Stress distributions in plasma-sprayed thermal barrier coati(3)

Stress distributions in plasma-sprayed thermal barrier coatings as a function of interface roughness and oxide scale thickness

28M.Ahrensetal./SurfaceandCoatingsTechnology161(2002)26–35

Stress distributions in plasma-sprayed thermal barrier coatings as a function of interface roughness and oxide scale thickness

M.Ahrensetal./SurfaceandCoatingsTechnology161(2002)

26–3529

Fig.3.Radialstressatthebottomofthevalleyasafunctionofamplitude(left)andperiodlength(right)ofthesinusoidalroughnessprofile.Dots:FEcalculation,dashedline:analyticalfit.Parametersacc.toEq.(1):sros17MPa,c1sy425MPa,c2s0.004,ps2.3.

thatsrisafunctionofthequotientLyA.ThefitfunctionsareadditionallydepictedinFigs.2and3(dashedlines).ThedependencesofsronAandLcanbeapproximatedwiththesameEq.(1)forbothpeakandvalleylocationbyusingdifferentexponentsandconstants(c1,c2).AccordingtothehigherexponentpwealreadyobtainsaturationofsrforintermediatevaluesofLyAinthecaseofthevalleyposition.Forexample,concerningthedependenceonamplitude(leftdiagramofFig.3)saturationbehaviourisobservedwithincreasingAintheinvestigatedamplituderangewhileinthecaseofthepeakposition(Fig.2)thereisstilladistinctincreaseofsr.

Thefactthattheradialstressis(asagoodapproxi-mation)afunctionofLyAwseeEq.(1)xshowsthatsrdoesnotsimplydependontheradiusofcurvatureofpeakorvalley,respectively.InthiscasesrshouldbeafunctionofL2yAsincetheradiusofcurvatureatthepeaktipandatthebottomofavalleyofasinusoidalinterfaceisgivenbyL2y(4p2A).

Wheninvestigatingtheinfluenceofthecurvatureoftheinterfaceroughnessonthestresslevelsthetwo-concentric-cylindersmodelalreadymentionedissome-timesusedintheliteraturew13,14x.Fromourownanalyticalcalculationsweobtainthefollowingfortheradiallocaldependenceoftheradialstressintheoutershell

B

K111E

2

sr r.sRiCyFDT

1qK2RiyRaDr2R2aG

coatingwrsRa,seeEq.(2)x.Asstatedabovetheradius

ofcurvatureofasinusoidalinterfacewithamplitudeAandperiodlengthLisequaltoL2y(4p2A).FortypicalvaluesAf10mmandLf50mmthisgivesf6mmfortheradiusofcurvature,wellbelowRa.PerformingthesubstitutionRsryRiEq.(2)canbeapproximatedinthecaseRi<Raby:REy2

sr R.sK1C1qF

RiGD

B

(3)

Consideringthestressesdirectlyattheinterface(Rs

0),itcanbeseenthatsrnolongerdependsonRiandhenceisindependentofthecurvatureoftheroughnessprofile.ThisisincontradictiontotheFEresults,whichshowadefinitedependenceofsr(Rs0)onAandL.Itisnotpossibletopredicttheinfluenceofthecurvatureonthestressesattheinterfacebyapplyingthesimpletwo-cylinders-model(usingrealisticvaluesforRiandRa).Obviouslyabondcoatpeakcannotsimplybetreatedasametallicinclusioninaceramicmatrix.Nevertheless,Eq.(3)canbeusedtogaininsightintothelocaldependenceoftheradialstress.Thiswillbeshowninthefollowing.

3.1.2.Radialstressabovepeakandvalleylocations3.1.2.1.Peak.Fig.4showsthelocaldependencesoftheradialstressabovethepeaklocationwhichwereobtainedbyFEcalculationsfordifferentAandL.Theoriginoftheradialco-ordinateRisdirectlypositionedattheBC-topcoatinterfaceattheasperitytip(labelled‘P’inFig.1).InFig.5theresultsareplottedagain,butnownormalisedto1atRs0.

Additionalanalyticalfitsweremadewithsr(R);(1qRyRi)y2accordingtoEq.(3).TheresultsareshowninFig.5.Theplotsrevealthathighlycurvedpeakshavehighstresslevelsdirectlyattheinterfacethatdecreaseoverarathershortdistancetothelevelwithoutinterfaceroughness.IfAisvaried(keepingLconstant)thisisshownmoredistinctlyinFig.5.Inthis

(2)

whereRiandRaaretheradiioftheinnerandoutercylinder,respectively.K1andK2areconstantsdependingonmaterialspropertieswhichareindependentoftem-peratureinthisapproach.Thebond-coatpeakistreatedasa(cylindrical)metallicinclusionwithinaceramicmatrixwhileRirepresentstheradiusofcurvatureatthetipoftheroughnesspeak.Thedistancerismeasuredfromtheaxisofthecylindricalinclusion.Raiscompa-rabletothethicknessofthetopcoat(f300mm)toprovidesr(r) 0whenapproachingthesurfaceofthe