Characterization and modeling of a martensitic transformation in a platinum modified diffusion aluminide bond coat for thermal barrier coatings

Acta Materialia 51 (2003) 4279–4294 www.actamat-journals.com

Characterization and modeling of a martensitic transformation in a platinum modified diffusion aluminide bond coat for thermal barrier coatings M.W. Chen a,∗, M.L. Glynn a, R.T. Ott b, T.C. Hufnagel b, K.J. Hemker a,b a

Department of Mechanical Engineering, Johns Hopkins University, 3400 N Charles Street, Baltimore, MD 21218, USA b Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Received 12 April 2003; received in revised form 12 April 2003; accepted 5 May 2003

Abstract Phase transformations in a platinum modified nickel aluminide bond coat were investigated by in situ high temperature X-ray diffraction analysis. Three phases, L10 martensite, B2 (β-(Ni,Pt)Al) and L12 (γ⬘-Ni3Al), were identified at different temperature ranges. The martensite is stable at temperatures below 620 °C, and the β-phase is stable at elevated temperatures. The reversible transformation, M↔β, is the principal reaction occurring throughout the bond coat layer during thermal cycling. Quantitative measurements indicate that the molar volume of the β-phase is approximately 2% larger than that of the martensite. Finite element simulations incorporating the volume change associated with this transformation indicate that the transformation significantly influences the distribution of stresses and strains in TBC systems. The effect of the martensite on TBC life is sensitive to the transformation temperatures relative to the creep strength of the bond coat.  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Thermal barrier coating (TBC); X-ray diffraction; Thermal cycling; Phase transformation; Martensite; Transformation strain

1. Introduction Thermal barrier coatings (TBCs) for Ni-base superalloys are widely used in aircraft engine and power generation gas turbines because the ceramic coatings provide excellent thermal insulation, thereby improving the efficiency and prolonging the life of the turbine components [1,2]. A TBC is com-

Corresponding author. Tel.: +1-410-516-6108; fax: +1410-516-4316. E-mail address: [email protected] (M.W. Chen). ∗

posed of three layers: a ceramic top coat, a thermally grown oxide (TGO) layer, and a metallic bond coat on a superalloy substrate. The top coat is the thermal insulator, the TGO provides oxidation resistance, the bond coat aids in the formation of the TGO and enhances bonding to the substrate, and the superalloy carries the loads. The useful life of this multilayered coating is determined by its ability to resist spallation. Detailed studies of this failure process in platinum modified nickel aluminide bond coat/yittria stabilized zirconica (YSZ) TBCs have identified the importance of out-of-plane displacements of the TGO prior to spallation [3–6].

1359-6454/03/$30.00  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00255-6

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Studies aimed at modeling TBC failures associated with the formation of TGO instabilities have historically focused on two main driving forces: thermal strains generated by the thermal expansion mismatch upon cooling and heating, and growth strains related to the lateral expansion of the TGO during service [2,3,6,7]. Tolpygo and Clarke [6] have drawn attention to the importance of microstructural evolution by highlighting local strains associated with the formation of γ⬘ precipitates in the bond coat. The importance of microstructural evolution has been amplified by a recent TEM study of thermally cycled platinum modified nickel aluminide bond coats [8–10]. We used post mortem TEM observations to show that the entire bond coat transforms from its as-fabricated B2 structure to an L10 martensite as a result of inter-diffusion with the underlying substrate during thermal cycling [8,9]. We also presented in situ TEM observations that illustrated that the newly formed martensite transforms to its parent β-phase and back (M↔β) upon heating and cooling [9]. The importance of the strains associated with this martensitic transformation appears to be magnified by the fact that the entire bond coat is transformed in each thermal cycle. The present study has been undertaken in an attempt to quantify the role of the martensitic transformation in the development of stresses and strains in TBC systems. The Ni–Al binary equilibrium phase diagram (Fig. 1) indicates that the ordered B2 structure (βphase) is stable between 45 and 59 at.% Ni at room temperature and that the maximum Ni concentration increases to 68 at.% at 1400 °C [11]. Ni-rich NiAl alloys with 61–68% Ni have been reported to transform into a tetragonally distorted L10 martensite, instead of the equilibrium phases upon modest quenching from temperatures above 1000 °C [12– 15]. As-produced commercial platinum modified nickel aluminide bond coats have the B2 structure, but the L10 martensite is observed in thermally cycled bond coats [8,9]. The transformation strains, temperatures and kinetics of heavily alloyed commercial bond coats are, however, expected to be significantly different than in the binary NiAl alloy. Here, we employ high temperature X-ray diffraction (HT-XRD) to characterize the martensitic transformation in a commercially produced plati-

num modified nickel aluminide bond coat that was thermally cycled to 28% of the furnace cycle test life of the TBC. The results of this analysis are combined with a finite element (FE) model of the multilayered bond coat in a way that illustrates the importance of this martensitic transformation in governing the development of stresses and strains in the bond coat. 2. Experimental approach Thermal barrier coated Rene´ N5 single crystalline buttons (25 mm diameter and 3 mm thick) were prepared by electrodepositing a thin layer of platinum, aluminizing and subsequent annealing. A YSZ top coat was grown by a standard electron beam physical vapor deposition (EBPVD) process, and the as-fabricated buttons were subjected to furnace cycle tests (FCT) with 1-h cycles that included: a rapid (5-min) heat up, a 45-min hold at approximately 1150 °C and a 10-min cool down. Buttons cycled to 28% of their FCT life were prepared for the in situ HT-XRD analysis by grinding off the ceramic top coat and TGO, and mechanically polishing the exposed surface of the underlying bond coat. HT-XRD analysis was carried out using a Rigaku TTRAXS θ/θ rotating anode diffractometer with Cu Kα radiation (l = 0.154 nm). The samples were heated in an Anton-Paar HTK 1200 hot stage under modest vacuum (~10⫺3 Torr). The heating rate between target temperatures was ~40 °C/min and 2-min holds were used to reach a uniform temperature at each target. The collected spectra were treated with standard background subtraction and peak fitting procedures that are incorporated in commercial XRD software. To account for experimental errors associated with displacement of the sample surface from the focusing circle as the temperature changes during the HT-XRD measurement, an extrapolation method, Bradley and Jay’s Extrapolation against cos2q [16], was used to calculate the lattice parameters of the phases present at different temperatures. In this method, the systematic errors are minimized by plotting the lattice parameter obtained from each peak against cos2q and extrapolating to cos2q = 0, where the error is minimized.

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Fig. 1.

Binary phase diagram of Ni–Al [11].

The volume fractions of each phase in the twophase regions were calculated from the X-ray peak intensities, according to the Eq. (1) [17], VA IARB ⫽ VB IBRA

(1)

where IA and IB are the measured integrated intensity of phases A and B, respectively. The term RA and RB are correction factors defined as: Ri ⫽

冉

1 2 1 ⫹ cos22qi,hkl |F |·p · i,hkl i,hkl n2i sin2qi,hkl·cosqi,hkl

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冊

(1a)

where i = A or B; n is the volume of the unit cell of phase i; Fi,hkl is the structure factor of the (hkl) peak for phase i; and pi,hkl is the multiplicity of peak (hkl) for phase i; and qi,hkl is one-half of the scattering angle for peak (hkl) of phase i.

3. Experimental results 3.1. Phase transformations during thermal cycling The phase transformations that occur during thermal cycling were identified from HT-XRD pat-

terns, examples are shown in Fig. 2. At room temperature (Fig. 2(a)), the major phase in the thermally cycled bond coat was indexed as L10 martensite with fundamental diffraction peaks of (1 1 1)L10, (2 0 0)L10, (2 2 0)L10, (3 1 1)L10 and superlattice peaks of (1 1 0)L10, (2 0 1)L10 and (2 2 1)L10. After heating to 1150 °C (Fig. 2(b)), the observed XRD peaks were significantly different and indicative of the ordered B2 structure, with fundamental diffraction peaks of (1 1 0)B2, (2 0 0)B2, (2 1 1)B2, and superlattice peaks of (1 0 0)B2, (1 1 1)B2, and (2 1 0)B2. These findings are in good agreement with previously reported in situ TEM observations of the transformation from L10 to B2 upon heating from room temperature to high temperatures [9]. After the full-range scan at 1150 °C, turning off the heater and filling the chamber with helium cooled the sample. The initial cooling rate from 1150 to 400 °C was ~60 °C/min, and from 400 °C to room temperature, the nominal cooling rate was slower at ~10 °C/min. After cooling back to room temperature, a full-range scan (Fig. 2(c)) showed that the bond coat had transformed back to the martensitic phase during cooling. Small amounts of the L12 (γ⬘-phase) are also apparent in the three scans in Fig. 2, see for

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cycle test, influences the substructure and the density of defects in the martensite. It is worth noting that the martensitic transformation does not take place when the sample is cooled from temperatures below 1000 °C, suggesting that the critical temperature for the austenitization of the bond coat alloy is above 1000 °C, which is consistent with the observations in Ni-rich binary NiAl [12]. In an effort to capture more intermediate temperature data but limit the time that the bond coats were exposed to intermediate temperatures, partial range scans were conducted by scanning from 38 to 58° at several temperatures, as is shown in Fig. 3. The martensitic phase was observed to be stable

Fig. 2. Full range X-ray diffraction patterns of the thermally cycled sample at (a) room temperature, (b) heated to 1150 °C, and (c) after cooling back to room temperature.

example the low intensity peaks indexed as (1 1 1)L12, (2 0 0)L12, and (1 1 0)L12. The volume fraction of L12 was determined from the peak intensities in these scans and found to be approximately 6% for all three scans. In these full-scan HT-XRD experiments, the martensitic transformation (M↔B2) that accompanies thermal cycling was found to be much more dramatic than variations in the L12 phase over the same thermal cycle. Closer inspection of the scans in Fig. 2 indicates that the peaks in Fig. 2(b) and (c) are narrower than those in Fig. 2(a). The broad nature of the peaks in the original room temperature scan, Fig. 2(a), can be related to crystal defects and fine substructure associated with the martensite. In that regard the sharpness of the peaks in the second scan, Fig. 2(b), may be explained by large grains and a low density of crystal defects in the high temperature B2 phase. The observation of relatively sharp peaks in the third scan, Fig. 2(c), suggests that the rate of cooling, which was much slower in the XRD chamber than in the furnace

Fig. 3. X-ray diffraction patterns with larger temperature steps on heating.

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Table 1 Temperature dependence of the Ni3Al volume fractions and the simplified composition based on the Ni-Al phase diagram Temperature (°C)

Volume fraction (%) Ni3Al

700 800 900 1100 1150 Averaged chemical composition

31.5 25.48 23.2 9.1 6.5

Chemical composition (at.%) NiAl

Ni

Al

68.5 74.52 76.8 90.9 93.5

64.40 64.15 64.36 64.49 64.56 64.39

35.60 35.85 35.64 35.51 35.44 35.61

at 400 °C, but at 700 °C it disappeared and β- and γ⬘-phases were identified. Evidence for both phases (β and γ⬘) remained during further heating from 700 to 1150 °C, but the relative intensity of the γ⬘ peaks was observed to change as a function of temperature. The change in the volume fraction of γ⬘ was calculated from the measured intensities of the (1 1 0)B2 and (1 1 1)L12 peaks and is reported in Table 1 and Fig. 4. As the temperature increased from 700 to 1150 °C, the volume fraction of L12 gradually decreased from a maximum of 31.5% to 6.5%, indicating that the L12 phase dissolves into the B2 with increasing temperature. The Ni–Al binary phase diagram shown in Fig. 1 explains this change in the amount of the γ⬘-phase. Above 700 °C, the bond coat composition falls into

a two-phase (β + γ⬘) region that spans from approximately 30–38 at.% Al. With increasing temperatures, the composition range of β gradually expands to the more Ni-rich side, which corresponds to a gradual reduction of the volume fraction of γ⬘. Using the lever rule and the binary Ni– Al phase diagram (Fig. 1), the simplified bond coat compositions were calculated from the measured volume fractions of β and γ⬘. These compositions were calculated at each temperature (Table 1) and were found to be self-consistent. Moreover, the simplified average Al concentration (35.6 at.%) is in good agreement with to the value (35.9 at.%) measured by quantitative micro-probe analysis and given in Table 2 [9], which suggests that most of the alloying elements in the bond coat occupy the Ni sites in the ordered B2 and L10 structures. 3.2. Martensite to B2 transformation

Fig. 4. The volume fraction change of the L12 phase with temperature.

The HT-XRD experiments (Fig. 3) confirm that the transformation from martensite to β occurs in the temperature range from 400 to 700 °C. More rapid HT-XRD scans over a smaller range, 2q of 41–48°, were conducted at smaller temperature steps in order to more accurately characterize the austenitization start temperature (As) and to measure the martensitic transformation strain. A series of scans taken in the range of 450–685 °C is shown in Fig. 5. The formation of the B2 peaks occurs between 600 and 650 °C, as shown by the increase in the relative intensity of the (1 1 0)B2 peak and the corresponding reduction in the intensity of the (2 0 0)L10 peak. The change in the intensity of the (1 1 1)L10 peak is harder to ascertain because it

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Table 2 Chemical composition of the bond coat with 28% of the cycle life measured by micro-probe [9] Phase Ni3Al NiAl Averaged

⌬V/V(%) 6.5 93.5

Ni

Al

Pt

Cr

Co

Ta

Re

W

65.6 44.65 46.01

17.95 37.17 35.92

3.7 8.4 8.09

3.91 4.45 4.45

6.13 5.11 5.11

2.08 0.15 0.15

0.104 0.045 0.045

0.53 0.024 0.024

Fig. 5. Transformation from martensite to B2 with increasing temperature. The transformation can be identified from the intensity change of the (1 1 0) peak of B2.

overlaps with the (1 1 1)L12 peak. A full-range scan of the bond coat taken at 675 °C has been indexed to show that all three phases (β, M and γ⬘) are present in appreciable amounts at this temperature (Fig. 6). The combined (1 1 1)L10–(1 1 1)L12 peak in Fig. 5 changes very little as the bond coat is heated from 450 to 650 °C, but the height of this peak was observed to increase by 60% as the temperature increased from 650 to 685 °C. Given the significant volume fraction of γ⬘ that has been observed at 700 °C (Table 1 and Fig. 3), and the decrease in the intensity of the (2 0 0)L10 peak, the observed increase in the (1 1 1)L10–(1 1 1)L12 peak cannot be taken as an indication of increasing amounts of L10. These observations indicate that a certain fraction of the martensite will transform directly to γ⬘ if held at approximately 700 °C for a sufficiently long time. In this regard it is important to note that the HT-XRD experiment

Fig. 6. X-ray diffraction pattern at 675 °C. Three phases, L10, B2 and L12, can be identified at this temperature.

held the bond coat at 600–675 °C for longer than 30-min, while FCT and engine applications spend much less time at these temperatures. Since the (1 1 0)B2 and (1 1 1)L10–(1 1 1)L12 are the most intense diffraction peaks (Fig. 5), the relative amount of β in the coating was estimated from the ratio of the intensity of these peaks. The temperature dependence of this ratio is plotted in Fig. 7, which indicates that minimal β is present at temperatures below 600 °C and that the volume fraction of β increases dramatically in the range of 600–675 °C. Linear extrapolation of this curve indicates that the start temperature (As) for the transformation from martensite to β is approximately 620 °C. 3.3. Transformation strain and temperature dependence of lattice parameters HT-XRD can be used to determine the lattice parameters as a function of temperature, and coef-

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Fig. 7. The temperature dependence of volume fraction of B2. The start temperature of the transformation is estimated by linear extrapolation analysis.

ficient of thermal expansion (CTE) values can be obtained from a series of high temperature XRD scans. The thermal strain produced by the thermal expansion of a material in which the temperature has changed from T1 to T2 can be calculated by measuring the lattice parameters at the two temperatures, eth ⫽

aT2⫺aT1 aT1

,

(2)

and the CTE (α) can be determined following Eq. (3): a⫽

aT2⫺aT1 ethermal ⫽ ⌬T (T2⫺T1)aT1

(3)

The measured changes in the lattice parameters (a and c) of the non-cubic L10 martensite are plotted as a function of temperature in Fig. 8(a,b), showing that the thermal expansion is different along the a and c directions [18]. The variation in the lattice parameters (a and c) below 400 °C are not well understood, but are believed to relate to the microstructure and stress relaxation on heating. An effective lattice parameter (a∗), a∗ ⫽ 3 冑VL10 ⫽ 3 冑a2 ⫻ c,

(4)

is used to calculate the CTE of the L10 martensite.

Fig. 8. The temperature dependence of the lattice parameters of L10 phase in the temperature ranging from 25 to 600 °C. (a) a; (b) a/c; and (c) a∗.

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The effective lattice parameter is plotted as a function of temperature in Fig. 8(c) and a linear fit to this data shows the average CTE of the martensite to be (11.3 ± 1.2) × 10⫺6 °C⫺1 between 25 and 600°C. At temperatures above 700 °C, the cubic βphase is the dominant phase. The lattice parameter of β exhibits a nearly linear increase with temperature in the range of 700–1000 °C, as shown in Fig. 9. The average CTE for this phase is (12.4 ± 0.3) × 10⫺6 °C⫺1 in this temperature range. The difference in the molar volume between the martensite and its parent phase will result in a significant volume change (⌬V) when the martensitic transformation occurs. Because β and martensite coexist at temperatures ranging from 620 to 675 °C, the difference in molar volume can be calculated from the lattice parameter measurements at a given temperature:

冉

⌬V ⫽ VB2⫺VL10 ⫽ N

2 a3B2 aL10 ⫻ cL10 ⫺ NB2 NL10

冊

ume fraction accompanying the transformation from L10 to B2 is given by Eq. (6): 2a3B2⫺a2L10 ⫻ cL10 ⌬V ⫽ VL10 a2L10 ⫻ cL10

(6)

The measured fractions at different temperatures are shown in Fig. 10. The HT-XRD data indicate that the molar volume of the B2 structure is 2.0 ± 0.3% larger than that of L10. The linear strain generated by the phase transformation is approximated by Eq. (7): etr ⫽

1 ⌬V , 3 V

(7)

giving a transformation strain (etr) of 0.7 ± 0.1%. This is comparable to the magnitude of the thermal strains causes by the CTE mismatch between the bond coat and the underlying superalloy substrate (see Section 5.1).

(5) 4. Finite element modeling results

Here, N is the total number of atoms in the bond coat layer; N B2 = 2, is the number of atoms in the B2 unit cell; NL10 = 4, is the number of atoms in the L10 unit cell; aB2 is the lattice parameter of the B2 phase; and aL10 and cL10 are the lattice parameters of the L10 structure. The change in the vol-

A finite element (FE) analysis was undertaken to assess the importance of the transformation strain in the development of local stresses and strains in the bond coat layer. The numerical simulations were performed using the FE code

Fig. 9. The temperature dependence of the lattic parameter of B2 phase.

Fig. 10. The volume difference between L10 and B2 in the transformation temperature range.

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ABAQUS. The TBC geometry was modeled using 4-node axisymmetric, bilinear (CAX4) elements, as shown in Fig. 11. To study the effect of the transformation on local instabilities, a semi-spherical undulation in the oxide layer penetrates the bond coat. The substrate, located beneath the bond coat, is large enough to dominate the displacement of the TBC system due to its thermal expansion. An axis of radial symmetry is located at the center of the undulation, on the left side of the model. Periodic boundary conditions were placed on the right side of the model. The boundary conditions were placed far enough away from the undulation to avoid significant interaction between undulations. The top surface of the top coat was left traction free. All elastic properties were taken to be temperature independent and are summarized in Table 3. Power law creep present in the bond coat was considered to be the only inelastic deformation in the TBC system. It was provided according to

Fig. 11.

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Table 3 Summary of elastic properties

Oxide Bond coat Substrate

E (GPa)

n

a (ppm/°C)

375 115 186

0.20 0.27 0.27

8.5 16 14

· e¯ cr ⫽ Bs¯ n, · where e¯ cr is the uniaxial equivalent creep strain rate, √2 / 3e˙ cr:e˙ cr; s¯ is the uniaxial equivalent deviatoric stress, and B and n are defined by the user as functions of temperature. Measured values of B and n at different temperatures were taken from [10] and are summarized in Table 4. A temperature cycle from a typical furnace cycle test was imposed on the FE model. The TBC system was initially stress free at the maximum temperature to simulate the fabrication process, and the system was cooled

FE model of the TBC system including an instability in the oxide layer penetrating into the bond coat.

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Table 4 Summary of bond coat inelastic properties T (°C)

B (MPa⫺n s⫺1)

400 650 900 1150

1.00 2.27 1.03 1.06

× × × ×

10⫺15 10⫺13 10⫺13 10⫺15

n 2.7 3.7 4.7 6.8

and then reheated. The temperature ranged from 1135 to 150 °C, and heat up and cool down time were ~10 min each. 4.1. Numerical results of transformation strain and stress Three separate numerical analyses were performed to study the effect of the martensitic transformation. One analysis was performed without the phase transformation, and the other two were performed with the transformation occurring at 600 and 800 °C, respectively. The results of these simulations are shown in Fig. 12. For each of the analyses, the most severe stresses in the bond coat develop directly below the undulation where only the in-plane and the out-of-plane stresses are acting due to the confined state of stresses at this point. The von Mises stress is equal to the magnitude of the difference between the in-plane stress, sIP, and the out-of-plane stress, sOP. The difference between the stresses, (sIP⫺sOP), at this point was plotted as a function of temperature (Fig. 12a,c,e). During cool down, there was an initial period of high temperature creep, followed by elastic loading at temperatures below which creep shuts down. In samples that did not undergo the martensitic transformation the maximum von Mises stress observed in the bond coat occurred at low temperature and was found to be approximately 800 MPa for the geometry studied (Fig. 12a). Incorporating a martensitic transformation (β→M on cooling and M→β on heating) at 600 °C resulted in the stresses of over 2 GPa at low temperature (Fig. 12c) when bond coat yielding was assumed to be negligible, which was deemed reasonable for temperatures below the bond coat ductile-to-brittle transition temperature (DBTT). By contrast, introducing the

transformation at 800 °C resulted in bond coat creep during the transformation and the low temperature stress was similar to that obtained without considering transformation (Fig. 12e). After cool down, the TBC system was heated back to the high temperature. There is an initial period of elastic unloading, followed by elastic loading and ending with high temperature creep. The bond coat unloads elastically until the transformation begins. Once the transformation occurs, the bond coat unloads elastically to zero stress and continues to load elastically with the opposite sign. Once the transformation is complete, the bond coat stress was relaxed by creep at high temperatures. The attendant out-of-plane top coat stress was shown in Fig. 12(b,d,f). Without the transformation this stress reached a modest value of ~85 MPa and was highest at low temperature. Reheating the TBC resulted in a modest hysterisis of the stress in the top coat. Introducing the martensitic transformation at 600 °C reduced the out-of-plane stress in the top coat. However, introducing the transformation at 800 °C allowed the bond coat to creep and effectively transfer its loads to the top coat. The highest out-of-plane stress was observed in the top coat when the martensitic transformation occurred at temperatures high enough to allow for bond coat creep. Thus the occurrence of the martensitic transformation (or not) and the phase transformation temperatures were found to be important factors in determining the out-of-plane stress in the top coat and influencing the driving force for TBC spallation.

5. Discussion 5.1. Importance of martensitic transformation strains The HT-XRD results presented in this paper confirm that the martensite observed in thermally cycled platinum modified nickel aluminide bond coats is stable at low temperatures and transforms back to its parent β-phase at elevated temperatures. The β-phase has been shown to have a larger molar volume than the martensite, and the transformation (M→β) that occurs upon heating increases the vol-

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Fig. 12. The calculated von Mises stresses in bond coat (a,c,e) and out-of-plane stresses in top coat (b,d,f). (a) and (b) Without phase transformation; (c) and (d) the phase transformation at 600 °C; and (e) and (f) phase transformation at 800 °C.

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ume of the bond coat in a manner that enhances the thermal expansion of the bond coat. Conversely, the reverse transformation (B2→M) that occurs on cooling decreases the volume of the bond coat and enhances the thermal contraction. The strain measured by HT-XRD and associated with heating the bond coat from RT to 1150 °C is plotted as a function of temperature in Fig. 13. This figure combines the effects of thermal expansion in both phases with the martensitic transformation, and illustrates a methodology for incorporating these strains into FE models of thermal cyclic behavior. The magnitude of the transformation strain is comparable to the thermal strain that occurs upon heating, and both can be modeled by using a non-linear variation of CTE with temperature. For a thin film on a flat substrate the elastic strain and stress generated by a change in temperature and a difference in CTE (a) are given by: ethermal ⫽ (af⫺as)(⌬T),

(8)

sthermal ⫽ [E / (1⫺n)]f(af⫺as)(⌬T)

(9)

Estimating of the CTE (abond coat=15.5 ppm/°C [10] and asuperalloy=16.3 ppm/°C [19]), a change in temperature of 1100 °C and the elastic constants of the thermally cycled bond coat (Ebond coat=180 GPa and n = 0.3) yield values on the order of

Fig. 13. Thermal cycling strain of the bond coat caused by thermal expansion and phase transformation during a thermal cycle.

ethermal = 0.1% and sthermal=225 MPa. By comparison, the transformation strain measured in the HTXRD experiments is etrans = 0.7%, which would translate to a transformation stress of strans=1.8 GPa. This simple calculation is based on the assumption of a flat interface; the stresses around a perturbation in the TGO are more complicated. The FE analysis presented in Section 4 was undertaken to more accurately determine the importance of the martensitic transformation on the development of stresses and strains in the vicinity of TGO out-of-plane perturbations. These calculations indicate that the stresses developed in the bond coat lead to elevated temperature plasticity, which facilitates penetration into the bond coat by the TGO and enlarges the perturbations. This motion of the TGO results in out-of-plane tensile stresses in the ceramic top coat that are highest at the central point above the perturbation. Comparisons with observations of failed TBC buttons indicate that this point of maximum out-of-plane stress corresponds with the position of crack nucleation [20], and the general finding that the cracks propagate in the top coat near to the interface is also consistent with the FE analysis. Introduction of the martensitic transformation into the FE simulations shows that the presence of the martensite has a significant effect on plastic strains and stresses in the bond coat, and the development of out-of-plane stresses in the top coat. When the transformation occurs at 600 °C, which is below the DBTT, the von Mises stress in the bond coat rises to ~2 GPa, but the out-of-plane stress in the top coat is reduced, not increased, by the transformation. This effect arises because of the three dimensionality of the perturbation. By contrast, when the transformation occurs at 800 °C the stress in the bond coat begins to increase but is then relaxed due to elevated temperature creep and the low temperature stresses are the same as those observed with no transformation. Upon reheating the reverse transformation at 800 °C causes the bond coat to creep and results in a spike in the out-of-plane stresses in the top coat. We conclude that influence of the martensite on TBC life is extremely sensitive to the transformation temperatures (Ms and As) relative to the creep strength of the bond coat.

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5.2. Effect of alloying on the martensitic transformation For binary Ni–Al alloys the Ms temperature has a strong dependence on chemical composition; decreasing the Al concentration from 39 to 32 at.% has been shown to result in a corresponding increase in the Ms temperature from ⫺230 to over 500 °C [13]. This dramatic temperature swing suggests that the transformation temperatures in commercial bond coats may also vary as a function of composition. Chemical analysis of the platinum modified nickel aluminide bond coat used in this study has shown that the Al concentration in the bond coat decreases with thermally cycling as a result of inter-diffusion with the underlying superalloy substrate [9]. Comparison with the binary alloys suggests that the martensitic reaction is expected to shift to higher temperatures with increased thermally cycling until the composition of the bond coat moves into the β and γ⬘ two phase region at the highest temperature during the FCT. Because it is difficult to control the sample temperature on cooling, the Ms temperature of the bond coat was not resolved by the present HT-XRD analysis. Differential thermal analysis (DTA) was conducted and used to measure the temperatures associated with the exothermic and endothermic peaks of both transformations (M→B2 and B2→M), see Fig. 14. The DTA temperature asso-

Fig. 14. DTA curve of the thermally cycled bond coat showing the transformation peaks during a thermal cycle.

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ciated with the peak in the M→B2 transformation was measured to be ~680 °C, which is in resonable agreement with the As of 620 °C measured by HTXRD. The DTA temperature associated with the peak in the B2→M transformation was determined to be ~530 °C. Following the empirical equation M s = (4990–124C Al) K, where CAl refers to atomic percent of Al, derived by Smialek and Hehemann for binary NiAl [13], the Ms temperature of the bond coat is predicted to be 265 °C for the minimum Al concentration (35.9 at.%) in the B2 phase at 1150 °C, or 300 °C for the simplified bond coat composition (35.6 at.%) given in Table 1. The fact that the measured value of the Ms temperature is much higher than the values estimated from the binary NiAl studies indicates that the additional 20 at.% of alloying elements (Pt, Cr, Co, etc.) strongly influence these transformation temperatures. In binary NiAl alloys, the As (M→β) temperature is 10–30 °C higher than the Ms (β→M) temperature [21]. The peaks measured in the DTA scan shown in Fig. 12 suggest that this difference is close to 50–100 °C for the bond coat. This finding is in agreement with previous studies that have shown that alloying additions can enlarge the difference between these transformation temperatures [22,23]. To date, limited information regarding alloying effects on the transformation temperatures has been reported [22–25]. There is evidence to suggest that alloying elements decrease the transformation temperatures in ternary Ni–Al–X (X = Cr, Mo, Ta and W) alloys [22]. By contrast, Co was found to significantly increase the transformation temperatures. Because the elements in VIII group of the periodic table, such as Co, preferentially increase the transformation temperatures, it is likely that Pt increases the transformation temperatures as well. In that light, the higher transformation temperatures measured in this study may be attributed to the 8 at.% Pt and 5 at.% Co found in the bond coat. Inter-diffusion would also be expected to result in changes in the composition and thus the transformation temperatures, but the tertiary and quaternary alloying effects are not understood. More work on the role of alloying is needed.

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5.3. Influence of g⬘ on the transformation strain and CTE measurements It has been suggested that the formation of γ⬘ may influence TGO roughening and durability [6]. In the current study, at 28% of FCT life the room temperature bond coat contains ~6 vol% γ⬘, which appears preferentially in the inter-diffusion zone, along grain boundaries, and at the bond coat-TGO interface [8,9]. Upon heating, the HT-XRD measurements indicate that the volume fraction of γ⬘ increases to as high as ~31% at intermediate temperatures. The phase-diagram in Fig. 1 suggests that the martensite transforms into two phases (β and γ⬘) at intermediate temperatures and then to single-phase β at high temperatures. Lattice parameter measurements indicate that the molar volume of γ⬘ is ~2% smaller than that of L10 martensite, and ~4% smaller than that of β. But the volume change induced by the reaction of M→γ⬘ or γ⬘→β is expected to have a minor effect, as compared to the martensitic transformation, because the precipitation and dissolution of γ⬘ is a transitional reaction. This point is confirmed in Fig. 3, and the volume reduction associated with the M→γ⬘ transformation will be compensated by the reaction from γ⬘ to B2, and the total volume change is determined by the volume difference between the martensite and the β-phase. One influence of this transitional reaction would be to partially spread the volume difference between the martensite and β-phase to higher temperatures, as represented by the dashed line in Fig. 13. However, the heating rates are much higher, ~5 min from room temperature to 1150 °C, for real hardware and during the FCT, and the volume fraction of γ⬘ formed directly from martensite may be much lower in these cases. The measured CTE value of the β-phase in the thermally cycled bond coat is smaller than reported values for the as-fabricated bond coat [3,10]. The smaller CTE value that was measured in the X-ray experiments can be attributed to the γ⬘→β reaction by considering the fact that the γ⬘-phase gradually dissolves into β-phase (Fig. 4), which becomes more Ni-rich with increasing temperature. Because Ni atoms are smaller than Al atoms, increasing the Ni content by substituting Ni on Al sites decreases

the lattice parameter in Ni-rich NiAl [26–28]. By fitting the experimental data [26–28], the composition dependence of NiAl lattice parameter a can be expressed as a ⫽ a0⫺0.00195(1⫺CAl)

(10)

where a0 is the lattice parameter of stoichiometric NiAl and CAl is the concentration of Al in a binary Ni–Al alloy. Thus, the decrement of the lattice parameter with decreasing Al concentration from C1 to C2 is given by: ⌬a ⫽ 0.00195(C2⫺C1)

(10a)

If the bond coat is simplified as a binary Ni– Al alloy, the Al concentrations in β at different temperatures can be obtained from the binary phase diagram. After correcting the temperature dependence of the lattice parameter by considering the composition effect, the average CTE of B2 is calculated to be ~16.4 × 10⫺6 °C⫺1, which is in good agreement with the value of the as-received bond coat (~15.5 × 10⫺6 °C⫺1) [10], in which neither chemical composition change nor phase transformation occurs on heating. However, it is important to note that when the composition of the bond coat moves into the β + γ⬘ two-phase region, the smaller CTE value, including the effect of the reaction, is the effective value of the bond coat. Annealing L10 martensite at moderate temperature from 400 to 700 °C usually results in the appearance of other phases such as N5Al3 and Ni2Al as reported by XRD analyses and TEM observations [18,29–31]. However, excluding γ⬘, these phases have not been observed in the current work, which may be due to the large amount of alloying elements stabilizing the martensitic phase. 5.4. Conditions for formation of martensite Diffusionless martensitic transformations are generally associated with high cooling rates that preclude diffusive transformations. But the L10type martensitic transformation that occurs in NiAl alloys has a much lower critical cooling rate, and air-cooling has been reported to be fast enough for the formation of martensitic [32]. For the commercial bond coat, the formation of martensite during the HT-XRD experiments suggests that the reac-

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tion occurs over a wide range of cooling rates. Separate DTA measurements have demonstrated that the martensitic transformation takes place at cooling rates as low as ~25 °C/min (Fig. 12). The cooling rates in commercial gas turbine engines are high enough to form the martensite [33]. Formation of the martensite is also highly sensitive to the Ni content of the β-phase. As-fabricated commercial bond coats do not have enough Ni to form the martensite, but inter-diffusion with the Ni-base superalloy substrate leads to ingress of Ni and the appearance of the martensite. It follows that the operating temperature must be high enough to promote this inter-diffusion. Moreover, bond coats held at intermediate temperatures will form two phases (β and γ⬘) microstructures and the Ni concentration of the β-phase will be considerably lower than that of the overall bond coat. For this reason, bond coats that are heated past the β-solvus temperature will be much more likely to form martensite on cooling. The importance of operating temperature on the formation of the martensite has been illustrated by recent investigation of a turbine blade that had been removed from service [33]. Careful inspection of the bond coat and TBC at various locations around the circumference of the blade indicated that martensite formed in the hotter regions of the blade but was less prevalent where the temperature was lower [33] 6. Summary and conclusions 1. HT-XRD experiments have confirmed a reversible transformation, β↔M martensite that accompanies thermal cycling. The critical cooling rate for the formation of the martensite was observed to be less than 25 °C/min. 2. The transformation temperatures determined by HT-XRD and DTA are much higher as compared with binary NiAl. This is attributed to the large amount of alloying elements in the commercial bond coat, particularly Pt and Co. 3. The molar volume of β-phase is ~2% larger than that of the martensite. The β↔M transformation, which occurs on each thermal cycle, results in an effective strain of 0.7%, which is comparable to the thermal strain that arises from the CTE mismatch.

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4. Incorporating the transformation strain into a FE model of the TBC suggests that the martensitic transformation plays an important role in the formation of stresses and strains in the TBC system. The effect of the martensite on TBC life was also found to be sensitive to the transformation temperatures (Ms and As) relative to the creep strength of the bond coat.

Acknowledgements This work was supported by the National Science Foundation under grant No. DMR9986752. The support of Dr. MacDonald and Dr. Murty and the NSF GOALI Program are greatly appreciated. RTO and TCH gratefully acknowledge support for the high-temperature diffraction work from the Department of Energy under Grant DE-FG02-98ER45699. Acquisition of the high-temperature diffractometer was made possible by the Army Research Office, through Grant DAAG55-97-1-0061.

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