Louis J. Ghosn

Ohio Aerospace Institute, Brook Park, Ohio

Dongming Zhu

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Robert A. Miller

Glenn Research Center, Cleveland, Ohio

Crack Driving Forces in a Multilayered Coating

System for Ceramic Matrix Composite Substrates

NASA/TM—2005-213835

September 2005
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Louis J. Ghosn

Ohio Aerospace Institute, Brook Park, Ohio

Dongming Zhu

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Robert A. Miller

Glenn Research Center, Cleveland, Ohio

Crack Driving Forces in a Multilayered Coating

System for Ceramic Matrix Composite Substrates

NASA/TM—2005-213835

September 2005

National Aeronautics and

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Glenn Research Center

Prepared for the

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NASA/TM—2005-213835 1

Crack Driving Forces in a Multilayered Coating System 

for Ceramic Matrix Composite Substrates 

Louis J. Ghosn 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Dongming Zhu 

U.S. Army Research Laboratory 

Glenn Research Center 

Cleveland, Ohio 44135 

Robert A. Miller 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The effects of the top coating thickness, modulus and shrinkage strains on the crack driving forces for 

a baseline multi-layer Yttria-Stabilized-Zirconia/Mullite/Si thermal and environment barrier coating 

(TEBC) system for SiC/SiC ceramic matrix composite substrates are determined for gas turbine 

applications. The crack driving forces increase with increasing modulus, and a low modulus thermal 

barrier coating material (below 10 GPa) will have no cracking issues under the thermal gradient condition 

analyzed. Since top coating sintering increases the crack driving forces with time, highly sintering 

resistant coatings are desirable to maintain a low tensile modulus and maintain a low crack driving force 

with time. Finite element results demonstrated that an advanced TEBC system, such as ZrO2/HfO2, which 

possesses improved sintering resistance and high temperature stability, exhibited excellent durability. A 

multi-vertical cracked structure with fine columnar spacing is an ideal strain tolerant coating capable of 

reducing the crack driving forces to an acceptable level even with a high modulus of 50 GPa. 

Introduction 

Significant progress has been achieved in improving the quality of SiC/SiC composite materials for 

hot section components in gas turbine applications (ref. 1). Melt infiltrated (MI) SiC/SiC composites are 

emerging as the leading material for shrouds, vanes and combustor liners in commercial gas turbines 

because of their high thermal conductivity, excellent thermal shock resistance, creep resistance, and 

oxidation resistance compared to other ceramic matrix composites (CMC) and to nickel and cobalt-based 

super alloys used in current engines (ref. 2). Durability has been demonstrated in excess of 9,000 hr at 

combustor temperatures and stresses within the current designs (ref. 1). A risk, that can significantly 

reduce the lives of the SiC/SiC composites in an engine environment, is the lack of environmental 

durability (ref. 3) in the presence of water vapor. Oxide coatings have shown promise in providing an 

environmental protection for these SiC/SiC composites due to their resistance to a corrosive environment 

up to 1250 °C (ref. 3). To further extend the thermal capability of SiC/SiC ceramic composite 

components to the hot wall surface temperatures up to 1650 °C, thermal and environmental barrier 

coatings (TEBC)s are being developed under the NASA Ultra-Efficient Engine Technology (UEET) 

Program (refs. 4 and 5). One of the UEET program goals is to improve the fuel efficiency and reduce the 

NOx emission of future gas turbine engines by allowing for even higher gas temperature with little or no 

film cooling compared to current engines. 
NASA/TM—2005-213835 2

Baseline plasma-sprayed Yttria-Stabilized Zirconia (YSZ: ZrO2-8wt.%Y2O3) thermal barrier and 

BSAS+mullite/Si environment barrier layered coatings showed excellent adherence to the SiC/SiC 

ceramic matrix composite substrates under thermal cycling in burner rig tests up to 1250 °C (ref. 3). But 

the same coating system tested to higher temperatures (up to 1480 °C), especially under a temperature 

gradient condition, resulted in coating delamination failures which were attributed to an increase in the 

crack driving forces in the coating (refs. 6 and 8). Therefore, research is being performed to develop 

advanced thermal and environmental barrier coating systems, which can last for tens of thousands hours 

as required for gas turbine applications. The ideal candidate TEBC system should have a low thermal 

conductivity, good high-temperature stability and resistance to sintering. Current research efforts are 

underway at NASA Glenn to screen various candidate coating materials such as hafnia-, pryochlore-, and 

magnetoplumbite-based TEBC (refs. 4 and 5) as well as advanced bond coat systems that can meet the 

1650 °C durability requirements. 

TABLE I.—ASSUMED MATERIAL PROPERTIES 

 Thermal 

conductivity, 

k 

Coefficient of 

thermal expansion, 

CTE 

Elastic 

modulus, 

E 

Specific 

heat, 

c 

Density, 

ρ

Poisson’s 

ratio, 

ν

 W/m-K 1/°C GPa J/kg-K Kg/m3 

MI SiC/SiC 

CMC 20 5.20x10–6 125 620 @20 °C 

1200@1000 °C 3100 0.3 

Si 83.7 5.00x10–6 200 700 2330 0.27 

EBC 2 5.50x10–6 90 750 2500 0.25 

TBC 1 1.00x10–6 ~5 to 50 582 5236 0.2 

In this study, the effects of temperature gradients and coating configurations are analyzed using finite 

element analysis (FEA) models based on the observed cracking in an YSZ baseline TEBC system. The 

only applied loadings are thermal loads. The crack driving forces as a function of crack length, coating 

layer thickness, top coating modulus and sintering time are reported to provide an insight into the material 

properties required in minimizing the cracking and delamination observed in the baseline TEBC 

protecting system for SiC/SiC composite material. 

Finite Element Approach 

The temperature and stress distributions are calculated as a function of coating layer thickness and 

thermal heat flux using the finite element method. ABAQUS-6.4 (ref. 9) was the platform employed to 

run the FEA models. The idealized specimen geometry was assumed to be a 2D structure formed from a 

2 mm thick substrate with a three layer baseline TEBC system deposited on the top face. The top coating 

layer, which is the thermal barrier coating (TBC) layer, consisted of a ZrO2-8wt.%Y2O3 layer with a 

thickness ranging between 0.127 to 0.508 mm. The second coating layer, which is the environmental 

barrier coating (EBC) layer, consisted of a mullite layer with a thickness ranging from 0.508 to 0.127 

mm. The third layer is assumed to be a bond coat (BC) layer of 0.127 mm thick Si. The sum of the TBC 

and EBC thickness was a constant in this study, always equal to 0.635 mm. Four different combinations 

of TBC and EBC thickness were considered ranging from 0.127 to 0.508 mm. The assumed material 

properties are presented in table I. A range of the YSZ elastic modulus was assumed in this study since 

the TBC tensile modulus was observed to vary with sintering time (ref. 10). 

Thermal loading was the only load applied in this study. The assumed stress free condition in the 

coated system was taken at the maximum applied temperature, and the stresses were actually developed 

upon cool down to room temperature. A comparison between the in-plane stress profiles developed under 

a uniform temperature and a temperature gradient is shown in figure 1 for a TBC and EBC layer thickness 

of 0.381 and 0.254 mm, respectively. A constant temperature of 1350 °C results in a uniform stress 
NASA/TM—2005-213835 3

Si

CMC

TBC

EBC

1100oC

1600oC

1350oC

Si

CMC

TBC

EBC

1100oC

1600oC

1350oC

Figure 1.—In-plane stress profile comparison between a 

uniform and a gradient applied temperature. 

distribution within each layer due the CTE mismatch between the various materials. The temperature 

gradient between the 1600 °C TBC hot side surface wall and the 1100 °C cooler substrate backside wall 

resulted in higher stresses due to a combination of uniform and bending load components in each layer 

generated by the addition of the 500 °C through the thickness temperature gradient. 

To study the effects of sintering on the developed stresses, a time dependent shrinkage strain rate as a 

function of the temperature and hold time was implemented in the finite element program as a volumetric 

shrinkage in a Creep type user defined subroutine. The total shrinkage strain and the resulting stresses 

were then calculated incrementally given a hold time and temperature in the YSZ top coat based on the 

experimentally measured shrinkage rates. The assumed equation relating the shrinkage strain rate to the 

temperature (T) and time followed the classical arrhenius type relation between strain rate and 

temperature, given as (refs. 11 and 12): 

A e f ( )t

dt

d RT

Q − = ε

ε& = (1) 

where A, R are constants, Q is the activation energy, and f(t) is a functional relation of time as 

determined by a best fit curve of the experimental data. Figure 2 shows the comparison between the 

experimental data shown as solid symbols and the curve-fit relations using equation 1 shown as open 

symbols for the shrinkage rate of YSZ for temperatures ranging from 1200 °C up to 1500 °C. 

The cracked geometries assumed are shown in figure 3 for a crack propagating near either the EBC/Si 

(fig. 3(a)) or TBC/EBC (fig. 3(b)) interfaces, simulating experimentally observed TEBC cracks under a 

cyclic laser heat-flux test. The crack driving forces were calculated using the contour integral technique 

through the virtual motion of a block of element surrounding the crack tip as implemented in ABAQUS. 

The depth of the crack was always assumed to be 0.0254 mm above the interface. The crack tip 

singularity was modeled using the standard “quarter point node” technique, by degenerating the eightnode biquadratic elements surrounding the crack tip into wedge elements and by moving the mid-sided 

nodes adjacent to the crack tip to one quarter of the edge length (ref. 13). The crack length analyzed in 

this study ranged from 0.2 to 6 mm. To vary the crack length, a routine was formulated to scale the node 

locations surrounding the crack tip in proportion to the desired crack length and crack depth. 
NASA/TM—2005-213835 4

Crack Driving Forces 

The variations of the Mode I and Mode II stress intensity factors as a function of the crack length are 

shown in figure 4 for a 0.381 mm TBC thick layer and a 0.254 mm EBC thick layer under constant and 

temperature gradient cases and a TBC tensile modulus of 10 GPa. The variation of the stress intensity 

factors (SIF)s for the constant temperature profile is almost independent of the crack length, with a 

constant ratio of the stress intensity factors KI/KII equal to 1.3. For the temperature gradient case, the 

Mode I and Mode II stress intensity factors increase with increasing crack length. For short cracks up to 

0.5 mm, the Mode II SIF for the temperature gradient case is almost equal to the Mode II of the constant 

temperature case. But the Mode I SIF is about 50 percent higher for the temperature gradient case 

compared to the constant temperature case. This variation reaches a high of 300 percent for a crack length 

of 3 mm. 

-6E-08

-5E-08

-4E-08

-3E-08

-2E-08

-1E-08

0E+00

0 50000 100000 150000 200000 250000 300000 350000 400000

Time (sec)

Shrinkage strain rate, de/dt (1/sec)

1500 C

1400 C

1300 C

1200 C

Figure 2.—Experimental and modeled shrinkage strain for the baseline 

YSZ thermal barrier coating as a function of time and temperature. 

BSAS+Mullite

Zirconia

Coating

Si

SiC/SiC

Si EBC

TBC

2W

TBC Crack

2 C 

EBC Crack

2 C 

2W

BSAS+Mullite

Zirconia

Coating

Si

SiC/SiC

Si EBC

TBC

2W

TBC Crack

2 C 

EBC Crack

2 C 

2W

Si EBC

TBC

2W

TBC Crack

2 C 

Si EBC

TBC

2W

TBC Crack

2 C 

EBC Crack

2 C 

2W

 (a) (b) (c) 

Figure 3.—Assumed crack geometry; (a) EBC crack, (b) TBC crack and (c) actual. 
NASA/TM—2005-213835 5

The variation of the effective SIF is also shown in figure 4 based on the maximum principal stress 

mixed mode criterion as derived by Erdogan and Shih (ref. 14) given below for completeness: 

2

sin

2

3 cos

2

cos3 2 m m II m Keff KI K θ θ − θ = (2) 

where θm is defined as the direction of the maximum principal stress given by: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= + +

θ 8

4

1

2

tan 2

2

II

I

II

m I

K

K

K

K (3) 

The trend of the effective SIF variation with crack length follows closely the Mode I and Mode II SIF 

trends. These trends emphasize the need to always test a new TEBC system for gas turbine applications 

under a temperature gradient simulating the actual engine thermal environment, rather under a uniform 

temperature. 

The variation of the effective SIF with TBC coating thickness is shown in figure 5 for a constant 

TEBC total thickness of 0.635 mm and a constant crack length of 0.5 mm for the temperature gradient 

case. A crack developed in the TBC results in an increasing SIF with increasing TBC thickness due to the 

increase in the bending load component in that layer with increasing thickness. The effective SIF for a 

crack growing in the EBC shows a minimum at 0.254 mm TBC thickness. The magnitudes of the SIF in 

the EBC layers are always higher than the magnitudes for a crack in the TBC layer, due to the additional 

stresses transferred from the fully cracked TBC into the partially cracked EBC ligament. These results 

demonstrate the need for a higher fracture toughness EBC material than the TBC material. 

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

01234

Crack Length c, mm

Stress Intensity Factor K, MPa m0.5

Mode I

Mode II

Mixed Mode

tTBC=0.381mm

tEBC=0.254mm

ETBC=10GPa

TBC Crack

Gradient

Constant

Temperature

Figure 4.—Stress intensity factor as a function of the crack length. 
NASA/TM—2005-213835 6

Next, the variation of the effective SIFs with sintering time is calculated as a function of the TBC 

elastic modulus. The analysis assumed a constant crack length of 0.5 mm in the TBC layer for a TEBC 

geometric construction of a 0.381 mm thick TBC layer and a 0.254 mm thick EBC under the thermal 

gradient condition. The effective SIF increases with increasing TBC modulus starting from 1MPa.

m1/2 for 

a TBC modulus of 5 GPa to well above 10 MPa.

m1/2 for a 50 GPa TBC modulus (above any measured 

fracture toughness of plasma sprayed YSZ (ref. 10)), (see fig. 6). As the TBC layer sintered during 

exposure, the effective SIF increases with time upon cool down. The crack driving forces increase quickly 

within the first 50 hours of exposure and then increase more gradually with increasing time. The initial 

rise of the SIF is gentler for a low modulus TBC material in the range of 5 to 10 GPa and is steeper for 

the higher modulus TBC (20 to 50 GPa). The results show that highly compliant materials are desirable in 

a TEBC system to accommodate the CTE mismatch and the temperature gradient. The ideal coating needs 

also to retain the low modulus after sintering during exposure to high temperature which is a clear 

challenge to the material developers as shown by Choi et al. in reference 10. Figure 7 shows a comparison 

between experimental measurements of the coating thermal conductivity with time for the baseline YSZ 

coating and an advanced HfO2 based sintering resistance coating. The measured thermal conductivity 

reduction for the YSZ coating can be related to an increase in the delamination area along the interfaces 

with increasing cycles. 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.1 0.2 0.3 0.4 0.5 0.6

TBC thickness, mm

Effective Stress Intensity Factor Keff, MPa 

m0.5

EBC-Crack

TBC-Crack

Figure 5.—Effective stress intensity factor as a function of the TBC thickness. 

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 50 100 150 200 250

Sintering Time, hr

Effective Stress Intensity Factor Keff, MPa m0.5

50

20

10

 5

ETBC, GPa

tTBC=0.381mm

tEBC=0.254mm

a=0.5mm

Crack in the TBC Layer

Typical

Measured

KIC Range

Figure 6.—Stress intensity factor variation with time and TBC modulus. 
NASA/TM—2005-213835 7

The final simulation is to study the effects of multi-vertical cracked structure for a crack in the TBC 

layer, also under a temperature gradient condition. In this simulation, the TBC coating is sectioned 

vertically for various spacing λ ranging from 50 to 200 μm horizontally for a 50 GPa TBC modulus. 

The effective SIF decreases with decreasing vertical spacing λ and increasing crack length, as shown in 

figure 8. The magnitudes of the SIF for the multi-vertical cracked structure are now in the range of 1 to 

2 MPa.

m1/2 even with a 50 GPa elastic modulus, which are almost in the ranges of a single crack case with 

a 5 GPa modulus as shown in figure 6. 

Conclusion 

The crack driving forces in a baseline line TEBC system were determined as a function of the coating 

layer thickness, elastic modulus and sintering time. The crack driving forces increase with increasing 

modulus. An elastic modulus of less than 10 GPa is required to reduce the crack driving forces to an 

acceptable level. The ideal TBC coating must possess a low thermal conductivity, high strain tolerance 

and high sintering resistance. A multi-vertical cracked structure with fine columnar spacing is an ideal 

strain tolerant coating capable of reducing the crack driving forces to an acceptable level even with a high 

modulus of 50 GPa. 

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 20 40 60 80 100 120

ZrO2-8wt%Y2O3(15mil)/mullite(10mil)

HfO2-(Y,Gd,Yb)2O3

Normalized thermal conductivity

 (15mil)/mullite(10mil)

Time, hours

30 min cycles

Figure 7.—Thermal conductivity variation with time. 

0.0

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8

Normalized Crack Length a/⎠

Effective Stress Intensity Factor Keff, MPa 

m0.5

200

150

100

 50

ETBC=50GPa

tTBC=0.381mm

tEBC=0.254mm

Figure 8.—Effective stress intensity factor as a function 

of crack length and columnar spacing. 

2λ, μm

2λ

Normalized Crack Length a/λ
NASA/TM—2005-213835 8

References 

1. D. Brewer, “HSR/EPM Combustor Materials Development Program,” Mater. Sci. Eng., A261, 284–

291 (1999). 

2. K.L. Luthra and G.S. Corman, “Melt Infiltrated (MI) SiC/SiC Composites for Gas Turbine 

Applications,” GE Research & Development Center Report 2001-CRD112, October (2001). 

3. K.N. Lee and R.A. Miller, “Development and Environmental Durability of Mullite and Mullite/YSZ 

Dual Layer Coatings for SiC and Si3N4 Ceramics,” Surface and Coatings Technology, 86–87, 142–

148 (1996). 

4. D.M. Zhu, N.P. Bansal and R.A. Miller, “Thermal Conductivity and Stability of HfO2-Y2O3 and 

La2Zr2O7 Evaluated for 1650 °C Thermal and Environmental Barrier Coatings,” Advances in Ceramic 

Matrix Composites IX, N.P. Bansal, J.P. Singh, W.M. Kriven and H. Schnneider (eds.), The American 

Ceramic Society, Westerville, Ohio, 153, 331–343, (2003). 

5. D.M. Zhu, D.S. Fox, N.P. Bansal and R.A. Miller, “Advanced Oxide Material Systems for 1650C 

Thermal/Environmental Barrier Coating Applications,” NASA TM-2004-213219, December (2004). 

6. K.N. Lee, “Current Status of Environmental Barrier Coatings for Si-Based Ceramics,” Surface and 

Coatings Technology, 133–134, 1–7 (2000). 

7. D.M. Zhu, K.N. Lee, and R.A. Miller, “Thermal Gradient Cyclic Behavior of a 

Thermal/Environmental Barrier Coating System on SiC/SiC Ceramic Matrix Composites,” 

Proceedings of ASME Turbo Expo 2002, June 3–6, 2002, ASME Paper GT–2002–30632, 

Amsterdam, The Netherlands (2002). 

8. D.M. Zhu, S.R. Choi, J.I. Eldridge, K.N. Lee and R.A. Miller, “Surface Cracking and Interface 

Reaction Associated Delamination Failure of Thermal and Environmental Barrier Coatings,” 

NASA/TM—2003-212318, April (2003). 

9. ABAQUS/STANDARD Finite Element Program. Version 6.4, Hibbitt, Karlsson & Sorensen Inc., 

Pawtucket, RI. 

10. S.R. Choi, D.M. Zhu and R.A. Miller, “Mechanical Properties/Database of Plasma-Sprayed ZrO2-

8wt% Y2O3 Thermal Barrier Coatings,” Int. J. Appl. Ceram. Technol., 1 [4], 330–342 (2004). 

11. D.M. Zhu and R.A. Miller, “Determination of Creep Behavior of Thermal Barrier Coatings under 

Laser Imposed High Thermal and Stress Gradient Conditions,” J. of Materials Research, 14 [1], 

146–161, (1999). 

12. D.M. Zhu and R.A. Miller, “Thermal-Barrier Coatings for Advanced Gas-Turbine Engines,” MRS 

Bulletin, 25 [7], 43–47, July (2000). 

13. R.S. Barsoum, “On the Use of Isoparametric Finite Elements in Linear Fracture Mechanics,” Int. J. 

Num. Methods in Engr., 10 [1], 25–37 (1976). 

14. F. Erdogan and G.C. Shih, “On the Crack Extension in plates under Plane loading and Transverse 

Shear,” J. Basic Eng., 85, 510–527 (1963). 
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E–15205

WBS–22–714–30–26

14

Crack Driving Forces in a Multilayered Coating System for Ceramic Matrix

Composite Substrates

Louis J. Ghosn, Dongming Zhu, and Robert A. Miller

Oxide coating; Crack driving forces; Ceramic composites; Finite element; Effects of

sintering

Unclassified -Unlimited

Subject Categories: 39 and 24

Prepared for the 29th International Conference on Advanced Ceramics and Composites sponsored by the American

Ceramic Society, Cocoa Beach, Florida, January 23–28, 2005. Louis J. Ghosn, Ohio Aerospace Institute, 22800 Cedar

Point Road, Brook Park, Ohio 44142; Dongming Zhu, U.S. Army Research Laboratory, NASA Glenn Research

Center; and Robert A. Miller, NASA Glenn Research Center. Responsible person, Louis J. Ghosn, organization code

RSL, 216–433–3822.

The effects of the top coating thickness, modulus and shrinkage strains on the crack driving forces for a baseline multilayer Yttria-Stabilized-Zirconia/Mullite/Si thermal and environment barrier coating (TEBC) system for SiC/SiC ceramic

matrix composite substrates are determined for gas turbine applications. The crack driving forces increase with increasing modulus, and a low modulus thermal barrier coating material (below 10 GPa) will have no cracking issues under the

thermal gradient condition analyzed. Since top coating sintering increases the crack driving forces with time, highly

sintering resistant coatings are desirable to maintain a low tensile modulus and maintain a low crack driving force with

time. Finite element results demonstrated that an advanced TEBC system, such as ZrO2/HfO2, which possesses improved sintering resistance and high temperature stability, exhibited excellent durability. A multi-vertical cracked

structure with fine columnar spacing is an ideal strain tolerant coating capable of reducing the crack driving forces to an

acceptable level even with a high modulus of 50 GPa.