Contact mechanics of rough surfaces in tribology m

TribologyLetters4(1998)1–351PerspectivesContactmechanicsofroughsurfacesintribology:multipleasperitycontactBharatBhushanComputerMicrotribologyandContaminationLaboratory,DepartmentofMechanicalEngineering,TheOhioStateUniversity,Columbus,OH43210-1107,USAReceived16June1997;accepted3September1997Contactmodelingoftworoughsurfacesundernormalapproachandwithrelativemotioniscarriedouttopredictrealareaofcontactandsurfaceandsubsurfacestressesaffectingfrictionandwearofaninterface.Whentwomacroscopicallyflatbodieswithmicroroughnesscomeincontact,thecontactoccursatmultipleasperitiesofarbitraryshapes,andvaryingsizesandheights.Deformationattheasperitycontactscanbeeitherelasticand/orelastic–plastic.Ifathinliquidfilmispresentattheinterface,attractivemeniscusforcesmayaffectfrictionandwear.Historically,statisticalmodelshavebeenusedtopredictcontactparameters,andthesegenerallyrequiremanyassumptionsaboutasperitygeometryandheightdistributions.Withtheadventofcomputertechnology,numericalcontactmodelsof3-Droughsurfaceshavebeendeveloped,particularlyinthepastdecade,whichcansimulatedigitizedroughsurfaceswithnoassumptionsconcerningtheroughnessdistribution.Inthisarticle,acomprehensivereviewofmodelingofmultiple-asperitycontactsindryandwetconditionsispresented.Contactmodelsforhomogeneousandlayered,elasticandelastic–plasticsolidswithandwithouttangentialloadingarepresented.Themodelsreviewedinthispaperfallintotwogroups:(a)analyticalsolutionsforsurfaceswithwell-definedheightdistributionsandasperitygeometryand(b)numericalsolutionsforrealsurfaceswithasperitiesofarbitraryshapeandvaryingsizeandheightdistributions.Implicationsofthesemodelsinfrictionandwearstudiesarediscussed.Keywords:contactmechanics,tribology,asperitycontact,surfacedeformation,contactarea,roughsurfaces1.IntroductionSolidsurfaces,irrespectiveoftheirmethodofformation,containirregularitiesordeviationsfromaprescribedgeo-metricalform.Thehighpointsonthesurfacesarereferredtoasasperities,peaks,summits,orhillsandthelowpointsarereferredtoasvalleys.Whentwonominallyflatsurfacesareplacedincontact,surfaceroughnesscausescontacttooccuratdiscretecontactspots(junctions).Deformationoc-cursintheregionofthecontactspots,establishingstressesthatopposetheappliedload.Thesumoftheareasofallthecontactspotsconstitutesthereal(true)areaofcon-tact,andformostmaterialswithappliedload,thiswillbeonlyasmallfractionoftheapparent(nominal)areaofcon-tact(thatwhichwouldoccurifthesurfaceswereperfectlysmooth).Therealareaofcontactisafunctionofthesurfacetopography,materialpropertiesandinterfacialloadingcon-ditions.Theproximityoftheasperitiesresultsinadhesivecontactscausedbyinteratomicinteractions.Whentwosur-facesmoverelativetoeachother,theadhesionoftheseas-peritiesandothersourcesofsurfaceinteractionscontributetofrictionforce.Repeatedsurfaceinteractionsandsurfaceandsubsurfacestresses,developedattheinterface,resultintheformationofwearparticlesandeventualfailure.Thus,thecontactmodelingoftworoughsurfacesisofconsider-ableinterestinthestudyoffrictionandwear[1–3].Roughnessmapsofaceramicsubstratemeasuredusingthreedifferentmeasuringinstrumentswithdifferentsam-plingintervals(lateralresolutions)areshowninfigure1.Thefigureshowsthatroughnessisfoundatscalesrangingfrommillimetertonanometer(atomic)scales.Althoughsurfaceroughnessisintrinsic,measuredroughnessisex-trinsic.Instrumentsusingdifferentsamplingintervalsmea-surefeatureswithdifferentlengthscales.Itcanbecon-cludedthatasurfaceiscomposedofalargenumberoflengthscalesofroughnessthataresuperimposedoneachother[4–6].Therefore,“Itisnotthatdifferentasperitiescomeindifferentsizesbutitisthatoneasperitycomesindifferentsizes”.Distributionofsizeandshapeofasper-itiesisdependentonthemeasurementtechnique.Whenthesamplingintervalatwhichthesurfaceisexaminedisreduced,thenumberofasperitiesdetectedandtheircur-vatureappeartorisewithoutalimitdowntotheatomicscale.Thismeansthatanasperityisnota“definiteobject”.Attemptshavebeenmadetoidentifyacorrectsamplingin-tervalwhichyieldstherelevantnumberofsummitsandtherelevantcurvatureforaparticularapplication(functionalfiltering)[7,8].Anasperityrelevantforcontactmechan-icsisdefinedasthatwhichmakesacontactinaparticularapplication(contactingasperity).Asthetwosurfacesarebroughtincontact,nanoscaleasperitiesarethefirsttocomeintocontact,instantlydeformingplastically,andmergingtoformmicro-tomacrocontacts,whichuponfurtherapplica-tionofloadmaydeformbyelasticorelastic–plasticdefor-mation[9].Thus,sizeandnumberofcontactingasperitiesaredependentontheinterfaceconditions.Bothfrictionandweararestronglyinfluencedbythedegreeofplasticinteractionofthecontactingasperities.©J.C.BaltzerAG,SciencePublishers2B.Bhushan/ContactmechanicsofroughsurfacesFigure1.Surfaceroughnessprofilesofaglass-ceramicsubstratemeasuredusinganatomicforcemicroscope(lateralresolution15nm),stylusprofiler(SP)P2withastylustipof0.2mradius(lateralresolution0:2m),andAlpha-step200(-200)withastylustipof5mradius(lateralresolution2m),andnoncontactopticalprofiler(NOP)(lateralresolution1m)[29].Modelingofthecontactofroughsurfacesisdifficultandhasbe