Investigation of TBCs on turbine blades by photoluminescence piezospectroscopy

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Acta Materialia 57 (2009) 182–195 www.elsevier.com/locate/actamat

Investigation of TBCs on turbine blades by photoluminescence piezospectroscopy X. Wang *, G. Lee, A. Atkinson Department of Materials, Imperial College London, London SW7 2BP, UK Received 7 February 2008; received in revised form 19 August 2008; accepted 20 August 2008 Available online 1 October 2008

Abstract Thermal barrier coating (TBC) blade specimens with Pt diffusion bond coats were subjected to thermal cycling with periodic measurements of the residual stress in the thermally grown oxide (TGO) using photoluminescence piezospectroscopy. Two distinct stress levels were generally found to coexist in the probed volume, i.e. a high stress (4 GPa) and a low stress (500 MPa) level. Both the high and low stress levels were independent of the curvature of the blade surface, in agreement with numerical modelling based on a composite cylinder stress model. The relative contributions of the two stress levels appear to be correlated with the h-Al2O3 content of the TGO, which was dependent on the position on the blade. The TBCs tended to fail along the TGO/bond coat interface in thermal cycling. This was modified by the presence of mixed transition metal oxides in the TGO. The results are interpreted in terms of a likely failure mechanism. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Thermal barrier coatings; Residual stresses; Ceramics; Transformation; Fracture

1. Introduction Thermal barrier coatings (TBCs) offer the potential to improve significantly efficiencies of aero engines as well as stationary gas turbines for power generation [1]. It is therefore desirable to develop models to predict remaining life and total lifetime for TBCs [2,3]. Photoluminescence piezospectroscopy (PLPS) can be employed to measure the residual stress in alumina ceramics, such as the thermally grown oxide (TGO) in TBCs, in a non-destructive way. The spectrum of unstressed alpha alumina displays two characteristic R lines (R1/R2 doublet) from Cr impurities which shift in frequency if the alumina is subjected to a uniform stress field. The peak shift is directly related to the stress [4–8]. It has been observed in some TBC systems with Pt–Al b phase bond coats that the average TGO stress and its stan*

Corresponding author. Tel. +44 0 207 5946771; fax: +44 0 207 5946757. E-mail address: [email protected] (X. Wang).

dard deviation show systematic changes with thermal cycling and suggested that the rate of change of the stress can be related to coating life [9,10]. However, more generally there exists no definite relationship between TGO residual stress and coating life. The residual stress in the TGO has been observed to either increase [9] or decrease [10] with thermal cycling, or increase first and then gradually decrease to a certain level until spallation [11]. In other words, luminescence peak shift evolution is not in itself universally reliable as a measure of damage or damage accumulation [12]. Earlier research was successful in relating the degradation of TBCs with platinized cc0 bond coats to an increase in the contribution from low TGO stress regions in luminescence stress mapping [13]. If localized damage is present, a PLPS spectrum often exhibits a bimodal character, from both a low stress (or even stress-free) component and a high stress component [9,14–17]. Upon deconvolution of the spectrum, both the high and low stress contributions can be obtained [13–15]. Apart from local damage, there are a variety of other possibilities for stress relaxation or redistribution in the

1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.08.053

X. Wang et al. / Acta Materialia 57 (2009) 182–195

TGO, e.g. rumpling, curvature, microstructural changes in the TGO. Different stress relaxation mechanisms may give rise to characteristic features or changes in the luminescence spectra. It is desirable for understanding TBC degradation if different stress relaxation mechanisms can be distinguished. Although much research has been reported on using PLPS in investigating the TBCs on simple button or plate specimens, no research has been reported using it on real turbine blades. Surfaces on a blade generally are not flat, having either concave or convex curvatures. Curvatures are expected to give rise to more complications in stress distribution and stress evolution than a standard laboratory test specimen with a flat surface. In this contribution, luminescence mapping was conducted on blade specimens with Pt diffusion cc0 bond coats. Our particular interest was to look at the effect of surface curvature on the stress evolution and coating failure behaviour. 2. Experimental 2.1. Specimens and thermal cycling

CV

F

CC Fig. 1. Schematic of analysis positions on blade specimens (shown in cross-section).

were chosen for mapping measurements. As shown schematically in Fig. 1, position CV had a convex curvature, position CC had a concave curvature and position F had a flat surface. TGO often contains h-Al2O3 as well as a-Al2O3, as shown in Fig. 2a. It is well established that h-Al2O3 produces R lines (doublet) at 14,575 and 14,650 cm1 [16]. In this study, apart from a doublet from a-Al2O3, three additional distinguishable peaks, at 14,330, 14,546 and

a

1

Alpha

Fitting

0.8

0.6

Theta

0.4

0.2

0

14320

14420

14520

14620

Wave number (cm-1)

2.2. Luminescence measurement and data processing

b

1

Experimental Fitting

0.8

0.6

I

Cr3+ luminescence spectra were acquired using a Renishaw Raman optical microprobe (model 2000) fitted with a motorized mapping stage. The laser source was a green Ar+ laser with a wavelength of 514.5 nm. An air conditioning unit was used to maintain a stable room temperature at 22 ± 0.3 °C. Before and after each experiment, the spectrometer was calibrated by taking a spectrum from a strain-free single crystal sapphire sample. In luminescence measurements, an acquisition time of one second was used for each spectrum. Measurements were taken on a square grid of 200  200 lm with a pitch of 20 lm. One ‘‘map” thus comprised 121 measurement points. For the button specimen, the mapping area was at the centre of the specimen. For the blade specimens, three representative positions with three different surface curvatures

Experimental

I

Two blade specimens and one button specimen were studied. The blade specimens were in the form of 1 cm sections cut from complete blades. The yttria-stabilized zirconia (YSZ) topcoat, applied by electron beam physical vapor deposition (EBPVD) at 1000 °C in an argon/oxygen atmosphere, was 200 lm in thickness. The thermal cycling tests were conducted by moving the specimens periodically in and out of a furnace by a computer-controlled motorized stage. The temperature of the furnace was maintained at 1150 °C. Immediately after being removed from the furnace the specimens were fancooled by laboratory air. The thermal cycling was run with a 20 h/1 h scheme, i.e. the specimen dwelt at high temperature for 20 h and stayed outside the furnace for 1 h. The specimens were removed at specified intervals from the cyclic heating rig for the luminescence measurements.

183

0.4

0.2

0

14360

14400

14440

Wave number (cm-1) Fig. 2. (a) A typical luminescence spectrum from TGO containing both hAl2O3 and a-Al2O3 and its fitting; (b) ‘‘pure” a-Al2O3 spectrum and its fitting.

184

X. Wang et al. / Acta Materialia 57 (2009) 182–195

1.2

Fitting 1 0.8 0.6 0.4 0.2 0 -0.2 14350

14400

Wave number

b

14450

(cm-1)

1.2

Fitting

1 0.8

I

where Ii is the intensity calculated from the fitted equation for a given frequency, Ii,exp is the intensity measured at this frequency and I i is the mean value of Ii calculated for the full spectrum; n is the number of data points for the spectrum to be fitted, which was 436; v is the residual degrees of freedom: v = n  m. With m, the number of fitted coefficients, equal to 8 for fitting two unconstrained peaks, the residual degrees of freedom v = 428. A perfect fitting gives the index: adjrsquare = 1. In reality, the goodness index is always smaller than one. Generally speaking, if a fitting generates an index of larger than 0.999, then the fitting can be regarded as a successful fitting. When the goodness of fit is smaller than 0.999, the fitting should be considered unsuccessful as the residual (Ii,exp  Ii) becomes significant. Fig. 3a gives an example of a spectrum which, when fitted by two unconstrained peaks, gave adjrsquare = 0.9964. Doublet splitting is evident in that three peaks are clearly present in the spectrum and the residual appears to give two noticeable humps, indicating that two extra peaks have probably been neglected. In this case, the spectrum should be deconvoluted using the constrained fitting procedure to two doublets – one with high shift (stress) and the other with low shift (stress) – as detailed in earlier publications [13,17]. The procedure takes into account the constraints that must be preserved regarding the relative height, width and separation of the R1 and R2 lines as determined in Ref. [17]. Fig. 3b shows the result of fitting this spectrum by two constrained doublets. It can be seen that curve fitting is much improved, with the goodness index = 0.9996 and the residual is decreased significantly.

a

I

14,626 cm1, respectively, were found to exist in the TGO. Of these, the 14,546 and 14,626 cm1 peaks can be confidently ascribed to h-Al2O3. They are at lower frequencies than those found in Ref. [16], due to the different residual stresses in the TGO. According to Ref. [16], it is less certain as to whether the 14,330 cm1 peak can be attributed to h-Al2O3. In this work it was observed that the intensity ratio of the peak at 14,330 cm1 to those at 14,546 and 14,626 cm1 was fairly constant in most cases, which indicates the peak at 14,330 cm1 is at least related to the h-Al2O3. For this reason, the peak at 14,330 cm1 was also treated as from h-Al2O3. A MatLab program was written for spectrum curve fitting and map plotting. In the first step, the program fits all the peaks corresponding to both a- and h-Al2O3 plus a polynomial background without applying any constraints. The ‘‘pure” a-Al2O3 spectrum can be obtained by subtracting the h-Al2O3 and background contributions from the original experimental spectrum. The ‘‘pure” alpha spectrum was then fitted to two unconstrained peaks (as shown in Fig. 2b). The goodness of fit was quantified by a statistical function called degrees of freedom adjusted r-square: Pn1 2 i¼1 ðI i;exp  I i Þ ; ð1Þ adjrsquare ¼ 1  m P n1 2 i¼1 ðI i;exp  I i Þ n1

0.6 0.4 0.2

Residual

0 -0.2

14350

14400

14450

Wave number (cm-1) Fig. 3. A representative spectrum showing doublet splitting fitted by (a) two unconstrained peaks, giving a goodness of fit of 0.9967 and (b) two constrained doublets, giving a goodness of fit of 0.9996.

The fitting using two doublets would find two stress levels, a high stress (with relatively larger peak shift) and a low stress (with relatively smaller peak shift). The mean peak shift (stress) in the probed volume was calculated by S¼

A H S H þ AL S L A H þ AL

ð2Þ

where A is the peak area and S is the R2 peak shift, and the subscripts H and L refer to high and low shift, respectively. When spectra are fitted by two unconstrained peaks, only one peak shift can be obtained. However, there could still be more than one stress level in the probed volume. We find that the peak width ratio from unconstrained fitting is sensitive to the multiplicity of the stress level. The peak width ratio (PWR) is defined as the ratio of the full width at half maximum of the R1 peak to that of the R2 peak. If only one significant stress level is present in the probed vol-

X. Wang et al. / Acta Materialia 57 (2009) 182–195

185

ume, the PWR follows the previously established relationship [17]:

3. Results

PWR ¼ 1:235 þ 3:762  103 Dm  4:286  104 Dm2

3.1. Button specimen

A14330 þ A14546 þ A14626 A14330 þ A14546 þ A14626 þ AR1 þ AR2

ð4Þ

where A14330, A14546 and A14626 are the peak areas at 14,330, 14,546 and 14,626 cm1, respectively, and AR1 and AR2 are the peak areas of the characteristic R1 and R2 peaks. A standard sapphire specimen was seen to give a pure aAl2O3 spectrum, without showing any noticeable h-Al2O3 peaks. However, when the standard Matlab program was used to analyse its spectrum, Ch was found to be a non-zero value (about 0.01), resulting from residual curve fitting error by the fitting program. This indicates the fitting program cannot be used to detect the presence of h-Al2O3 when the h-Al2O3 content is very low (e.g. less than 2%). It is not known how Ch is related to the actual fraction of h-Al2O3 in the TGO. However, it is reasonable to assume a monotonic relationship exists: a higher Ch indicates a higher h-Al2O3 content, a lower Ch a lower hAl2O3 content. Since the R2 line has a nearly linear dependence on stress [8,13], all the peak shift data in this contribution are R2 peak shift with respect to the sapphire sample used for the calibration. According to Ref. [19], the R2 peak position of a strain-free a-Al2O3 material is dependent on chromium content: mCr = mo + 0.827xCr, where xCr is Cr content (wt.%) and frequency is in cm1. To assess the difference, TGO pieces spalled from the blades were checked and found to have shifts varying from +1 to 3 cm1 (as compared to sapphire). However, the spalled TGO was always attached to pieces of YSZ topcoat, and are thus subject to a residual stress arising from the thermal mismatch between TGO and YSZ topcoat. To fully release the residual stress in the TGO, spalled pieces from a blade specimen were ground using a pestle and mortar to 200 mesh. The peak shift of the pulverized TGO pieces was found to be +1.4 ± 0.7 cm1. This indicates that in the current work the peak shift of the TGO in the final stage might have been underestimated by 1.4 cm1. Since the Cr content is expected to change (very likely to increase) with thermal exposure time, for the early and inter-mediate stages this error is likely to be smaller than 1.4 cm1. Since under most circumstances the TGO has a compressive stress or a negative peak shift, for convenience the peak shift data in the following are negative peak shift.

a

2

Fitting 1.5

1

Ref 0.5

0 13

13.5

14

14.5

15

Peak shift (cm-1)

b

0.4

20

15 0.3 10 0.2

Cθ

Ch ¼

The button specimen failed at 8 cycles (160 h at 1150 °C), with about 80% of the coating spalled off. The spectra were all fitted by two unconstrained peaks (goodness index > 0.999), throughout the lifetime of the specimen. Fig. 4a gives the peak width ratio as a function of peak shift. The fitting results follow Eq. (3) (the reference line) quite well, indicating single stress level in the probed volume. The changes of peak shift and h-Al2O3 content with thermal cycling are shown in Fig. 4b. Note that the error bars in Fig. 4b represent the standard deviation of the data measured at all 121 mapping locations. The average residual stress was seen to have increased in the first two cycles and then remained almost constant for the rest of its life time. In contrast, the average h-Al2O3 content index Ch decreased in the first two cycles and then remained at about 0.06 for the rest of the lifetime, indicating a detectable small quantity of h-Al2O3 persisted throughout the lifetime.

PWR

where Dm is the negative peak shift of the TGO. If PWR does not follow Eq. (3), then multiple stress levels exist in the probed volume [13,17,18]. The relative intensities of the h-Al2O3 and a-Al2O3 luminescence lines provide a semi-quantitative indicator of the h-Al2O3 content. The h-Al2O3 content in the TGO was estimated using the following equation:

Peak shift (cm-1)

ð3Þ

5 0.1 0

0.0

-5 0

2

4

6

Number of thermal cycles Fig. 4. (a) Peak width ratio vs. peak shift for spectra at cycle 4 of the button specimen, with the reference line representing Eq. (3); (b) the evolution of peak shift and h-Al2O3 content with cyclic thermal treatment for the button specimen. The error bars represent the standard deviation of the data measured at 121 mapping locations.

X. Wang et al. / Acta Materialia 57 (2009) 182–195

a

1.000

F1

Goodness of fit

0.999

20

0.4

15

Cθ

Peak shift (cm-1)

25

Position CC1 10 0.2 5 0 0.0 0

2

4

6

8

10

12

14

Thermal cycles

b

25

0.6

Peak shift (cm-1)

20 0.4 15

Position CV1 10 0.2 5

0.0

0 2

4

6

10

8

12

14

Thermal cycles

c

Peak shift (cm-1)

This blade specimen had a lifetime of 15 cycles (300 h at 1150 °C). The lifetime was judged as being when P20% of the coating area spalled off. Local spallation first occurred at position CV (hereafter referred to as CV1) after 13 cycles. At cycle 15, most coating area, including position CC (referred to as CC1 hereafter), had spalled off. However, position F (referred to as F1 hereafter) remained adherent to the substrate. The luminescence spectra at CC1 and F1 appeared to consist of two peaks without peak splitting. The goodness of fit by two unconstrained peaks fitting is shown in Fig. 5. It can be seen the adjrsquare index for position CC1 and F1 was consistently large (>0.999), independent of the number of thermal cycles. The spectra at CC1 and F1 could therefore be fitted satisfactorily by two unconstrained peaks. In contrast, the spectra at position CV1 in the early stage (<8 cycles) tended to show doublet splitting, which had to be fitted by two pairs of doublets In the later stage the spectra at position CV1 looked similar to those at other positions. As shown in Fig. 5, the goodness of fit for unconstrained fitting is quite small (<0.996) for CV1 in the early stage, while in the late stage it increased to a value quite close to 0.999. The evolution of peak shift and h-Al2O3 content with thermal cycling for blade specimen one is shown in Fig. 6a–c. As the spectra at CC1 and F1 were fitted by two unconstrained peaks, only one peak shift was obtained. The spectra at CV1 were fitted by two pairs of doublets, therefore the average peak shift was calculated using Eq. (2). As shown in Fig. 6b, the average shift gradually increased over the first 7 cycles and then showed a slight decrease at later stage. Meanwhile, the h-Al2O3 content at CV1 was seen to decrease gradually in the first 6 cycles and then remained practically unchanged until the coating failed. For positions CC1 and F1 (Fig. 6a and c) the peak shift increased in the first two cycles and then remained almost

0.6 30

Cθ

3.2. Blade specimen one

0.6 30

20

0.4

Cθ

186

Position F1

10

0.2

CC1

0.998

0

0.997

0.0 0

0.996

2

4

6

8

10

12

14

Number of thermal cycles

CV1

Fig. 6. Evolution of peak shift and h-Al2O3 content with thermal cycles for blade specimen 1 at positions (a) CC1, (b) CV1 and (c) F1 (20 h cycles at 1150 °C).

0.995 0.994 0

2

4

6

8

10

12

14

Thermal Cycles Fig. 5. Goodness of fit for two unconstrained peaks vs. thermal cycles for blade specimen 1.

constant for the rest of its lifetime, while the h-Al2O3 content Ch was almost constant (about 0.06) throughout the lifetime. A representative peak width ratio vs. peak shift

X. Wang et al. / Acta Materialia 57 (2009) 182–195 2

a

0.6 25

Ref

Position CC2

20

1

0.5

0.4

15

Cθ

Peak shift (cm-1)

1.5

PWR

187

10

0.2

5 0.0

0 0

0 21

22

23

24

25

b

20

25

10

0.6

Position CV2 0.4

6

Cθ

Peak shift (cm-1)

8

relationship for a single map is given in Fig. 7. The peak width ratio for both positions CC1 and F1 were found to deviate significantly from Eq. (3). This deviation indicates that there is a significant contribution from a lower stress component.

15

Number of thermal cycles

Peak shift (cm-1) Fig. 7. A representative profile of peak width ratio vs. peak shift for CC1 and F1.

10

4 0.2

3.3. Blade specimen two

2

This blade specimen had a lifetime of 26 cycles (520 h at 1150 °C). Local spallation first occurred at position CV (CV2) after 25 cycles. After 26 cycles, the coating in most areas, including position F (F2), spalled off, but remained adherent at position CC (CC2). All the spectra for specimen two were found to show doublet splitting. The goodness of fit when fitted using two unconstrained peaks always gave the goodness of fit <0.999. Therefore, all the spectra had to be fitted by two pairs of doublets. The evolution of average shift and h-Al2O3 content with thermal cycling are shown in Fig. 8 for the different positions. For position CC2 (Fig. 8a), the peak shift showed a gradual increase from 10 to 18 cm1 after 12 cycles and then remained fairly constant to the end of life. Meanwhile the h-Al2O3 content decreased to about 0.05 at cycle 12 and remained unchanged thereafter. For position CV2 (Fig. 8b), the peak shift was highest (7 cm1) at cycle 4. It remained at approximately 5 cm1 during the rest of the lifetime. The h-Al2O3 content was remarkably high, being 0.4 initially and decreasing in the early stage, but retaining a relative high value (about 0.1), indicating the h-Al2O3 persistently stayed in the TGO until the end of life. For position F2 (Fig. 8c), the peak shift gradually increased from 5 to 10 cm1 when the h-Al2O3 content decreased from 0.22 at cycle 2 to 0.1 at cycle 12. After 12 cycles, both the peak shift and the h-Al2O3 content remained unchanged.

0

0.0 0

5

10

15

20

25

Thermal cycles

c

12

0.6

Peak shift (cm-1)

9 0.4

Position F2

6

Cθ

20

5

0.2 3

0.0

0 0

5

10

15

20

25

Number of thermal cycles Fig. 8. Evolution of peak shift and h-Al2O3 content as a function of thermal cycling for blade section 2 at (a) position CC2; (b) position CV2; and (c) position F2 (20 h cycles at 1150 °C).

3.4. Coating failure mode SEM was conducted on the substrate and spalled topcoat pieces to examine the locations of coating failure. It was found that, in all cases except CV2, failure was at the bond coat/TGO interface, whereas CV2 had the failure path within the TGO.

188

X. Wang et al. / Acta Materialia 57 (2009) 182–195

Fig. 9. Backscattered images of (a) the underside of a spalled piece (the grey area being alumina and the bright area zirconia) and (b) the exposed surface of substrate (the grey area being Ni, Cr, Co, Al and Pt, but without O, and the dark area being alumina according to element analyses) for position CC2.

Fig. 9 shows the backscattered images of the underside of the spalled coating and the exposed substrate for position CC2. The underside of the spalled topcoat pieces was covered mainly by the TGO (alumina), whereas the exposed surface on the substrate showed mainly bond coat (a mixture of Ni, Cr, Co, Al and Pt, but without O) (Fig. 9b). Therefore, the failure was along the TGO/bond coat interface. The button specimen and positions CC1, CC2, CV1, F1 and F2 on blade specimens showed very similar images to Fig. 9, indicating the button specimen and all positions except CV2 on the blade specimens showed the same failure path, i.e. along the TGO/bond coat interface. In contrast, position CV2 had a different failure path. Fig. 10a shows the underside of a spalled piece which was from an area close to the edge of CV2. Element mapping confirmed that the CV2 area was covered by a mixture of Ni, Co, Cr, Al and O on the underside of the spalled piece, while the neighbouring area was covered by alumina. Fig. 10b shows an area on the exposed substrate that was near to the edge of CV2. This reveals that at CV2 the substrate was covered by the mixed oxides, but at a neighbouring position the bond coat was exposed. Therefore, the coating at position CV2 failed within the TGO, which was composed of mixed oxides of aluminium, nickel, cobalt and chromium.

4. Discussion The residual stress in the TGO arises from the thermal expansion mismatch between the substrate and the TGO and, to a lesser degree, from the TGO growth stresses. For the TGO formed on a flat surface, the elastic thermal mismatch stress is equibiaxial and can be approximated by: rmis ¼

ETGO ðas  aTGO ÞðT f  T R Þ 1  mTGO

ð5Þ

where aS is the thermal expansion coefficient of the substrate, aTGO mTGO, ETGO are the thermal expansion coefficient, Poisson’s ratio and Young’s modulus of the TGO layer, TR is the room temperature and Tf is the freezing temperature (i.e. the temperature below which the stress starts to build up without being relaxed by creep or plastic deformation). The elastic thermal mismatch stress is expected to be influenced by the curvature. The influence of curvature can be assessed using a composite cylinder model (see Appendix). The input parameters required for the model are given in Table 1, which are chosen according to Refs. [20,21]. The Young’s modulus and Poisson ratio are at room temperature and the coefficient of thermal expansion was averaged over room temperature to 1150 °C. For a concave curvature, layer 1 is YSZ (200 lm thick),

Fig. 10. Backscattered images of (a) the underside of a spalled piece (b) the exposed surface of substrate at the edge of CV2 position.

X. Wang et al. / Acta Materialia 57 (2009) 182–195 Table 1 Input parameters for the composite cylinder model Parameters

YSZ

TGO

Substrate

Young’s modulus (GPa) Poisson ratio Thermal expansion coefficient Temperature difference (Tf  TR) (K)

20 0.25 10.5  106 [19] 1125

350 0.26 8.5  106 [19]

150 0.27 17  106 [20]

layer 2 is the TGO (4 lm thick) and layer 3 is the substrate (100 mm thick). The calculated radial stress, rr, hoop stress, rh, and axial stress, rz, in TGO are shown

x 105

a

189

in Fig. 11a–c, in which the stresses of a flat surface are also shown for the purpose of comparison. For a flat surface, the radial stress is zero, and the plane stress was calculated according to Eq. (5). Fig. 11a reveals a compressive radial stress is associated with a concave curvature, but this stress, typically <1 MPa, is very small compared to the hoop stress and axial stress, which are larger than 4.5 GPa (Fig. 11b and c). The radial compressive stress also quickly diminishes as the radius of curvature increases. Both the hoop stress and axial stress (as in Fig. 11b and c) approach the same level as the plane stress of a flat surface as the radius of curvature increases. The influence of

b

x 109 -4.5205

Hoop Stress (Pa)

Radial Stress (Pa)

0

-2

Concave Flat

-4 0

2

4

Concave Flat

-4.521

-4.5215

6

0

x 109

6

23

Peak shift (cm-1)

-4.5215

Concave -4.5216

Flat

-4.5217

4

d

-4.5214

22.5

Concave Flat

22 0

2

4

6

0

Radius of Curvature (mm)

2

4

Radius of Curvature (mm)

x 108

e

2

Radial stress (Pa)

Axial Stress (Pa)

c

2

Radius of Curvature (mm)

Radius of Curvature (mm)

1

0

0

2

4

6

Radius of curvature (mm) Fig. 11. (a) Radial TGO stress, (b) hoop TGO stress, (c) axial TGO stress and (d) peak shift vs. radius for concave curvature.

6

X. Wang et al. / Acta Materialia 57 (2009) 182–195

a Radial stress (Pa)

2

x 10

8

1

0

0

2

4

6

Radius of curvature (mm)

b

x 109

Hoop Stress (Pa)

-3.5

-4

-4.5

-5

0

2

4

6

Radius of Curvature (mm)

c Axial stress (Pa)

the curvature on hoop stress and axial stress exists, but is small: when the radius of curvature changes from an infinitely large value to 0.1 mm, the hoop stress changes by <0.02% and axial stress changes by <0.002%. According to Ref. [8], the peak shift (Dm) of the R2 line can be calculated as: Dm = 2.536(rr + rh + rz) (the units for peak shift and stress are in cm1 and GPa, respectively). The peak shift as a function of radius of curvature is shown in Fig. 11d, which indicates that the peak shift on a concave curvature should be essentially the same as that on a flat surface. For a convex curvature, assuming layer 1 is the substrate whose thickness was set to be r1 (as in Fig. A1), layer 2 is the TGO (4 lm thick) and layer 3 is YSZ (200 lm thick). The stresses as a function of the curvature radius are given in Fig. 12a–c. Fig. 12a reveals a tensile radial stress is associated with the convex curvature. The tensile stress is about 50 MPa when the curvature radius is about 0.5 mm and can go up to approximately 150 MPa when the curvature radius is 0.1 mm. Meanwhile, Fig. 12b and c indicates that both the hoop stress and axial stress increase in magnitude as the radius of curvature increases. The peak shift as a function of the radius of curvature is shown in Fig. 12d for the convex curvature. It can be seen that the peak shift is significantly influenced by the radius of the curvature only when the radius is smaller than 2 mm. For the case of the real blade specimens, the radius at the CV positions was larger than 2 mm; therefore the peak shift at CV positions should be the same as that on a flat surface. Based on the modelling results shown in Figs. 11d and 12d, the peak shift is expected to be about 23 cm1, which is fairly close to the maximum observed peak shift for the blade specimens (e.g. in Fig. 6a and c). The button specimen had a significantly smaller peak shift (15 cm1 as in Fig. 4b). This might be due to different material properties from those listed in Table 1. In addition, a number of other factors could influence the residual stress in the TGO (such as surface roughness). An important conclusion here from the composite cylinder model is that the elastic stress difference associated with the curvature should not make a significant difference to the peak shift. This seems to agree with the peak shift results for blade specimen one as shown in Fig. 5a–c, for which all positions gave a similar peak shift (20 cm1) in the stable stage. However, the experimental results for specimen two (Fig. 8a–c) indicate that both the CV and F positions had much lower average shifts than expected for a flat surface. However, when there are multiple stress levels in the probed volume, it may be more appropriate to look at the individual contributing stress levels instead of the average stress. The high and low stresses obtained by deconvoluting the spectra from positions CV2, CC2 and F2 are plotted in Fig. 13b. It is clear that both the high and low stress components were independent of position. Furthermore, the high shift component has a value close to that

x 109 -2

-3

-4

-5

0

2

4

6

Radius of curvature (mm)

d

24

Peak shift (cm-1)

190

22

20

18

16

0

2

4

6

Radius of curvature (mm) Fig. 12. (a) Radial stress, (b) hoop stress, (c) axial stress and (d) peak shift vs. radius for convex curvature.

calculated for a flat surface assuming linear elastic behaviour, and the low shift component has a shift of only a few cm1.

X. Wang et al. / Acta Materialia 57 (2009) 182–195

a

30

CV1

1.0

CV2 0.8

20 0.6

F2

CL

Peak shift (cm-1)

25

a

F1 CC1

191

15

0.4

10 0.2

5

CC2 0.0

0

0

b

5

30

CV2

25

0

15

10 Thermal Cycles

5

10

15

20

25

20

25

Thermal Cycles

b

F2 CC2

0.4

CV2

F2

Cθ

Peak shift (cm-1)

0.3

20 15

0.2

10 0.1

5

CC2 0.0

0

0

5

10

15 20 X Axis Title

25

30

0

5

10

15

Thermal cycles

Fig. 13. Evolution of high and low stresses vs. thermal cycles.

Fig. 14. (a) The low stress contribution; (b) h-Al2O3 content vs. thermal cycles for blade specimen 2.

The spectra from CC1 and F1 were fitted by two unconstrained peaks, but the peak width ratio profiles in Fig. 7 indicate that multiple stress levels existed in the probed volume even in these cases. The reason that the spectra from CC1 and F1 could be fitted by one doublet was because the high stress contribution was dominant in the spectra. When the spectra from CC1 and F1 were forced to fit to two constrained doublets, the high stress (Fig. 13a) was very similar to those shown in Fig. 13b, but the low stress data had a large relative scattering. Such a large uncertainty in the low stress was because the low stress contribution in the spectra of CC1 and F1 was particularly weak. In such cases, the low stress data are not reliable. Therefore, the low stress data for CC1 and F1 are not plotted in Fig. 13a. The low shift (stress) contribution was calculated by the peak areas: CL = AL/(AH + AL), where CL is the low shift contribution, AL is the integrated peak area corresponding to the low shift contribution and AH is that of the high shift. Fig. 14 gives the low shift contribution for CC2, CV2 and F2 as a function of thermal cycles. The CV2 gave the highest low stress contribution and CC2 gave the lowest low stress contribution amongst the three positions. The low shift contribution at all positions on the blades decreased with the number of thermal

cycles, indicating that the low stress contribution was not due to accumulation of local damage or degradation of the coating system. Upon comparing the low stress contribution in Fig. 14a to the h-Al2O3 content given in Fig. 8a–c, it appears that the low stress contribution is correlated with the h-Al2O3 content. For ease of comparison, the h-Al2O3 content given in Fig. 8a–c is replotted in Fig. 14b. The evolution of low stress contribution with thermal cycles is similar to the evolution of h-Al2O3 content, indicating the low stress contribution might be caused by the h-Al2O3 in the TGO. TGO growth involves the nucleation and growth of h-Al2O3 [22–24], which tends to subsequently transform to the thermodynamic stable phase a-Al2O3. h-Al2O3 formation is more favourable in the initial stage and at relatively lower temperatures [25,26], so the rate of heating is likely to influence the h content in the TGO. Considering the larger thermal mass of the blades, the higher h content found for them might be a result of the relatively slower heating rate. Therefore a small section (about 2 wt.%) of a blade specimen was also tested. It was found there was no substantial difference in the h content between the small and large specimens. Therefore the heating rate does not seem

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X. Wang et al. / Acta Materialia 57 (2009) 182–195

to be a primary factor influencing the h content in the current study. The h to a transformation can be affected by a number of factors. For example, due to a higher solubility of ZrO2 in h-Al2O3 than in a-Al2O3, the h to a transformation is kinetically hindered by the presence of the YSZ topcoat because concurrent ZrO2 precipitation is required [27,28]. The Cr level can also affect the h to a transformation [29]. Furthermore, it has been reported that the h content depends on the bond coat surface condition prior to topcoat deposition: a polished surface appears to favour a formation, while a rough surface encourages h formation [30]. The h to a transformation also depends on how the surface is prepared and the O2 partial pressure of oxidation [29]. Overall it is fair to say that the kinetics of h to a transformation are far from being fully understood. In the current study, despite the two blade specimens being subjected to identical thermal treatment and having nominally the same chemical composition and manufacturing procedure, they produced TGO having significantly different h contents. This indicates that the kinetics of the formation of the h-Al2O3 and its transformation to a-Al2O3 could be changed significantly by subtle changes in chemical composition, interface morphology or defect content in the TBC system. Since h-Al2O3 is formed by outward Al diffusion [27], when the TGO is formed in the early stage, new TGO is in contact with YSZ, which will delay its transformation to a-Al2O3. At a later stage, the outward Al diffusion can be blocked by a continuous layer of a-Al2O3 with a sufficient thickness, so that TGO can be formed between the TGO and the bond coat by inward diffusion of oxygen and a-Al2O3 is then more likely to be formed. This is in agreement with the observation that the h-Al2O3 content decreased with thermal cycles, as shown in Fig. 14b. However, according to Fig. 14b, the h-Al2O3 content was also dependent on the position on the blade: the convex surface had a higher h-Al2O3 content and the concave surface a lower h-Al2O3 content than the flat surface. SEM examination (Fig. 10a and b) revealed that in one case mixed oxides were formed at the convex surface (CV2), whereas in other positions no mixed oxides were detected. This implies that the curvature has some influence on the manner of oxide formation. Further systematic experiments are needed to investigate this. Cracking of the TGO and depletion of aluminium in the bond coat with concurrent enrichment of the oxide in Cr, Co and Ni were found to be the reasons for the formation of the mixed oxides [31]. The convex surface is more susceptible to aluminium depletion and microcracking (e.g. due to the tensile stress arising from the h-Al2O3 to a-Al2O3 transformation). In this sense, it is not too surprising to see the mixed oxides on convex curvature at a relative early oxidation exposure. The TGO formed in the EBPVD system has been reported to have microstructural variations through the

Fig. 15. Fine maps on the cross-section of a blade specimen thermally cycled for 7 cycles (140 h): (a) intensity map; (b) peak shift map; and (c) h-Al2O3 content map.

thickness [28,32–34]. h-Al2O3 was not uniformly distributed through the thickness of the TGO, but instead was found to exist mainly in the TGO near the TGO/topcoat interface [28,29,35], consistent with the stabilizing effect of the YSZ. The presence of two distinct stress levels at nearly all analysis points is also consistent with there being two different layers in the TGO on the blade specimens. Additional luminescence experiments were performed to examine whether there were different layers through the thickness of the TGO in the blade specimen. Fine mapping (with a pitch size of 1 lm) was carried out on the cross-section of a blade specimen which had been thermally cycled at 1100 °C for 7 cycles (140 h). In Fig. 15a–c, the X and Y scales are in micrometres and the greyscale levels represent the normalized signal intensity (%, as in Fig. 15a), peak shift (cm1 in b) and the content of the h-Al2O3 (% in c). When the laser beam hit the TGO, the luminescence signal increased remarkably. Therefore, the TGO layer can be identified

X. Wang et al. / Acta Materialia 57 (2009) 182–195

easily in terms of the intensity (as shown in Fig. 15a). The luminescence intensity (in Fig. 15a) is highest in the centre of the layer. This is because the TGO layer was only 3–4 lm thick: when the laser spot (1–2 lm in diameter) hits the centre, the maximum amount of material can be probed. When the spot hits places other than the centre of the layer, the signal is weakened as a result of either blocking by the bond coat or scattering by YSZ. From Fig. 15a, the luminescence intensity in the TGO near the bond coat interface is very similar to (if not lower than) that near the YSZ. Therefore, the possibility of significant Cr gradient in the TGO can be ruled out. Fig. 15b and c shows the variation of a-Al2O3 peak shift and h-Al2O3 content within the TGO layer. According to Fig. 15b, it is clear that a relatively lower stress (lower shift, darker in colour) existed in the layer immediately adjacent to the YSZ, while a higher stress (shift) existed in the layer next to the bond coat. The maximum shift in Fig. 15b is much less than the value of 20 cm1 measured through the YSZ, probably due to partial stress relaxation caused by exposure of the TGO in the cross-section. Fig. 15c confirms that the TGO adjacent to the YSZ had a high h-Al2O3 content, although the distribution appears to be non-uniform in thickness. By comparing Fig. 15b and c, it can be seen that the positions with high h-Al2O3 content always have a lower a-Al2O3 shift. a-Al2O3 has been observed to nucleate within the h-Al2O3 [36], and a volumetric shrinkage accompanies the h- to a-Al2O3 phase transformation. Therefore, regions within the TGO where h-Al2O3 has recently transformed to a-Al2O3 have an additional tensile strain contribution resulting from the transformation. When cooled, the mixed h-Al2O3/a-Al2O3 layer is subject to the same thermal mismatch strain with the superalloy as is the underlying a-Al2O3 layer. Thus one would expect a bimodal stress to be detected by luminescence: one from the a-Al2O3 layer and the other

193

(with a lower stress) from the a-Al2O3 nucleated within the h-Al2O3. It is known that bond coat rumpling can create a normal tensile stress in the TGO, leading to the initiation of local delamination. According to the modelling carried out by Davis and Evans [37], the rumpling of the TGO with a Pt aluminide bond coat could lead to a 16% decrease in the TGO residual stress (from 4.6 to 3.9 GPa). However, according to Fig. 13a and b, both high stress and low stress components were fairly stable with thermal cycling at all positions except CV2. Furthermore, our SEM examination of the cross-sections of the specimens (a representative SEM image is shown in Fig. 16) did not reveal significant rumpling. Thus the low stress observed at position CV2 cannot be attributed to rumpling. Coating failure took place at the TGO/bond interface at all positions except CV2 irrespective of whether or not there was a mixed a-Al2O3/h-Al2O3 layer above the aAl2O3 TGO. This implies that the mechanical integrity of the TGO layer is not compromised too much by the presence of the mixed a-Al2O3/h-Al2O3 layer, although h to a transformation is accompanied by a tensile stress which could lead to microcracking or a microporous structure. The results in this work also imply that the driving force for coating failure has a significant contribution from the stored energy in the TGO. The fact that blade two had a higher h-Al2O3 content and had a significantly longer life time than blade one (520 vs. 300 h at 1150 °C) may be attributed to the lower stored energy in the TGO in blade two (due to the low stress of the mixed a-Al2O3 /h-Al2O3 layer). Position CV2 failed differently because the TGO layer and the TGO/YSZ interface were severely damaged by the formation of the mixed transitional metal oxides. In this case the stored elastic strain energy in the YSZ could be the main driving force for coating failure along TGO/ YSZ interface. Sintering of the YSZ increases its elastic modulus and hence the stored elastic energy on cooling. YSZ sintering will be enhanced on a concave surface due to the way in which the YSZ columns grow toward each other during deposition in these locations. Hence the YSZ stored energy on thermal cycling will be greater at a concave surface. 5. Summary and conclusions

Fig. 16. A representative SEM image of a cross-section of blade specimens, with the TGO layer (the dark layer in the middle) showing no significant rumpling.

Button specimens showed luminescence spectra that could be fitted with a simple R1/R2 doublet. There was some h-Al2O3 detectable as received, but this quickly disappeared with thermal cycling and the TGO stress rose to approximately 3 GPa, then remained constant to failure. There was no clear evidence of low stress features of the type reported previously [13]. In contrast, two stress levels coexisted in the TGO on blade specimens: a high stress of 4 GPa and a low stress of 500 MPa. Neither stress value was affected by the cur-

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X. Wang et al. / Acta Materialia 57 (2009) 182–195

The authors are grateful to D. Rickerby and R. Jones of Rolls-Royce plc, and J. Nicholls and R. Wellman of Cranfield University for provision of specimens.

3 2

Appendix A. Composite cylinder stress model

1

r0

r1

r2

r3

Fig. A1. Geometry of layers in the concentric cylinder model.

vature on the blade surface, in agreement with predictions based on a composite cylinder model. The fractional contribution of the low stress component decreased with thermal cycling and therefore was not related to local damage accumulation in the TGO. Furthermore, the two blade specimens showed very different fractions of low stress contribution. The low stress contribution decreased as the h-Al2O3 content decreased with thermal cycling. The existence of the h-Al2O3 is a major factor giving rise to the low stress contributions in the TGO. Both the low stress contribution and the h-Al2O3 content varied with position on the blade surface. The position with the convex curvature had a higher h-Al2O3 content and a larger low stress contribution, whereas the position with concave curvature had a lower h-Al2O3 content and a smaller low stress contribution. Luminescence maps on cross-sections indicate that the high and low stress contributions probably come from two different layers in the TGO: a dense inner a-Al2O3 layer and an outer h-Al2O3 containing layer. These TBCs with Pt diffusion bond coats failed along the TGO/bond coat interface in thermal cycling. This was modified by the presence of mixed transitional metal oxides in the TGO. There was no evidence of rumpling, and both the high and low stress contributions stayed fairly stable throughout the lifetime of the specimens. Acknowledgements The authors thank EPSRC for financial support grants GR/S26149/01 and GR/T07329/01. The authors also thank Prof. L. Cohen of the Department of Physics at Imperial College for access to the Raman microprobe.

The effect of substrate curvature on the stresses in the different layers of the TBC system can be analysed semiquantitatively using a model of concentric cylinders as illustrated in Fig. A1. The analysis is all elastic and the basic method is described in standard text books on mechanics (e.g. [38]). This approach has been used previously to understand the stresses generated by local curvature (surface roughness) of the TGO growing on metal substrates in the absence of the ceramic topcoat [39] and also for plasma-sprayed coatings on cylindrical substrates [40]. In Fig. 1 the region inside r0 and outside r3 is void. For a TBC on a convex surface, region 1 is superalloy, region 2 is TGO and region 3 is YSZ. In principle, an extra layer could be inserted for the bond coat, but this is not done here since its properties are similar to those of the superalloy. For a TBC on a concave surface, region 1 is YSZ, region 2 is TGO and region 3 is superalloy. Stresses are generated as a result of the thermal expansion mismatch between the materials in the different layers. These are radial stress, rr; hoop stress, rh; and axial stress, rz. The stresses and strains (assuming isotropic properties) are related by 2 3 32 3 2 er 1 m m rr 6 7 16 76 7 ðA1Þ 4 eh 5 ¼ 4 m 1 m 54 rh 5 þ DaDT E ez rz m m 1 where Da is the difference in thermal expansion coefficient with respect to a reference value (for convenience taken as that of region 1) and DT is the temperature excursion. The assumption of isotropic properties is known not to be valid for EBPVD YSZ, but is made here in order to simplify the analysis. The stresses take the general form rr ¼ A 

B ; r2

rh ¼ A þ

B ; r2

and

rz ¼ C

ðA2Þ

where r is the radial coordinate. Thus, for each region there are thee unknowns (A, B and C), making a total of nine, requiring nine independent equations for solution. These come from the boundary conditions. At each interface there is continuity of radial traction (four equations) and for each interface between the solid materials there is continuity of both hoop and radial strain (four equations). The final equation comes from the condition of zero net axial force: 3 X

C i ðr2i  r2i1 Þ ¼ 0

ðA3Þ

i¼1

The nine equations can be arranged in matrix form as

X. Wang et al. / Acta Materialia 57 (2009) 182–195

2

1

0

6 6 0 0 6 6 6 1 1 6 6 6 0 1 6 6 6 2m1 2m2 6  E1 E2 6 6 2  2m 6 0 E2 6 6 0 0 6 6 ð1m Þ ð1m2 Þ 6 1  E2 6 E1 4 ð1m2 Þ 0 E2

 r12

0

0

0

0

1

0

0

 r12

0

0

0

 r12

1 r21

0

0

0

1

0

 r12

1 r22

0

0

0

0

0

3

1

2

0

0

0

0

1 E1

 E12

2m3 E3

0

0

0

0

1 E2

0

0

0

0

r21  r20

r22  r21

0

ð1þm1 Þ E1 r21

2Þ  ð1þm E r2

0

 Em11

m2 E2

3Þ  ð1m E3

0

ð1þm2 Þ E2 r22

3Þ  ð1þm E r2

0

 Em22

2 1

3 2

In this equation the subscripts refer to the materials in the different regions and Daij is the difference in TEC between the i and j layers. The simultaneous equations can be solved analytically, but the results are unwieldy [40]. We chose to invert the matrix to solve for the coefficients Ai, etc. using Matlab. References [1] Schulz U, Leyens C, Fritscher K, Peters M, Saruhan-Brings B, Lavigne O, et al. Aerosp Sci Technol 2003;7:73. [2] Martena M, Botto D, Fino P, Sabbadini S, Gola MM, Badini C. Eng Fail Anal 2006;13:409. [3] Gell M, Sridharan S, Wen M, Jordan EH. J Appl Ceram Technol 2004;1:316. [4] Ma Q, Clarke DR. J Am Ceram Soc 1993;76:1433. [5] Christensen RJ, Lipkin DM, Clarke DR, Murphy K. Appl Phys Lett 1996;69:3754. [6] Clarke DR, Christensen RJ, Tolpygo V. Surf Coat Technol 1997;94(5):89. [7] Ma Q, Clarke DR. J Am Ceram Soc 1994;77:298. [8] He J, Clarke DR. J Am Ceram Soc 1995;78:1347. [9] Wen M, Jordan EH, Gell M. Mater Sci Eng A Struct 2005;398:99. [10] Sridharan S, Xie LD, Jordan EH, Gell M. Surf Coat Technol 2004;179:286. [11] Xie LD, Sohn YH, Jordan EH, Gell M. Surf Coat Technol 2003;176:57. [12] Nychka JA, Clarke DR. Surf Coat Technol 2001;146:110. [13] Selcuk A, Atkinson A. Acta Mater 2003;51:535. [14] Sohn YH, Vaidyanathan K, Ronski M, Jordan EH, Gell M. Surf Coat Technol 2001;146:102. [15] Wen M, Jordan EH, Gell M. Surf Coat Technol 2006;200:5193.

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

3

72 A 3 2 0 7 1 76 7 6 7 6 A2 7 6 0 7 6 0 7 76 7 6 0 76 6 A3 7 6 7 6 0 7 76 0 B1 7 6 76 7 6 76 7 6 6 Da ¼ B 0 76 2 7 6 12 DT 76 7 6 7 B3 7 6 Da23 DT  E13 76 7 6 76 6 C1 7 6 0 6 6 r23  r22 7 76 7 6 74 C 2 7 5 4 Da12 DT 0 7 7 5 C3 Da23 DT 0

195

3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5

ðA4Þ

m3 E3

Wen QZ, Lipkin DM, Clarke DR. J Am Ceram Soc 1998;81:3345. Selcuk A, Atkinson A. Mater Sci Eng A Struct 2002;335:147. Wang X, Atkinson A. Mater Sci Eng A Struct 2007;465:49. Yu HJ, Clarke DR. J Am Ceram Soc 2002;85:1966. Ali MY, Nusier SQ, Newaz GM. J Mater Sci Lett 2004;39:3383. Sieborger D, Brehm H, Wunderlich F, Moller D, Glatzel U. Zeitschrift Fur Metallkunde 2001;92:58. Grabke HJ. Intermetallics 1999;7:1153. Doychak J, Smialek JL, Mitchell TE. Metall Trans A 1989;20:499. Doychak J, Ruhle M. Oxid Met 1989;31:431. Mennicke C, Mumm DR, Clarke DR. Zeitschrift Fur Metallkunde 1999;90:1079. Tolpygo VK, Clarke DR. Mater High Temp 2000;17:59. Pint BA, Martin JR, Hobbs LW. Solid State Ionics 1995;78:99. Zhao X, Hashimoto T, Xiao P. Scripta Mater 2006;55:1051. Levi CG, Sommer E, Terry SG, Catanoiu A, Ruhle M. J Am Ceram Soc 2003;86:676. Wang X, Atkinson A, Chirivı´ L, Nicholls JR. Surf Coat Technol, submitted for publication. Shillington EAG, Clarke DR. Acta Mater 1999;47:1297. Hu M, Guo S, Tomimatsu T, Ikuhara Y, Kagawa Y. Surf Coat Technol 2006;200:6130. Brickey MR, Lee JL. Oxid Met 2000;54:237. Nijdam TJ, Jeurgens LPH, Chen JH, Sloof WG. Oxid Met 2005;64:355. Stiger MJ, Yanar NM, Jackson RW, Laney SJ, Pettit FS, Meier GH, et al. Metall Mater Trans A 2007;38:848. Lipkin DM, Schaffer H, Adar F, Clarke DR. Appl Phys Lett 1997;70:2550. Davis AW, Evans AG. Acta Mater 2005;53:1895. Rees DWA. Mechanics of solids and structures. London: McGrawHill; 1990. Gong XY, Clarke DR. Oxid Met 1998;50:355. Tsui YC, Clyne TW. Thin Solid Films 1997;306:34.