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1、Proc.R.Soc.A(2006)462,319–348doi:10.1098/rspa.2005.1563Publishedonline22November2005Elastic–plasticcontactofaroughsurfacewithWeierstrassprofileBYYAN-FEIGAOANDA.F.BOWER*DivisionofEngineering,BrownUniversity,Providence,RI02912,USAWeanalysecontactbetweenarigidcy
2、lindricalindenterandanelastic–perfectlyplasticsolidwithafractalsurfaceroughness,whichisidealizedasaWeierstrassprofile.Ahierarchicalschemeisusedtocalculatequantitiessuchasthenumberofcontactspots;theirsize;thetruecontactpressureactingonthecontactspots,andthetot
3、altrueareaofcontact.Inaddition,wecalculatecriticalconditionsthatwillinitiateplasticflowintheasperities,anddeterminetheextentofthisplasticflowasafunctionoftheappliedloading,thematerialpropertiesofthedeformingsolid,andthesurfaceroughness.Animportantconclusionofo
4、urstudyisthataperfectlyfractaldescriptionofsurfaceroughnessappearstoleadtounphysicalpredictionsofthetruecontactsizeandnumberofcontactspots,forbothelasticandelastic–plasticsolids.Possibleapproachestoresolvingthesedifficultiesarediscussed.Keywords:self-affinefra
5、ctal;contactmechanics;surfaceroughness;plasticity1.IntroductionWhentworoughsurfacesarepressedintocontact,theymeetonlyatthehighestpointsonthetwosurfaces.Topredictthesizeoftheresultingcontactspots,thetruecontactpressure,andthetrueareaofcontactisavenerableprobl
6、emincontactmechanics,andisclearlyofconsiderablepracticalimportance,sincephenomenasuchasfriction,wear,andcontactfatiguearecontrolledbythenatureofasperitycontacts.Nevertheless,afullysatisfactorysolutionremainselusive.Difficultiesinmodellingcontactbetweenroughsu
7、rfacesarisebecauseofthefractalnatureofsurfaceroughness.Earlymodels,suchastheclassicworkofGreenwood&Williamson(1966)andsubsequentrefinementsbyWhitehouse&Archard(1970),Nayak(1971),Bushetal.(1975),Greenwood(1984)andMcCool(1986)amongothers,idealizedaroughsurfacea
8、sacollectionofasperitieswithsphericaltipsofequalradius,butwithaGaussiandistributionofheights.Thesemodelspredictawell-definednumberoftotalcontactspots,contactsize,contactpressureandcontactarea,whi
