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Acta Materialia 57 (2009) 2349–2361

The influence of bondcoat and topcoat mechanical propertieson stress development in thermal barrier coating systems

E.P. Busso a,*, Z.Q. Qian b, M.P. Taylor c, H.E. Evans c

a Centre des Materiaux, Mines ParisTech, B.P. 87, CNRS-UMR 7633, 91003 Evry, Franceb Department of Mechanical Engineering, Imperial College, London, UK

c Department of Metallurgy and Materials, The University of Birmingham, Birmingham, UK

Received 21 September 2008; received in revised form 15 January 2009; accepted 15 January 2009Available online 13 March 2009

Abstract

A finite-element study has been undertaken to investigate the stress development within a TBC system consisting of an EB-PVD YSZtopcoat and a Pt-aluminized diffusion bondcoat. Particular attention has been paid to the role of variables such as the elastic anisotropywithin the topcoat, interface roughness, variation in creep strength of the bondcoat and the volumetric strains associated with the for-mation of the thermally grown oxide (TGO). Bond coat oxidation and thermal loading during cooling give rise to significant tensile stres-ses within the topcoat and tensile tractions at the TGO interfaces. Bondcoat creep, as distinct from yield and plastic behaviour, was thedominant stress relaxation process, and strong bondcoats (in creep) tended to show higher tensile stress levels. Another important factordetermining thermal barrier coating stress levels was the level of elastic anisotropy of the topcoat: an elastic isotropic yttria-stabilizedzirconia gave rise to considerably higher stresses than a transversely isotropic topcoat.� 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Finite element analysis; Thermal barrier coating system; TBC; Stress analysis; Sintering

1. Introduction

Thermal barrier coatings (TBCs) are widely used inaerospace and land-based gas turbines to improve the per-formance and efficiency of the engine. A typical TBC sys-tem consists of an outer yttria-stabilized zirconia (YSZ)ceramic layer and an aluminium-rich intermediate metalliclayer which serves as an oxidation-resistant bondcoat (BC).A thermally grown oxide (TGO) layer develops along themetal–ceramic interface at elevated temperatures.Fig. 1(a) is a typical cross-section showing the main com-ponents of an EB-PVD/Pt-aluminide TBC system andthe TGO developed after 3 h of oxidation at 1200 �C.

Failures of TBC systems occur by the delamination ofthe YSZ topcoat resulting from the slow growth and even-

1359-6454/$36.00 � 2009 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2009.01.017

* Corresponding author. Tel.: +33 1 60 76 30 01; fax: +33 1 60 76 31 50.E-mail address: esteban.busso@ensmp.fr (E.P. Busso).

tual coalescence of sub-critical cracks. These cracks canform within the topcoat at its base (e.g. Fig. 1(a)), at theTGO/YSZ interface, within the TGO or at the TGO/BCinterface [1–6]. The formation of such cracks can be relatedto local high values of principal tensile stresses or to inter-facial tractions. Finite-element (FE) methods can be usedto estimate the magnitude and location of such stressesbut it is important to allow, within the FE model, for thevolume expansion associated with TGO formation [6–8].This is particularly important when realistic non-planarBC surfaces are considered since the volume change associ-ated with TGO formation will then result in out-of-planestress development at temperature [5]. Further examinationof the influence of BC surface roughness, given by the ratio(b/a) in Fig. 1(b), will be made in this present FE study.

The quality of FE predictions depends also on the use ofappropriate mechanical properties for the BC, TGO andYSZ topcoat. The BC, in particular, will creep readily attypical operating temperatures [9–12] but, for simplicity,

rights reserved.

Fig. 1. (a) SEM micrograph of a TBC system containing an EB-PVD YSZ topcoat and a Pt-aluminide bondcoat after 3 h of oxidation at 1200 �C. (b) Therepresentative periodic unit cell used in the finite-element analysis. (Arrows in (a) point at TBC microcracks.)

Table 1Pt-aluminide bondcoat elastic and yield strength, ry, values used in theanalyses.

T (K) 293 473 673 873 1073 1273 1373

ry (MPa) 426 412 396 362 284 202 114E (GPa) 117 113 108 104 99 94 92a/10�6 (K�1) 12.3 13.2 14.2 15.2 16.3 17.2 17.7

2350 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

some researchers [13,14] have treated this nonlinear behav-iour of the bondcoat by using elastic/perfectly plastic prop-erties. This idealistic behaviour has been modelled,however, using time-dependent stress relaxation data [11].Nevertheless, more recent creep data [12] have indicatedthat a significant batch-to-batch variation in creep strengthcan exist. Higher creep strength can be expected when alu-minium and platinum contents favour the precipitation ofa fine dispersion of c0 (nominally, Ni3Al) particles. Theobjectives of the present work are twofold. The first objec-tive is to assess the sensitivity of predictions of stresseswithin the TBC system to the assumed flow properties ofthe bondcoat. Accordingly, computations will be under-taken for an EB-PVD TBC system containing a Pt-alumi-nide bondcoat (Fig. 1(a)) which deforms by either of thecreep characteristics [11,12] reported for that bondcoat,and by assuming either an ideal elasto-plastic or an idealelastic behaviour.

It is noted that, in previous studies [13,15], the topcoathas been treated either as a homogeneous isotropic mate-rial or considered to be a fully compliant one [16]. In fact,the properties of the transversely isotropic YSZ materialwhich results from EB-PVD deposition depend on manyfactors, such as the sintering time, sintering temperatureand the orientation of the local transversely isotropic mate-rial axis [8]. Thus the second objective of this work is toassess the effects of YSZ morphology resulting from depo-sition and its sintering behaviour on the TBC stresses. Tothat purpose, the effects of YSZ sintering will be incorpo-rated into the FE model.

2. Material properties

2.1. Creep and thermo-mechanical properties

The TBC system considered consists of a Pt-aluminideoxidation-resistant BC, a YSZ topcoat deposited by EB-PVD (Fig. 1(a)) and a TGO consisting of a -alumina. Thiscoating system is bonded to a superalloy substrate.

The (Ni,Pt)Al bondcoats considered in this work aretreated as isotropic materials having a Young’s modulusdescribed by [11]:

E ¼ 1000ð118� 0:024T Þ ð1Þwhere T (K) is the temperature and E (MPa) is the Young’smodulus. Some values are given in Table 1, together withvalues of the linear expansion coefficients, a. The Poisson’sratio was taken as 0.3, invariant with temperature. Theyield strengths, ry, at different temperatures are obtainedfrom Cheng et al. [13] and are also summarized in Table 1.

As described earlier, the creep behaviour for the bond-coat were taken either from Taylor et al. [12] or fromPan et al. [11]. In the former case, the creep rate (s�1) isdescribed by:

_eC ¼ 8:75� 108r6:82 exp � 616000

8:314T

� �ð2Þ

where the equivalent Mises stress, r, is in MPa and the tem-perature, T, is in K. This algorithm will be referred to laterin the paper as (Ni,Pt)Al-1. Two different creep equationswere suggested by Pan et al. [11], namely

_eC ¼ 9:1� 1027 rE

� �4

exp � 400000

8:314T

� �ð3Þ

and

_eC ¼ 6:3� 1013 rE

� �4

exp � 125000

8:314T

� �ð4Þ

where the symbols have the same meaning and units as inEqs. 1 and 2. Note that, from a physical point of view, a

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2351

creep exponent close to 4 is associated with dislocationcreep. Eqs. 3 and 4 will be referred to as (Ni,Pt)Al-2aand (Ni,Pt)Al-2b, respectively.

Eqs. (2)–(4) show a wide variation in activation energy,even within the same data set (Eqs. 3 and 4), and stressdependence of creep rate and serve to demonstrate the needto assess the sensitivity of predictions of stress to these val-ues. A graphical comparison of the three equations at1100 �C (1473 K) is given in Fig. 2. For the stress rangeshown, the range of predicted creep rates extends overmany orders of magnitude illustrating the level of uncer-tainty in BC creep behaviour. Also included in this figureis a generic creep curve [7] describing the behaviour of aNiCoCrAlY bondcoat. Its creep response falls within therange associated with Pt-aluminide behaviour (see Fig. 2).It should be noted that, of necessity, Eqs. (2)–(4) will needto be extended beyond their experimentally validated rangeat stages during the numerical computations (i.e. toapproximately 200 MPa).

As with the bondcoats, the a -alumina TGO is assumedto be an isotropic and homogeneous material. The Young’smodulus and other elastic properties at various tempera-tures are listed in Table 2 [13]. It should pointed out thatall the data shown in this section were fitted to polynomialfunctions when used in the finite element calculations.

The creep properties of the alumina TGO are taken as[17]:

_eC ¼ 6:80� 103r2:3 exp � 424000

8:314T

� �ð5Þ

where stress, r, is again in MPa and temperature, T, is in K.It can be appreciated from Fig. 2 that the creep strength ofthe TGO is expected to be appreciably higher than that ofthe bondcoat for the stresses and strain rates of interest.

Due to its columnar microstructure, the EB-PVD YSZtopcoat is treated as a transversely isotropic elastic mate-rial, with its elastic moduli taken to be a function of sinter-

1,E-12

1,E-10

1,E-08

1,E-06

1,E-04

1,E-02

1,E+00

1,E+02

1,E-01 1,E+00 1,E+01 1,E+02 1,E+03Stress (MPa)

Stra

in R

ate

(1/s

)

(Ni,Pt)Al-1 (Ni,Pt)Al-2a

(Ni,Pt)Al-2b NiCoCrAl Al2O3

Fig. 2. Creep properties of the different bondcoats and of the a -aluminaTGO at 1100 �C. The creep data of (Ni,Pt)Al-1 were obtained from Ref.[12] (Eq. 2) and those of (Ni,Pt)Al-2a and b were taken from Ref. [11](Eqs. 4 and 3, respectively). The creep data for the NiCoCrAlY coatingwas taken from Ref. [7] and that for the TGO from Ref. [17].

ing time and temperature. The sintering behaviour and thethermo-mechanical properties of the YSZ topcoat areobtained from Ref. [8]. The elastic properties after 100 hsintering at 1473 K are summarized in Table 3; it shouldbe noted that the bulk Young’s modulus of YSZ is210 GPa according to Schulz et al. [18]. In the sinteringmodel of Qian and Busso [8], it is assumed that the elasticstiffness in the local X10 and X30 directions (see Fig. 1b) arethe same, but that in the X20 direction may be different. Theaxes X10 and X30 are assumed to be parallel and perpendic-ular, respectively, to the TGO/YSZ interface in the vicinityof that interface (see Fig. 1(b)). When considering locationswithin the YSZ remote from the interface (about threetimes the magnitude of the amplitude of the BC surfaceroughness), the orientation of the YSZ columns adoptsthat of the global material axes, i.e. X10 becomes parallelto X1 and X20 becomes parallel to X2. The elastic constantsof the YSZ are given in Table 3 at different temperaturesand after 100 h exposure at 1473 K. Here, E10 and E20 arethe elastic moduli along the local X10 and X20 axes, respec-tively, and mp is the in-plane Poisson’s ratio. Further detailsrelated to the sintering behaviour of the YSZ and the def-inition of the YSZ material axes may be found elsewhere[8]. Note that EB-PVD TBCs often exhibit a fine equiaxedmicrostructure at the TGO-YSZ interface (e.g. see Refs.[6,8]). This region has not been accounted for in this studydue to its relatively small size.

2.2. Bondcoat oxidation

From SEM measurements of TGO thickness, the fol-lowing equation was found to describe oxide thickness, h

(in m), as a function of exposure time, t (in s), at 1100 �C:

h ¼ Aþ Bt0:5 ð6Þwhere A = 0.5 � 10�6 m is the TGO thickness in the as-received condition prior to testing and B = 4.77 � 10�9 ms�0.5. The growth exponent in Eq. 6, typical of Pt-aluminized bondcoats, is rather high when compared withthe typical value of 0.3 obtained from simple theory ofoxidation/diffusion. This expression is shown as the solidline in Fig. 3 and predicts a total alumina TGO thicknessof approximately 3.4 lm after 100 h of exposure at1100 �C.

The formation of this oxide by selective oxidation ofaluminium from the bondcoat results in a volume increasedescribed by the Pilling–Bedworth ratio, U. A particularfeature of the present approach is that the progressivetransformation of the bondcoat to oxide can be modelledduring the FE analysis. This means that the effect of thecorresponding transformation strains on stress develop-ment can be assessed at the oxidation temperature in theabsence of any thermally induced strains. Due to this, itis important to use realistic values for the Pilling–Bedworthratio and some consideration needs to be given to this.

For simple pure metals, this ratio is readily defined asthe volume of oxide formed from the metal ion divided

Table 2Elastic properties of the TGO at different temperatures, T (from Ref. [13]).

T (K) 293 473 673 873 1073 1273 1373

E (GPa) 400 390 380 370 355 325 320m 0.23 0.23 0.24 0.24 0.25 0.25 0.25a/10�6 (K�1) 8.0 8.2 8.4 8.7 9.0 9.3 9.5

Table 3Elastic properties of the YSZ at different temperatures after 100 h exposure at 1473 K [7].

T (K) 293 473 773 973 1173 1373 1473

E20 (GPa) 205 196 188 182 178 174 173E10 (GPa) 67 64 61 59 58 56 56mp 0.10 0.10 0.10 0.11 0.11 0.12 0.12a/10�6 (K�1) 9.7 9.8 9.9 9.9 10.0 10.1 10.1

For comparison, the Young’s modulus of fully dense YSZ is 210 GPa [18].

0

1

2

3

4

0 20 40 60 80 100Oxidation Time (hrs)

TGO

Thi

ckne

ss (μ

m)

External TGO

Internal TGO

Total

Fig. 3. Measured total alumina thickness (including that preformed) as afunction of oxidation time at 1100 �C for the Pt-aluminized bondcoat. Theinternal and external components of the new oxide are also shown.

1 These computations were performed for NiAl, but it is assumed thatthey are relevant also to (Ni,Pt)Al.

2352 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

by the volume of the ion in the metal. For the oxidation ofaluminium via the reaction A:

2Alþ 3

2O2 ! Al2O3 ðAÞ

the Pilling–Bedworth ratio is given as

U ¼ V Al2O3

2V Al¼

V �Al2O3ZAl

2V �AlZAl2O3

ð7Þ

Here, the subscripts Al2O3 and Al refer to oxide and metal,respectively, and V is the corresponding ionic volume. Thiscan be calculated from the volume V* of the unit cell, avail-able in standard XRD data banks (e.g. [19]), by dividingthe cell volume by the number of ions in the unit cell, Z.In the case of the oxide, this is then an ‘‘average” ionic vol-ume. Thus, using V �Al ¼ 6:64� 10�29m3; ZAl ¼ 4; V �Al2O3

¼25:47� 1029m3; ZAl2O3

¼ 6 gives for reaction A from Eq. 7:

U ¼ 1:28

This is the generally accepted value for the oxidation ofpure aluminium. An identical value is obtained if the calcu-lation were done using molar volumes.In the present con-text of the selective oxidation of the b-(Ni,Pt)Albondcoat, the removal of an aluminium ion will reduce

the stoichiometry of the b layer but not necessarily causea phase transition. This arises because there is a wide com-position range over which the b phase is stable [20], transi-tion to the c0 structure occurring only at aluminiumcontents <�38 at.% Al at 1100 �C. First principles calcula-tions [21] show that vacancies on the aluminium sub-latticeare viable defects in the b-phase, as are nickel ions on alu-minium sites.1 The selective oxidation of aluminium fromthe bondcoat in the present system can then be consideredto occur by the removal of an aluminium ion, its replace-ment with a viable point defect within the b-structure andthe oxidation of the removed ion. The sequence is de-scribed by reaction B for the case of aluminium vacancies:

ðNi;PtÞxAly þ3

2O2 ! ðNi;PtÞxAly�2 þ 2Alþ 3

2O2

! ðNi;PtÞx Aly�2 þAl2 O3 ðBÞ

The volume change, DV1, associated with the first step inthis reaction is:

DV 1 ¼ V ðNi;PtÞxAly�2þ 2V Al � V ðNi;PtÞxAly ð8Þ

where V represents the atomic or molecular volumes of therespective species. It is expected that this volume changewill be dominated to first order by the extra volume ofthe aluminium ions removed from the b phase. The factthat a vacancy is actually created as a result of this removal[20] indicates that relaxation within the (Ni,Pt) sub-latticeis likely to be small. It then follows from reaction B thatthe first-order volume change in the oxidation process isdetermined simply by that associated with the oxidationof aluminium to alumina. The Pilling–Bedworth ratio isthen given as

U ffi V Al2O3

2V Alffi 1:28 ð9Þ

At later stages in the oxidation exposure, when appreciablealuminium depletion has occurred in the near-surface

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2353

region of the bondcoat, the removal of further aluminiumcan be envisaged to initiate a phase transformation:

6NiAlþ 3O2 ! 2Ni3Alþ 2Al2 O3 ðCÞFor the purposes of this discussion, the reaction has beenwritten in terms of the simple Ni–Al, rather than (Ni,Pt)–Al phases because the volumes of the unit cells are reason-ably well established for the simpler system. The substitu-tion of platinum for nickel is likely to have some effecton these volumes, however. As before, usingV*Al2O3 = 25.47 � 10�29 m3 and ZAl2O3 = 6 together withV*NiAl = 2.41 � 10�29 m3, ZNiAl = 1, V*Ni3Al = 4.69 �10�29 m3 and ZNi3Al = 1 gives the effective Pilling–Bed-worth ratio for reaction C as:

U ¼2V�Ni3 Al=ZNi3Al

� �2V�Al2O3

=ZAl2O3

� �6V�NiAl=ZNiAl

� � ð10Þ

This is a similar value to that for the oxidation of both purealuminium and the b-(Ni,Pt)Al phase as discussed above.Again, an identical value is obtained if molar volumes, cal-culated from molecular weights and bulk densities, areused. This indicates that there will be no dramatic changesin the volume strains produced during the formation ofalumina on Pt-aluminide coatings even when the phasetransition of reaction C occurs. This differs from the argu-ment of Tolpygo and Clarke [22] who considered the vol-ume decrease associated with the transformation from bto c0 phase to be important to the formation of rumpleson the bondcoat surface. It should be recognized, though,that this transformation, at the surface of the bondcoatwhere aluminium diffusion into the alloy substrate is negli-gible, occurs as a result of the selective oxidation of alumin-ium. The volume increase associated with aluminaformation was neglected in their calculation of volumechange but needs to be included. When this is done, as inreaction C, an overall volume increase is found which is lit-tle different from that occurring on adjacent b phases.

In this present work, a value of the Pilling–Bedworthratio, U, of 1.28 for the formation of alumina has then beenused throughout. The mean volumetric strain, eV, due tothe transformation from metal to oxide is then 0.08 (=‘n(U)). This strain is not isotropic but is partitioned suchthat the component, eT

n ; normal to the TGO/BC interfaceis much larger than the in-plane transverse strain, eT

t . Thevalue of the ratio eT

n=eTt ¼ 87 incorporated into the present

analysis is the same as that used elsewhere [8] and derivesfrom the results of Huntz et al. [23]. The kinetics of growthof the internal and external components of the total oxidethickness at 1100 �C, based on Eq. 6, are shown in Fig. 3.

3. The finite element model

Full details of the FE model used in this work can befound elsewhere [7,8]. It is based on the commercial FEcode ABAQUS, but with the novel feature of allowingfor the volume changes occurring at temperature during

the oxidation of the bondcoat. In addition, creep of boththe bondcoat and TGO is permitted, as is progressive sin-tering of the YSZ topcoat. For the present work, theTBC system was held isothermally at 1100 �C, duringwhich time the TGO continued to thicken, before coolingto 25 �C. The transformation strains associated withTGO growth and the thermal strains during subsequentcooling were the only loads applied to the system.

The FE model was developed by first identifying repre-sentative YSZ-TGO interfacial regions (e.g. see Fig. 1) andthen repeating these as two-dimensional periodic unit cellswith appropriate periodic and symmetry boundary condi-tions. Two aspect ratios, defined as the ratio b/a inFig. 1(b), of 0.25 and 0.52, were used to study the effectof bondcoat roughness on the stresses developed withinthe TBC system. Fig. 4 shows the FE mesh and the bound-ary conditions when the aspect ratio (b/a) is 0.25. The ini-tial thicknesses of the BC and YSZ are 50 and 125 lm,respectively. The mesh consisted of about 5000 quadraticgeneralized plane strain elements with full integration.The displacement of the plane L (see Fig. 4) in the x1 direc-tion during cooling was imposed by the thermal expansionof the substrate [2].

4. Results and discussion

4.1. TGO thickness

Fig. 5(a) and (b) shows the computed thickness of theTGO layer after 100 h oxidation at 1100 �C for coatingswith roughness ratios of (a) b/a = 0.25 and (b) b/a = 0.52. In the figures, the internal and external compo-nents of the oxide are identified. Shown as the dark inter-mediate layer between these is the original alumina layerformed during processing. This, together with the entireTBC system, is assumed to be stress-free prior to the oxida-tion exposure. The lower interface of this original oxidelayer corresponds to the outer surface of the bondcoatobtained after coating deposition. It can be appreciatedfrom Fig. 5 how the bondcoat is partially consumed byoxide formation during the course of the FE analysis.For computational efficiency, it is assumed that the exter-nal oxide forms above the original oxide layer, whereas,in reality, it would be expected to form at its base as aresult of inward oxygen transport. This assumption hasno effect on calculated stresses, however, since the wholealumina layer is considered to be an isotropic solid withuniform properties. The total oxide thickness of 3.3 lmshown in Fig. 5 agrees with that predicted by Eq. 6.

4.2. Effects of bondcoat creep and plasticity

Fig. 6 shows contour plots of the out-of-plane stresscomponent, r22, at 1100 �C after 100 h of oxidation forboth values of initial TGO aspect ratio, namely (a) b/a = 0.25 and (b) b/a = 0.52. Here creep of the bondcoatand TGO and also the sintering of the YSZ are considered

Fig. 4. Typical FE mesh used in the TBC model for a bondcoat surface roughness ratio, b/a, of 0.25, with b = 11.06 lm.

Fig. 5. FE predictions showing the TGO layer after 100 h of oxidation at 1100 �C.

2354 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

in the stress analysis. The bondcoat creep properties usedare those of Taylor et al. [12] (Eq. 2). The stresses shownare those predicted at the test temperature of 1100 �C priorto cooling and confirm an earlier suggestion [5] that tensilewings will develop at temperature at the flanks of bondcoatprotuberances. These are a result of continuity strains aris-

ing from the volume expansion on oxide formation. Themagnitude of the tensile stress in these wings clearlyincreases with bondcoat surface roughness and maybecome sufficient to nucleate cracks within the topcoat atlocation A (see Fig. 6(a)) isothermally at the oxidationtemperature. Cracks at such locations are certainly found

Fig. 6. Contour plots of r22 at 1100 �C for two different TGO roughness ratios after 100 h of oxidation at the same temperature when creep of thebondcoat and TGO and the sintering of the topcoat are considered in the stress analysis. Here, the bondcoat creep properties used are those of Taylor et al.[12] (Eq. 2).

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2355

during post-test examination (see Fig. 1(a), for example),but it cannot be confirmed at this stage that these occurredat temperature. Another point of interest from Fig. 6 isthat out-of-plane tensile stresses are also expected, at theoxidation temperature, to occur above valleys of the bond-coat (location B). Their presence could help propagate a

Fig. 7. Contour plots of r22 at 25 �C after 100 h of oxidation at 1100 �C whencreep properties used are those of Taylor et al. [12] (Eq. 2).

crack across steep-sided valleys; again, examples can befound in Fig. 1(a).

Fig. 7(a) and (b) shows the contour plot of the out-of-plane stress component, r22, on cooling to 25 �C afteroxidation for 100 h at 1100 �C for two different TGOroughness ratios when, again, the creep effects of the

the creep effects of bondcoat and TGO are accounted for. The bondcoat

2356 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

bondcoat and the TGO are considered. Tensile wings arestill present (arrowed in Fig. 7(a)) but, as with the situationat the oxidation temperature, only on the rougher bond-coat interface (b/a = 0.52). The largest out-of-plane tensilestresses after cooling arise within the topcoat above the val-leys (arrowed in Fig. 7(a)). Either of these locations couldprovide, in principle, sites for crack nucleation within theYSZ topcoat or near the YSZ/TGO interface, at least withthe rougher bondcoat. It is also clear from Fig. 7 that sig-nificant out-of-plane stresses also develop in the bondcoatat the apex of protuberances. These stresses are absent atthe oxidation temperature (Fig. 6) and arise solely duringcooling as a result of thermal mismatch strains. In princi-ple, cracks could form in these locations during coolingat the TGO/BC interface due to the high tensile interfacetractions. The formation of tensile stress-driven crackswithin the bondcoat, however, is less likely due to the duc-tile nature of the bondcoat. The magnitudes of these tensilestresses/tractions increase with TGO thickness, as has beenshown in Ref. [8].

In order to understand the driving force responsible forthe nucleation of cohesive cracks entirely within the TGO,it is necessary to analyse the distribution of the maximumprincipal stresses in the TGO. This is given in Fig. 8(a)and (b), which shows the maximum principal stress con-tours for the two different TGO roughness ratios at1100 �C after 100 h of oxidation at the same temperature.Note that, following standard convention, a negative valueof the maximum principal stress implies that it is the leastnegative of the three components. The contour plots corre-sponding to those shown in Fig. 8 for the condition aftercooling to 25 �C are given in Fig. 9(a) and (b). As with

Fig. 8. Contour plots of the maximum principal stress at 1100 �C after 100 h oTGO creep are considered: (a) b/a = 0.52 and (b) b/a = 0.25. The bondcoat c

the out-of-plane stress, tensile regions exist at both temper-atures and surface roughness ratios within the TGO, inboth the apex and valley regions. The highest tensile prin-cipal stresses are found in the valley regions near the YSZ-TGO interface upon cooling (see Fig. 9(a)).Tensile wingswithin the YSZ topcoat have formed at both temperaturesfor the rougher bondcoat surface (b/a = 0.52) but areabsent, or much less pronounced, when b/a = 0.25.

Figs. 10 and 11 show the predicted normal tractionsalong the (a) TGO/YSZ and (b) the TGO/BC interfacesat 1100 and 25 �C, respectively, after 100 h of oxidationat 1100 �C for a TBC system, with bondcoat and TGOcreep behaviour taken into account and with the rougherinterface (b/a = 0.52). Three different types of bondcoatcreep properties are used, namely those reported by Tayloret al. [12] (Eq. 2) and by Pan et al. [11] (Eqs. 3 and 4) (seealso Fig. 2). It can be seen that, for all the different creepbehaviour, a tensile stress region develops across theTGO/YSZ interface around the valley regions both at theoxidation temperature and after cooling to 25 �C. In con-trast, tensile stresses across the TGO/BC interface occurappreciably around the bondcoat peak regions but onlyin the cooled specimen. These findings are consistent withregions where interfacial TGO cracks are known to nucle-ate [4].

Fig. 10(a) shows that the influence of the bondcoat creepbehaviour on the stress acting across the TGO/YSZ inter-face at 1100 �C is important: there is a nearly factor twodifference in this traction at the bondcoat valley betweenthe low-strength bondcoat variant, (Ni,Pt)Al-2b, given byEq. 4, and the stronger variant given by Eq. 2, (Ni,Pt)Al-1. It is the stronger bondcoat which develops the higher

f oxidation at the same temperature in a TBC system when bondcoat andreep properties used are those of Taylor et al. [12] (Eq. 2).

Fig. 9. Contour plots of the maximum principal stress at 25 �C after 100 h of oxidation at 1100 �C in a TBC system when bondcoat and TGO creep areconsidered: (a) b/a = 0.52 and (b) b/a = 0.25. The bondcoat creep properties used are those of Taylor et al. [12] (Eq. 2).

Fig. 10. Normal tractions along the (a) TGO/YSZ and (b) TGO/bondcoat interfaces at 1100 �C after 100 h of oxidation at the same temperature for aTBC system with three different bondcoat creep strengths and TGO creep behaviour (b/a = 0.52).

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2357

tensile traction at the TGO/YSZ interface since it will expe-rience lower stress relaxation rates. By contrast, there isnegligible difference in the peak tensile tractions betweenthe three bondcoat strengths examined after cooling to25 �C (Fig. 11(a)). This observation suggests that the finalstress values shown in each of the bondcoats are developedlargely at temperatures where creep relaxation rates arenegligible.

A similar pattern arises at the TGO/BC interface at theoxidation temperature (Fig. 10(b)) except that the strongestbondcoat experiences an approximately factor 10 highertensile stress at the bondcoat valley than does the weakestbondcoat. Absolute values of stress at this interface arelower, however, than at the TGO/YSZ interface. Another

difference is that the location of the maximum tensile trac-tion at the TGO/BC interface moves to the apex of thebondcoat protuberance after cooling to 25 �C. The stron-gest bondcoat exhibits the highest tensile stress in this casealso, although there is little difference in the predicted stresslevels between the creep behaviour given by Eqs. 3 and 4.

The effects of different bondcoat elastic-plastic-creepmechanical behaviour have also been studied in this workto investigate the relative effects of each deformation mech-anism. Three different cases were considered: (i) the BCdeforms only elastically; (ii) the BC has elasto-creep defor-mation; and (iii) the BC exhibits elasto-plasto-creep defor-mation. The strongest bondcoat creep property is used,namely that of Taylor et al. [12] ((Ni,Pt)Al-1 in Fig. 2).

Fig. 11. Normal tractions along the (a) TGO/YSZ and (b) TGO/bondcoat interfaces at 25 �C after 100 h of oxidation at 1100 �C for a TBC system withthree different bondcoat creep strengths and TGO creep behaviour (b/a = 0.52).

Fig. 12. Normal tractions along the TGO interfaces at 1100 �C after 100 h of oxidation at the same temperature in a TBC system when the BC wasconsidered to have (1) elastic deformation only, (2) elasto-creep deformations and (3) elasto-plasto-creep deformations, and the TGO had elasto-creepbehaviour. The creep data corresponds to (Ni,Pt)Al-1 (Eq. 2). b/a = 0.52.

2358 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

The normal tractions along the TGO interfaces at 1100 �Care plotted in Fig. 12 and at 25 �C in Fig. 13. As before, (a)refers to the TGO/YSZ interface and (b) to the TGO/BC.It can be appreciated from Fig. 12 that purely elasticbehaviour can lead to significant discrepancies in predictedstress at the creep temperature since relaxation processesare not accounted for. This is particularly noticeable atpeak regions where, at the TGO/YSZ interface, essentiallyzero stress is expected under elastic conditions but a signif-icant compressive traction (��60 MPa) is predicted underrelaxed conditions. The converse holds at the TGO/BCinterface for here the peak regions experience large tensiletractions under elastic deformation but approximately zerostress when elasto-creep or elasto-plasto-creep conditionsexist. It should be noted that, at each interface, the predic-tions of both of these latter are essentially identical indicat-ing that the mechanical response is dominated by creeprather than by yield and athermal plasticity.

Similar trends develop on cooling to 25 �C, as can beseen from Fig. 13. The most striking feature here is the

large tensile stress (�0.9 GPa) predicted to develop underelastic conditions across the TGO/BC interface above peakregions. This is significantly relaxed to �400 MPa by bond-coat creep (Fig. 13(b)) and further to �300 MPa if bond-coat athermal plasticity is permitted in addition to creep.This result indicates that creep remains the importantrelaxation process even during cooling although there isclearly a contribution from athermal plasticity.

4.3. Effect of YSZ material properties

In order to study the effects of the YSZ elastic propertieson the stress state of the TBC system, three types of YSZtopcoat were considered. The properties of the first, termedYSZ1, were obtained from the sintering model of Bussoand Qian [8]. In this case, the Young’s modulus along thelocal in-plane and out-of-plane directions are differentand vary with time and temperature, as summarized inTable 3. Here, E01 = f 1 (time,T) – E20 = f 2 (time,T). It isthis model of the YSZ which has been used in the preceding

Fig. 13. Normal tractions along the TGO interfaces at 25 �C after 100 h of oxidation at 1100 �C in a TBC system when the bondcoat was considered tohave (1) elastic deformation only, (2) elasto-creep deformations and (3) elasto-plasto-creep deformations, and the TGO had elasto-creep behaviour. Thecreep data corresponds to (Ni,Pt)Al-1 (Eq. 2). b/a = 0.52.

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2359

sections. For the second topcoat variant, termed YSZ2, thelocal out-of-plane modulus, E20, was again obtained fromthe sintering model [8] and hence it is the same as forYSZ1, E20 = f 2 (time,T). However, the local in-plane mod-ulus, E10, was taken as 0.6 E20 throughout the sintering pro-cess, thus giving a stiffer in-plane behaviour than YSZ1.Finally, the elastic properties of the third topcoat variant,YSZ3, were assumed to be isotropic with E10 = E20 = f 2

(time,T).Fig. 14 shows the in-plane Young’s modulus, E10, of the

first three YSZ materials (YSZ1, YSZ2 and YSZ3) used inthis study. It can be seen that YSZ1 has the smallest in-plane modulus and that YSZ3 has the largest. It shouldalso be noted that the out-of-plane elastic modulus, E20,is the same for all the YSZ variants considered. In theresults to be shown in this section, the bondcoat materialcreep properties were always taken as those of (Ni,Pt)Al-1 (Eq. 2) and the TGO was also always assumed to creepaccording to Eq. 5. Stress development within the TBC sys-tem was then examined for each of the topcoat variantsdescribed above.

0

50

100

150

200

250

0 20 40 60 80 100Sintering Time (hrs)

E'1

(GPa)

YSZ3 (E1′=E2′= 2f (t,T))

YSZ2 (E2′= 2f (t,T), E1′=0.6 E2′)

YSZ1 (E1′= 1f (t,T) ≠ E2′= 2f (t,T)

Fig. 14. Evolution of in-plane Young’s modulus, E10, at room temperaturefor the various YSZ materials (YSZ1: transversely isotropic as per Table 3;YSZ2: transversely with stiff in-plane behaviour; and YSZ3: isotropic).

Fig. 15 shows the contour plot of r22 at 25 �C after 100 hof oxidation at 1100 �C when the YSZ material has ratiosof (a) E10/E20 = 0.6 (YSZ2) and (b) E10/E20 = 1.0 (YSZ3).Note that the corresponding r22 contour plot at 25 �Cwhen the topcoat is modelled as YSZ1 is given inFig. 7(a). A comparison between Figs. 15 and 7(a) revealsthat the maximum tensile out-of-plane stresses are lower inmagnitude in the former than those in Fig. 7(a), where theratio of E10/E20 is 0.32 after 100 h of oxidation (and sinter-ing) at 1100 �C. It can be seen that the maximum out-of-plane stress is equal to 717 MPa for YSZ1 (E10 = 0.32E20

after the oxidation exposure of 100 h at 1100 �C), toapproximately 500 MPa for YSZ2 (E10 = 0.6 E20), and to250 MPa for YSZ3 (E10 = E20). These results show thatthe magnitude of the maximum out-of-plane tensile stressin the TBC after cooling increases as the YSZ in-planeYoung’s modulus is reduced for a fixed value of the out-of-plane modulus. A similar trend was found for the max-imum principal stress within the TGO. Thus an elastic iso-tropic assumption for an EB-PVD topcoat will severelyunderestimate the local TBC stresses upon cooling.

The normal tractions along the TGO/YSZ interface forthe three different topcoat variants after cooling to 25 �Care shown in Fig. 16. These results confirms the trendobserved from Figs. 7(a) and 15, and show that the normaltensile tractions along the TGO/YSZ interface are concen-trated near the valley of the bondcoat undulation and reacha maximum at the valley. The magnitude of this maximumtensile stress depends very much on the YSZ properties.When the topcoat has the greatest in-plane compliance(YSZ1), the maximum tensile normal traction reaches 700MPa, but this decreases to 210 MPa as the in-plane Young’smodulus increases to that of the isotropic case (YSZ3).

5. Conclusions

A finite-element-based mechanistic study of stress devel-opment within a TBC system consisting of an EB-PVDYSZ topcoat and a Pt-aluminized diffusion BC has been

Fig. 15. Contour plot of r22 at 25 �C after 100 h of oxidation at 1100 �C when the YSZ material is (a) YSZ2: transversely with stiff in-plane behaviour; and(b) YSZ3: isotropic. Here, b/a = 0.52 and the bondcoat creeps according to (Ni,Pt)Al-1.

Fig. 16. Normal tractions along the TGO/YSZ interface at 25 �C after100 h of oxidation at 1100 �C when the properties of the topcoat are YSZ1(E10 = 0.32E20), YSZ2 (E10 = 0.6E20) and YSZ3 (E10 = E20). In each case, b/a = 0.52 and the bondcoat creeps according to (Ni,Pt)Al-1.

2360 E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361

undertaken. Particular attention has been paid to the roleof materials properties, especially elastic anisotropy withinthe topcoat and variation in creep strength of the bond-coat. Volumetric strains associated with the TGO at theBC/YSZ interface at temperature have also been incorpo-rated into the mechanistic approach. Two different BC sur-face roughnesses, characterized by amplitude, b, to half-wavelength, a, ratios (b/a) of 0.25 and 0.52, respectively,were also considered.

As a consequence of oxide growth, produced isother-mally at 1100 �C, it was found that tensile stresses devel-oped within the topcoat localized near the flanks ofbondcoat protuberances. These ‘‘tensile wings” result from

thermo-elastic mismatch strains and those produced by theanisotropic volume changes caused by oxide growth andrequired to maintain continuity within the TBC structure.The magnitude of the stresses obtained increased with BCsurface roughness. It is shown that the location of maxi-mum out-of-plane tensile stress within the YSZ correspondto sites of sub-critical cracking, observed at room temper-ature, but it cannot be determined at this stage whethersuch cracks formed at temperature or during cooling. Ten-sile tractions acting across the actual TGO interfaces at theoxidation temperature were found to be a maximum at val-ley regions. These tractions were highest across the TGO/YSZ interface (�85 MPa) but, at both TGO interfaces,they decreased by as much as 40% with reducing BC creepstrength. Yield and athermal plasticity, as distinct fromtime-dependent creep, did not contribute significantly tothis relaxation process.

The effect of thermal loading, caused by differential ther-mal contraction during cooling from 1100 to 25 �C, hasbeen examined in some detail. It was found that out-of-plane tensile stresses developed within YSZ regions overly-ing BC valleys. Again, these stresses increased substantiallywith BC surface roughness, e.g. from the range 125–250 MPa at (b/a) = 0.25 to 500–717 MPa at (b/a) = 0.52.Maximum interfacial tensile tractions were predicted tooccur at valley regions for the TGO/YSZ interface and atthe apex of protuberances for the TGO/BC interface. Bothlocations correspond to previously reported sites for sub-critical crack formation. Bondcoat creep during coolingwas again the principal deformation mode determiningthese interfacial stresses, although athermal plasticity nowalso made a contribution.

E.P. Busso et al. / Acta Materialia 57 (2009) 2349–2361 2361

The stresses within the YSZ and the tractions along theTGO/YSZ interface were found to depend on the elasticanisotropy of the topcoat. The FE predictions showed thatthe magnitudes of tensile stresses decreased when the ratiobetween the YSZ in-plane and out-of-plane stiffnessincreased. For instance, when the greatest in-plane compli-ance of the topcoat is considered, i.e. one that is typical ofan EB-PVD YSZ, the maximum TGO/YSZ interface trac-tion reaches 700 MPa; however, this decreases to 210 MPaif elastic isotropy with a 205 GPa elastic modulus isassumed. These findings, which can arguably be consideredto be the most important in this study, show that if an elas-tic isotropic behaviour is assumed for a transversely isotro-pic EB-PVD topcoat, the local TBC stresses upon coolingcan be severely underestimated.

Acknowledgements

Financial support for this work from the United King-dom’s Engineering and Physical Sciences Research Councilthrough Grants GR/R48056/01 and GR/R47653/01 isgratefully acknowledged.

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