A numerical procedure for simulating the distortions exhibited by a thermally grown oxide (TGO) upon temperature cycling has been adapted to incorporate the microstructure of the bond coat. The focus is on the dual phase β/γ′ microstructure that develops upon oxidation of a system with a Pt-aluminide bond coat. The results reveal that the presence of the γ′-phase next to the TGO reduces its distortion locally, because of the superior high-temperature strength of γ′, relative to β. Conversely, in regions where the β-phase exists adjacent to the TGO, it distorts and the TGO propagates downward, while simultaneously lengthening. These results from the simulations are in direct correspondence with experimental observations

Darzens, S.

Karlsson, Anette M

English

EngagedScholarship @ Cleveland State University

Cleveland State University
EngagedScholarship@CSU
Mechanical Engineering Faculty Publications Mechanical Engineering Department
1-30-2004
On the Microstructural Development in Platinum-
Modified Nickel-Aluminide Bond Coats
S. Darzens
University of Delaware
Anette M. Karlsson
Cleveland State University, a.karlsson@csuohio.edu
Follow this and additional works at: https://engagedscholarship.csuohio.edu/enme_facpub
Part of the Mechanical Engineering Commons
How does access to this work benefit you? Let us know!
Publisher's Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Surface and
Coatings Technology. Changes resulting from the publishing process, such as peer review, editing,
corrections, structural formatting, and other quality control mechanisms may not be reflected in this
document. Changes may have been made to this work since it was submitted for publication. A
definitive version was subsequently published in Surface and Coatings Technology, 177, ,
(01-30-2004); 10.1016/j.surfcoat.2003.09.001
This Article is brought to you for free and open access by the Mechanical Engineering Department at EngagedScholarship@CSU. It has been accepted
for inclusion in Mechanical Engineering Faculty Publications by an authorized administrator of EngagedScholarship@CSU. For more information,
please contact library.es@csuohio.edu.
Original Citation
Darzens, S., and Karlsson, A. M., 2004, "On the Microstructural Development in Platinum-Modified Nickel-Aluminide Bond Coats,"
Surface and Coatings Technology, 177-178pp. 108-112.
On the microstructural development in platinum-modified nickel-
aluminide bond coats 
S. Darzens, A.M. Karlsson* 
Dl'partmem of Mech(lIIical Engineering, Universify of Delaware. Nelwlrk. DE 19716, USA 
I. Introduction 
Incorporating thermal barrier coatings (TBes) in gas 
turbines for propulsion and power generation potentially 
allows for increase in both gas temperalUres and gas 
turbine life, thus increasing fuel economy and reducing 
life cycle cost. However, this potential is compromised 
by premature fail ures of TSes that are frequent ly 
observed in commercial systems. The premature fa ilures 
are typically associated with spalling of the coating, but 
the details of the mechanisms are not completely under-
stood. These fa ilures can only be avoided by developing 
a fundamenta l understanding of the failure mechanisms 
to guide redesign of the coating systems. 
The lack of understanding of the fai lure mechan isms 
is due to the complex, multilayered structure of TBCs, 
consisting of a superalloy substrate, a bond coat, a 
thennally grown oxide (TOO) and a ceramic top coat. 
The superalloy sustains the mechanical load, while the 
top coat acts as the thennal insulator. The TOO is a 
reaction product, fonned by oxidation of the bond coal 
and consists of a-alumina . In order to protect the 
superalloy from ox idation, the bond coat provides the 
system with aluminum to fonn the TOO. Consumption 
of Al in fonning AI20 ) leads to depletion of Al in the 
·Com:sponding author. Tel.: + 1·302·831-6437; fax: + 1-302·831-
3619. 
E·mail address: karlsson@mc.udc1.cdu (A.M. Karlsson). 
bond coat, resulting in the evolution of the bond-coat 
microstructure. Thus, the thenno-mechanical properties 
of the bond coat change during use. As a consequence, 
the overall properties of the thennal barrier system also 
evolve during service. 
A large class of failures is associated with the growth 
of the TOO [1 - 6]. As this layer is fonned at high 
temperature, it is subjected to thicken ing as well as 
lengthening growth (7]. The lengthening component 
may be interpreted as new alumina fonn ing at the grain 
boundaries of the existing grains (Fig. 1) (4,7- 9] . 
A particularly interesting failure mode occurs when 
the lengthening component of the TOO growth results 
in out-of-plane displacements that change on a cycle-
by-cycle basis. This eventually leads to system fai lure. 
This phenomenon has recently received considerable 
attention [4,8- 12], for Pt-modified nickel-aluminide (Pt-
NiA I), and has also been observed for MCrA IYs (13,14]. 
The current understanding of the failure mode-based 
on experimental, numerical and analytical stud ies-
shows that there are several essential conditions that 
together cause the development of the morphological 
features [12]. These are (i) thennal mismatch between 
bond coat and TOO; (ij) thennal cycling; (i ii) initial 
imperfections in the bond-coat/TBC interface; (jv) 
lengthening component of TOO growth; (v) yielding of 
the bond coat and (vi) high temperature creep of the 
TOO. In addition to these essential conditions, there are 
Fig. 1. Formation of new oxide during TGO growth. The lengthening 
of the oxide scale observed experimentally may be due to new oxide 
forming at the grains boundaries w4,7–9x. 
a range of conditions and properties that may accelerate 
or dampen the change in morphology. Of particular 
interest for this study will be one type of phase trans-
formation that occurs in the platinum–aluminide bond 
coat. 
Two types of phase transformations are observed in 
Pt-NiAl: martensitic phase transformation of the b-phase 
w15,16x, which is reversible during thermal cycling, and 
transformation from the initial b-phase to g9-phase, 
which is non-reversible. 
The response of the systemdue  to the martensitic 
transformation was investigated in Refs. w17,18x, and it 
was seen that it creates a complicated, non-linear system 
response. For example, the thermal mismatch between 
the bond coat and the substrate can be enhanced by the 
phase transformation, resulting in accelerated morpho-
logical changes. 
The transformation of b-phase to g9-phase near the 
TGOybond-coat interface is mainly due to the depletion 
of aluminum as the Al diffuses out to form the TGO at 
the bond-coat surface w20x, but also due to diffusion of 
Ni to the bond coat fromthe  superalloy. The thermo-
mechanical properties—such as thermal expansion and 
yield strength—are quite different for the two phases. 
Observations indicate that, when both phases are contig-
uous with the TGO, instability propagations occur pref-
erentially next to the b-phase (Fig. 2) w4,20x. 
In the following, we will present numerical simula-
tions that rationalize the observations relating to the 
presence of b-phase and g9-phase, while simultaneously 
provide insights about the role of bond-coat microstruc-
ture in TBC failure. 
The interplay between the TGO instability and crack 
growth in the TBC defines the scope of the present 
analysis. Namely, upward displacements of the TGO at 
the periphery of interface imperfections cause the TGO 
to ‘push-up’ the TBC, causing cracks in the TBC to 
extend and coalesce w4,5,8,10x. In this paper, the top 
coat is ignored in the simulations. The effect of the top 
coat is investigated in a separate study w21x. 
2. Simulation protocol 
The simulation protocol has been described in detail 
elsewhere w9x. The main features are as follows. 
The bond coat has a temperature-dependent yield 
strength that diminishes rapidly with increase in temper-
ature from ambient to approximately 800 8C and there-
after remains essentially invariant w19x. In this case, 
Fig. 2. Optical image of an etched cross-section of a furnace cycle 
test specimen at different fraction of life, showing the location of the 
byg9-phases relative to the TGO instability. (a) 8% of life; (b) 34% 
of life and (c) 76% of life w20x. 
Fig. 3. The axisymmetric model used for the present calculations 
showing the location of the byg9-phases. 
different values of the high-temperature strengths are 
assigned to the b- and g9-phases. In the following, the 
high-temperature yield strengths will simply be referred 
to as ‘yield strength’. 
At the temperature maximum, the TGO experiences 
thickening and lengthening strains. The lengthening 
strain dominates the TGO instability. Accordingly, to 
simplify the calculations, the thickness can be held 
constant (at its average) and the lengthening strain 
imposed during each thermal cycle. In this case, the 
lengthening strain is taken to be representative of that 
for a furnace cycle test, ´ gs10y3. 
At the highest temperature in the cycle, the TGO has 
a maximum sustainable stress, governed by creepy 
yielding. This stress is equated to the experimentally 
determined TGO growth stress. Once this stress is 
reached in the TGO, in-elastic deformation prohibits 
further elongation, causing the growth strain to be 
redistributed as thickening. At temperatures below the 
maximum, the TGO is elastic. 
The bond coat is considered to have a different 
thermal expansion coefficient than the substrate. In 
addition, different values are assigned to the b- and g9-
phases. 
Initial geometric imperfections are introduced at the 
bond-coatyTBC interface, with shape and size typical 
of that associated with the interface roughness created 
by grit blasting of the bond coat, prior to TBC deposi-
tion. The shape assumed is shown in Fig. 3. These 
dimensions and shapes are based on observations made 
on this specific thermal barrier system (Fig. 2). The 
shape sensitivity was studied in Ref. w11x, and that the 
total amplitude change invariant with respect to initial 
shape. The amplitude growth is monitored in the numer-
ical investigations, corresponding to the growth of the 
imperfection. 
The calculations follow the bond-coatyTGO defor-
mation upon thermal cycling while the TGO is subject 
to an elongation strain per cycle. In the following 
simulations, the superalloy is elastic. 
3. Simulation results 
3.1. Preliminary results 
First of all, a simplified model without the substrate 
and the TBC layer has been used (Fig. 4a). The 
curvature of the TGO layer is identical for the above 
two phases, b and g9. The b-phase has significantly 
lower yield stress than the g9-phase. For modeling 
purposes we selected to use high-temperature yield 
strengths of 20 and 120 MPa, respectively. 
After 12 cycles, the displacement of the TGO layer 
in the normal direction is an order of magnitude higher 
in the b-phase than in the g9-phase (Fig. 4b). (The 
tangential displacement is negligible.) This is mainly 
due to the higher yield stress of the g9-phase but also to 
a lower extent to its smaller thermal expansion mismatch 
with the TGO layer. 
Fig. 4. The simplified axisymmetric model used for the preliminary 
simulations. (a) The location of the b- and g9-phases of the bond coat 
is symmetric. (b) The deformation of the TGO after 12 cycles: larger 
deformation downward in the b-phase. (sY(b)s20 MPa, a(b)s18 
ppmy8C, sY(g9)s120 MPa, a(g9)s14 ppmy8C.) 
Table 1 
Material properties used in the model 
E (GPa) n a 
TGO 400 0.2 8.6 
Bond coat 200 0.3 14 
Substrate 200 0.3 16 
The displacement of the TGO layer mainly occurs at 
high temperature. The system endures an increase of 
stress fromtwo  sources: (i) the mismatch of thermal 
expansion coefficient between the TGO and the bond 
coat, (ii) and the lateral growth of the TGO. Under 
these test conditions, the yield stress of the b-phase is 
reached rapidly, implying the plastic deformation of the 
b-phase. Simultaneously, the lateral growth of the TGO 
takes place, and is readily accommodated by the yielding 
of the b-phase. On the contrary, the yield stress of the 
TGO above the g9-phase is reached before the yield 
stress of the g9-phase, inducing a large plastic deforma-
tion of the TGO above the g9-phase. Consequently, the 
lateral growth of the TGO is limited above the g9-phase. 
Only a slight deformation of the g9-phase occurs, where-
as the larger deformation is localized in the middle of 
the b-phase. 
These preliminary results are consistent with the 
experimental observations, which show that the propa-
gation of the instabilities occurs preferentially down-
wards, in the b-phase. 
3.2. Layered model 
In the following, the layered model (Fig. 3) will be 
considered, taking into account the effect of the substrate 
but ignoring the TBC layer. (The effect of the TBC 
layer will be discussed in a later study w21x.) Based on 
experimental observation and on the preliminary report 
discussed above, the instability will be located above 
the b-phase. The geometry of this model represents the 
system after approximately 30% of its lifetime. At this 
lifetime, the g9-phase domains are large relative to the 
instabilities and cannot be neglected. We will compare 
to the case when the instability is located above the g9. 
In the following, the (high-temperatures) yield strengths 
b  g9  are assumed to be sYs20 MPa and sY s120 MPa, for 
the b- and g9-phases, respectively. The properties used 
are summarized in Table 1. 
Before proceeding, we note that the thermal expansion 
misfit of the bond coat, abc, to the substrate, asub , 
influences the development of the instability. It causes 
the bond coat to become fully plastic upon thermal 
cycling, rather than exhibiting the local plasticity around 
the imperfection found in the case of absent misfit 
w9,17x. In this case, we will assume that the misfit 
between the two bond-coat phases vanishes, abcsag9s 
y6abs14=10 y8C, while the misfit between bond coat 
and substrate is constant, abcyasub sy2=10y6y8C 
w23x. 
Benchmark results are obtained for the case of homo-
geneous bond coat (Fig. 5). Two cases of bond-coat 
yield strength are studied: (i) the bond coat consist of 
bc bpure b-phase: sY ssYs20 MPa and (ii) the bond coat 
bc g9consist of pure g9-phase: sY ssY s120 MPa. The case 
of lower yield strength results in larger amplitude chang-
es (Fig. 5), which is consistent with previous published 
results w9x. However, the deformation is not self-similar, 
i.e. the deformation obtained for the lower yield strength 
cannot be achieved by magnifying the deformation 
obtained fromthe  higher yield strength. This is primarily 
related to two factors: (i) for higher yield strength, the 
yielding tends to be limited to high stress areas around 
the imperfection, and (ii) for the lower yield strengths, 
larger regions are affected by the yielding and in 
addition, yielding occurs during oxidation. Thus, the 
simulations show that morphological instabilities are 
more likely to occur in the b-phase. This is consistent 
with experimental observations. 
The influence on the amplitude change of b- and g9-
phase locations is investigated in Fig. 6. When the b-
phase is located at the bottomof  the imperfection (Fig. 
6a) significantly larger downwards deflection are 
Fig. 5. The deformation of the TGO–bond-coat interface and the accu-
mulation of plastic strain after 24 cycles for various bond-coat yield 
bc bstrength for a homogeneous bond coat: (a) sY ssYs120 MPa and 
bc g9 y6(b) sY ssYs20 MPa. (abc  sag9sabs14=10 y8C, abcyasub s 
y2=10y6y8C.) 
4. Conclusion 
Fig. 6. The deformation of the TGO–bond-coat interface and the accu-
mulation of plastic strain after 24 cycles for microstructures: (a) b-
phase at the bottomof  the undulation and (b) g9-phase at the bottom 
of the undulation. (sb Ys20 MPa, sg9  Ys120 MPa. abc  sag9sabs 
y6	 y614=10 y8C, abcyasub sy2=10 y8C.) 
achieved compared to when g9 is located at the bottom 
(Fig. 6b). Fromthe  contours corresponding to accumu-
lation of plastic strain, it is seen that when b is located 
in the bottom, the plastic field extends downwards. If 
the g9 is located at the bottom, the high strength g9 acts 
almost as rigid body, pushing the softer b aside. Thus, 
in this case, significantly more plastic strain is accu-
mulated on the side of the imperfection resulting in 
upwards motion at the periphery of the imperfection.1 
In summary, by comparing the downwards deflection 
of a bond coat where the location of the b- and g9-
phases is varied, it is seen that the case of b-phase at 
the bottom of the undulation promotes morphological 
instabilities. 
1 The peripheral upwards motion will be prevented if the interface 
between top coat and TGO is intact and has been seen to interact 
with the growth and coalescence of cracks w22x. The interaction with 
the top coat is explored in Ref. w21x. 
The present article has shown that a previously 
developed simulation procedure can be used to incor-
porate microstructure in the bond coat and that the 
effects duplicate experimental observations. In particu-
lar, the presence of the g9-phase next to the TGO reduces 
its distortion, attributed to its superior high-temperature 
strength. In regions where the b-phase exists adjacent 
to the TGO, it distorts and the TGO propagates down-
ward, as it lengthens, in direct correspondence with 
experimental observations. Moreover, upward displace-
ments can also take place depending on the thermo-
mechanical properties of the different phases. These 
displacements may play a role in the propagation of the 
cracks, and therefore the lifetime of the system. 
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On the Microstructural Development in Platinum-Modified Nickel-Aluminide Bond Coats

Cleveland-Marshall College of Law

Cleveland State UniversityEngagedScholarship@CSUMechanical Engineering Faculty Publications Mechanical Engineering Department1-30-2004On the Microstructural Development in Platinum-Modified Nickel-Aluminide Bond CoatsS. DarzensUniversity of DelawareAnette M. KarlssonCleveland State University, a.karlsson@csuohio.eduFollow this and additional works at: https://engagedscholarship.csuohio.edu/enme_facpubPart of the Mechanical Engineering CommonsHow does access to this work benefit you? Let us know!Publisher's StatementNOTICE: this is the author’s version of a work that was accepted for publication in Surface andCoatings Technology. Changes resulting from the publishing process, such as peer review, editing,corrections, structural formatting, and other quality control mechanisms may not be reflected in thisdocument. Changes may have been made to this work since it was submitted for publication. Adefinitive version was subsequently published in Surface and Coatings Technology, 177, ,(01-30-2004); 10.1016/j.surfcoat.2003.09.001This Article is brought to you for free and open access by the Mechanical Engineering Department at EngagedScholarship@CSU. It has been acceptedfor inclusion in Mechanical Engineering Faculty Publications by an authorized administrator of EngagedScholarship@CSU. For more information,please contact library.es@csuohio.edu.Original CitationDarzens, S., and Karlsson, A. M., 2004, "On the Microstructural Development in Platinum-Modified Nickel-Aluminide Bond Coats,"Surface and Coatings Technology, 177-178pp. 108-112.On the microstructural development in platinum-modified nickel-aluminide bond coats S. Darzens, A.M. Karlsson* Dl'partmem of Mech(lIIical Engineering, Universify of Delaware. Nelwlrk. DE 19716, USA I. Introduction Incorporating thermal barrier coatings (TBes) in gas turbines for propulsion and power generation potentially allows for increase in both gas temperalUres and gas turbine life, thus increasing fuel economy and reducing life cycle cost. However, this potential is compromised by premature fail ures of TSes that are frequent ly observed in commercial systems. The premature fa ilures are typically associated with spalling of the coating, but the details of the mechanisms are not completely under-stood. These fa ilures can only be avoided by developing a fundamenta l understanding of the failure mechanisms to guide redesign of the coating systems. The lack of understanding of the fai lure mechan isms is due to the complex, multilayered structure of TBCs, consisting of a superalloy substrate, a bond coat, a thennally grown oxide (TOO) and a ceramic top coat. The superalloy sustains the mechanical load, while the top coat acts as the thennal insulator. The TOO is a reaction product, fonned by oxidation of the bond coal and consists of a-alumina . In order to protect the superalloy from ox idation, the bond coat provides the system with aluminum to fonn the TOO. Consumption of Al in fonning AI20 ) leads to depletion of Al in the ·Com:sponding author. Tel.: + 1·302·831-6437; fax: + 1-302·831-3619. E·mail address: karlsson@mc.udc1.cdu (A.M. Karlsson). bond coat, resulting in the evolution of the bond-coat microstructure. Thus, the thenno-mechanical properties of the bond coat change during use. As a consequence, the overall properties of the thennal barrier system also evolve during service. A large class of failures is associated with the growth of the TOO [1 - 6]. As this layer is fonned at high temperature, it is subjected to thicken ing as well as lengthening growth (7]. The lengthening component may be interpreted as new alumina fonn ing at the grain boundaries of the existing grains (Fig. 1) (4,7- 9] . A particularly interesting failure mode occurs when the lengthening component of the TOO growth results in out-of-plane displacements that change on a cycle-by-cycle basis. This eventually leads to system fai lure. This phenomenon has recently received considerable attention [4,8- 12], for Pt-modified nickel-aluminide (Pt-NiA I), and has also been observed for MCrA IYs (13,14]. The current understanding of the failure mode-based on experimental, numerical and analytical stud ies-shows that there are several essential conditions that together cause the development of the morphological features [12]. These are (i) thennal mismatch between bond coat and TOO; (ij) thennal cycling; (i ii) initial imperfections in the bond-coat/TBC interface; (jv) lengthening component of TOO growth; (v) yielding of the bond coat and (vi) high temperature creep of the TOO. In addition to these essential conditions, there are Fig. 1. Formation of new oxide during TGO growth. The lengthening of the oxide scale observed experimentally may be due to new oxide forming at the grains boundaries w4,7–9x. a range of conditions and properties that may accelerate or dampen the change in morphology. Of particular interest for this study will be one type of phase trans-formation that occurs in the platinum–aluminide bond coat. Two types of phase transformations are observed in Pt-NiAl: martensitic phase transformation of the b-phase w15,16x, which is reversible during thermal cycling, and transformation from the initial b-phase to g9-phase, which is non-reversible. The response of the systemdue  to the martensitic transformation was investigated in Refs. w17,18x, and it was seen that it creates a complicated, non-linear system response. For example, the thermal mismatch between the bond coat and the substrate can be enhanced by the phase transformation, resulting in accelerated morpho-logical changes. The transformation of b-phase to g9-phase near the TGOybond-coat interface is mainly due to the depletion of aluminum as the Al diffuses out to form the TGO at the bond-coat surface w20x, but also due to diffusion of Ni to the bond coat fromthe  superalloy. The thermo-mechanical properties—such as thermal expansion and yield strength—are quite different for the two phases. Observations indicate that, when both phases are contig-uous with the TGO, instability propagations occur pref-erentially next to the b-phase (Fig. 2) w4,20x. In the following, we will present numerical simula-tions that rationalize the observations relating to the presence of b-phase and g9-phase, while simultaneously provide insights about the role of bond-coat microstruc-ture in TBC failure. The interplay between the TGO instability and crack growth in the TBC defines the scope of the present analysis. Namely, upward displacements of the TGO at the periphery of interface imperfections cause the TGO to ‘push-up’ the TBC, causing cracks in the TBC to extend and coalesce w4,5,8,10x. In this paper, the top coat is ignored in the simulations. The effect of the top coat is investigated in a separate study w21x. 2. Simulation protocol The simulation protocol has been described in detail elsewhere w9x. The main features are as follows. The bond coat has a temperature-dependent yield strength that diminishes rapidly with increase in temper-ature from ambient to approximately 800 8C and there-after remains essentially invariant w19x. In this case, Fig. 2. Optical image of an etched cross-section of a furnace cycle test specimen at different fraction of life, showing the location of the byg9-phases relative to the TGO instability. (a) 8% of life; (b) 34% of life and (c) 76% of life w20x. Fig. 3. The axisymmetric model used for the present calculations showing the location of the byg9-phases. different values of the high-temperature strengths are assigned to the b- and g9-phases. In the following, the high-temperature yield strengths will simply be referred to as ‘yield strength’. At the temperature maximum, the TGO experiences thickening and lengthening strains. The lengthening strain dominates the TGO instability. Accordingly, to simplify the calculations, the thickness can be held constant (at its average) and the lengthening strain imposed during each thermal cycle. In this case, the lengthening strain is taken to be representative of that for a furnace cycle test, ´ gs10y3. At the highest temperature in the cycle, the TGO has a maximum sustainable stress, governed by creepy yielding. This stress is equated to the experimentally determined TGO growth stress. Once this stress is reached in the TGO, in-elastic deformation prohibits further elongation, causing the growth strain to be redistributed as thickening. At temperatures below the maximum, the TGO is elastic. The bond coat is considered to have a different thermal expansion coefficient than the substrate. In addition, different values are assigned to the b- and g9-phases. Initial geometric imperfections are introduced at the bond-coatyTBC interface, with shape and size typical of that associated with the interface roughness created by grit blasting of the bond coat, prior to TBC deposi-tion. The shape assumed is shown in Fig. 3. These dimensions and shapes are based on observations made on this specific thermal barrier system (Fig. 2). The shape sensitivity was studied in Ref. w11x, and that the total amplitude change invariant with respect to initial shape. The amplitude growth is monitored in the numer-ical investigations, corresponding to the growth of the imperfection. The calculations follow the bond-coatyTGO defor-mation upon thermal cycling while the TGO is subject to an elongation strain per cycle. In the following simulations, the superalloy is elastic. 3. Simulation results 3.1. Preliminary results First of all, a simplified model without the substrate and the TBC layer has been used (Fig. 4a). The curvature of the TGO layer is identical for the above two phases, b and g9. The b-phase has significantly lower yield stress than the g9-phase. For modeling purposes we selected to use high-temperature yield strengths of 20 and 120 MPa, respectively. After 12 cycles, the displacement of the TGO layer in the normal direction is an order of magnitude higher in the b-phase than in the g9-phase (Fig. 4b). (The tangential displacement is negligible.) This is mainly due to the higher yield stress of the g9-phase but also to a lower extent to its smaller thermal expansion mismatch with the TGO layer. Fig. 4. The simplified axisymmetric model used for the preliminary simulations. (a) The location of the b- and g9-phases of the bond coat is symmetric. (b) The deformation of the TGO after 12 cycles: larger deformation downward in the b-phase. (sY(b)s20 MPa, a(b)s18 ppmy8C, sY(g9)s120 MPa, a(g9)s14 ppmy8C.) Table 1 Material properties used in the model E (GPa) n a TGO 400 0.2 8.6 Bond coat 200 0.3 14 Substrate 200 0.3 16 The displacement of the TGO layer mainly occurs at high temperature. The system endures an increase of stress fromtwo  sources: (i) the mismatch of thermal expansion coefficient between the TGO and the bond coat, (ii) and the lateral growth of the TGO. Under these test conditions, the yield stress of the b-phase is reached rapidly, implying the plastic deformation of the b-phase. Simultaneously, the lateral growth of the TGO takes place, and is readily accommodated by the yielding of the b-phase. On the contrary, the yield stress of the TGO above the g9-phase is reached before the yield stress of the g9-phase, inducing a large plastic deforma-tion of the TGO above the g9-phase. Consequently, the lateral growth of the TGO is limited above the g9-phase. Only a slight deformation of the g9-phase occurs, where-as the larger deformation is localized in the middle of the b-phase. These preliminary results are consistent with the experimental observations, which show that the propa-gation of the instabilities occurs preferentially down-wards, in the b-phase. 3.2. Layered model In the following, the layered model (Fig. 3) will be considered, taking into account the effect of the substrate but ignoring the TBC layer. (The effect of the TBC layer will be discussed in a later study w21x.) Based on experimental observation and on the preliminary report discussed above, the instability will be located above the b-phase. The geometry of this model represents the system after approximately 30% of its lifetime. At this lifetime, the g9-phase domains are large relative to the instabilities and cannot be neglected. We will compare to the case when the instability is located above the g9. In the following, the (high-temperatures) yield strengths b  g9  are assumed to be sYs20 MPa and sY s120 MPa, for the b- and g9-phases, respectively. The properties used are summarized in Table 1. Before proceeding, we note that the thermal expansion misfit of the bond coat, abc, to the substrate, asub , influences the development of the instability. It causes the bond coat to become fully plastic upon thermal cycling, rather than exhibiting the local plasticity around the imperfection found in the case of absent misfit w9,17x. In this case, we will assume that the misfit between the two bond-coat phases vanishes, abcsag9s y6abs14=10 y8C, while the misfit between bond coat and substrate is constant, abcyasub sy2=10y6y8C w23x. Benchmark results are obtained for the case of homo-geneous bond coat (Fig. 5). Two cases of bond-coat yield strength are studied: (i) the bond coat consist of bc bpure b-phase: sY ssYs20 MPa and (ii) the bond coat bc g9consist of pure g9-phase: sY ssY s120 MPa. The case of lower yield strength results in larger amplitude chang-es (Fig. 5), which is consistent with previous published results w9x. However, the deformation is not self-similar, i.e. the deformation obtained for the lower yield strength cannot be achieved by magnifying the deformation obtained fromthe  higher yield strength. This is primarily related to two factors: (i) for higher yield strength, the yielding tends to be limited to high stress areas around the imperfection, and (ii) for the lower yield strengths, larger regions are affected by the yielding and in addition, yielding occurs during oxidation. Thus, the simulations show that morphological instabilities are more likely to occur in the b-phase. This is consistent with experimental observations. The influence on the amplitude change of b- and g9-phase locations is investigated in Fig. 6. When the b-phase is located at the bottomof  the imperfection (Fig. 6a) significantly larger downwards deflection are Fig. 5. The deformation of the TGO–bond-coat interface and the accu-mulation of plastic strain after 24 cycles for various bond-coat yield bc bstrength for a homogeneous bond coat: (a) sY ssYs120 MPa and bc g9 y6(b) sY ssYs20 MPa. (abc  sag9sabs14=10 y8C, abcyasub s y2=10y6y8C.) 4. Conclusion Fig. 6. The deformation of the TGO–bond-coat interface and the accu-mulation of plastic strain after 24 cycles for microstructures: (a) b-phase at the bottomof  the undulation and (b) g9-phase at the bottom of the undulation. (sb Ys20 MPa, sg9  Ys120 MPa. abc  sag9sabs y6	 y614=10 y8C, abcyasub sy2=10 y8C.) achieved compared to when g9 is located at the bottom (Fig. 6b). Fromthe  contours corresponding to accumu-lation of plastic strain, it is seen that when b is located in the bottom, the plastic field extends downwards. If the g9 is located at the bottom, the high strength g9 acts almost as rigid body, pushing the softer b aside. Thus, in this case, significantly more plastic strain is accu-mulated on the side of the imperfection resulting in upwards motion at the periphery of the imperfection.1 In summary, by comparing the downwards deflection of a bond coat where the location of the b- and g9-phases is varied, it is seen that the case of b-phase at the bottom of the undulation promotes morphological instabilities. 1 The peripheral upwards motion will be prevented if the interface between top coat and TGO is intact and has been seen to interact with the growth and coalescence of cracks w22x. The interaction with the top coat is explored in Ref. w21x. The present article has shown that a previously developed simulation procedure can be used to incor-porate microstructure in the bond coat and that the effects duplicate experimental observations. In particu-lar, the presence of the g9-phase next to the TGO reduces its distortion, attributed to its superior high-temperature strength. In regions where the b-phase exists adjacent to the TGO, it distorts and the TGO propagates down-ward, as it lengthens, in direct correspondence with experimental observations. Moreover, upward displace-ments can also take place depending on the thermo-mechanical properties of the different phases. These displacements may play a role in the propagation of the cracks, and therefore the lifetime of the system. References w1x M. Gell, K. Vaidyanathan, B. Barber, J. Cheng, E. Jordan, Metall. Mater. Trans. A 30 (1999) 427–435. w2x P.K. Wright, A.G. Evans, Curr. Opin. Solid State Mater. Sci. 4 (1999) 255–265. w3x D.R. Mumm, A.G. Evans, Acta Mater. 48 (2000) 1815–1827. w4x D.R. Mumm, A.G. Evans, I. Spitsberg, Acta Mater. 49 (2001) 2329–2340. w5x A.G. Evans, D.R. Mumm, Prog. Mater. Sci. 46 (2001) 505–553. w6x V.K. Tolpygo, D.R. Clarke, Acta Mater. 48 (2000) 3283–3293. w7x V.K. Tolpygo, J.R. Dryden, D.R. Clarke, Acta Mater. 46 (1998) 927. w8x M.Y. He, A.G. Evans, J.W. Hutchinson, Acta Mater. 48 (2000) 2593–2601. w9x A.M. Karlsson, A.G. Evans, Acta Mater. 49 (2001) 1793–1804. w10x A.M. Karlsson, J.W. Hutchinson, A.G. Evans, J. Mech. Phys. Solids 50 (2002) 1565–1589. w11x A.M. Karlsson, C.G. Levi, A.G. Evans, Acta Mater. 50 (2002) 1263–1273. w12x A.M. Karlsson, J.W. Hutchinson, A.G. Evans, Mater. Sci. Eng. A 351 (2003) 244–257. w13x	 M. Bartsch, B. Baufeld, E.R. Fuller, Proceedings of the 27th Annual Conference on Composites, Advance Ceramics and Materials, January (2003), in press. w14x R.C. Pennefather, D.H. Boone, Surf. Coat. Technol. 1–3 (1995) 45–57. w15x M.W. Chen, R.T. Ott, T.C. Hufnagel, P.K. Wright, K.J. Hemker, Surf. Coat. Technol. 163–164 (2003) 25–30. w16x Y. Zhang, J.A. Haynes, B.A. Pint, I.G. Wright, W.Y. Lee, Surf. Coat. Technol. 163–164 (2003) 19–24. w17x A.M. Karlsson, J. Eng. Mater. Technol., in press. w18x A.M. Karlsson, Proceedings of the 27th Annual Conference on Composites, Advance Ceramics and Materials, January, 2003. w19x D. Pan, M.W. Chen, P.K. Wright, K.J. Hemker, Acta Mater. 51 (2003) 2205–2217. w20x S. Darzens, D.R. Mumm, D.R. Clarke, A.G. Evans, Metall. Mater. Trans. A 34 (2003) 511–522. w21x S. Darzens, A.M. Karlsson, A.G. Evans, in preparation. w22x T. Xu, M.Y. He, A.G. Evans, Acta Mater. 51 (2003) 2807–3820. w23x J.A. Haynes, B.A Pint, W.D. Porter, I.G. Wright, Materials at High Temperature, January, submitted for publication. 

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On the Microstructural Development in Platinum-Modified Nickel-Aluminide Bond Coats

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