Louis J. Ghosn

Ohio Aerospace Institute, Brook Park, Ohio

Sai V. Raj

Glenn Research Center, Cleveland, Ohio

Residual Stresses in Thermal Barrier Coatings

for a Cu-8Cr-4Nb Substrate System

NASA/TM—2002-211561

July 2002

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Louis J. Ghosn

Ohio Aerospace Institute, Brook Park, Ohio

Sai V. Raj

Glenn Research Center, Cleveland, Ohio

Residual Stresses in Thermal Barrier Coatings

for a Cu-8Cr-4Nb Substrate System

NASA/TM—2002-211561

July 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

26th Annual International Conference on Advanced Ceramics and Composites

sponsored by the American Ceramic Society

Cocoa Beach, Florida, January 13–18, 2002

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NASA/TM2002-211561 1 

RESIDUAL STRESSES IN THERMAL BARRIER COATINGS FOR A Cu-8Cr-4Nb 

SUBSTRATE SYSTEM 

Louis J. Ghosn 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Sai V. Raj 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

ABSTRACT 

 Analytical calculations were conducted to determine the thermal stresses developed in a 

coated copper-based alloy, Cu-8(at.%)Cr-4%Nb (designated as GRCop-84), after plasma spraying 

and during heat-up in a simulated rocket engine environment. Finite element analyses were 

conducted for two coating systems consisting of a metallic top coat, a pure copper bond coat and 

the GRCop-84. The through thickness temperature variations were determined as a function of 

coating thickness for two metallic coatings, a Ni-17(wt%)Cr-6%Al-0.5%Y alloy and a Ni50(at.%)Al alloy. The residual stresses after low-pressure plasma spraying of the NiCrAlY and 

NiAl coatings on GRCop-84 substrate were also evaluated. These analyses took into consideration 

a 50.8 μm copper bond coat and the effects of an interface coating roughness. The through the 

thickness thermal stresses developed in coated liners were also calculated after 15 minutes of 

exposure in a rocket environment with and without an interfacial roughness. 

INTRODUCTION 

Since 1998, various studies have been conducted to significantly improve the performance of 

rocket engines and to reduce the weight of specific engine components under NASA’s third 

generation Reusable Launch Vehicle (RLV) program [1]. Efforts have focused on reducing the 

weight of the thrust chamber as well as improving the component life at higher operating gas 

temperatures. One candidate material under consideration for the thrust chamber component is a 

NASA-developed copper-based alloy known as GRCop-84 (Cu-8(at.%)Cr-4Nb) [2] that is being 

considered as a replacement for the NARloy-Z alloy currently used in various thrust chambers [3]. 

Table I compares the material properties of extruded GRCop-84 with those for NARloy-Z at 

538 °C [2–3]. As shown in Table I, the GRCop-84 has a lower density than the NARloy-Z, higher 

strength at elevated temperatures, and longer fatigue and creep life. These properties suggest the 

advantages of GRCop-84 as a liner material to achieve longer component life. 

Although, GRCop-84 shows an improvement in its high temperature properties compared to 

the current liner material, a coating is still desirable to further increase the operating temperature 

by protecting the substrate hot-wall from oxidation and blanching. Various metallic and ceramic 

coatings are being considered as coating materials for the GRCop-84 liner. Two metallic top 

overlay coatings will be considered in this paper: a nickel-based alloy with Ni-17(wt.%) 

Cr-6Al-0.5%Y used primarily as a bond coat for ceramic thermal barrier coatings on superalloys 

[4] and a Ni50(at.%)-Al alloy. Furthermore, a 50.8 μm copper bond coat layer is also applied 

between the two top coats and the GRCop-84 substrate to promote bonding. The NiCrAlY 

coating has been successfully used with NARloy-Z liners and was applied to the GRCop-84 

substrate for comparison. The NiAl intermetallic alloy is of interest as a coating due to its ability 
NASA/TM2002-211561 2 

to form a protective Al2O3 scale on the surface while maintaining the mechanical properties of the 

underlying substrate [5]. Table II summarizes key material properties for the two coating systems 

at 900 °C. The NiCrAlY has a lower thermal conductivity but a higher coefficient of thermal 

expansion (CTE) compared to NiAl. The NiAl shows higher yield and tensile strengths, but lower 

creep resistance, compared to NiCrAlY. 

Table I. Comparison of the 538 °C Material Properties of GRCop-84 and NARloy-Z. 

Table II. Material Properties of NiAl and NiCrAlY at 900 °C 

 For the combustor liner design, the variation of the substrate temperature with coating 

thickness is first determined using the finite element method for the two top coats, under typical 

steady-state thermal conditions expected in the rocket chamber liner. Furthermore, the residual 

stresses built up after cool down from the plasma spraying conditions are determined in the 

coatings and the substrate. A precise determination of these residual stresses after processing is 

key to understanding the behavior of these coatings after cool down from the processing 

temperature, as well as the response to subsequent thermo-mechanical loads. The effect of the 

surface roughness of the interfaces on the residual stresses is also determined for the two coatings. 

The surfaces of the substrate materials are usually grit blasted prior to the application of the 

coating in order to improve the coating adherence through a mechanical interlock. The presence 

of this surface roughness was shown to introduce a complex stress field that can lead to cracking 

along the coating-substrate interface and ultimately to the spallation of the coating [6–9]. Hence, 

the perturbations of the residual stress distribution with the presence of interfacial asperities are 

also delineated for the two coatings in this investigation. Finally, the thermal stresses developed 

in a simulated engine environment are determined with and without interfacial roughness. 

HEAT-TRANSFER ANALYSIS 

 The steady-state temperature distributions through the thickness of coated GRCop-84 

substrates were determined as a function of the coating thickness using the finite element method. 

The applied thermal boundary conditions simulating the gas temperature conditions in the rocket 

chamber are shown in Fig. 1(a). The hot gases are estimated to reach temperatures as high as 

3,277 °C. The liquid hydrogen fuel provides the back face cooling for the liner. The variations of 

the temperatures along the various interfaces as well as the hot and cold outer walls at steady-state 

conditions are shown in Figs. 2(a) and (b) for the NiCrAlY and NiAl coatings, respectively. It is 

noted that similar thermal analyses were conducted by Holmes and co-workers on a copper alloy 

Material Density Thermal 

Conductivity

Yield 

Strength

Tensile 

Strength

CTE 

×10–6

Fatigue Life at 

0.7%∆εtotal

Creep Life 

at 500 °C

σ = 84 MPa

(kg/m3) (W/m °C) (MPa) (MPa) (1/°C) (Cycles) (h)

NARloy-Z (wrought) 9130 351 90 117 22 3,601 12

GRCop-84 (extruded) 8756 290 120 155 20 10,990 250

Material Density 

Thermal 

Conductivity 

Yield 

Strength 

Tensile 

Strength 

Elastic 

Modulus 

CTE 

×10–6

Time to 1% 

Strain at 900 °C

σ = 40 MPa

(kg/m3) (W/m °C) (MPa) (MPa) (GPa) (1/°C) (h) 

NiCrAlY 5500 13 49 69 135 18 32 

NiAl 5900 80 78 141 157 15 0.3 
NASA/TM2002-211561 3 

Fig. 1.—(a) Geometry and convective heat transfer boundary conditions, (b) rough interfaces.

X

Y

tgas = 3,277 °C

h = 12,363 W/m2 °C

50.8 μm

GRCop-84

Bond Coat

(Cu)

Top coat

(NiAl or NiCrAlY)

1.016 mm

Coating 

thickness

(a)

(b)

Amplitude

Wavelength

Valley Peak

Asperity

slopes

Rough interfaces

Line through

top coat valley

Line through

tLH2 = –176 °C top coat peak

h = 58,283 W/m2 °C

tLH2 = –176 °C

Top coat

Bond coat

Substrate

coated only with NiCrAlY at lower hot gas temperatures [10]. The bond coat material for both 

coatings is a 50.8 μm pure Cu. The hot outer surface temperature of the NiCrAlY top coat 

increases rapidly for higher thicknesses, starting at 593 °C for a 25.4 μm coating thickness to 

993 °C for a 228.6 μm coating thickness. The temperature of the GRCop-84 along the GRCop/Cu 

interface decreases from 513 to 411 °C for coating thicknesses of 25.4 μm and 228.6 μm, 

respectively. The resulting temperature difference observed through the thickness of the coating 

increases from 50 to 444 °C for a coating thickness of 25.4 and 228.6 μm, respectively. The 

variation in temperature of the GRCop-84 with the NiAl top coat is not as pronounced as the 

NiCrAlY top coat due to its higher thermal conductivity. The effect of the high NiAl thermal 

conductivity is to reduce the hot wall coating temperature with a corresponding reduction in the 

temperature difference through the thickness of the coating. Furthermore, the NiAl top coat 

increases slightly the temperature along the GRCop-84/Cu interface as well as the GRCop cold 

wall temperature, as shown in Fig. 2(b), compared to the NiCrAlY top coat. For example, at a 

coating thickness of 101.6 μm, the overall temperature difference through the thickness for the 

NiAl coating is 164 °C compared to 400 °C for the NiCrAlY, (a factor of 2). In addition, the NiAl 

hot surface coating temperature reaches only 564 °C compared to the 758 °C for the NiCrAlY 

coating. The temperature difference through the coating is only 43 °C for the NiAl compared to 

283 °C for the NiCrAlY, for the same coating thickness of 101.6 μm. 

COOL DOWN RESIDUAL STRESSES 

 The residual stresses developed in the coated GRCop-84 play an important role in the 

production and performance of the coatings. Their precise determination is essential to study the 

coating behavior upon cool down from the processing temperatures and its subsequent behavior 

under the thermo-mechanical loading observed in the rocket chamber environment. The residual 

stresses were determined upon cool down from plasma spraying using the finite element method. 

As the temperature of the coated substrate is dropped to room temperature, thermal residual 

stresses are developed in the various layers. Two-dimensional eight-node quadratic finite element 

meshes were generated for flat interfaces as well as for rough interfaces to model the various 

layers shown in Fig. 1(b). It should be noted that edge effects are not considered in the present 
NASA/TM2002-211561 4 

analysis for simplicity. The assumed bond coat/top coat wavelength is 48 μm with a 10 μm 

amplitude, and the substrate/bond coat roughness is assumed to have a 152 μm wavelength and a 

6 μm amplitude. These values were estimated from microstructures of coated substrates. The 

stresses in each layer in the Y-direction, corresponding to Fig. 1(a) are shown in Table III 

assuming flat interfaces for three top coat thicknesses of 25.4, 101.6, and 228.6 μm, for both alloy 

top coats. The assumed bond coat thickness for both top coats was 50.8 μm thick pure copper 

deposited on a 1.016 mm thick GRCop-84 substrate. The stress distribution is constant in each 

layer. The stresses in the coating in the Y-direction are compressive and decrease with increasing 

coating thickness. The Y-stresses in the substrate are tensile and increase with increasing coating 

thickness. The stress in the copper bond coat is almost independent of the top coat composition 

and thickness. The magnitude of the stresses in the NiCrAlY is about a factor of 2~3 times the 

stress magnitude in the NiAl. For flat interfaces, the stresses in the X-direction are zero. 

Fig. 2. (a)—Temperatures at the various interfaces as a function of 

 the NiCrAlY top coat thickness.

Fig. 2. (b)—Temperatures at the various interfaces as a function of

 the NiAl top coat thickness.

300

400

500

600

700

800

900

1000

0.00 0.05 0.10 0.15 0.20 0.25

Coating thickness (mm)

Coating thickness (mm)

GRCop-Cold Wall

GRCop/Cu-Interface

Cu/NiAl-Interface

NiAl-Hot Wall

GRCop-Cold Wall

GRCop/Cu-Interface

Cu/NiAl-Interface

NiAl-Hot Wall

300

400

500

600

700

800

900

1000

0.00 0.05 0.10 0.15 0.20 0.25

Temperature (°C) Temperature (°C)
NASA/TM2002-211561 5 

Table III. Variation of the Y-direction stress with coating thickness for flat interfaces. 

When the interface roughness is taken into consideration, the stresses near the interfaces are 

perturbed as shown in Figs. 3 and 4 for the NiAl and NiCrAlY top coats, respectively where the 

coating thickness was assumed to be 101.6 μm. The stress distributions along the thickness 

through a valley and a peak corresponding to Fig. 1(b), of the bond coat/top coat interface are 

shown as a function of the normalized distance, x/t, where t is the total substrate and coatings 

thickness, i.e., t = 1.1684 mm. Due to the shallowness of the interface roughness of 

substrate/bond coat, no appreciable stress perturbation was calculated. Along the valley of the 

bond coat/top coat, the stress perturbation is also minimal. But along the peak, there is a sharp 

decrease in the stress in the top coat associated with a corresponding increase in stress in the bond 

coat, but limited to a small region of less than 25 μm. The presence of the roughness also 

introduces X-direction stresses, but of relatively small magnitude on the order of ±5 and ±15 MPa 

for the NiAl and the NiCrAlY coatings, respectively. The tensile stresses occur in the valley of 

the top coat and the compressive stresses occur at the peak of the top coat. Furthermore, the 

presence of the rough interfaces also introduces a shear stress along the slopes of the asperities 

with magnitudes of ±38 and ±77 MPa along the bond coat/top coat interfaces for the NiAl and 

NiCrAlY coatings, respectively, (see Fig. 1(b)). 

Fig. 3. Y-direction post processing stress variation for a 101.6 μm 

 rough interfaces.

–100

–80

–60

–40

–20

0

20

40

60

0.80 0.85 0.90 0.95 1.00

Normalized distance x/t

Stress (MPa)

Flat

Valley

Peak

Total thickness t = 1.1684 mm

Substrate Bond Coat Top Coat

Coating 

Thickness

Substrate 

Stress σyy

Bond Coat 

Stress σyy

Top Coat 

Stress σyy

Substrate 

Stress σyy

Bond Coat 

Stress σyy

Top Coat 

Stress σyy

(μm) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa)

25.4 0.2 30 –53 2 31 –148

101.6 3 29 –47 11 32 –121

228.6 7 29 –39 19 32 –93

NiAl Coating NiCrAlY Coating
NASA/TM2002-211561 6 

Fig. 4. Y-direction post processing stress variation for a 101.6 μm 

 NiCrAlY top coat with flat and rough interfaces.

0.80 0.85 0.90 0.95 1.00

Normalized distance x/t

Stress (MPa)

Total thickness t = 1.1684 mm

Substrate Bond Coat Top Coat

–250

–200

–150

–100

–50

0

50

100

Flat

Valley

Peak

HEAT-UP THERMAL STRESSES 

 The steady-state stresses developed after exposing the coated GRCop-84 to a simulated rocket 

combustion chamber environment and subjected to the convective heat transfer boundary 

conditions shown in Fig. 1(a) were calculated subsequent to the build-up of the residual stress 

after plasma spraying for only a 101.6 μm thick top coating. It is considered that these simulations 

assume that the liner surfaces are flat. Realistic simulations would require curvature effects and 

thickness variation be considered in the analyses. The Y-direction stresses after 15 minutes of 

exposure time are shown in Figs. 5 and 6 for the NiAl and NiCrAlY top coats, respectively. After 

exposure, the coated GRCop-84 reached the steady state temperatures shown in Fig. 2. The 

overall temperature difference is only 164 °C as seen in Fig. 2(b), for the NiAl top coat. Hence, 

the resulting stress distribution in the GRCop-84 substrate (Fig. 5) reveals a bending stress due to 

the effects of the thermal gradient producing tensile stresses at the cooled surface and compressive 

stresses towards the bond coat hotter region. The stresses in the bond coat are almost zero, 

showing a reduction of the stresses from the cool down conditions after processing (Fig. 3). The 

stresses in the NiAl top coat are now tensile (Fig. 5) compared to the compressive post-processing 

stresses (Fig. 3) and have a slight gradient. Nevertheless, the tensile stresses in the NiAl coating 

are much smaller than the room temperature fracture stress of about 300 MPa [11]. The presence 

of the rough surface results in a sharp increase of the top coat tensile stresses along the bond coat 

interface at the peak of the asperity, while through the valley no appreciable stress perturbation is 

observed. 

 For the NiCrAlY coating, with the larger temperature difference shown in Fig. 2(a) and lower 

yield stress (Table I), plastic deformation occurred in the coating outer region causing an 

unloading of the stress along the outer surface. The stress variation in the NiCrAlY coating is 

tensile at the bond coat/NiCrAlY interface, which decreases to a high compressive stress of 

–390 MPa before increasing slightly to reach –150 MPa at the outer surface (Fig. 6). The stresses 

through the bond coat are again close to zero, and the stress distribution in the substrate follows a 

similar trend as the NiAl coating, (Fig. 5). 

 Again, the presence of the interfacial asperities introduces X-direction stresses along the valley 

and the peak path with tensile stresses along the peak and compressive stresses along the valley 

with a magnitude of 5 and 20 MPa, for the NiAl and NiCrAlY coatings, respectively. The 

introduction of interfacial roughness leads to shear stresses along the slopes of the asperities. The 
NASA/TM2002-211561 7 

00 0.20 0.40 0.60 0.80 1.00 –60

–40

–20

0

20

40

60

80

0.

At 25 °C, after plasma spraying

Total thickness t = 1.1684 mm

Top

coat Bond coat

Fig. 5. Y-direction stress as a function of the normalized distance for a NiAl

 top coat with flat andrough interfaces.

Normalized distance x/t

Stress (MPa)

Substrate

Flat

Valley

Peak

0.00 0.20 0.40 0.60 0.80 1.00

At 25 °C, after plasma spraying

Total thickness t = 1.1684 mm

Top

Bond coat coat

Stress (MPa)

Substrate

Flat

Valley

Peak

Fig. 6. Y-direction stress as a function of the normalized distance for a 

 NiCrAlY top coat with flat and rough interfaces.

Normalized through the thickness distance x/t

–500

–400

–300

–200

–100

0

100

200
NASA/TM2002-211561 8 

shear stress magnitudes are 22 and 61 MPa for the NiAl and NiCrAlY coatings, respectively. The 

direction of shearing stresses along the slopes is reversed during heat up cycle as compared to the 

cool down shearing direction thereby leading to an alternating shear stress. 

SUMMARY 

 A steady-state heat transfer analysis of coated GRCop-84 revealed that both coatings provide 

adequate protection of the substrate. The NiAl coating’s high thermal conductivity provided 

protection almost independent of the coating thickness. The temperature of the substrate hot wall 

temperature with a NiAl coating decreased by only 15 °C for a coating thickness ranging from 

25.4 to 228.6 μm. The through thickness temperature difference is also small relative to the 

difference for the NiCrAlY top coat. In contrast, the NiCrAlY coating provides a better heat 

shield to the GRCop-84 substrate due to its low thermal conductivity, but at the expense of a high 

temperature difference in the coating reaching almost 578 °C at a coating thickness of 228.6 μm. 

 The residual stresses developed during cool down from plasma spraying showed that the Ydirection stresses are compressive for both coatings, while the stresses in the copper bond coat and 

the GRCop-84 are tensile. The stress magnitude for the NiAl coating is almost a factor of 2 

smaller than the stresses for the NiCrAlY top coat. The presence of interfacial asperity introduces 

a X-direction stress along the peak and valley of the asperities as well as a shear stress along the 

slopes of the asperities. The stress perturbation is limited to a small region of less than 25 μm for 

a 101.6 μm coating. 

 The through thickness thermal stresses developed after exposure to a simulated rocket liner gas 

temperature are tensile in the NiAl top coat. The stress distribution for the NiCrAlY coatings is 

more complex due to the large thermal gradient developed from the low conductivity of the 

coating. The stress gradient in the NiCrAlY coating changes dramatically after heat up, and 

plastic yield occurs in the outer region of the NiCrAlY coating. Again, the presence of rough 

interfaces perturbs the Y-stress distribution as well as introducing X-direction stress along the 

peaks and valleys and shear stresses along the slopes. 

REFERENCES 1

S. Elam, J. Lee, R. Holmes and F. Zimmerman, “Lightweight Chambers for Thrust 

Assemblies,” Presented at the 52nd International Astronautical Congress, 1–5 Ocober 2001, 

Toulouse, France. 2

D. Ellis and D. Keller, “Thermophysical Properties of GRCop-84,” NASA/CR2000-

210055, NASA Glenn Research Center, Cleveland, OH, June 2000. 3

D.L. Ellis and G.M. Michal, “Mechanical and Thermal Properties of Two Cu-Cr-Nb Alloys 

and NARloy-Z,” NASA CR–198529, NASA Lewis Research Center, Cleveland, OH, Oct. 1996. 4

P.A. Siemers and R.L. Mehan, Mechanical and Physical Properties of Plasma Sprayed 

Stabilized Zirconia,” GE Technical Information Series, Report No. 83CRD149, July 1983. 5

R.D. Noebe, R.R. Bowman, and M.V. Nathal, “Physical and Mechanical Properties of the B2 

Compound NiAl,” International Materials Reviews, 38 [4] 193–232 (1993). 6

R.A. Miller and C.E. Lowell, “Failure Mechanisms of Thermal Barrier Coatings Exposed to 

Elevated Temperature,” Thin Solid Films, 95 [3] 265–273 (1982). 7

G.C. Chang, W. Phucharoen and R.A. Miller, “Behavior of Thermal Barrier Coatings for 

Advanced Gas Turbine Blades,” Surface and Coatings Technology, 30 13–28 (1987). 8

B.L. Ferguson, G.J. Petrus and T.M. Krauss, “Modeling of thermal barrier coatings,” NASA 

CR–195365, NASA Lewis Research Center, Cleveland, OH, Nov. 1992. 

9

M.J. Pindera, J. Aboudi and S.M. Arnold, “The Effect of Interface Roughness and Oxide Film 

Thickness on the Inelastic Response of Thermal Barrier Coatings to Thermal Cycling,” NASA 

TM1999-209770, NASA Glenn Research Center, Cleveland, OH, Dec. 1999. 10R. Holmes, Private Communications, NASA Marshall Space Flight Center, Huntsville, AL, 

April 2001. 11S.V. Raj, R.D. Noebe, and R. Bowman, “Observations on the Brittle to Ductile Transition 

Temperatures of B2 Nickel Aluminides With and Without Zirconium,” Scripta Metall., 23 

2049–2054 (1989). 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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14

Residual Stresses in Thermal Barrier Coatings for a Cu-8Cr-4Nb

Substrate System

Louis J. Ghosn and Sai V. Raj

Finite element method; Residual stress; Rocket engines; Surface roughness;

Plasma spraying; Thermal stresses; Coating

Unclassified -Unlimited

Subject Category: 39 Distribution: Nonstandard

Prepared for the 26th Annual International Conference on Advanced Ceramics and Composites sponsored by the

American Ceramic Society, Cocoa Beach, Florida, January 13–18, 2002. Louis J. Ghosn, Ohio Aerospace Institute,

Brook Park, Ohio; and Sai V. Raj, NASA Glenn Research Center. Responsible person, S.V. Raj, organization code 5160,

216–433–8195.

Analytical calculations were conducted to determine the thermal stresses developed in a coated copper-based alloy,

Cu-8%(at.%)Cr-4%Nb (designated as GRCop-84), after plasma spraying and during heat-up in a simulated rocket engine

environment. Finite element analyses were conducted for two coating systems consisting of a metallic top coat, a pure

copper bond coat and the GRCop-84. The through thickness temperature variations were determined as a function of

coating thickness for two metallic coatings, a Ni-17%(wt%)Cr-6%Al-0.5%Y alloy and a Ni-50%(at.%)Al alloy. The

residual stresses after low-pressure plasma spraying of the NiCrAlY and NiAl coatings on GRCop-84 substrate were also

evaluated. These analyses took into consideration a 50.8 mm copper bond coat and the effects of an interface coating

roughness. The through the thickness thermal stresses developed in coated liners were also calculated after 15 minutes of

exposure in a rocket environment with and without an interfacial roughness.