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

Transcription

1 Available online at Acta Materialia 57 (2009) The influence of bondcoat and topcoat mechanical properties on 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 Matériaux, Mines ParisTech, B.P. 87, CNRS-UMR 7633, Evry, France b 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 2009 Available 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 YSZ topcoat and a Pt-aluminized diffusion bondcoat. Particular attention has been paid to the role of variables such as the elastic anisotropy within the topcoat, interface roughness, variation in creep strength of the bondcoat and the volumetric strains associated with the formation of the thermally grown oxide (TGO). Bond coat oxidation and thermal loading during cooling give rise to significant tensile stresses within the topcoat and tensile tractions at the TGO interfaces. Bondcoat creep, as distinct from yield and plastic behaviour, was the dominant stress relaxation process, and strong bondcoats (in creep) tended to show higher tensile stress levels. Another important factor determining thermal barrier coating stress levels was the level of elastic anisotropy of the topcoat: an elastic isotropic yttria-stabilized zirconia gave rise to considerably higher stresses than a transversely isotropic topcoat. Ó 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 * Corresponding author. Tel.: ; fax: address: esteban.busso@ensmp.fr (E.P. Busso). Thermal barrier coatings (TBCs) are widely used in aerospace and land-based gas turbines to improve the performance and efficiency of the engine. A typical TBC system consists of an outer yttria-stabilized zirconia (YSZ) ceramic layer and an aluminium-rich intermediate metallic layer which serves as an oxidation-resistant bondcoat (BC). A thermally grown oxide (TGO) layer develops along the metal ceramic interface at elevated temperatures. Fig. 1(a) is a typical cross-section showing the main components of an EB-PVD/Pt-aluminide TBC system and the TGO developed after 3 h of oxidation at 1200 C. Failures of TBC systems occur by the delamination of the YSZ topcoat resulting from the slow growth and eventual coalescence of sub-critical cracks. These cracks can form within the topcoat at its base (e.g. Fig. 1(a)), at the TGO/YSZ interface, within the TGO or at the TGO/BC interface [1 6]. The formation of such cracks can be related to local high values of principal tensile stresses or to interfacial tractions. Finite-element (FE) methods can be used to estimate the magnitude and location of such stresses but it is important to allow, within the FE model, for the volume expansion associated with TGO formation [6 8]. This is particularly important when realistic non-planar BC surfaces are considered since the volume change associated with TGO formation will then result in out-of-plane stress development at temperature [5]. Further examination of the influence of BC surface roughness, given by the ratio (b/a) infig. 1(b), will be made in this present FE study. The quality of FE predictions depends also on the use of appropriate mechanical properties for the BC, TGO and YSZ topcoat. The BC, in particular, will creep readily at typical operating temperatures [9 12] but, for simplicity, /$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi: /j.actamat

2 2350 E.P. Busso et al. / Acta Materialia 57 (2009) 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) The representative periodic unit cell used in the finite-element analysis. (Arrows in (a) point at TBC microcracks.) some researchers [13,14] have treated this nonlinear behaviour of the bondcoat by using elastic/perfectly plastic properties. This idealistic behaviour has been modelled, however, using time-dependent stress relaxation data [11]. Nevertheless, more recent creep data [12] have indicated that a significant batch-to-batch variation in creep strength can exist. Higher creep strength can be expected when aluminium and platinum contents favour the precipitation of a fine dispersion of c0 (nominally, Ni 3 Al) particles. The objectives of the present work are twofold. The first objective is to assess the sensitivity of predictions of stresses within the TBC system to the assumed flow properties of the bondcoat. Accordingly, computations will be undertaken for an EB-PVD TBC system containing a Pt-aluminide bondcoat (Fig. 1(a)) which deforms by either of the creep characteristics [11,12] reported for that bondcoat, and by assuming either an ideal elasto-plastic or an ideal elastic behaviour. It is noted that, in previous studies [13,15], the topcoat has been treated either as a homogeneous isotropic material or considered to be a fully compliant one [16]. In fact, the properties of the transversely isotropic YSZ material which results from EB-PVD deposition depend on many factors, such as the sintering time, sintering temperature and the orientation of the local transversely isotropic material axis [8]. Thus the second objective of this work is to assess the effects of YSZ morphology resulting from deposition and its sintering behaviour on the TBC stresses. To that purpose, the effects of YSZ sintering will be incorporated into the FE model. 2. Material properties 2.1. Creep and thermo-mechanical properties The TBC system considered consists of a Pt-aluminide oxidation-resistant BC, a YSZ topcoat deposited by EB- PVD (Fig. 1(a)) and a TGO consisting of a -alumina. This coating system is bonded to a superalloy substrate. Table 1 Pt-aluminide bondcoat elastic and yield strength, r y, values used in the analyses. T (K) r y (MPa) E (GPa) a/10 6 (K 1 ) The (Ni,Pt)Al bondcoats considered in this work are treated as isotropic materials having a Young s modulus described by [11]: E ¼ 1000ð118 0:024T Þ ð1þ where T (K) is the temperature and E (MPa) is the Young s modulus. Some values are given in Table 1, together with values of the linear expansion coefficients, a. The Poisson s ratio was taken as 0.3, invariant with temperature. The yield strengths, r y, at different temperatures are obtained from Cheng et al. [13] and are also summarized in Table 1. As described earlier, the creep behaviour for the bondcoat were taken either from Taylor et al. [12] or from Pan et al. [11]. In the former case, the creep rate (s 1 )is described by: _e C ¼ 8: r 6:82 exp ð2þ 8:314T where the equivalent Mises stress, r, is in MPa and the temperature, T, isink. This algorithm will be referred to later in the paper as (Ni,Pt)Al-1. Two different creep equations were suggested by Pan et al. [11], namely _e C ¼ 9: r exp ð3þ E 8:314T and _e C ¼ 6: r exp E 8:314T where the symbols have the same meaning and units as in Eqs. 1 and 2. Note that, from a physical point of view, a ð4þ

3 E.P. Busso et al. / Acta Materialia 57 (2009) creep exponent close to 4 is associated with dislocation creep. Eqs. 3 and 4 will be referred to as (Ni,Pt)Al-2a and (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 stress dependence of creep rate and serve to demonstrate the need to assess the sensitivity of predictions of stress to these values. A graphical comparison of the three equations at 1100 C (1473 K) is given in Fig. 2. For the stress range shown, the range of predicted creep rates extends over many orders of magnitude illustrating the level of uncertainty in BC creep behaviour. Also included in this figure is a generic creep curve [7] describing the behaviour of a NiCoCrAlY bondcoat. Its creep response falls within the range associated with Pt-aluminide behaviour (see Fig. 2). It should be noted that, of necessity, Eqs. (2) (4) will need to be extended beyond their experimentally validated range at stages during the numerical computations (i.e. to approximately 200 MPa). As with the bondcoats, the a -alumina TGO is assumed to be an isotropic and homogeneous material. The Young s modulus and other elastic properties at various temperatures are listed in Table 2 [13]. It should pointed out that all the data shown in this section were fitted to polynomial functions when used in the finite element calculations. The creep properties of the alumina TGO are taken as [17]: _e C ¼ 6: r 2:3 exp ð5þ 8:314T Strain Rate (1/s) 1,E+02 1,E+00 1,E-02 1,E-04 1,E-06 1,E-08 1,E-10 (Ni,Pt)Al-2b NiCoCrAl Al 2 O 3 (Ni,Pt)Al-2a (Ni,Pt)Al-1 1,E-12 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03 Stress (MPa) Fig. 2. Creep properties of the different bondcoats and of the a -alumina TGO 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 coating was taken from Ref. [7] and that for the TGO from Ref. [17]. where stress, r, is again in MPa and temperature, T,isinK. It can be appreciated from Fig. 2 that the creep strength of the TGO is expected to be appreciably higher than that of the bondcoat for the stresses and strain rates of interest. Due to its columnar microstructure, the EB-PVD YSZ topcoat is treated as a transversely isotropic elastic material, with its elastic moduli taken to be a function of sintering time and temperature. The sintering behaviour and the thermo-mechanical properties of the YSZ topcoat are obtained from Ref. [8]. The elastic properties after 100 h sintering at 1473 K are summarized in Table 3; it should be noted that the bulk Young s modulus of YSZ is 210 GPa according to Schulz et al. [18]. In the sintering model of Qian and Busso [8], it is assumed that the elastic stiffness in the local X 1 0 and X 3 0 directions (see Fig. 1b) are the same, but that in the X 2 0 direction may be different. The axes X 1 0 and X 3 0 are assumed to be parallel and perpendicular, respectively, to the TGO/YSZ interface in the vicinity of that interface (see Fig. 1(b)). When considering locations within the YSZ remote from the interface (about three times the magnitude of the amplitude of the BC surface roughness), the orientation of the YSZ columns adopts that of the global material axes, i.e. X 1 0 becomes parallel to X 1 and X 2 0 becomes parallel to X 2. The elastic constants of the YSZ are given in Table 3 at different temperatures and after 100 h exposure at 1473 K. Here, E 1 0 and E 2 0 are the elastic moduli along the local X 1 0 and X 2 0 axes, respectively, and m p is the in-plane Poisson s ratio. Further details related to the sintering behaviour of the YSZ and the definition of the YSZ material axes may be found elsewhere [8]. Note that EB-PVD TBCs often exhibit a fine equiaxed microstructure at the TGO-YSZ interface (e.g. see Refs. [6,8]). This region has not been accounted for in this study due to its relatively small size Bondcoat oxidation From SEM measurements of TGO thickness, the following equation was found to describe oxide thickness, h (in m), as a function of exposure time, t (in s), at 1100 C: h ¼ A þ Bt 0:5 ð6þ where A = m is the TGO thickness in the asreceived condition prior to testing and B = m s 0.5. The growth exponent in Eq. 6, typical of Ptaluminized bondcoats, is rather high when compared with the typical value of 0.3 obtained from simple theory of oxidation/diffusion. This expression is shown as the solid line in Fig. 3 and predicts a total alumina TGO thickness of approximately 3.4 lm after 100 h of exposure at 1100 C. The formation of this oxide by selective oxidation of aluminium from the bondcoat results in a volume increase described by the Pilling Bedworth ratio, U. A particular feature of the present approach is that the progressive transformation of the bondcoat to oxide can be modelled during the FE analysis. This means that the effect of the corresponding transformation strains on stress development can be assessed at the oxidation temperature in the absence of any thermally induced strains. Due to this, it is important to use realistic values for the Pilling Bedworth ratio and some consideration needs to be given to this. For simple pure metals, this ratio is readily defined as the volume of oxide formed from the metal ion divided

4 2352 E.P. Busso et al. / Acta Materialia 57 (2009) Table 2 Elastic properties of the TGO at different temperatures, T (from Ref. [13]). T (K) E (GPa) m a/10 6 (K 1 ) Table 3 Elastic properties of the YSZ at different temperatures after 100 h exposure at 1473 K [7]. T (K) E 2 0 (GPa) E 1 0 (GPa) m p a/10 6 (K 1 ) For comparison, the Young s modulus of fully dense YSZ is 210 GPa [18]. TGO Thickness (μm) by the volume of the ion in the metal. For the oxidation of aluminium via the reaction A: 2Al þ 3 2 O 2! Al 2 O 3 the Pilling Bedworth ratio is given as U ¼ V Al 2 O 3 2V Al ¼ V Al 2 O 3 Z Al 2V Al Z Al 2 O 3 Total Internal TGO External TGO Oxidation Time (hrs) Fig. 3. Measured total alumina thickness (including that preformed) as a function of oxidation time at 1100 C for the Pt-aluminized bondcoat. The internal and external components of the new oxide are also shown. ðaþ Here, the subscripts Al 2 O 3 and Al refer to oxide and metal, respectively, and V is the corresponding ionic volume. This can be calculated from the volume V * of the unit cell, available in standard XRD data banks (e.g. [19]), by dividing the cell volume by the number of ions in the unit cell, Z. In the case of the oxide, this is then an average ionic volume. Thus, using V Al ¼ 6: m 3 ; Z Al ¼ 4; V Al 2 O 3 ¼ 25: m 3 ; Z Al2 O 3 ¼ 6 gives for reaction A from Eq. 7: U ¼ 1:28 This is the generally accepted value for the oxidation of pure aluminium. An identical value is obtained if the calculation were done using molar volumes.in the present context of the selective oxidation of the b-(ni,pt)al bondcoat, the removal of an aluminium ion will reduce ð7þ the stoichiometry of the b layer but not necessarily cause a phase transition. This arises because there is a wide composition range over which the b phase is stable [20], transition to the c 0 structure occurring only at aluminium contents <38 at.% Al at 1100 C. First principles calculations [21] show that vacancies on the aluminium sub-lattice are viable defects in the b-phase, as are nickel ions on aluminium sites. 1 The selective oxidation of aluminium from the bondcoat in the present system can then be considered to occur by the removal of an aluminium ion, its replacement with a viable point defect within the b-structure and the oxidation of the removed ion. The sequence is described by reaction B for the case of aluminium vacancies: ðni; PtÞ x Al y þ 3 2 O 2!ðNi; PtÞ x Al y 2 þ 2Al þ 3 2 O 2!ðNi; PtÞ x Al y 2 þ Al 2 O 3 ðbþ The volume change, DV 1, associated with the first step in this reaction is: DV 1 ¼ V ðni;ptþx Al y 2 þ 2V Al V ðni;ptþx Al y ð8þ where V represents the atomic or molecular volumes of the respective species. It is expected that this volume change will be dominated to first order by the extra volume of the aluminium ions removed from the b phase. The fact that a vacancy is actually created as a result of this removal [20] indicates that relaxation within the (Ni,Pt) sub-lattice is likely to be small. It then follows from reaction B that the first-order volume change in the oxidation process is determined simply by that associated with the oxidation of aluminium to alumina. The Pilling Bedworth ratio is then given as U ffi V Al 2 O 3 ffi 1:28 ð9þ 2V Al At later stages in the oxidation exposure, when appreciable aluminium depletion has occurred in the near-surface 1 These computations were performed for NiAl, but it is assumed that they are relevant also to (Ni,Pt)Al.

5 E.P. Busso et al. / Acta Materialia 57 (2009) region of the bondcoat, the removal of further aluminium can be envisaged to initiate a phase transformation: 6NiAl þ 3O 2! 2Ni 3 Al þ 2Al 2 O 3 ðcþ For the purposes of this discussion, the reaction has been written in terms of the simple Ni Al, rather than (Ni,Pt) Al phases because the volumes of the unit cells are reasonably well established for the simpler system. The substitution of platinum for nickel is likely to have some effect on these volumes, however. As before, using V* Al2O3 = m 3 and Z Al2O3 = 6 together with V* NiAl = m 3, Z NiAl =1, V* Ni3Al = m 3 and Z Ni3Al = 1 gives the effective Pilling Bedworth ratio for reaction C as: 2V Ni 3 Al =Z Ni 3 Al 2V Al 2 O 3 =Z Al2 O 3 U ¼ 6V NiAl =Z ð10þ NiAl This is a similar value to that for the oxidation of both pure aluminium and the b-(ni,pt)al phase as discussed above. Again, an identical value is obtained if molar volumes, calculated from molecular weights and bulk densities, are used. This indicates that there will be no dramatic changes in the volume strains produced during the formation of alumina on Pt-aluminide coatings even when the phase transition of reaction C occurs. This differs from the argument of Tolpygo and Clarke [22] who considered the volume decrease associated with the transformation from b to c 0 phase to be important to the formation of rumples on the bondcoat surface. It should be recognized, though, that this transformation, at the surface of the bondcoat where aluminium diffusion into the alloy substrate is negligible, occurs as a result of the selective oxidation of aluminium. The volume increase associated with alumina formation was neglected in their calculation of volume change but needs to be included. When this is done, as in reaction C, an overall volume increase is found which is little different from that occurring on adjacent b phases. In this present work, a value of the Pilling Bedworth ratio, U, of 1.28 for the formation of alumina has then been used throughout. The mean volumetric strain, e V, due to the transformation from metal to oxide is then 0.08 (= n(u)). This strain is not isotropic but is partitioned such that the component, e T n ; normal to the TGO/BC interface is much larger than the in-plane transverse strain, e T t. The value of the ratio e T n =et t ¼ 87 incorporated into the present analysis is the same as that used elsewhere [8] and derives from the results of Huntz et al. [23]. The kinetics of growth of the internal and external components of the total oxide thickness at 1100 C, based on Eq. 6, are shown in Fig The finite element model Full details of the FE model used in this work can be found elsewhere [7,8]. It is based on the commercial FE code ABAQUS, but with the novel feature of allowing for the volume changes occurring at temperature during the oxidation of the bondcoat. In addition, creep of both the bondcoat and TGO is permitted, as is progressive sintering of the YSZ topcoat. For the present work, the TBC system was held isothermally at 1100 C, during which time the TGO continued to thicken, before cooling to 25 C. The transformation strains associated with TGO growth and the thermal strains during subsequent cooling were the only loads applied to the system. The FE model was developed by first identifying representative YSZ-TGO interfacial regions (e.g. see Fig. 1) and then repeating these as two-dimensional periodic unit cells with appropriate periodic and symmetry boundary conditions. Two aspect ratios, defined as the ratio b/a in Fig. 1(b), of 0.25 and 0.52, were used to study the effect of bondcoat roughness on the stresses developed within the TBC system. Fig. 4 shows the FE mesh and the boundary conditions when the aspect ratio (b/a) is The initial thicknesses of the BC and YSZ are 50 and 125 lm, respectively. The mesh consisted of about 5000 quadratic generalized plane strain elements with full integration. The displacement of the plane L (see Fig. 4) in the x 1 direction during cooling was imposed by the thermal expansion of the substrate [2]. 4. Results and discussion 4.1. TGO thickness Fig. 5(a) and (b) shows the computed thickness of the TGO layer after 100 h oxidation at 1100 C for coatings with roughness ratios of (a) b/a = 0.25 and (b) b/ a = In the figures, the internal and external components of the oxide are identified. Shown as the dark intermediate layer between these is the original alumina layer formed during processing. This, together with the entire TBC system, is assumed to be stress-free prior to the oxidation exposure. The lower interface of this original oxide layer corresponds to the outer surface of the bondcoat obtained after coating deposition. It can be appreciated from Fig. 5 how the bondcoat is partially consumed by oxide formation during the course of the FE analysis. For computational efficiency, it is assumed that the external oxide forms above the original oxide layer, whereas, in reality, it would be expected to form at its base as a result of inward oxygen transport. This assumption has no effect on calculated stresses, however, since the whole alumina layer is considered to be an isotropic solid with uniform properties. The total oxide thickness of 3.3 lm shown in Fig. 5 agrees with that predicted by Eq Effects of bondcoat creep and plasticity Fig. 6 shows contour plots of the out-of-plane stress component, r 22, at 1100 C after 100 h of oxidation for both values of initial TGO aspect ratio, namely (a) b/ a = 0.25 and (b) b/a = Here creep of the bondcoat and TGO and also the sintering of the YSZ are considered

6 2354 E.P. Busso et al. / Acta Materialia 57 (2009) Fig. 4. Typical FE mesh used in the TBC model for a bondcoat surface roughness ratio, b/a, of 0.25, with b = lm. Fig. 5. FE predictions showing the TGO layer after 100 h of oxidation at 1100 C. in the stress analysis. The bondcoat creep properties used are those of Taylor et al. [12] (Eq. 2). The stresses shown are those predicted at the test temperature of 1100 C prior to cooling and confirm an earlier suggestion [5] that tensile wings will develop at temperature at the flanks of bondcoat protuberances. These are a result of continuity strains arising from the volume expansion on oxide formation. The magnitude of the tensile stress in these wings clearly increases with bondcoat surface roughness and may become sufficient to nucleate cracks within the topcoat at location A (see Fig. 6(a)) isothermally at the oxidation temperature. Cracks at such locations are certainly found

7 E.P. Busso et al. / Acta Materialia 57 (2009) Fig. 6. Contour plots of r 22 at 1100 C for two different TGO roughness ratios after 100 h of oxidation at the same temperature when creep of the bondcoat 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). during post-test examination (see Fig. 1(a), for example), but it cannot be confirmed at this stage that these occurred at temperature. Another point of interest from Fig. 6 is that out-of-plane tensile stresses are also expected, at the oxidation temperature, to occur above valleys of the bondcoat (location B). Their presence could help propagate a crack across steep-sided valleys; again, examples can be found in Fig. 1(a). Fig. 7(a) and (b) shows the contour plot of the out-ofplane stress component, r 22, on cooling to 25 C after oxidation for 100 h at 1100 C for two different TGO roughness ratios when, again, the creep effects of the Fig. 7. Contour plots of r 22 at 25 C after 100 h of oxidation at 1100 C when the creep effects of bondcoat and TGO are accounted for. The bondcoat creep properties used are those of Taylor et al. [12] (Eq. 2).

8 2356 E.P. Busso et al. / Acta Materialia 57 (2009) bondcoat and the TGO are considered. Tensile wings are still present (arrowed in Fig. 7(a)) but, as with the situation at the oxidation temperature, only on the rougher bondcoat interface (b/a = 0.52). The largest out-of-plane tensile stresses after cooling arise within the topcoat above the valleys (arrowed in Fig. 7(a)). Either of these locations could provide, in principle, sites for crack nucleation within the YSZ topcoat or near the YSZ/TGO interface, at least with the rougher bondcoat. It is also clear from Fig. 7 that significant out-of-plane stresses also develop in the bondcoat at the apex of protuberances. These stresses are absent at the oxidation temperature (Fig. 6) and arise solely during cooling as a result of thermal mismatch strains. In principle, cracks could form in these locations during cooling at the TGO/BC interface due to the high tensile interface tractions. The formation of tensile stress-driven cracks within the bondcoat, however, is less likely due to the ductile nature of the bondcoat. The magnitudes of these tensile stresses/tractions increase with TGO thickness, as has been shown in Ref. [8]. In order to understand the driving force responsible for the nucleation of cohesive cracks entirely within the TGO, it is necessary to analyse the distribution of the maximum principal stresses in the TGO. This is given in Fig. 8(a) and (b), which shows the maximum principal stress contours for the two different TGO roughness ratios at 1100 C after 100 h of oxidation at the same temperature. Note that, following standard convention, a negative value of the maximum principal stress implies that it is the least negative of the three components. The contour plots corresponding to those shown in Fig. 8 for the condition after cooling to 25 C are given in Fig. 9(a) and (b). As with the out-of-plane stress, tensile regions exist at both temperatures and surface roughness ratios within the TGO, in both the apex and valley regions. The highest tensile principal stresses are found in the valley regions near the YSZ- TGO interface upon cooling (see Fig. 9(a)).Tensile wings within the YSZ topcoat have formed at both temperatures for the rougher bondcoat surface (b/a = 0.52) but are absent, or much less pronounced, when b/a = Figs. 10 and 11 show the predicted normal tractions along the (a) TGO/YSZ and (b) the TGO/BC interfaces at 1100 and 25 C, respectively, after 100 h of oxidation at 1100 C for a TBC system, with bondcoat and TGO creep behaviour taken into account and with the rougher interface (b/a = 0.52). Three different types of bondcoat creep properties are used, namely those reported by Taylor et al. [12] (Eq. 2) and by Pan et al. [11] (Eqs. 3 and 4) (see also Fig. 2). It can be seen that, for all the different creep behaviour, a tensile stress region develops across the TGO/YSZ interface around the valley regions both at the oxidation temperature and after cooling to 25 C. In contrast, tensile stresses across the TGO/BC interface occur appreciably around the bondcoat peak regions but only in the cooled specimen. These findings are consistent with regions where interfacial TGO cracks are known to nucleate [4]. Fig. 10(a) shows that the influence of the bondcoat creep behaviour on the stress acting across the TGO/YSZ interface at 1100 C is important: there is a nearly factor two difference in this traction at the bondcoat valley between the low-strength bondcoat variant, (Ni,Pt)Al-2b, given by Eq. 4, and the stronger variant given by Eq. 2, (Ni,Pt)Al- 1. It is the stronger bondcoat which develops the higher Fig. 8. Contour plots of the maximum principal stress at 1100 C after 100 h of oxidation at the same temperature in a TBC system when bondcoat and TGO creep are considered: (a) b/a = 0.52 and (b) b/a = The bondcoat creep properties used are those of Taylor et al. [12] (Eq. 2).

9 E.P. Busso et al. / Acta Materialia 57 (2009) 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 are considered: (a) b/a = 0.52 and (b) b/a = 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 a TBC system with three different bondcoat creep strengths and TGO creep behaviour (b/a = 0.52). tensile traction at the TGO/YSZ interface since it will experience lower stress relaxation rates. By contrast, there is negligible difference in the peak tensile tractions between the three bondcoat strengths examined after cooling to 25 C (Fig. 11(a)). This observation suggests that the final stress values shown in each of the bondcoats are developed largely at temperatures where creep relaxation rates are negligible. A similar pattern arises at the TGO/BC interface at the oxidation temperature (Fig. 10(b)) except that the strongest bondcoat experiences an approximately factor 10 higher tensile stress at the bondcoat valley than does the weakest bondcoat. Absolute values of stress at this interface are lower, however, than at the TGO/YSZ interface. Another difference is that the location of the maximum tensile traction at the TGO/BC interface moves to the apex of the bondcoat protuberance after cooling to 25 C. The strongest bondcoat exhibits the highest tensile stress in this case also, although there is little difference in the predicted stress levels between the creep behaviour given by Eqs. 3 and 4. The effects of different bondcoat elastic-plastic-creep mechanical behaviour have also been studied in this work to investigate the relative effects of each deformation mechanism. Three different cases were considered: (i) the BC deforms only elastically; (ii) the BC has elasto-creep deformation; and (iii) the BC exhibits elasto-plasto-creep deformation. The strongest bondcoat creep property is used, namely that of Taylor et al. [12] ((Ni,Pt)Al-1 in Fig. 2).

10 2358 E.P. Busso et al. / Acta Materialia 57 (2009) 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 with three 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 was considered to have (1) elastic deformation only, (2) elasto-creep deformations and (3) elasto-plasto-creep deformations, and the TGO had elasto-creep behaviour. The creep data corresponds to (Ni,Pt)Al-1 (Eq. 2). b/a = The normal tractions along the TGO interfaces at 1100 C are plotted in Fig. 12 and at 25 C infig. 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 elastic behaviour can lead to significant discrepancies in predicted stress at the creep temperature since relaxation processes are not accounted for. This is particularly noticeable at peak regions where, at the TGO/YSZ interface, essentially zero stress is expected under elastic conditions but a significant compressive traction ( 60 MPa) is predicted under relaxed conditions. The converse holds at the TGO/BC interface for here the peak regions experience large tensile tractions under elastic deformation but approximately zero stress when elasto-creep or elasto-plasto-creep conditions exist. It should be noted that, at each interface, the predictions of both of these latter are essentially identical indicating that the mechanical response is dominated by creep rather than by yield and athermal plasticity. Similar trends develop on cooling to 25 C, as can be seen from Fig. 13. The most striking feature here is the large tensile stress (0.9 GPa) predicted to develop under elastic conditions across the TGO/BC interface above peak regions. This is significantly relaxed to 400 MPa by bondcoat creep (Fig. 13(b)) and further to 300 MPa if bondcoat athermal plasticity is permitted in addition to creep. This result indicates that creep remains the important relaxation process even during cooling although there is clearly a contribution from athermal plasticity Effect of YSZ material properties In order to study the effects of the YSZ elastic properties on the stress state of the TBC system, three types of YSZ topcoat were considered. The properties of the first, termed YSZ1, were obtained from the sintering model of Busso and Qian [8]. In this case, the Young s modulus along the local in-plane and out-of-plane directions are different and vary with time and temperature, as summarized in Table 3. Here, E 0 1 = ^f 1 (time,t) E 2 0 = ^f 2 (time,t). It is this model of the YSZ which has been used in the preceding

11 E.P. Busso et al. / Acta Materialia 57 (2009) 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 to have (1) elastic deformation only, (2) elasto-creep deformations and (3) elasto-plasto-creep deformations, and the TGO had elasto-creep behaviour. The creep data corresponds to (Ni,Pt)Al-1 (Eq. 2). b/a = sections. For the second topcoat variant, termed YSZ2, the local out-of-plane modulus, E 2 0, was again obtained from the sintering model [8] and hence it is the same as for YSZ1, E 2 0 = ^f 2 (time,t). However, the local in-plane modulus, E 1 0, was taken as 0.6 E 2 0 throughout the sintering process, 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 E 1 0 = E 2 0 = ^f 2 (time,t). Fig. 14 shows the in-plane Young s modulus, E 1 0, of the first three YSZ materials (YSZ1, YSZ2 and YSZ3) used in this study. It can be seen that YSZ1 has the smallest inplane modulus and that YSZ3 has the largest. It should also be noted that the out-of-plane elastic modulus, E 2 0, is the same for all the YSZ variants considered. In the results to be shown in this section, the bondcoat material creep properties were always taken as those of (Ni,Pt)Al- 1 (Eq. 2) and the TGO was also always assumed to creep according to Eq. 5. Stress development within the TBC system was then examined for each of the topcoat variants described above. E'1 (GPa) YSZ3 (E 1 =E 2 = ˆf 2 (t,t)) YSZ2 (E 2 = ˆf 2 (t,t), E 1 =0.6 E 2 ) YSZ1 (E 1 = ˆf 1 (t,t) E 2 = ˆf 2 (t,t) Sintering Time (hrs) Fig. 14. Evolution of in-plane Young s modulus, E 1 0, at room temperature for 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 r 22 at 25 C after 100 h of oxidation at 1100 C when the YSZ material has ratios of (a) E 1 0/E 2 0 = 0.6 (YSZ2) and (b) E 1 0/E 2 0 = 1.0 (YSZ3). Note that the corresponding r 22 contour plot at 25 C when the topcoat is modelled as YSZ1 is given in Fig. 7(a). A comparison between Figs. 15 and 7(a) reveals that the maximum tensile out-of-plane stresses are lower in magnitude in the former than those in Fig. 7(a), where the ratio of E 1 /E is 0.32 after 100 h of oxidation (and sintering) at 1100 C. It can be seen that the maximum out-ofplane stress is equal to 717 MPa for YSZ1 (E 1 0 = 0.32E 2 0 after the oxidation exposure of 100 h at 1100 C), to approximately 500 MPa for YSZ2 (E 1 0 = 0.6 E 2 0), and to 250 MPa for YSZ3 (E 1 0 = E 2 0). These results show that the magnitude of the maximum out-of-plane tensile stress in the TBC after cooling increases as the YSZ in-plane Young s modulus is reduced for a fixed value of the outof-plane modulus. A similar trend was found for the maximum principal stress within the TGO. Thus an elastic isotropic assumption for an EB-PVD topcoat will severely underestimate the local TBC stresses upon cooling. The normal tractions along the TGO/YSZ interface for the three different topcoat variants after cooling to 25 C are shown in Fig. 16. These results confirms the trend observed from Figs. 7(a) and 15, and show that the normal tensile tractions along the TGO/YSZ interface are concentrated near the valley of the bondcoat undulation and reach a maximum at the valley. The magnitude of this maximum tensile stress depends very much on the YSZ properties. When the topcoat has the greatest in-plane compliance (YSZ1), the maximum tensile normal traction reaches 700 MPa, but this decreases to 210 MPa as the in-plane Young s modulus increases to that of the isotropic case (YSZ3). 5. Conclusions A finite-element-based mechanistic study of stress development within a TBC system consisting of an EB-PVD YSZ topcoat and a Pt-aluminized diffusion BC has been

12 2360 E.P. Busso et al. / Acta Materialia 57 (2009) Fig. 15. Contour plot of r 22 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 after 100 h of oxidation at 1100 C when the properties of the topcoat are YSZ1 (E 1 0 = 0.32E 2 0), YSZ2 (E 1 0 = 0.6E 2 0) and YSZ3 (E 1 0 = E 2 0). In each case, b/ a = 0.52 and the bondcoat creeps according to (Ni,Pt)Al-1. undertaken. Particular attention has been paid to the role of materials properties, especially elastic anisotropy within the topcoat and variation in creep strength of the bondcoat. Volumetric strains associated with the TGO at the BC/YSZ interface at temperature have also been incorporated into the mechanistic approach. Two different BC surface roughnesses, characterized by amplitude, b, to halfwavelength, a, ratios (b/a) of 0.25 and 0.52, respectively, were also considered. As a consequence of oxide growth, produced isothermally at 1100 C, it was found that tensile stresses developed within the topcoat localized near the flanks of bondcoat protuberances. These tensile wings result from thermo-elastic mismatch strains and those produced by the anisotropic volume changes caused by oxide growth and required to maintain continuity within the TBC structure. The magnitude of the stresses obtained increased with BC surface roughness. It is shown that the location of maximum out-of-plane tensile stress within the YSZ correspond to sites of sub-critical cracking, observed at room temperature, but it cannot be determined at this stage whether such cracks formed at temperature or during cooling. Tensile tractions acting across the actual TGO interfaces at the oxidation temperature were found to be a maximum at valley 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 creep strength. Yield and athermal plasticity, as distinct from time-dependent creep, did not contribute significantly to this relaxation process. The effect of thermal loading, caused by differential thermal contraction during cooling from 1100 to 25 C, has been examined in some detail. It was found that out-ofplane tensile stresses developed within YSZ regions overlying BC valleys. Again, these stresses increased substantially with BC surface roughness, e.g. from the range MPa at (b/a) = 0.25 to MPa at (b/a) = Maximum interfacial tensile tractions were predicted to occur at valley regions for the TGO/YSZ interface and at the apex of protuberances for the TGO/BC interface. Both locations correspond to previously reported sites for subcritical crack formation. Bondcoat creep during cooling was again the principal deformation mode determining these interfacial stresses, although athermal plasticity now also made a contribution.

13 E.P. Busso et al. / Acta Materialia 57 (2009) The stresses within the YSZ and the tractions along the TGO/YSZ interface were found to depend on the elastic anisotropy of the topcoat. The FE predictions showed that the magnitudes of tensile stresses decreased when the ratio between the YSZ in-plane and out-of-plane stiffness increased. For instance, when the greatest in-plane compliance of the topcoat is considered, i.e. one that is typical of an EB-PVD YSZ, the maximum TGO/YSZ interface traction reaches 700 MPa; however, this decreases to 210 MPa if elastic isotropy with a 205 GPa elastic modulus is assumed. These findings, which can arguably be considered to be the most important in this study, show that if an elastic isotropic behaviour is assumed for a transversely isotropic EB-PVD topcoat, the local TBC stresses upon cooling can be severely underestimated. Acknowledgements Financial support for this work from the United Kingdom s Engineering and Physical Sciences Research Council through Grants GR/R48056/01 and GR/R47653/01 is gratefully acknowledged. References [1] Bouhanek K, Adesanya OA, Stott FH, Skeldon P, Lees DG, Wood GC. Mater Sci Forum 2001;615: [2] Tolpygo VK, Clarke DR, Murphy KS. Surf Coat Technol 2001;124: [3] Mumm DR, Evans AG, Spitsberg IT. Acta Mater 2001;49:2329. [4] Padture NP, Gell M, Jordan EH. Science 2002;296:280. [5] Evans HE, Taylor MP. J Corros Sci Eng 2003; Paper H011. [6] Busso EP, Wright L, Evans HE, McCartney LN, Saunders SRJ, Osgerby S, Nunn J. Acta Mater 2007;55:1491. [7] Busso EP, Lin J, Sakurai A, Nakayama M. Acta Mater 2001;49:1515. [8] Busso EP, Qian ZQ. Acta Mater 2006;52: [9] Brindley WJ, Whittenberger JD. Mater Sci Eng A 1993;33:163. [10] Taylor MP, Evans HE, Ponton CB, Nicholls JR. Surf Coat Technol 2000;13:124. [11] Pan D, Chen MW, Wright PK, Hemker KJ. Acta Mater 2003;51:2205. [12] Taylor MP, Evans HE, Busso EP, Qian ZQ. Acta Mater 2006;54:3241. [13] Cheng J, Jordan EH, Barber B, Gell M. Acta Mater 1998;46:5839. [14] He MY, Hutchinson JW, Evans AG. Mater Sci Eng 2003;172:A345. [15] Karlsson AM, Xu T, Evans AG. Acta Mater 2002;50:1211. [16] Darzens S, Karlsson AM. Surf Coat Technol 2004;108: [17] Lin HT, Becher PF. J Am Ceram Soc 1990;73:1378. [18] Schulz U, Fritscher K, Leyens C, Peters M. J Eng Gas Turbines Power 2002;124:229. [19] PANalytical BV. Version 1.0d [20] Gleeson B, Wang W, Hayashi S, Sordelet D. Mater Sci Forum 2004;213: [21] Lozovoi AY, Alavi A, Finnis MW. Phys Rev Lett 2000;85:610. [22] Tolpygo VK, Clarke DR. Acta Mater 2000;48:3283. [23] Huntz AM, Amiri G, Evans HE, Cailletaud G. Oxid Metals 2002;57:499.