Stress–strain state of multiwall carbon nanotube under internal pressure

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1、JournalofNanoparticleResearch4:207214,2002.©2002KluwerAcademicPublishers.PrintedintheNetherlands.Stress–strainstateofmultiwallcarbonnanotubeunderinternalpressureB.A.Galanov,S.B.GalanovandY.Gogotsi*InstituteforProblemsinMaterialsScience,NationalAcadem

2、yofScience,Kiev,Ukraine;UkrainianResearchandDesignInstituteofSteelConstruction,Kiev,Ukraine;DepartmentofMaterialsEngineering,DrexelUniversity,∗3141Chestnutstreet,Philadelphia,PA19104,USA;Authorforcorrespondence(Tel.:215-895-6446;Fax:215-895-6760;E-ma

3、il:gogotsi@drexel.edu)Received6September2001;acceptedinrevisedform11December2001Keywords:nanotubes,strength,nanoscalemechanics,modeling,nanofluidics,hydrothermalsynthesis,internalpressureAbstractAconsideredapplicationofcarbonnanotubesisnanopipinginnan

4、ofluidicdevices.Theuseofnanotubesforfluidtransportrequireslarge-diametertubesthatcansustainprescribedloadingwithoutfailure.Twomodelsofthestressstrainstateoflongmultiwallcarbonnanotubes,subjectedtointernalpressure,aredescribed.Cylindricalnanotubeshaving

5、aRussiandollstructurehavebeenconsidered.Itisassumedthatthedeformationsarelinearelasticandnegligiblealongthetubeaxis(incomparisonwiththeradialdeformations).Thisassumptionisnotrestrictiveforpotentialapplicationsofnanotubes,wheretheirdeformationsmustbes

6、mallandreversible.Thedistancebetweenthelayersissmallincomparisontotheradiiofcurvatureofgraphitelayers.Inthecaseofseveralcarbonlayers,adiscretemodel(DM)isproposed.ThesolutionsofDMequations,withcorrespondingboundaryconditions,determinethestressesbetwee

7、nthelayers,theforcesinthelayers,andthedeformationofthelayers.Forthecaseofthickwallsbuiltofnumerouscarbonlayers,acontinuousmodel(CM)isproposed.ThemainCMequationistheEulersdifferentialequationwithcorrespondingboundaryconditions.Itssolutiondefinesthecont

8、inuousdistributionofthestressesandstrainsacrossthewallthicknessofthetube.NotationsE2radialYoungsmodulusTitangential(hoop)stressinlayeri,mea-a0distancebetweentwoadjacentlayersbeforedefor-suredinPa·m(στi=Ti/a0)mation(a0=const)(Figure2)εi=στi/E1tangenti