Interaction of molten silicates with thermal barrier coatings under

Interaction of molten silicates with thermal barrier coatings
under temperature gradients
R. Wesley Jacksona,∗, Elisa M. Zaleskia,c , David L. Poerschkea ,
Brian T. Hazelc , Matthew R. Begleya,b , Carlos G. Levia,b
a
b
Materials Department, University of California, Santa Barbara, CA 93106-5050, USA
Mechanical Engineering Department, University of California, Santa Barbara, CA 93106-5070, USA
c
Pratt and Whitney, East Hartford, CT, 06108, USA
Abstract
This paper examines the effect of temperature gradients on the interaction between silicate deposits
and thermal barrier coating (TBC) systems. A dedicated test facility, in which a CO2 laser is
employed to impose a controllable thermal gradient through the coating and underlying substrate,
is used to investigate the interaction between two silicate compositions with state-of-the-art 7YSZ
EB-PVD TBCs. The experimental results are then used to guide the development of expressions
that describe the nature of silicate infiltration in the TBCs, the evolution of coating elastic modulus,
and the generation and release of stresses.
Keywords: thermal barrier coating; delamination; CMAS; thermal gradient; Infiltration;
∗
Corresponding Author
Email address: [email protected], F ax :(805) 893-8486 (R. Wesley Jackson)
Preprint submitted to Acta Materialia
October 20, 2014
1. Introduction
The rising operating temperature of aero-engines has increased the prevalence of molten deposits of calcium magnesium alumino-silicates (CMAS) on the hardware surfaces surrounding the
hot gas path [1–4]. The combustor and airfoils in the high-pressure turbine, where CMAS deposition is most prevalent, are typically protected by thermal barrier coatings (TBCs). These coatings
have microstructures with tailored porosity designed to impart high in-plane compliance to minimize thermal stresses, and low thermal conductivity, to maximize the temperature drop across the
coating. Both of these properties are generally degraded by CMAS infiltration [1, 5].
Capillarity drives the penetration of CMAS into the coating as molten silicates readily wet oxide
ceramics [6, 7]. The depth to which CMAS penetrates depends upon the temperature gradient
across the coating as well as the composition of the melt through its effects on viscosity, and the
chemical interaction with the TBC. As the temperature at the TBC-bond coat interface is typically
greater than the glass transition temperature, Tg , infiltration into the coating is either controlled
by viscous flow and therefore the time at which the TBC is above Tg , or by the crystallization
kinetics. Both of these factors depend on the composition of the glass, with the Si:O ratio [8, 9]
having a controlling effect on the viscosity and the concentration of minor elements, particularly,
Fe [8], and Ti [10], playing a strong role on the crystallization kinetics.
As the molten silicate penetrates into the cooler interior of the coating, crystallization may occur
even in the absence of any interaction with the TBC as long as the undercooling is sufficient to
activate the crystallization kinetics. Typical crystallization products for CMAS include anorthite,
diopside, one of the wollastonite variants, and either tridymite or gehlenite depending on the silica
concentration [1, 11, 12]. More often, however, melt penetration leads to dissolution of the TBC at
the interface with the melt [7], and subsequent reprecipitation of one or more crystalline phases. For
state-of-the-art TBCs based on 7wt.% yttria partially-stabilized zirconia (7YSZ), the reprecipitated
phases may be Y-lean tetragonal zirconia, transformable to monoclinic on cooling, Y-rich cubic
zirconia [7] and zircon, calcium zirconate or garnet [12, 13], depending on the composition of the
melt.
Once infiltrated, the modulus of the TBC is expected to markedly increase due to the presence
crystalline silicates and/or residual solid glass in the original pores. The rise in modulus increases
the magnitude of the stresses in the TBC that are generated from the inherent CTE mismatch
2
between the ceramic topcoat and the superalloy component [4]. It is therefore of interest to analyze
how the CMAS induced variation in stiffness through the coating couples with the temperature
gradient to generate thermal stresses in the TBC and how these stresses drive delamination [14, 15].
This work is part of a broader investigation to elucidate the effect that CMAS has on the
durability of TBC systems and to identify possible mitigation approaches. A novel, laser based,
thermal gradient testing facility is used to thermally cycle 7YSZ TBCs with prescribed temperature gradients. The microstuctural changes observed in these experiments are then paired with
analytical expressions that capture key features of the TBC-CMAS interaction, namely: the rate
of CMAS infiltration in a thermal gradient, the evolution of CMAS induced TBC stiffening, and
the development of thermal stresses.
2. Experimental approach
2.1. Thermal gradient test
The TBCs examined in this work were thermally cycled in a facility specially designed to impose
a tunable temperature gradient. This experimental set-up is capable of modulating both surface
temperatures by using a 2 kW, 10.6 µm, CO2 laser to heat the surface of the TBC, and an air jet
to cool the uncoated backside of the substrate, Figure 1. To homogenize the incident energy, the
laser beam was passed through a ZnSe facetted lens that was rotated at 300 rpm with the center
of the lens translated 3 mm off of the beam axis. Additionally, the TBC was raised 6 mm above
the focal plane to further enhance the uniformity of the heating profile, Figure 1(b) [16].
7YSZ TBCs are semi-transparent in the visible and near infrared range (λ=0.3-5 µm), but the
absorptivity increases with expanding wavelength and above λ > 7 µm TBCs are highly adsorptive
[17, 18]. Eldridge and co-workers measured the transmittance of 10.6 µm radiation through a
60 µm thick coating to be 0.2% at 1170◦ C and attributed the low transmittance to the large
absorption coefficient, which is in excess of 1000 cm−1 at temperatures greater than 1000◦ C [18,
19] which corresponds to an optical penetration depth of less than 10µm. Further, unlike the
scattering coefficient, that is markedly decreased by CMAS infiltration, the absorption coefficient
is not expected to be influenced by the presence of CMAS [5]. The highly absorptive nature of the
TBC minimizes the need to consider radiative heat transfer through the coating in the analysis.
3
The surface temperature of the TBC was monitored by a far-infrared, (7-10 µm) imaging pyrometer. A single surface temperature was calculated by averaging the temperature in a region of
interest covering the majority of the surface of TBC specimen. The long wavelength pyrometer
was used to minimize the collection of radiation from the interior of the coating, which, in the
thermal gradient, can skew temperature readings to lower values. Thin, 250 µm diameter, k-type
thermocouples were used to measure the temperature on the back surface of the substrate and,
notably, within the substrate at a short distance below the substrate/TGO interface. The thermal
cycle used in this investigation consisted of three segments, a heating stage, a dwell period and
a cooling stage. In all cases, the dwell period was 10 minutes, and the surface temperature of
the TBC was approximately 1300◦ C. The heating and cooling stages are prescribed by the rate at
which the laser power was changed, while the cooling air velocity remained constant resulting in
the TBC surface heating at a rate of 110◦ C/min and the bottom surface of the substrate heating
at a rate of 90◦ C/min.
Measured temperatures for a 7YSZ TBC with CMAS that was cycled 5 times are shown in
Figure 2. This thermal cycle is typical of all experiments conducted in this investigation with the
temperature gradient across the TBC approximately 0.7◦ C/µm and surface, coating/bond coat
interface, and backside temperatures for each experiment are listed in Table 3 along with the
calculated heat fluxes.
2.2. Specimen details
The TBC specimens were fabricated especially for this study by Pratt and Whitney and comprise of a 3 mm thick superalloy substrate, PW 1484, coated with a 30 µm thick NiCoCrAlY-Hf-Si
bond coat and a 350 µm thick EB-PVD 7YSZ top coat. Using electro-discharge machining (EDM),
a 300 µm diameter hole was drilled into the substrate directly below the bond coat, and a 300 µm
wide trench was cut into bottom surface of the substrate to allow thermocouples to be placed in the
specimen. The unique specimen design, schematically illustrated in Figure 1, allowed the temperature gradient through the multi-layer TBC system to be monitored through the test. In some tests,
the backside thermocouple became separated from the substrate surface during exposure, resulting
in erroneously low temperature reads. In these cases TBack is estimated with the calculated heat
flux and substrate thermal conductivity and these values are listed in parentheses in Table 3.
4
2.3. CMAS preparation and deposition
Two silicate compositions characterized in a previous study [8], denoted C33 M9 A13 S45 and
C13 F10 A18 S59 were used in this investigation; their composition, glass transition temperature, Tg ,
and the incipient melting temperature, TIM , are listed in Table 1. The CMAS composition has
been used in previous investigations [7, 8, 20] and is a simplified version of the intruding melt
found within airfoil coatings by Borom et al.[1]. The C13 F10 A18 S59 composition was selected for its
higher viscosity estimated by literature models and more active crystallization behavior measured
by differential-scanning calorimetry[8] .
The synthesis of the C33 M9 A13 S45 and C13 F10 A18 S59 powders followed the procedures described
by Zaleski et al.[8]. The constituent oxides (99.95% CaO, 99.95% MgO, 99.8% SiO2 and 99.99%
Fe2 O3 from Alfa Aesar, and 99.99% AKP-50 Al2 O3 from Sumitomo Chemical) were mixed in deionized water, creating a thick paste. The mixtures were then ball milled for 4 h, dried, crushed
in a mortar and pestle and pre-reacted by heating in air for 24 hours at 1200◦ C for C33 M9 A13 S45
and at 1000◦ C for C13 F10 A18 S59 . Both mixtures were then crushed a second time in a mortar and
pestle.
The powders were mixed in ethanol at a concentration of 200 mg/ml and suspended by ultrasonic
agitation. The suspended mixtures were then deposited on the TBC surface dropwise and dried
under a heat lamp for 30 minutes to drive off the ethanol resulting in a C(M/F)AS loading of
approximately 5 mg/cm2 .
2.4. Characterization techniques
Microstructural characterization of the TBCs was performed using scanning electron microscopy
(SEM, XL30 Sirion FEG, FEI, Hillsboro, OR). Lamellae for transmission electron microscopy
(TEM, Technai G2 Sphera, FEI) were extracted using focused ion beam (FIB, Helios, FEI) to
examine the infiltrated silicate and the TBC. Compositional analysis was performed using energy
dispersive spectroscopy in the TEM (TEM-EDS, Oxford, Concord, MA). The concentrations were
calibrated with CMAS and CFAS standards verified by inductively coupled plasma mass spectrometry (ICP-MS, Dirats Laboratories, Westfield, MA).
5
3. Results
Experimental observations of 7YSZ TBCs exposed to the two different silicate melts under
a thermal gradient will be described below. The infiltration behavior and the microstructural
evolution of the coating due to interactions with the silicate melt will be detailed followed by a
description of cracking in the coating.
3.1. 7YSZ-C33 M9 A13 S45
Following a single thermal cycle with the schedule described in Figure 2, C33 M9 A13 S45 was
found to completely penetrate the TBC, Figure 3(a). The YSZ-C33 M9 A13 S45 interaction near the
surface of the TBC was consistent with previous investigations [7, 11] in which the initially featherlike TBC columns evolve into the globular structure depicted in Figure 3(b). The spatial extent
of the C33 M9 A13 S45 attack increased with additional cycles, as a dense outer zirconia shell and
a string of rounded pockets of residual CMAS particles are present on the TBC column surfaces,
Figure 4(a-b).
TEM analysis of a FIB lamella parallel to the base of the coating, Figure 4(d) shows the open
porosity in the TBC structure has been filled with CMAS. Convergent-beam diffraction of the
CMAS filled pores indicates that the silicate is amorphous. Compositional analysis, performed
using EDS in both the SEM and TEM found that the composition of the infiltrated silicate was
similar to the bulk composition, both of which are listed in Table 1. In contrast with the observations
at the top of the TBC, the extent of the reaction between the 7YSZ and C33 M9 A13 S45 was minimal,
as reflected in the presence of facetted nano-pores remaining in the TBC in close proximity to the
CMAS/TBC interface. A 80 nm intermixed zone (IMZ) of zirconia and alumina is present between
the TGO and the TBC, Figure 3(c), typical of TBCs deposited before the TGO has transformed
to α-Al2 O3 [21], but no observable reaction product developed at the TBC/TGO interface despite
the complete penetration of the silicate. Following 5 thermal cycles, the thickness of the IMZ
has not measurably increased and there is still no observable reaction product at the TGO/TBC
interface, Figure 4(c). Additionally, SEM-EDS measurements identify CMAS constituents in the
intercolumnar gaps extending to the base of the coating, but not within the TGO.
No cracks were observed in the TBC following a single thermal cycle, but delaminations were observed after 5 cycles, as illustrated in Figure 4. The largest crack was found at the bond coat/TGO
6
interface above which the TBC had buckled away from the bond coat, Figure 4(a)(c). Additionally, cracks running parallel to bond coat/TGO interface formed in the TBC approximately 100
µm above end of the interface delamination, Figure 4(c). These cracks grew from a vertical separation descending from the surface of the TBC. None of these delaminations, however, extended
sufficiently to exfoliate the coating from the substrate. The occurrence of the delamination at the
BC/TGO interface and not the TGO/TBC interface is expected as a significant amount of strain
energy is released when the TGO separates from the bond coat. The energetics of both cracking
events will be discussed in section 4.3.
3.2. 7YSZ-C13 F10 A18 S59
TBC specimens were also loaded with C13 F10 A18 S59 and thermally cycled. The C13 F10 A18 S59
deposit was visually observed to undergo two melting events during the heat-up stage of the thermal
cycle. As the second melting event begins, the molten C13 F10 A18 S59 appeared to partially de-wet
the from TBC surface and form droplets of molten silicate. Cross-sectional images show that the
TBCs were only partially penetrated by the C13 F10 A18 S59 after a single cycle, Figure 5, and five
cycles, Figure 6. Following a single cycle a large amount of residual C13 F10 A18 S59 remained in
the surface. Iron-rich phases were found to have precipitated on the tips of the TBC columns and
zircon, ZrSiO4 , was found in the intercolumnar spaces near the surface, Figure 6, consistent with
observations by Mechnich et al [22]. C13 F10 A18 S59 penetration extended 250 µm into the coating.
This corresponds to a temperature of approximately 1150◦ C. TEM analysis on a FIB lamella
parallel to the substrate, extracted slightly above the bottom of the infiltrated region, found the
silicate to be amorphous and the composition denuded in Fe. The inference is that the penetration
was limited by the rate of viscous flow, rather than by crystallization, consistent in principle with
the higher viscosity of the C13 F10 A18 S59 melt. Following 5 thermal cycles the C13 F10 A18 S59 -YSZ
interaction was more extensive as the column tips have been dissolved to a greater extent and
there was minimal residual CFAS left on the surface of the coating. Importantly, the depth of
CFAS penetration does not measurably increase between the 1st and the 5th cycles despite the
glassy nature of the penetrant. This finding will be discussed in terms of temperature-dependent
infiltration model developed in section 4.1.
7
4. Discussion
The thermo-mechanical degradation of TBCs by silicates is envisaged to involve the following
sequence of events: (i) oxide deposits are held above the incipient melting temperature1 (ii) the
molten silicate penetrates the coating; (iii) upon cooling below the “softening point” [23] the coating
stiffness increases rapidly and; (iv) the thermal strains generated during cooling induce delamination
cracks driven by the elastic strain energy stored in the stiffened coating. The nature of each of these
phenomena can be significantly affected by the temperature gradient that exists in TBC systems.
The effect that temperature gradients have on each of these factors will be subsequently analyzed
by extending previously developed models to incorporate through-thickness temperature variation.
The predictions of these models will be compared with the experimental results detailed above.
4.1. Silicate infiltration
The energy available for delamination is dependent on the extent to which the molten silicate
flows into the coating [4]. The penetration depth is governed by the competition between the flow
dynamics of the viscous silicate, which diminishes with decreasing temperature down the coating thickness, and the kinetics of crystallization as influenced by any dissolution of the thermal
barrier oxide. First, consider the infiltration rate of the silicate into the coating under a temperature gradient. At the simplest level, the rate of penetration can be calculated by extending
the isothermal capillary flow through porous media analysis in Kramer et al. [7, 24] assuming
that the melt rapidly achieves thermal equilibrium with its local surroundings. During the high
temperature dwell, a linear steady-state temperature gradient is imposed across the coating. At a
given location, h, measured from the coating surface, the temperature, T (h), can be expressed in
terms of the temperature drop across the coating ∆TT BC = TSurf − TSub , the temperature at the
substrate/coating interface, TSub , and the coating thickness, HT BC .
T (h) =
1
−∆TT BC
h + TSurf
HT BC
(1)
In this investigation, the exposure temperature exceeds the liquidus of C33 M9 A13 S45 and is close to the
C13 F10 A18 S59 liquidus so that the majority of the deposit is molten and compositional shift of the liquid from
that of the bulk is negligible.
8
This temperature distribution can be combined with the temperature dependent melt viscosity2 ,
approximately given by:
η(T ) = ηo exp(−βT )
(2)
The viscosity does not follow the behavior predicted by Equation 2 over a wide temperature range,
but within the relevant temperatures it can be approximated using values calculated from the model
proposed by Giordano et al [9]. Based on the assumption of rapid thermal equilibration with the
local surroundings, the instantaneous melt viscosity profile through the coating may be written as
η(h) = ηo exp[β(
−∆TT BC
h + TSurf )]
HT BC
(3)
The penetration velocity as a function of distance can then be expressed as [7]
32r
ω
σLV cos(θ)
dh
=
2
dt
kt (ω − 1)
η(h)h
(4)
where, σLV , is the surface tension of the melt, cos(θ), is the contact angle between the melt
and the TBC, ω, is the porosity, kt , is a tortuosity factor, and r is a hydraulic radius or dimension
representative of the area available for flow between columns. The relationship between penetration
depth and time can be determined by integrating Equation 4 with application of the boundary
condition that at t=0, h=0.
t=
∆T
kt (1 − ω)2 ηSurf + η(h)(−1 + β HT BC h)
32σLV r
ω
( β∆T )2
(5)
HT BC
The calculated infiltration depth is plotted as a function of time for the C33 M9 A13 S45 and
C13 F10 A18 S59 melts in Figure 7. In these calculations, perfect wetting is asummed, i.e. cos(θ) = 1,
the porosity is assumed constant (ω = 0.1), the liquid surface tension (σLV = 0.4) is calculated
based on heuristic models reported elsewhere [25] and the tortuosity factor is calculated using the
Kozeny model of permeability (kt = 2)[24]. If the viscosity were to remain constant η = ηSurf ,
both the C33 M9 A13 S45 and C13 F10 A18 S59 melts would be predicted to fully penetrate the coating.
2
To describe the viscosity over a wide range of temperature Giordano et al.
[9] use the expression η =
A
10−4.55 exp T −B
where the constants A and B depend on melt composition. For mathematical expedience, a simple
exponential description is used in Equation 3 which fits the Giordano expression when interpolating between known
viscosities.
9
If the temperature dependence of viscosity in Equations (2,3) is considered, then the C33 M9 A13 S45
melt would be expected to completely penetrate the coating at the end of the 10 minute dwell,
while the C13 F10 A18 S59 melt would only penetrate 200 µm. The silicate infiltration depths can
be compared with the experimental results in Figures 4 and 5. In Figure 4, the YSZ coating has
been completely penetrated by C33 M9 A13 S45 as illustrated by the dense cross section. On the
other hand, the C13 F10 A18 S59 melt has only partially penetrated the coating. A glass transition
is not expected during the high temperature dwell because the base of the coating, approximately
1050◦ C, is hotter than Tg for both compositions. The experimental results also suggest that the
crystallization kinetics of the two silicates compositions are not sufficient to impede penetration.
4.2. The effect of silicate penetration on coating modulus and thermal expansion coefficient
The effect of silicate penetration on coating compliance and thermal expansion is conceptually
understood but lacking significant experimental quantification in the literature; however, both
properties are of crucial importance in determining the driving force for coating delamination.
As a first approximation, the columnar structure of an infiltrated EB-PVD can be modeled as
a laminate with alternating YSZ and 2nd phase (i.e. CMAS) plates. The elastic modulus can be
estimated using the simple Reuss (series) rule-of-mixtures, EEf f,R
1
EEf f,R
= VY SZ
1
EY SZ
+ VP 2
1
EP 2
(6)
where VY SZ is the volume fraction of the YSZ columns in the TBC, VP 2 is the volume fraction of the
second phase, EY SZ , and EP 2 are the moduli of the YSZ columns and the second phase respectively
[26]. A uniaxial fiber composite serves as a better approximation of the TBC structure and Hashin
and co-workers[27–29] have found upper and lower bounds for the transverse elastic modulus. The
effective composite modulus, EEf f calculated using the Reuss model and Hashin transverse fiber
bounds using values for a typical EB-PVD TBC with VT BC = 90% and ET BC =200 GPa are plotted
as a function of EP 2 in Figure 8(a). For reference, the Voigt (parallel) rule-of-mixtures[26] is also
plotted.
For the case of the uninfiltrated coating, EP 2 =5-10 GPa which results in EEf f =30-50 GPa
which, is in good agreement with [30]. If the pores in the coating are then filled with glassy silicate
(GS), EGS =70-90 GPa [31, 32] the effective modulus increases to 155-170 GPa at temperatures
10
below Tg . If the silicate were to crystallize (CS) and stiffen to ECS =110-120 GPa [31] the effective
modulus will increase but only by ∼6% to 180 GPa.
The effective CTE, αEf f , of composite materials depends on the elastic properties and CTE of
the constituents [33, 34]. But as a first approximation, the simple Voigt rule-of-mixtures, αEf f,V =
αY SZ VY SZ + αP 2 VP 2 , which describes the transverse thermal expansion of the parallel laminate
structure inlaid in Figure 8(a), can be used to predict the CTE of a silicate penetrated EB-PVD
TBC. A more accurate representation of αEf f can be taken from the work of Schapery [34] where
the transverse CTE of unidirectional fiber composites is expressed in terms of the Ei , νi , and αi of
the constituents
αEf f = (1 + νY SZ )αY SZ VY SZ + (1 + νP 2 )αP 2 VP 2 +
EY SZ αY SZ VY SZ + EP 2 αP 2 VP 2
EY SZ VY SZ + EP 2 VP 2
(7)
The uniaxial fiber model predicts αEf f to be equal to the Voigt model when the elastic properties
of the constituents are equal and αEf f decreases with a reduction in EP 2 due to the insuffeceint
constraint of the less stiff CMAS matrix. The variation in αEf f as a function of αP 2 was calculated
with Equation 7 for EP 2 equal to 70 and 120 GPa, corresponding to a glassy and crystalline silicate
respectively, showing a weak dependence on EP 2 .
The CTE of most glasses is less than YSZ and (C,M)AS glasses range from 2-9 ppmK−1 with
the CTE decreasing with increasing SiO2 content [32]. αEf f as a function second phase CTE is
presented in Figure 8(c) using the Voigt rule-of-mixtures and Equation 7. The CTE of silicates in
the composition range of C33 M9 A13 S45 is approximately 7 ppmK−1 [32, 35] resulting in the reduction
of αEf f of the CMAS filled TBC would be approximately 5% with respect to 7YSZ.
The primary conclusions from this analysis is that the effective modulus of the TBC increases
dramatically when penetrated by a silicate melt but is not strongly influenced by the stiffness of
the second phase when EP 2 > 31 EY SZ . As such, the effective modulus of a TBC with less than 20%
porosity is not predicted to markedly change if the second phase were to crystallize from a silicate
glass. The effective CTE of a TBC will typically be reduced by silicate penetration with a reduction
of 5% for compositions in the range of C33 M9 A13 S45 and reductions approaching 15% for high SiO2
glasses with low CTE. Finally, the error in using the simple Reuss model for EEf f and Voigt model
for αEf f with respect to more complex composite models is small for the silicate-EB-PVD system.
11
4.3. Thermo-mechanical model
The evolution of stress and strain energy in the TBC multilayer following thermal cycling in the
laser gradient test is analyzed using the thermo-mechanical model recently presented by Jackson
and Begley [36]. The TBC system is modeled as a series of layers extending infinitely in the
xz−plane which are stacked in the y−direction, Figure 1(c). The total strain is described in terms
of the curvature, κ, and the axial stretch, o , of the multilayer about the reference axis, located at
the bottom of the superalloy at y = 0. The stress as a function of position in a layer, i, within the
multilayer is then defined by:
¯i [o − κ · y − c · θi (y)]
σi (y) = E
(8)
¯i is the effective modulus of layer-i (e.g. E
¯ = E/(1 − ν) under equi-biaxial conditions and
where E
¯ = E/(1 − ν 2 ) under plane strain conditions), νi is the Poisson’s ratio, and θ(y)i is the thermal
E
strain distribution, defined as θ(y) = α (T (y) − T o (y)). That is, the strain distribution is calculated
by determining the change in the local temperature, T (y), from a reference temperature T o (y) that
defines the stress-free state. This temperature change is then multiplied by the coefficient of thermal
expansion (CTE) of that layer αi and the term c, where c = 1 + ν for plain strain while c = 1 for
equi-biaxial conditions. The values o and κ are calculated through force and moment balances, as
described previously [36]. The strain energy, Ui , in each layer can then be calculated by integrating
σi (y) through the thickness of each layer, where yti and ybi respectively define the top and bottom
of the layer-i.
Z
Ui =
yti
ybi
1+v 2
v
2
2
σx + σz −
(σx + σz ) dy
2E
2E
(9)
The energy release rate for delamination, G, is calculated by finding the difference between the
strain energy in the two multilayers created by the interface crack, and the strain energy in the
intact (original) multilayer ahead of the crack.
h
i
G = U [o , κ] − U t to , κt + U b bo , κb
(10)
While the strain energy in the intact layer is calculated with the deformation constants associated
with biaxial deformation, the two multilayers created as the crack grows are allowed to relax in the
direction normal to the crack such that the resultant moment and axial force are zero, (i.e. x = 0)
but remain constrained in the z−direction with z (y) determined by the deformation constants
describing the deformation of fully intact multilayer under biaxial stress conditions.
12
4.4. Mechanical anaylsis
The material properties used in the analysis are listed in Table 2 where the values of the
infiltrated coating modulus and CTE were estimated with the Reuss and Voigt models, respectively.
It is assumed that the coating is completely relaxed under the thermal gradient during the high
temperature dwell and cooling is slow enough that the maximum stress and energy release rate
values develop when fully cooled to the ambient. (The cooling rates used in this investigation are
sufficiently slow such that thermal-shock induced delamination that results from rapid cooling are
not expected [36].)
In Figure 9(a), the stress profile through the TBC multilayer after cooling is plotted for noninfiltrated (YSZ), partially infiltrated (C13 F10 A18 S59 ) and fully infiltrated (C33 M9 A13 S45 ) coatings.
In all cases, the coating is in a state of compression and the magnitude of the compressive stress
increases as the fraction of the coating which has been infiltrated increases. The corresponding G
for delamination has also been plotted in Figure 9(b). The G values are plotted for EEf f =170 and
185 GPa.3 It is assumed for simplicity that the silicate infiltration does not markedly increase the
thermal conductivity of the coating as the measured temperatures did not dramatically decrease
for fixed laser power and cooling air velocity. While the molten C(M/F)AS will readily fill the
intercolumnar gaps, there is a large population of closed nano pores that will not be filled until the
coating surrounding the pores is dissolved. The phenomenon is observed near the column tips but
not in the interior of the coating, Figure 4(d). As it is the intracolumnar pores which give decrease
the thermal conductivity of the coating, little change in thermal conductivity is expected in the
short exposure time experienced by the TBCs in this investigation.
The energy release rate rises dramatically as the fraction of coating infiltrated increases, as
G is proportional to σ 2 . For comparison, the energy release rate for the same TBC multilayer
following cooling after an 1100◦ C isothermal dwell is plotted for a range of silicate penetration
depths. This comparison was chosen to represent the standard furnace cycle test widely used to
assess the durability of TBCs. The energy release rate is much higher in the isothermal case than
in the temperature gradient case as elaborated below.
3
During cooling, the modulus of a TBC infiltrated with a glassy silicate will increase when cooled below the glass
transition temperature. However, the point at which this transition occurs does not effect the amount of stored elastic
strain energy so long as deformation is purely elastic.
13
In the experiments, no delamination was observed for either the C33 M9 A13 S45 or the C13 F10 A18 S59
infiltrated coating following a single cycle. On first impression this is unexpected as an energy release rate of 400 J/m2 would exceed the fracture toughness of the interface. However, it is necessary
that a pre-existing flaw be present to give origin to a propagating crack. As thermal cycling progresses, there are a number of processes that will allow the micro-cracks present in the coating
and the discontinuities in the coating/alloy interface to propagate such that a critical flaw from
which delamination cracks can evolve. The exact mechanism behind this transition needs further
investigation. Nevertheless, as silicate penetration increases from 70% to 100% of the 350 µm coating the driving force for the delamination increases by 50%, suggesting that the likelihood of the
C33 M9 A13 S45 infiltrated coating delaminating is much greater than then that of the C13 F10 A18 S59
infiltrated coating as observed experimentally.
Finally, this analysis can be extended to examine how the temperature drop across the coating
and the depth of silicate infiltration influence the driving force for delamination. Figure 10 depicts
contours of constant driving force for delamination for a C(M/F)AS penetrated coating, G, normalized by the driving force for a non-penetrated TBC (EEf f =40 GPa), Go for a range of initial
temperature gradients and silicate penetration depths. In the map, the top surface of the coating is
fixed at 1300◦ C and the coating/substrate interface temperature is varied. That is, when ∆T = 0
the coating is isothermal and TSub = 1300◦ C, while ∆T = 200◦ C corresponds to TSub = 1100◦ C.
The ordinate of the map describes the depth of penetration. When h/HT BC = 0, no infiltration has
occurred and when h/HT BC = 1 the TBC is fully infiltrated by the silicate. As such, the map can
be viewed as an analog to a cross-sectional micrograph where increasing penetration depth moves
toward the horizontal axis of the map or toward the TGO in the micrograph.
Figure 10 shows that increasing the temperature gradient decreases the driving force for delamination. The decrease is due to the fact that the high temperature on the outer portion of the coating
makes the low CTE YSZ contract to greater extent when cooled, minimizing the difference in the
length change between the coating and the substrate, lowering the stress. The map also reiterates
the point, shown in Figure 9, that decreasing the penetration depth decreases the amount of stored
energy in the coating. Further, as was described in Section 4.1, the rate a which a silicate melt
will penetrate a coating decreases with an increasing temperature gradient, because the viscosity
increases markedly with decreasing temperature. The combination of these two effects shows that
14
increasing the temperature gradient across the coating (increasing the heat flux and decreasing the
substrate temperature) can markedly decrease the tendency for the infiltrated silicate to induce
delamination.
4.5. Thermochemical degradation
The C(M/F)AS induced microstructural evolution of 7YSZ TBCs has been presented in Figures
3-6. The short duration of some of the high-temperature exposures (10 min) allows the initiation of
interaction to be examined. As the molten silicate penetrates the TBC, the feathery arms that make
up the TBC columns begin to dissolve and subsequently reprecipitate after a critical supersaturation
is reached. Arguably, dissolution is most rapid initially at the feather tips and reprecipitation occurs
between the feathers producing a dense zirconia layer on the periphery of the TBC column and
a row of partially occluded spherical CMAS pockets running parallel to the column surface. This
microstructure is observed for TBCs loaded with C33 M9 A13 S45 or C13 F10 A18 S59 , Figures 3 and 5
respectively. The globular microstructure that results after longer exposures is envisaged to develop
from the continued dissolution and reprecipitation of the TBC into the CMAS pockets, which seem
to migrate inward gradually consuming the cores of the columns [7, 22].
The C33 M9 A13 S45 deposit was found not to yield crystallization products containing both oxides
from the TBC and the melt. This was not the case for the C13 F10 A18 S59 loaded TBC, as an Fe-rich
phase formed on the surface of the TBC columns and zircon grew in the intercolumnar gaps near the
TBC surface, Figure 5. The higher Si concentration in C13 F10 A18 S59 with respect to C33 M9 A13 S45
drives the zircon formation. However, the growth of zircon is relatively slow, unlike rare-earth
apatites (e.g. Gd8 Ca2 (SiO4 )6 O2 ) that form on TBCs with high concentration of a dissolved rareearth element and are capable of inhibiting infiltration by blocking the intercolumnar gaps [11, 37].
In consequence, the silicate penetration is not hindered by zircon formation. Additionally, the
formation of these phases does not markedly change the CFAS composition although some Fe
depletion is observed, Table 3.
Finally, no reaction was observed at the CMAS infiltrated TBC-TGO interface. CMAS-Al2 O3
reactions have been reported at the base of the TBC, notably in Kramer et al [7] where anorthite,
CaAl2 Si2 O8 , was was found to form following isothermal exposure at 1300◦ C. In the current investigation, no reaction was observed, Figures 3-4; the difference in behavior is ascribed to the lower
temperature of the TBC/TGO interface, 1050◦ C, which appears to be sufficiently low for the melt
15
presumably saturated with Y and Zr to react with the TGO. Nevertheless, most molten silicate
compositions will not be in equilibrium with the TGO and further work is merited to investigated
the tendency for reaction at the lower temperature of the TBC/TGO induced in an actively cooled
TBC.
5. Conclusions
A novel laser gradient facility was developed and used to investigate the influence that the
temperature gradient has on several facets of the interaction between silicate melts and thermal
barrier coatings. The key insights are as follows:
• The depth to which a silicate melt will penetrate a TBC is strongly affected by the temperature gradient across the coating as the melt viscosity increases exponentially with decreasing
temperature. A simple model was developed to calculate the penetration depth as a function
of time.
• Simple models of planar laminate composites were used to estimate the effect of silicate
penetration on the coating stiffness and thermal expansion. Filling the pores in the coating
with a second phase will markedly increase the effective stiffness even when this second phase
is substantially more compliant than the TBC material. Conversely, silicate infiltration will
only minimally decrease the effective CTE of TBCs even for low CTE glasses are considered.
These models were compared with more complex descriptions of the transverse properties of
uniaxial fiber composites finding only small differences.
• The increase in stiffness dramatically elevates the stresses in the coating and the driving force
for delamination. These calculations are consistent with observations from the laser gradient
experiments. Additionally, calculations were performed that illustrate the manner in which
increasing the temperature gradient across the TBC decreases the energy release rate.
• Both silicate compositions induce morphological evolution of the TBC through dissolution
and reprecipitation reactions. The Si concentration in C13 F10 A18 S59 is sufficient to react
with the TBC to form zircon. No zircon formation was observed on the TBC loaded with
C33 M9 A13 S45 .
16
Acknowledgements: Research supported by the Office of Naval Research under grant N00014-081-0522 monitored by Dr. D.A. Shifler. The modeling activity was performed through a collaboration
with MRB supported by NSF-DMR 1105672. The characterization work made use of the MRL
Shared Experimental Facilities, a member of the NSF-funded Materials Research Facilities Network
(www.mrfn.org) supported by the NSF MRSEC Program under Award DMR 1121053.
References
[1] M. P. Borom, C. A. Johnson, L. A. Peluso, Role of environment deposits and operating surface
temperature in spallation of air plasma sprayed thermal barrier coatings, Surf Coat Tech 86
(1996) 116–126.
[2] C. Mercer, S. Faulhaber, A. Evans, R. Darolia, A delamination mechanism for thermal barrier
coatings subject to calcium–magnesium–alumino-silicate (CMAS) infiltration, Acta Mater 53
(2005) 1029–1039.
[3] A. G. Evans, D. R. Clarke, C. G. Levi, The influence of oxides on the performance of advanced
gas turbines, J Euro Ceram Soc 28 (2008) 1405–1419.
[4] C. G. Levi, J. W. Hutchinson, M.-H. Vidal-S´etif, C. A. Johnson, Environmental degradation
of thermal-barrier coatings by molten deposits, MRS Bull 37 (2012) 932–941.
[5] L. Li, D. R. Clarke, Effect of cmas infiltration on radiative transport through an eb-pvd
thermal barrier coating, Inter. J Appl Ceram Tech 5 (2008) 278–288.
[6] N. Eustathopoulos, M. G. Nicholas, B. Drevet, Wettability at high temperatures, volume 3,
Elsevier, 1999.
[7] S. Kr¨amer, J. Yang, C. G. Levi, C. A. Johnson, Thermochemical interaction of thermal barrier
coatings with molten CaO–MgO–Al2 O3 –SiO2 (CMAS) deposits, J Am Ceram Soc 89 (2006)
3167–3175.
[8] E. M. Zaleski, C. Ensslen, C. G. Levi, Thermochemical interaction of thermal barrier coatings
with molten CMAS deposits, J Am Ceram Soc (2014) submitted.
17
[9] D. Giordano, D. B. Dingwell, Non-arrhenian multicomponent melt viscosity: a model, Earth
Planet Sci Lett 208 (2003) 337–349.
[10] A. Aygun, A. L. Vasiliev, N. P. Padture, X. Ma, Novel thermal barrier coatings that are
resistant to high-temperature attack by glassy deposits, Acta Mater 55 (2007) 6734–6745.
[11] S. Kr¨amer, S. Faulhaber, M. Chambers, D. R. Clarke, C. G. Levi, J. W. Hutchinson, A. G.
Evans, Mechanisms of cracking and delamination within thick thermal barrier systems in
aero-engines subject to calcium-magnesium-alumino-silicate (CMAS) penetration, Mater Sci
Eng A 490 (2008) 26–35.
[12] W. Braue, Environmental stability of the YSZ layer and the YSZ/TGO interface of an inservice EB-PVD coated high-pressure turbine blade, J Mater Sci 44 (2009) 1664–1675.
[13] P. Mechnich, W. Braue, Solid-state CMAS corrosion of an EB-PVD YSZ coated turbine blade:
Zr4+ partitioning and phase evolution, J Am Ceram Soc (2014).
[14] A. G. Evans, D. R. Mumm, J. W. Hutchinson, G. H. Meier, F. S. Pettit, Mechanisms controlling
the durability of thermal barrier coatings, Prog Mater Sci 46 (2001) 505–553.
[15] A. G. Evans, J. W. Hutchinson, The mechanics of coating delamination in thermal gradients,
Surf Coat Tech 201 (2007) 7905–7916.
[16] M. D. Novak, F. W. Zok, High-temperature materials testing with full-field strain measurement: Experimental design and practice, Rev Sci Inst 82 (2011) 115101–115101.
[17] J. Manara, M. Arduini-Schuster, H.-J. R¨atzer-Scheibe, U. Schulz, Infrared-optical properties
and heat transfer coefficients of semitransparent thermal barrier coatings, Surf Coat Tech 203
(2009) 1059–1068.
[18] J. I. Eldridge, C. M. Spuckler, Determination of scattering and absorption coefficients for
plasma-sprayed yttria-stabilized zirconia thermal barrier coatings, J Am Ceram Soc 91 (2008)
1603–1611.
[19] J. I. Eldridge, C. M. Spuckler, J. R. Markham, Determination of scattering and absorption
coefficients for plasma-sprayed yttria-stabilized zirconia thermal barrier coatings at elevated
temperatures, J Am Ceram Soc 92 (2009) 2276–2285.
18
[20] S. Kr¨amer, J. Yang, C. G. Levi, Infiltration-inhibiting reaction of gadolinium zirconate thermal
barrier coatings with cmas melts, J Am Ceram Soc 91 (2008) 576–583.
[21] M. J. Stiger, N. M. Yanar, R. W. Jackson, S. J. Laney, F. S. Pettit, G. H. Meier, A. S. Gandhi,
C. G. Levi, Development of intermixed zones of alumina/zirconia in thermal barrier coating
systems, Metall Mater Trans A 38 (2007) 848–857.
[22] P. Mechnich, W. Braue, U. Schulz, High-temperature corrosion of EB-PVD yttria partially
stabilized zirconia thermal barrier coatings with an artificial volcanic ash overlay, J Am Ceram
Soc 94 (2011) 925–931.
[23] H. R. Lillie, Viscosity of glass between the strain point and melting temperature, J Am Ceram
Soc 14 (1931) 502–512.
[24] D. R. Poirier, G. H. Geiger, Transport phenomena in materials processing, Minerals, Metals
& Materials Society, 1994.
[25] A. Kucuk, A. Clare, L. Jones, An estimation of the surface tension for silicate glass melts
at 1400c using statistical analysis, Glass Technology-European Journal of Glass Science and
Technology Part A 40 (1999) 149–153.
[26] Y.-M. Chiang, D. P. Birnie, W. D. Kingery, Physical ceramics, J. Wiley NY, 1997.
[27] Z. Hashin, S. Shtrikman, On some variational principles in anisotropic and nonhomogeneous
elasticity, J Mech Phys Solids 10 (1962) 335–342.
[28] Z. Hashin, B. W. Rosen, The elastic moduli of fiber-reinforced materials, J Appl Mech 31
(1964) 223–232.
[29] Z. Hashin, On elastic behaviour of fibre reinforced materials of arbitrary transverse phase
geometry, J Mech Phys Solids 13 (1965) 119–134.
[30] C. Johnson, J. Ruud, R. Bruce, D. Wortman, Relationships between residual stress, microstructure and mechanical properties of electron beam-physical vapor deposition thermal
barrier coatings, Surf Coat Tech 108 (1998) 80–85.
19
[31] J. D. Bass, Elasticity of minerals, glasses, and melts, Mineral Physics & Crystallography: A
Handbook of Physical Constants (1995) 45–63.
[32] N. P. Bansal, R. H. Doremus, Handbook of glass properties, Academic Press, Inc., Orlando,
FL, 1986.
[33] E. Kerner, The elastic and thermo-elastic properties of composite media, Proc Phys Soc B 69
(1956) 808.
[34] R. A. Schapery, Thermal expansion coefficients of composite materials based on energy principles, J Compos Mater 2 (1968) 380–404.
[35] S. N. Salama, H. Darwish, H. Abo-Mosallam, Ha forming ability of some glass-ceramics of the
CaMgSi2 O6 -Ca5 (PO4 )3 F-CaAl2 SiO6 system, Ceram Inter 32 (2006) 357–364.
[36] R. W. Jackson, M. R. Begley, Critical cooling rates to avoid transient-driven cracking in
thermal barrier coating (TBC) systems, Int J Solids Structures 51 (2014) 1364–1374.
[37] D. L. Poerschke, C. G. Levi, Effect of cation substitution and temperature on the interaction
between thermal barrier oxides and molten CMAS, J Euo Ceram Soc (2014) in press.
[38] J. A. Haynes, B. A. Pint, W. D. Porter, I. G. Wright, Comparison of thermal expansion and
oxidation behavior of various high-temperature coating materials and superalloys, Mater High
Temp 21 (2004) 87–94.
[39] T. M. Pollock, S. Tin, Nickel-based superalloys for advanced turbine engines: chemistry,
microstructure and properties, J Propulsion Power 22 (2006) 361–374.
[40] J. B. Wachtman, W. R. Cannon, M. J. Matthewson, Mechanical properties of ceramics, Wiley,
2009.
[41] T. R. Kakuda, A. M. Limarga, T. D. Bennett, D. R. Clarke, Evolution of thermal properties
of EB-PVD 7YSZ thermal barrier coatings with thermal cycling, Acta Mater 57 (2009) 2583–
2591.
[42] D. R. Clarke, S. R. Phillpot, Thermal barrier coating materials, Materials Today 8 (2005)
22–29.
20
Table 1: Composition and melt attributes of silicates investigated [8, 9].
CaO
MgO
AlO1.5
SiO2
FeOx
Tg
TIM
η1300
η1100
(cat. %)
(cat. %)
(cat. %)
(cat. %)
(cat. %)
(◦ C)
(◦ C)
Pa·s
Pa·s
nominal
33
9
13
45
0
966
1234
5.31
178
infiltrated
32
8
12
47
0
nominal
13
0
18
59
10
994
1101
371
22,090
infiltrated
11
0
12
62
6
C33 M9 A13 S45
C13 F10 A18 S59
Table 2: Properties of TBC system constituents [30, 38–42].
Thickness
E
ν
α
k
Layer
(µm)
(GPa)
(10−6 K −1 )
(W/mK)
Superalloy
3000
200
0.3
15
20
Bond coat
30
180
0.3
16
20
TGO
2
400
0.25
8
10
TBC
350
40
0.2
11
1.5
TBC+CMAS
0-350
170
0.25
10.6
1.5
Table 3: Laser gradient test data.
TSurf TSub TBack ∆TT BC Laser Power
Heat flux
Specimen
(◦ C)
(◦ C)
(◦ C)
(◦ C)
(kW)
(M W/m2 )
CMAS 1 cycle
1287
1030
862
247
1.1
1.1
CMAS 5 cycles
1286
1032
883
244
1.1
1.1
CFAS 1 cycle
1287
1001
(814)
286
1.1
1.2
CFAS 5 cycles
1324
994
(778)
331
1.2
1.4
21
(A)
(B)
2kW CW CO2 laser
λ =10.6 µm
Mirror
Beam
Path
Transmissive
Beam
Integrator
Imaging
Pyrometer:
7> λ >10 µm
y
(C)
25.4 mm
7YSZ
350 μm
Steel
specimen
fixture
25 mm
beam
30 μm
NiCoCrAlY-HfSi
Sample
Thermocouples
3 mm
Thermocouples
PW-1484
Cooling
Air
z
x
Figure 1: (a) Schematic illustration of the laser gradient testing apparatus. (b) Thermal image of the TBC surface
demonstrating the uniformity of the homogenized laser beam. (c) Schematic illustration of the TBC sample with the
ordinate system used in the mechanical analysis is overlaid.
22
Temperature °C
1300
1000
700
TIM(C33M9A13S45)
TIM(C13F10A18S59)
TSurf
TSub
TBack
10 mins
0
Time min
50
100
150
Figure 2: Temperatures of the TBC surface, TSurf , the TBC/bond coat interface, TSub and at the back substrate
surface, TBack during a 5 cycle exposure. A similar thermal cycle was performed on specimens that under went
a single cycle. TSurf was measured by a pyrometer while TSub and TBack were measure by thermocouples. The
incipient melting point, TIM , of CMAS and CFAS are indicated.
Figure 3: (a) Cross-sectional SEM image of the TBC exposed to C33 M9 A13 S45 after a single thermal cycle. (b)
Higher magnification images of the CMAS/YSZ interface (c) and the TBC/TGO interface with an inlaid image of
the TGO showing the presence of an intermixed zone (IMZ) adjacent to the TBC and the absence of reaction between
he penetrated CMAS and the TGO.
23
Figure 4: Cross-sectional SEM images of YSZ exposed to C33 M9 A13 S45 after 5 thermal cycles. (a) The complete
cross-section of the TBC showing buckling, with the image magnified five times in the vertical direction relative to
the horizontal scale. (b) Higher resolution images off the column tips showing CMAS/TBC reaction. (c) Higher
magnification image of the marked area in (a), showing delamination at the TGO/BC interface and cracks in the
TBC. (d) TEM micrograph taken from the base of the coating showing CMAS filling the inter-columnar gaps of the
coating. A convergent-beam electron diffraction pattern indicating the amorphous nature of the CMAS filled pore is
inlaid.
24
Figure 5: (a) Cross-sectional back-scattered electron SEM images of a YSZ TBC exposed to C13 F10 A18 S59 after a
single thermal cycle. (b) Secondary-electron with a dashed line overlaid to mark the extent of infiltration. (c) TEM
micrograph taken from bottom of the penetrated region showing CFAS filling the inter-columnar gaps of the coating
with an inlaid convergent-beam electron diffraction pattern indicating the amorphous nature of the CFAS filled pore.
25
Figure 6: (a) Cross-sectional SEM image of YSZ TBC exposed to C13 F10 A18 S59 after five thermal cycle. (b) Higher
resolution images off the column tips showing CFAS/TBC reaction. (c) A secondary-electron SEM image illustrating
the extent of penetration. The infiltrated TBC is dense (upper portion of the image) while uninfiltrated coating
remains porous.
26
1300
η=ηo exp[-βT]
η=ηSurf
50
1250
100
150
C13F10A18S59 1200
200
CFAS
250
300
350
Temperature ( °C)
Penetration depth, h (µm)
0
Measured h
C33M9A13S44
0
2
4
1150
CMAS
6
8
1100
10
Time (min)
Figure 7: The calculated infiltration depth, h, of CMAS and CFAS melts into the TBC under a 200◦ C temperature
gradient. The calculations are performed where it is assumed that the viscosity remains constant, dashed line, and
changes with the temperature gradient through the coating, solid line. The infiltration depths observed experimentally
in Figures 3 and 5 are overlaid.
27
(a) 200
185
170
YSZ
Voigt
r(+)
Fibe
YSZ
T
Re ran
us sF
s ib
er
(-)
s
Tran
EEff (GPa)
2 Phase
nd
crystalline
silicates
glassy
silicates
40
as-deposited
0
5
70
120
200
E P2 (GPa)
(b)
11
Voigt
Rule-of-mixtures
10
EP2=120 GPa
EP2=70 GPa
-1
α Eff (ppm K )
10.6
Transverse CTE
Uniaxial fiber composite
Fused
Silica
7
0.5
CMAS
YSZ
7
11
-1
α P2 (ppm K )
Figure 8: The effective TBC modulus EEf f (a) and CTE αEf f (b) for a fixed VY SZ = 0.9 are plotted as a function of second phase stiffness, EP 2 and CTE αP 2 respectively. In (a), EEf f is plotted using the Voigt and Reuss
approximations as well as the upper and lower bounds for the transverse modulus of a unidirectional fiber composite, labeled TransFiber(+) and TransFiber(-), respectively. EEf f of a TBC in the as-deposited, silicate infiltrated
(glassy and crystalline silicate) and fully densified states are highlighted for the Reuss approximation. In (b), αEf f
is plotted using the Voigt rule-of-mixtures as well as transverse CTE of a uniaxial fiber composite for values of EP 2
corresponding to glassy and crystalline silicates.
28
500
PW 1484
TBC
bond coat
0
Z
YS
YS
YS
Z+
Z+
CM
CF
AS
AS
Stress (MPa)
(a)
-500
σTGO=-3.2 GPa
σTGO=-3.3 GPa
σTGO=-3.5 GPa
-1000
2
(b)
3
3.4
Position, y (mm)
h (µm)
250
350
0
EEffective =185 GPa
EEffective =170 GPa
630
G (J/m2)
530
Isothermal T=1100°C
YSZ+CMAS
Temperature gradient
240
160
YSZ+CFAS
YSZ
1
0.75
0.5
0.25
0
h/HTBC
Figure 9: (a)The stress profile across the TBC multilayer following cooling from an initial temperature gradient
corresponds to TSurf = 1300◦ C and TBack = 800◦ C to 25◦ C for no infiltration, partial infiltration with CFAS and full
infiltration with CMAS. (b) The energy release rate for delamination at the TGO-bond coat interface as a function
of silicate penetration depth, h. The observed penetration depths of the CMAS and CFAS melts are marked. The
energy release rate is also plotted for a TBC thermally cycled from 1100◦ C to 25◦ C without a through-thickness
temperature gradient.
29
TSub (°C)
h/HTBC
1300
0.0
1200
1100
900 G/Go
5.
1000
0.2
4.
0.4
3.
0.6
2.
0.5
2
0.8
1
1.
3
4
1.0
0
100
200
300
400
0
ΔTTBC (°C)
Figure 10: The driving force for delamination is plotted for a range of CMAS penetration depth, h and temperature
drop across the TBC, ∆TT BC . When ∆TT BC = 0, the entire TBC is 1300◦ C and when h/HT BC = 1, the TBC is
fully infiltrated by the silicate. The energy release rate, G, is calculated for delamination at the bond coat/TGO
interface and is normalized by the energy release rate for the delamination, Go of an un-infilitrated, isothermal coating
following cooling from 1100◦ C.
30

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