Thermal barrier coating life models developed under the NASA Lewis Research Center's Hot Section Technology (HOST) Program are summarized. An initial laboratory model and three design-capable models are discussed. Current understanding of coating failure mechanisms are also summarized. The materials and structural aspects of thermal barrier coatings have been successfully integrated under the HOST program to produce models which may now or in the near future be used in design. Efforts on this program continue at Pratt and Whitney Aircraft where their model is being extended to the life prediction of physical vapor deposited thermal barrier coatings

Miller, R. A.

English

Thermal barrier coating life models developed under the NASA Lewis Research Center's Hot Section Technology (HOST) program are summarized. An initial laboratory model and three design-capable models are discussed. Current understanding of coating failure mechanisms are also summarized

Miller, Robert A.

NASA Technical Reports Server

Breton 

Life modeling of thermal barrier coatings for aircraft gas turbine engines

N09 20 1 4 3  
LIFE MODELING OF THERMAL BARRIER COATINGS FOR AIRCRAFT 
GAS TURBINE ENGINES 
R. A. Miller 
National Aeronautics and Space Administration 
Lewis Rerearch Center 
Cleveland, Ohio 
ABSTRACT 
Thermal barrier coating life models developed 
under the NASA Lewis Research Center's Hot Section 
Technology (HOST) program are summarized. An initial 
laboratory model and three design-capable models are 
discussed. Current understanding of coating failure 
mechanisms are also summarized. 
INTRODUCTION 
Thermal barrier coatings are being developed for 
protecting air-cooled turbine blades and vanes in air- 
craft gas turbine engines. 
coating system consists of about 0.25 mm of a zirconia- 
yttria ceramic over 0.13 mm of an MCrAlY alloy bond 
coat. Both layers are applied by plasma spraying. The 
benefits arise from the insulation provided by the 
ceramic layer. This insulation allows higher gas tem- 
peratures, lower component temperatures, reduced cool- 
ing air requirements, moderation o f  thermal transients, 
and/or a decrease in the severity of hot spots. 
yields improvements in performance, efficiency, and com- 
ponent durability. Future engine designs are expected 
t o  rely heavily on thermal barrier coatings. Thus life 
models are required to assess the risks associated with 
any given design and t o  insure that these coatings can 
be exploited fully. 
Miller (1987), DeMasi et al., (1988). Strangman et al., 
(1987). and Hillery (1987). 
The NASA thermal barrier coating life model devel- 
opment program consisted initially of an in-house pro- 
gram designed t o  improve understanding and t o  develop a 
model suitable for treating laboratory life data 
(Miller, 1987). This work was then extended via three 
contracts under the HOST program t o  the development of 
design-capable models (DeMasi et al., 1988; Strangman 
et al., 1987; Hillery et al., 1987). These contracts 
were devi sed determine thermomechanical properties, t o  
analyze coating stresses and strains, and t o  develop 
life models. Phase I of each contract has now been suc- 
cessfully completed, and the results will be summarized 
in this paper. 
The current state-of-the-art 
This 
Further details may be found in 
COATING FAILURE MECHANISMS 
A basic understanding of coating failure mechanisms 
i s  a prerequisite t o  the development of life prediction 
models. Failure mechanisms in gas turbine engines and 
in laboratory simulations have been discussed in detail 
elsewhere (e.g., Miller, 1987; DeMasi et al., 1988; 
Strangman et al., 1987, Hillery et al., 1987). There 
is now general agreement that these coatings fail pri- 
marily as a result of stresses induced by the thermal 
expansion mismatch between the ceramic and metallic 
layers, and that these stresses are greatly influenced 
by time-at-temperature processes such as oxidation and 
possibly sintering. The stress state in the ceramic 
layer which leads t o  crack propagation and eventual 
spalling is one of biaxial compression in the plane of 
the coating and radial tension. These stresses are fur- 
ther complicated by the wavy and irregular interface 
between the ceramic and metallic layers. In fact, 
HOST-sponsored calculations indicate that the radial 
stresses above a wavy interface may actually alternate 
between regions of compression and tension as illus- 
trated i n  Fig. 1 (Chang et al.. 1987). Figure 2 
illustrates that the behavior of plasma sprayed 
zirconia-based thermal barrier coatings differs signi f 1- 
cantly from the behavior of conventional ceramics. This 
behavior. which is believed t o  result from the splat 
structure, includes very low thermal conductivity and 
very high compressive strain tolerance. In-plane ten- 
sile strain tolerance of the coating system is also very 
high because such loading may lead to segmentation 
cracking in the ceramic with no degradation to the 
attachment strength. Plasma sprayed zirconia-yttria 
also exhibits creep-like behavior, presumably as a 
result of sliding at the splat boundaries, and fatigue- 
like behavior, presumably as a result of slow crack 
growth. Experimental evidence of slow crack growth (or 
microcrack link up), creep, and fatigue are presented 
in DeMasi et al., (1988). 
INITIAL LABORATORY MODEL DEVELOPMENT 
A preliminary life prediction model has been 
described (Miller, 1987; Miller, 1984; Miller et al., 
1984). This model assumed that the complex state of 
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s t r e s s  and s t r a i n  imposed on the  c o a t i n g  system by the  
thermal loads cou ld  be expressed i n  terms o f  a s i n g l e  
parameter.  Th is  parameter was l a b e l l e d  Cy -- which was 
taken t o  be t h e  r a d i a l  component o f  t he  thermal expan- 
s i o n  mismatch s t r a i n .  Next i t  was assumed t h a t  the  
t ime-a t - tempera ture  e f f e c t s  cou ld  be t r e a t e d  i n  terms 
o f  o x i d a t i o n  a lone and t h a t  o x i d a t i o n  cou ld  be charac- 
t e r i z e d  by the  we igh t  g a i n  a t  the conc lus ion  o f  eacn 
c y c l e  W N .  Then. we igh t  g a i n  and s t r a i n  were r e i l t e d  
u s i n g  e i t h e r  o f  two a l t e r n a t e  approaches. I n  t h e  f i r s t  
case, dep ic ted  i n  F i g .  3 (a ) .  an o x i d i z e d  c o a t i n g  i s  
assumed t o  behave as i f  an e f f e c t i v e  s t r a i n  Ee i s  
i nc reas ing .  A t  z e r o  we igh t  g a i n  t h i s  e f f e c t i v e  s t r a i n  
equals the  r a d i a l  s t r a i n  c y .  A t  a c r i t i c a l  we igh t  g a i n  
wc -- d e f i n e d  as the  we igh t  g a i n  r e q u i r e d  t o  f a i l  t he  
c o a t i n g  i n  a s i n g l e  c y c l e  -- the  e f f e c t i v e  s t r a i n  equa ls  
a f a i l u r e  s t r a i n  c f .  Th is  leads t o  the  exp ress ion  
h e r e  NfN i s  t he  apoarent  lumber of cyc les  rema in ing  
a f t e r  c y c l e  U and we igh t  g a i n  8 ~ .  
F igu re  4 i l l u s t r a t e s  :he f i t s  ob ta ined  u s i n g  
i x p r e s s i o n  4 and a p p l y i n g  ' t  t o  l i f e  aa ta  c o l l e c t e d  a t  
i i 0 0  " C  f o r  t h ree  d i f f e r e n t  c y c l e  !er lqths.  Tt should 
5e Tent lone0 t h a t  the  s e t  af Parameters g i ven  i n  the  
f i g u r e  a r e  7o t  un ique.  Yumerous o t n e r  s e r s  p r o v i d e  
e q u a i l y  gocd f i t s .  For evamole r a i s i n g  rhe assumed 
' ~ a l u e  c,f -7 m i l e  l ower ing  the  s t r a i n  r a t i o  aroduces 
an e q u a l l y  ;ood f i t .  A lso ,  the  l i f e  da ta  can be f i t  
e q u a l l y  w e i i  Js ing  express ions  4 o r  5.  
DESIGN-CAPASLE LIFE MODELING 
v ih i ie  the  above model rep resen ted  a f i r s t  s t e D  i t  
was n c t  i n  3 fo rm which would be o f  j s e  t o  an eng ine  
des igne r .  -he re fo re  r h r e e  c o n t r a c t s  were i n s t i t u t e d  
under :he HOST program which were aimed a t  t he  develop- 
ment o f  Gesign-capable moaels. 
P r a t t  & Whitney A i r c r a f t  (DeMasi e t  a l . ,  1988) ,  
a long  w i t h  subcon t rac to r  Southwest Research I n s t i t u t e .  
developed a fa t igue-based c o a t i n g  l i f e  model which ilses 
where the  exponent m has been added t o  a l l o w  the  curve  
i n  F i g .  3(a) t o  be n o n l i n e a r .  The a l t e r n a t e  assumption 
( M i l l e r .  1987) i s  t o  assume t h a t  t he  f a i l u r e  s t r a i n  
degrades from an i n i t i a l  va lue  c f o  t o  a f i n a l  va lue  
equal  t o  E t .  Th is  case, i l l u s t r a t e d  i n  F i g .  3 (b)  leads 
t o  the  exp ress ion  
M i n e r ' s  Law ( e  
r e w r i t t e n  as 
p;ession 7 )  a long -w i  t h  exp ress ion  6 
(8 )  
wnere A C i  i s  
AC 
the  i n e l a s t i c  s t r a i n  range d e f i n e d  by 
( 2 )  2 0  
= A ( a  A T )  + Ach + A c t  - E ( 9 )  
Cracks i n  the  ceramic l a y e r  may be assumed t o  grow 
acco rd ing  t o  a c rack  growth law o f  t he  fo rm 
The t e r m  A(a AT)  i n  t h e  above exp ress ion  i s  t h e  t h e r -  
mal expansion mismatch s t r a i n  (wh ich  was expressed i n  
t e r m s  o f  Cy i n  the  p rev ious  s e c t i o n ) ,  Ach is t he  
s t r a i n  r e s u l t i n g  f rom t h e  h e a t i n g  t r a n s i e n t ,  hC i s  
ti:e i t r a i n  r e s u l t i n g  f rom the  c o o l i n g  t r a n s i e n t ,  and 
o,,,/E i s  t he  e l a s t i c  s t r a i n  a t  y i e l d i n g .  The assumed 
rC1 a t  i onsh i  p between o x i d a t i o n  and s t r a i n ,  analogous t o  
exp ress ion  2.  was 
I , .d 
dA -dN = Aeebac (3 )  
where da/dN i s  t he  inc rementa l  c rack  growth per  c y c l e ,  
A i s  a cons tan t ,  b and c a re  exponents r e l a t e d  to 
t h e  s u b c r i t i c a l  c rack  growth exponent.  and a i s  t he  
c rack  l e n g t h .  The model r e s u l t i n g  from express ion  1 i s  
N, 
(10) 
where o x i d a t i o n  has been expressed i n  terms o f  t he  
o x i d e  l a y e r  th i ckness  6 r a t h e r  than the  s p e c i f i c  
h e i g h t  g a i n  w .  The i n e l a s t i c  s t r a i n  range was ca lcu-  
l a t e d  u s i n g  f i n i t e  element techn iques  Nhich employed a 
t ime dependent i n e l a s t i c  model developed by Na lke r  
(1983) .  F igu re  5 shows an example o f  the  use of t h i s  
model t o  c a l c u l a t e  compressive and t e n s i l e  s t r a i n s  which 
may be compared d i t h  exper imenta l  da ta .  I n  F i g .  6 t h e  
ceramic s t r e s s - s t r a i n  behav io r  i s  c a l c u l a t e d  f o r  a s i n -  
g l e  c y c l e .  Th is  f i g u r e  d i s p l a y s  the  l a r g e  amount o f  
reve rsed  i n e l a s t i c  s t r a i n  produced by thermal c y c l i n g .  
F igu re  7 shows a p l o t  o f  observed versus c a l c u l a t e d  
l i v e s  f o r  a wide range o f  t e s t  c o n d i t i o n s .  As shown i n  
the  f i g u r e  the  model i s  accu ra te  t o  p l u s  o r  minus a f a c -  
t o r  o f  3, which i s  cons idered adequate.  
Company (Strangman e t  a l . ,  1987) may be expressed as 
The model developed by t h e  G a r r e t t  Turb ine  Engine 
and the  a l t e r n a t i v e  model r e s u l t i n g  f rom exp ress ion  2 i s  
N, 
These models may a l s o  be de r i ved  f rom the  f a m i l i a r  
f a t i g u e  exp ress ion  ( M i l l e r  e t  a l . .  1984; Manson, 1966). 
-b 
Nf = (:) (6)  
and M i n e r ' s  Law 
( 7 )  
110 
N = l  
Equat ion  1 1  i s  expressed s c h e m a t i c a l l y  i n  F i g .  8 which 
shows t h a t  t h e  mode1 cons ide rs  bond coa t  o x i d a t i o n ,  z i r -  
con ia  toughness r e d u c t i o n ,  and damage due t o  mo l ten  s a l t  
depos i t s .  The model i s  d r i v e n  by t h e  thermal a n a l y s i s  
of t he  component of  i n t e r e s t  f o r  i t s  a n t i c i p a t e d  m i s -  
Z ion. The l e f t  s i d e  o f  t h e  denominator i n  exp ress ion  1 1  
as de termined from t e s t  d a t a  c a l i b r a t i o n s  i s  
ltO"' + 0.181) MTBREF 
- I  [exp[-0.015(1 + 273) + C l l ) - '  + (exp[-0.041( +273) + C,]) 
(12)  
where MTBREF i s  a m u l t i t e m p e r a t u r e  bu rne r  r i g  e x p e r i -  
ence f a c t o r  which f o r c e s  p r e d i c t i o n s  and exper iment  i n t o  
agreement. The r i g h t  s i d e  o f  t h e  denominator i n  expres- 
s i o n  1 1  i s  c a l c u l a t e d  u s i n g  a Gar re t t -deve loped  model 
(Strangman, 1984; Strangman e t  a l . ,  1987). I n  p r a c t i c e ,  
the  model i s  d r i v e n  by thermal  a n a l y s i s  of t h e  component 
o f  i n t e r e s t .  An example o f  t he  a p p l i c a t i o n  o f  t h e  t h e r -  
mal b a r r i e r  c o a t i n g  l i f e  model t o  l a b o r a t o r y  t e s t  d a t a  
i s  shown i n  F i g .  9, and m i s s i o n  a n a l y s i s  p r e d i c t i o n s  a re  
shown i n  F i g .  10. 
The approach used by  t h e  General E l e c t r i c  Company 
( H i l l e r y  e t  a l . ,  1987) employed time-dependent, n o n l i n -  
ear  f i n i t e  element mode l ing  of t h e  s t resses  and s t r a i n s  
p resen t  i n  t h e  thermal  b a r r i e r  c o a t i n g  system, f o l l o w e d  
by t h e  c o r r e l a t i o n  o f  these s t resses  and s t r a i n s  w i t h  
t e s t  l i v e s .  The l i f e  model developed u s i n g  t h i s  
approach may be expressed as 
A E ~ ~  + 0 .4  AcR = 0.121 Nf -0.486 (13)  
where AERZ i s  t h e  shear s t r a i n  range, AER i s  t he  nor -  
mal s t r a i n  range, and Nf i s  t h e  number o f  c y c l e s  t o  
f a i l u r e .  The above model i s  t h e  o n l y  one t o  cons ide r  
f a i l u r e  induced by edges and hence i s  t h e  o n l y  one t o  
cons ide r  shear s t r a i n .  Express ion  13 i s  i l l u s t r a t e d  
g r a p h i c a l l y  i n  F i g .  1 1  
CONCLUDING REMARKS 
I n  conc lus ion ,  t h e  m a t e r i a l s  and s t r u c t u r a l  aspects 
o f  thermal  b a r r i e r  c o a t i n g s  have been s u c c e s s f u l l y  i n t e -  
g r a t e d  under t h e  NASA HOST program to  produce models 
which may now or i n  the  near  f u t u r e  be used i n  des ign .  
E f f o r t s  on t h i s  program con t inue  a t  P r a t t  & Whitney A i r -  
c r a f t  where t h e i r  model i s  be ing  extended t o  the  l i f e  
p r e d i c t i o n  o f  p h y s i c a l  vapor depos i ted  thermal b a r r i e r  
c o a t i n g s .  
Whi le t h e  HOST program has been q u i t e  successful  i t  
shou ld  a l s o  be no ted  t h a t  many new and unanswered ques- 
t i o n s  have been r a i s e d  by t h i s  work. For example, t he  
e f f e c t s  o f  c reep and i n e l a s t i c i t y  i n  bo th  t h e  ceramic 
and bond coa t  l a y e r s  a re  p o o r l y  understood. The role o f  
shear ing  s t resses ,  i n c l u d i n g  the  r o l e  t h a t  shear ing  a t  
an edge may p l a y  i n  r e d u c i n g  t h e  f a t i g u e  exponent,  i s  
n o t  w e l l  unders tood.  The d e t a i l e d  mechanism by which 
o x i d a t i o n  c o n t r o l s  c o a t i n g  system l i f e  i s  n o t  w e l l  
understood e i t h e r .  Also, i t  i s  n o t  known whether t h e  
assumption o f  a smooth i n t e r f a c e ,  commonly employed to 
s i m p l i f y  f i n i t e  element ana lyses  can lead  t o  i n a c c u r a t e  
o r  even m i s l e a d i n g  r e s u l t s .  Other  areas o f  u n c e r t a i n t y  
i n v o l v e  t h e  importance o f  s i n t e r i n g  a t  h i g h  temperatures 
and h o t  c o r r o s i o n  a t  r e l a t i v e l y  low tempera tures .  
REFERENCES 
Chang, G.C. ,  Phucharoen, W.,  and M i l l e r ,  R .A . ,  1987. 
Behav io r  o f  Thermal B a r r i e r  Coat ings  for  Advanced Gas 
Turb ine  B lades , "  Su r face  and Coat ings  Technology, 
DeMasi, J .T . ,  O r t i z ,  M., and S h e f f l e r ,  K.D..1988, "Ther-  
mal B a r r i e r  Coa t ing  L i f e  P r e d i c t i o n  Model Development", 
NASA C o n t r a c t o r  Report ,  t o  be p u b l i s h e d  ( P r a t t  & N h i t -  
ney A i r c r a f t )  
H i l l e r y ,  R.V. ,  P i l s n e r ,  B.H., McKnight,  R.L., Cook, T .  
S . ,  and H a r t l e .  M. S., 1987, "Thermal B a r r i e r  Coa t ing  
L i f e  P r e d i c t i o n  Model, F l n a l  Repor t , "  NASA CR-180807. 
Manson, S . S . ,  1966, "Thermal S t ress  and Low Cyc le  
Fa t igue , "  McGraM-Hill Book Company, New York, 1966. 
M i l l e r ,  R .A . ,  1984. "Oxidat ion-Based Thermal B a r r i e r  
Coa t ing  L i f e  P r e d i c t i o n  Model" Jou rna l  o f  t h e  American 
Ceramic Science, Vol. 67, No. 8. pp. 517-521. 
M i l l e r ,  R . A . ,  Agarwal,  P . ,  and Duders tad t ,  E .C. ,  1984, 
L i f e  Mode i ing  o f  Atmospher ic and Low Pressure  Plasma 
Sprayed Thermal B a r r i e r  Coat ing , "  Ceramic Eng ineer ing  
Science Procedings, Vol 5 .  No. 7-8, pp. 470-478. 
M i l l e r ,  R .A . ,  1987, "Cur ren t  S ta tus  o f  Thermal B a r r i e r  
Coat ings  - An Overview," Sur face  and Coat ings  Technolo- 
Strangman, T . E . ,  1984. " L i f e  P r e d i c t i o n  and Development 
of Coat ings  for  Turb ine  A i r f o i l s . "  Workshop on  Gas Tur- 
b i n e  M a t e r i a l s  i n  a Mar ine  Environment,  Bath,  U. K .  
Strangman. T . E . ,  Neumann, J . ,  and L i u ,  A . ,  1987, "Ther- 
mal B a r r i e r  Coa t ing  L i f e  P r e d i c t i o n  Model Development, 
F i n a l  Report ,"  NASA CR-179648. 
Walker, K ,P. ,  1983, "Research and Development Program 
f o r  Non-Linear S t r u c t u r a l  Mode l ing  w i t h  Advanced Time- 
Temperature Dependent C o n s t i t u i t i v e  R e l a t i o n s h i p s , "  
NASA CR-165533. 
V O l .  30, pp. 13-28. 
gy,  V O l .  30, NO. 1 ,  pp. 1 - 1 1 .  
111 
CERMIC 
/- 01 = 0 
BOND COAT 
FIGURE 1. - SCHEMATIC REPRESENTATIUN OF CALCULATED RADIAL 
THERML EXPANSION MISR4TCH STRESS ABOVE A WAVY INTER- 
FACE. 
CONDUCT I V I TY 
FATIGUE 
J 
2 1  
LOG N t 
FIGURE 2. - SCtERATIC REPRESENTATION OF T H E R M  ECHANICAL 
PROPERTIES RESULTING FROW COATING SPLAT STRUCTURE. 
112 
I 
(A) ASSWD RELATIONSHIP BETMEN EFFECTIVE STRAIN 
AND OXIDATIVE HEIGHT GAIN. 
0 WC 
SPECIFIC MIGHT GAIN, W 
(B) ASSWD ALTERNATE RELATIONSHIP BEMEN FAILURE 
STRAIN AND OXIDATIVE MIGHT GAIN. 
FIGURE 3. - ASSUWED HEIGHT GAIN/STRAIN RELATIONSHIPS. 
200 t 
b = 17.00 
m =  1.00 
EI/Ef = 0.38 
Wc = 2.4 MG/CH2 
OPEN SYMBOLS DENOTE EASURED 
CLOSED SYMBOLS DENOTE NODELED 
m 
m 
0 5 10 15 20 
FIGURE 4. - COPPARISON OF CALCULATED AND MODELED LIFE AS 
A FUNCTION OF HEATING CYCLE DURATION ACCORDING TO NASA 
LABORATORY MODEL. 
10 
HEATING CYCLE LENGTH. t. h r  
t 
‘I &LAST IC 
(NAS3-22055 1 
I 
-3.0 -2.5 -2.0 -1.5 -1.0 
FIGURE 5. - CERMIC BEHAVIOR MODELED WITH WALKER EQUATION 
ACCORDING TO THE PRATT 8 WHITNEY NOEL. 
.113 
STRESS 
STRAIN - 10 000 W 
FIGURE 6. - SCHERATIC OF STRAINS CALCULATED FOR A TYPICAL 
CYCLE ACCORDING TO THE PRATT 8 WHITMY HODEL. 
0 DESIGN DATA TESTS 
SUBSTANTIATION TESTS - BURMR RIG 
SUBSTANTIATION TESTS - WARTZ L M '  
HEATER 
4 -  / -= 
-SALT >< SOLIDIFICATION 
. \  '
I \ 
'\ 
r BOND \ 
'\ / COATING 
OX IDAT I ON 
SALT 
FILA DAluIGE 
ZIRCONIA 
TOUGHESS 
TEMRATURE 
FIGURE 8. - SCHEMTIC OF PROCESSES CONSIDERED I N  THE 
GARRETT MODEL. 
ll:i 100 
10 L 
1 
6000 700 800 900 1000 1100 1200 1300 
TEPF'ERATURE. OC 
FIGURE 9. - CONSERVATIVE F I T  OF LABORATORY LIFE DATA 
TO THE GARRETT HODEL. 
114 
m SYSTEM 
PLASM SPRAY 
CHRMALLOY 
UNION CARBIDE 
EB-PVD 
TEKSCAL 
Bus I WESS 
JET, 
HR 
16 517 
6 6% 
49 644 
55 607 
M I T I E  
SURVEILLANCE. 
5 207 
29 973 
2 106 
FIGURE 10. - HISSION ANAlYSIS PREDICTIONS 
BY THE GARRETT MODEL. 
Nf 
FIGURE 11. - CORRELATION B E W E N  CALCULATED STRAIN RELA- 
TIONSHIP AND EXPERIENTAL CYCLES TO FAILURE ACCORDING 
TO THE GENERAL ELECTRIC MODEL. 
115 


Life modeling of thermal barrier coatings for aircraft gas turbine engines

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