Stress distributions in plasma-sprayed thermal barrier coati(2)

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

M.Ahrensetal./SurfaceandCoatingsTechnology161(2002)

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Fig.1.GeometryoftheTBCsystemusedintheFEcalculations.TheinsetshowsthesinusoidalroughnessprofileattheBC–TBCinterface.‘P’and‘V’indicatepeakandvalleylocations,respectively.

thestressstatesintheTBConamicroscopicalscalewithhelpofFEcalculationstakingintoaccountthebondcoatroughnessandthethermallygrownoxideattheBC–TBCinterface(butnotgrowthstressesduetobondcoatoxidation).Weanalysethespatialdependenceofstressesatpeakandvalleypositionsoftheinterfaceroughnessforvariousparameterscharacterisingthisroughness.Afurtherparameteristhethicknessoftheoxidelayer.Incontrasttotheabovementionedresearchonstressdistribution,weattempttoobtainapproximatedanalyticaldescriptionsofthecalculatedspatialdepend-ences.Suchanalyticalfunctions,comprisingparametersofroughnessandoxidethickness,willbeusedinafurtherstageofmodellingwhenweconsidercrackinitiationandpropagationcausedbystressevolutionduringthermalcycling.Theywillbepublishedinalaterpaper.

2.Modeldescription2.1.Experimentallymodelling

supported

assumptions

for

Heatinganas-sprayed,nearlystress-freeTBCsystemtoelevatedtemperatures(approx.10008C)willdeveloptensilein-planestressinthetopcoat.Taking40MPaasYoung’smodulusoftheTBC,thestresslevelcanbeestimatedbymeansofthesimpleformulasfETBC(aSubyaTBC)DTtobeapproximately200MPa(aSubf1.5=10y5yK,aTBCf1=10y5yK).Asporousplasma-sprayedceramiccoatingscannotresistsuchhighstressessegmentationcracksreducingthestresseshadtobeexpected.However,wehavenotyetobservedsegmentationcracksafterthermalcyclinginourexper-iments.Wethereforeassumethatothermechanismsofrelaxationmustoperate:thelayeredandcrackedstruc-tureoftheTBCallowstheslidingofthespraylamellaealongtheirinterfacestoacertainextent.ThisresultsinasmallaverageYoung’smodulusandlargecreeprates

oftheTBCathightemperaturesintheearlystagesofthermalcycling.Themoduluscanbefurtherdiminishedbytheopeningofmicrocrackslocatedwithinthespraysplatsw22x.Indeed,significantlylowereffectivevalues(f15GPa)fortheYoung’smodulusofas-sprayedTBCsinadditiontopronouncedcreephavebeenfoundrecentlyw23,24x.Even,ifcreepwereneglected,lowervaluesofYoung’smodulusalonewouldreducethethermalstresscausedbyheatingtovaluesbelow100MPa.DuringhightemperatureoperationsinteringattheinterfacesofthespraylamellaeaccompaniedbyhealingofintrasplatmicrocracksleadstoanincreaseofYoung’smodulusandareductionofcreepw24x.Throughoutthermalcyclingtheseprocessesincombinationwillcauseagradualincreaseofthein-planecompressivestresslevelatroomtemperature.

InourcalculationsweassumedforthesakeofsimplificationthattheTBCsystemisstressfreeathightemperature(10008C)ingthismethoditwaspossibletoexaminefactorswhichgovern,oratleastaffect,theresidualstressesintheTBC.Duringcoolingthebehaviourofallmaterialswasassumedtobefullyelastic.Thematerialspropertiesusedformodellingaregiveninw8,9x.2.2.Modellingdetails

ThecalculationsofthestresseswithintheTBCwereperformedbymeansofthefiniteelement(FE)codeABAQUSw21x.Totakeintoaccountthefactthatspallationofthecoatingsoftenoccursatthecurvedendsoftheturbinebladesweusedacylindricalgeom-etry,showninFig.1.Theradiusofthesubstratewasselectedas5mm,thethicknessoftheBCwas150mmandthethicknessofthetopcoatwas300mm.Thecylinderwasassumedtobelongincomparisontoitsdiameter.ThisleadtoasimplificationoftheFEcalcu-