Stress distributions in plasma-sprayed thermal barrier coati(5)

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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thecaseoflargerA.ThisalsoisincontrasttothebehaviouratthepeaklocationwherethedecreaseofsrisfasterforlargerA.Fig.7showsanotherpresenta-tionofthelocaldependenceofsratthevalleylocationforvariousamplitudes.Heretheoriginoftheradialco-ordinateisnotpositionedatthebottomofthevalleybutatthemidpointofalinethatconnectstwoadjacentpeaks(position‘T’inFig.1).ItisobviousthatapartfromratherlowvaluesofAthelocaldependencesoftheradialstressarequitesimilarfordifferentA.Thatmeansthestresslevelsoutsidethevalleyarealmostunaffectedbythedepth,ortheshape,ofthevalleyitself.

Thedifferencesinthelocaldependencesbetweenpeakandvalleylocationcanbeexplainedasfollows:contrarytothepeakthematerialofthetopcoatatthevalleypositionisflankedbybondcoatmaterialonbothsides.Narrowvalleys(largeA,smallL)willinparticularleadtoadifferentstressevolutionincomparisontothepeakwherethetopcoatmaterialisnotconfined.ObviouslyanalyticalfitsbasedonEq.(3)cannotdescribethelocalstressdependenceatthevalleyposition.

3.1.2.3.Isolatedpeaksandvalleys.Inadditiontothesinusoidal-shapedinterface,weperformedFEcalcula-tionsforsinglepeaksandsinglevalleys.Heretheheightofthepeakorthedepthofthevalleyisgivenby2AwhileLnowrepresentsthepeakwidthorthevalleywidth.Thedependenceoftheradialstressattheinter-faceonamplitudeandperiodlengthwasalsofittedwiththehelpofEq.(1).Theexponentphadtobeslightlylarger(e.g.ps1.1fortheroughnesspeak).AgainsrisafunctionofthequotientLyAasagoodapproximation.Theradialstresslevelsinthevicinityoftheinterfacearehigherforthesinglepeakcomparedtothepeakofthesinusoidalinterface(withthesameAandL).Incontrast,thedifferencesbetweenthestressesofthesinglevalleyandthevalleylocationofthesinusoidal

Fig.7.Localdependencesoftheradialstressabovethebottomofthevalleyfordifferentamplitudes(As1,5,10,20,30,40mm)withRs0atposition‘T’inFig.

1.

profilearerathersmall.Thelocaldependencesoftheradialstressesabovethesinglepeakandabovethebottomofthesinglevalleyarecomparabletothedependencesfoundforthesinusoidalprofile.Theresultsofthecalculationsonsinglepeaksandvalleysarenotpresentedinthispaper.3.2.Interfacewithoxidescale

Duringthehightemperaturephasesofthermalcyclingbondcoatoxidationleadstothegrowthofathermallygrownoxide(TGO)layerattheBC–TBCinterface.Thislayerconsistspredominantlyofa-Al2O3w1x.AgaininourcalculationstheTGOisassumedtobestress-freeatthesehightemperatures.Stressesthatariseduringgrowthoftheoxidescalew19,20xhavenotyetbeentakenintoaccount.

Asalreadymentioned,thethermalexpansioncoeffi-cientoftheoxideisrathersmallcomparedtothatof

Fig.6.Localdependencesoftheradialstressabovethebottomofthevalleyfordifferentamplitudes,A,andperiodlengths,L.Left:fixedL,amplitudes:5–40mm;right:fixedA,periodlengths:20–250mm.