingtribo-system.Theoretically,thesefeaturescanbe modelledbytheinteractivefrictionmodel,bythere-calibration ofthemodelparameters.Withthatsaid,itshouldberecognised thatthisstudyispreliminaryandrequiresfurtherexperimentson differenttypesofhardcoatinginordertooptimisethemodel.In addition,sincethemodelisbasedonweartestsofshortduration, theinfluenceoftheoxideasathirdbodyhasbeenignored. How-ever,oxideisoftengeneratedunderactualoperatingconditionand hasagreatinfluenceonthefrictionprocess[24].Toaddressthis problem,oxideformationwillbestudiedinasubsequentstudy,and willbeincorporatedintothefrictioncoefficientevolutionmodel. 4. Conclusions

Thefriction coefficientevolution ofTiN coatingwasstudied usingaballondiscweartestalongwithvariousother characteri-sationmethods.Thishasenabledanovelinteractivefrictionmodel tobedeveloped.

1)Theballondisctestresultsillustratethatthefrictionevolution processofTiNcoatingcomprisesofthreestagescorresponding todifferentwearbehavioursandmechanisms,namelystageI withlowfriction,stageIIwithdebrisfriction,andstageIIIwith coatingfailure.

2)ThewearparticlesofTiNcoatingplayedaveryimportantrole infrictionandwearprocess.Theinitiationofwearparticleflow markstheendofstageIwithlowfrictionandthestartofstage IIwithhighfriction,whichdirectlyaffectedthewearlifeofthe TiNcoating.

3)Theinteractivefrictionmodeldevelopedinthepresentresearch providesaneffective approachto modelthe coatingfriction andwear,astwointeractiveresponsesfromatribo-system.In addition,thismodelhasenabledthedescriptionofthefriction coefficientevolution and theestimation ofwearlife of hard coatings.In the subsequentstudy, furtherfriction and wear experimentsof different hard coatingswill beperformed in ordertooptimisethismodel.

Acknowledgements

ThestrongsupportfromAviationIndustryCorporationofChina (AVIC)inthisfundedresearchismuchappreciated.Theresearch

wasperformedattheAVICCentreforStructuralDesignand Manu-factureatImperialCollegeLondon.Inaddition,theauthorswould liketothankcolleagues(XingLiu,GangSunandHaibingZhou)at BAMTRIforprovidingsamples,andexpressspecialthankstoDobre OanaatImperialCollege,Londonforfriendlyhelpwithfrictionand weartesting.ThisworkwassupportedbyNationalInstrumentation grantprogramofchina(ContractNo.2011YQ120039).

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