The basic objective of this investigation is the quantitative determination of stress states in a model thermal barrier coating (TBC) as it cools in the air to 600 C from an assumed stress-free state at 700 C. This model is intended to represent a thin plasma-sprayed zirconia-yttria ceramic layer with a nickel chromium-aluminum-yttrium bond coat on a cylindrical substrate made of nickel-based superalloys typically found in gas turbines

Chang, George C.

Miller, Robert A.

Phucharoen, Woraphat

English

NASA Technical Reports Server

N89 - 1 1 3 3 0  
THERMAL EXPANSION MISMATCH AND PLASTICITY I N  
THERMAL BARRIER COATING 
George C .  Chang and Woraphat Phucharoen 
C l e v e l a n d  S t a t e  U n i v e r s i t y  
C l e v e l a n d ,  O h i o  
and 
Rober t  A .  M i l l e r  
NASA Lewis Research Center  
C l e v e l a n d ,  O h i o  
1. INTRODUCTION 
The basic objective of this investigation is the quantitative 
determination of stress states in a model thermal barrier coating 
(TBC) as it cools in the air to 600°C from an assumed stress-free 
state at 700°C. This model is intended to represent a thin plasma- 
sprayed zirconia-yttria ceramic layer with a nickel-chromium-alumi- 
num-yttrium bond coat on a cylindrical substrate made of nickel- 
based. superalloys typically found in gas turbines. 
The problem under study is a complex one due to layering, un- 
even interface between the ceramic and the bond, oxidation, and 
thermal expansion mismatch, as reported in references 1, 2, and 3. 
Thus, a concerted effort has been made to use the versatile finite 
element method to represent a cylindrical model TBC which resembles 
those that had been tested in a laboratory (refs. 1 and 3). The 
modeling concept is illustrated in figure 1. 
To implement this finite element scheme, a generic code called 
MARC (ref. 4 )  has been utilized with the aid of a supercomputer 
(known as CRAY-XMP) at NASA Lewis Research Center. The latest fi- 
nite element model which is known as TBCGEP, contains 1316 nodal 
points and 2140 generalized plane strain elements. This finite 
element model is now capable of representing both the ceramic layer 
arid the bond coat with classical elastic-perfectly plastic materi- 
als. 
Numerical results from previous studies have been reported in 
references 2, 3, 5, and 6. Parameters studied include: (1) varia- 
tion of material properties involved, (2) oxidation of the bond 
coat, ( 3 )  cracking at the ceramic-bond interface, ( 4 )  coefficient of 
thermal expansion and Poisson's ratio of bond coat, and (5 )  
plasticity in the bond coat. 
The newly revised code TBCGEP has been used to study the in- 
fluence of pl.asticity in ceramic layer on stress states, particu- 
larly on stresses in the "critical zone" shown in figure 2. De- 
tailed results from three lengthly computer runs are presented in 
section 3 of this paper. 
35 7 
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2 .  FINITE ELEMENT MODELING OF A CYLINDRICAL TBC 
The uncoated superalloy cylindrical test specimens used in 
reference 1 had a radius (R ) of 0.65 cm and a length of 7.60 cm. 
The specimens were plasma-sfirayed in air with a thin zirconia- 
yttria (Zr02 - 8 wt. % Y 0 ) layer on a thin nickel-chromium- 
aluminum-zirconium bond coat. The test specimen is sufficiently 
long, as compared to its radius, that the problem can be approxi- 
mated by a two-dimensional generalized plane-strain case in the 
context of classical elasticity. 
is illustrated in figure 2. Details for an early model (known as 
TBC) was given in reference 2. 
sinusoidal interface with an amplitude and a period of 50 micro- 
meters (pm). 
interface (15pm) than TBC. Detailed finite element discretization 
has been presented in reference 5. 
2 3  
The resulting finite element model 
That model features a rather sharp 
The next finite element model known as TBCGEP has a more smooth 
3. INFLUENCE OF PLASTICITY IN CERAMIC LAYER ON STRESS STATES 
\Jith the aid of the latest computer code named TBCGEP, the 
influence of plasticity in ceramic layer on stress states through- 
out the TBC has been studied on a preliminary basis. Three cases, 
i.e. T-17, T-18, and T-19, have been investigated. A s  shown in 
Table 1, these three cases are identically the same as that of Case 
B-2 with the sole exception of varying degree of plasticity. The 
plastic behavior, as known in the classical theory of plasticity, is 
controlled by the parameter called YP1 which is the measure in von 
Mises yeild criterion in an elastic-perfectly-plastic solid. 
The stress states have been calculated by using ten increments 
of -10°C each, starting at an assumed stress-free temperature of 
700°C. The results for Case T-18 are presented in figures 6-8. 
Also presented in figures 9-11 are results for Case T-19. 
parison purposes, corresponding stresses for the perfectly elastic 
case known as B-2 are also shown in figures 3-5. 
For com- 
From figures 3 ,  6, and 9, it can be seen that the x-stress in 
the ceramic layer experiences very significant reduction with in- 
creasing plasticity. Furthermore, a rather localized redistribu- 
tion in stresses is seen to have taken place in the vicinity of the 
critical zone. These results are expected within the realm of 
classical plasticity. The same can also be said about the x-stress 
in the bond coat adjacent to the ceramic-bond interface. Indeed, 
the experience with y-stress and shearing stress is substantially 
similar to the x-stress. In short, these results have shown the 
widespread influence of ceramic plasticity as well as the forgiven 
nature of plasticity in a solid material. 
358 
Now, figure 12 presents data on stresses in the critical zone 
in a model TBC as a function of temperature and plasticity. Stres- 
ses in x-direction increased linearly with decreasing temperature in 
Case B-2. These stresses, however, tend to increase with de- 
creasing temperature at a rate much slower than that of Case B-2 as 
more plasticity is involved. At 6OO0C, the x-stress in Case T-19 is 
only  about 40  percent of the corresponding stress in the elastic 
case, B-2. 
Similar reductions in y-stresses can be seen as a function of 
plasticity as well. The magnitudes of reduction, however, are even 
more pronounced than that of Case B-2. Much of the same can be said 
of shearing stresses as shown in figure 12. 
In short, data shown in figure 12 clearly illustrates the very 
significant influence ceramic plasticity has on stresses in the 
critical zone. Given the nature of plasticity in a medium, the re- 
sults are entirely expected. 
4 ,  CONCLUDING REMARKS 
In the present work, the computer code TBCGEP has been used to 
generate numerical solutions to the model thermal barrier coating, 
as shown in figures 3 to 12. 
In section 3 ,  nine stress-field contours and figure 12 illus- 
strate the very important influence ceramic plasticity has on the 
stresses in the critical zone as a coating system is cooled from an 
assumed stress free temperature. The importance is in marked con- 
trast with the slight impact bond coat plasticity had on stresses in 
the critical zone or elsewhere in the model TBC (ref. 6 ) .  None- 
theless, additional data will have to be generated and analyzed 
before a firm conclusion can be drawn. 
The question of combined influence of plasticity in both cera- 
mic layer and the bond coat, is of significant interest at present. 
Of equal importance is the determination of the effect of bond coat 
oxidation on stress states, in the presence of plasticity. Such are 
some of the major directions for future TBC investigations. 
359 
REFERENCES 
1. Miller, R. A.; and Lowell, C. E.: Failure Mechanism of Thermal 
Barrier Coatings Exposed to Elevated Temperatures. Thin Solid 
Films, 95, 1983, pp. 265-273. 
2. Chang, G. C.; Phucharoen, W.; and Miller, R. A.: Thermal Ex- 
pansion Mismatch and Oxidation in Thermal Barrier Coatings. 
NASA CP-2405, 1985, pp. 405-425. 
3 .  Chang, George C.; Phucharoen, Woraphat; and Miller, Robert A.: 
Behavior o f  Thermal Barrier Coatings for Advanced Gas Turbine 
Blades. Surface and Coatings Technology, 30, 1, 1987, pp. 13- 
28. 
4. Anonymous, MARC Finite Element Program User Manual, Version 
K-2, MARC Analysis Research Corporation, 1986. 
5. Chang, George C.; Phucharoen, Woraphat; and Miller, Robert A.: 
A Study on Thermal Barrier Coatings including Thermal Expansion 
Mismatch and Bond Coat Oxidation. NASA-CP-2444, 1986, pp. 415- 
434. 
6. Chang, G. C.; Phucharoen, W.; and Miller, R. A.: Finite Ele- 
ment Thermal Stress Solutions for Thermal Barrier Coatings. 
Paper presented at the 14th International Conference on Metal- 
lurgical Coatings, San Diego, CA., March 23-27, 1987. 
360 
TABLE 1 MATERIAL AND OTHER PARAMETERS 
Parameters Case A-2 Cases B-2, T-17, T-18, T-19 
Young's Modulus (MPa) 
6 Substrate 0.1758 x lo6 0.1758 x lo6 
Bond 0.1379 x lo6 0.1379 x lo6 
Ceramic 0.0276 x 10 0.0276 x 10 
Poisson's Ratio 
Substrate 0.25 0.25 
Bond 0.27 0.27 
Ceramic 0.25 0.25 
Coefficient of 
Thermal Expans ion 
(/"C> 
Substrate 
Bond 
Ceramic 
YP1 - value (MPa) 
Substrate 
Bond 
Ceramic 
Oxidat ion 
13.91 x 101; 
10.01 x 10 
15.16 x 10-6 
6 0.069 x lo6 
0.069 x lo6 
0.069 x 10 
NO 
Interface Roughness 
Amplitude (pm) 50 
*5 ,000 p s i .  
36 1 
13.91 x 101; 
10.01 x 10 
15.16 x 10-6 
0.069 x lo6 
0.069 x 10 
(B-2) 0.069 x lo6 
(T-17) 34.48" 
(T-18) 17.24 
(T-19) 8.62 
NO 
15 
Crr- -9 section 
Ceramic layer 
Bond coat 
Substrate 
Figure 1. CYLINDRICAL TBC TEST SPECIMEN 
Figure 2. THE TBCGEP FINITE ELEMENT MODEL 
362 
Ceramic 
Figure 3. STRESS IN X-DIRECTION DUE TO THERMAL EXPANSION MISMATCH 
Figure 4. STRESS IN Y-DIRECTION DUE TO THERMAL EXPANSION MISMATCH 
36 3 
- Ceramic 0 
Case 8-2 
Part: 2C 
Unit: MPa 
Figure 5. SHEARING STRESS DUE TO THERMAL EXPANSION MISMATCH 
364 
365 
Figure 8. SHEARING STRESS DUE TO THERMAL EXPANSION MISMATCH AND 
PLASTICITY 
Figure 9. STRESS IN X-DIRECTION DUE TO THERMAL EXPANSION MISMATCH 
AND INCREASED PLASTICITY 
366 
Figure 10. STRESS IN Y-DIRECTION DUE TO THERMAL EXPANSION MISMATCH 
AND INCREASED PLASTICITY 
Figure 11. SHEARING STRESS DUE TO THERMAL EXPANSION MISMATCH AND 
INCREASED PLASTICITY 
36 7 
A 
2 
E 
a 
zi 
W z 
0 
t a 
0 
z 
v) 
W 
u) m 
W 
I- u) 
a 
. 1 q  Cases 
-14 STRESSES V IIU*IIII* 8-2 (YrI= 6 9 . 0 0 1 1  W a )  " D19EC' CY - T-17 ( Y 1 ' 1 =  3 4 . 4 8  CIPaJ 
--- T-18 ( Y I ' 1 =  1 7 . 2 4  ClPa) 
'I ..... T-19 (Y1'1= 8 . 6 2  bll'a) 
600 650 700 
TEMPERATURE ("C) 
-16 G..' 
-'"i 20 
jure 12. VARIATION OF STRESSES WITH TEMPERATURE 
ORIGINAL PAGE IS 
OF POOR QUALITY 
368 


Thermal expansion mismatch and plasticity in thermal barrier coating

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