Proceedings of the World Congress on Engineering 2011 Vol III

WCE 2011, July 6 - 8, 2011, London, U.K.

Numerical Simulation of Thermal Barrier Coating

System under Thermo-mechanical Loadings
A. Moridi, M. Azadi, G.H. Farrahi

 Aluminum alloy cylinder heads are exposed to two types

Abstract— In the present paper, numerical simulation of of loading with low and high frequency. High frequency
thermal barrier coating system under thermo-mechanical loadings include combustion pressure on the combustion
loadings is performed, using the finite element method in chamber and low frequency loadings include initial static
ABAQUS software. The base material is Aluminum-silicon
alloy, A356.0 which is widely used in automotive components
forces (such as bolts forces) and thermal expansion. Due to
such as diesel engine cylinder heads. Thermal barrier coatings these loadings, cylinder heads should have suitable material
(TBCs) are applied to combustion chamber in order to reduce properties to endure high cycle fatigue (HCF) and thermo-
fuel consumption and pollutions and also improve fatigue life mechanical fatigue (TMF). In thermo-mechanical loading
of components. conditions, a combination of modern cooling methods or
The roughness effect of coating layers on stress distribution protective coatings such as TBCs can be used which leads to
of test specimens is investigated. Semi-ellipsoid roughness of
lower thermal stresses due to lower temperature gradient.
the interfaces between substrate/bond coat and bond coat/top
coat are simulated to get the stress distribution by considering To model and predict the fatigue life, different failure
different wave lengths and roughness amplitudes. Mutual mechanisms of TBC systems must be considered. A major
influence of waves positioning (in phase and out of phase) is weakness in the system, is the interfaces between
also studied in present investigation. Results show that substrate/BC and BC/TC. These interface regions undergo
separation of the TBC system from substrate (in cylinder heads high stresses due to the mismatch of thermal expansion
application) is more probable than separation of BC and TC between materials and due to interface roughness [6].
due to higher stresses in substrate/BC interface. Moreover the
magnitude of stress increases when the roughness amplitude Another failure mechanism is the development of TGO at
enhances and wave length shortens which leads to crack the interface formed as a result of bond coat oxidation at
initiation in TBC system. Crack propagation and failure in about 900 oC [7].
TBCs accelerate when the peak regions of asperities position The purpose of the present paper is to investigate the
on each other, leading to more tensile zones in BC layer. influence of the interfaces roughness on stress distribution
by using finite element (FE) modeling of TBC systems. FE
modeling of TBC systems on aluminum alloys is rare and
Index Terms—Finite element method, thermal barrier
coating, roughness profile, thermo-mechanical loading
most researches were about simulation of coating on super
alloys. High temperature application of these alloys cause
I. INTRODUCTION forming of TGO layer between BC and TC which is the
vital failure mechanism. Bengtsson and Persson [8] and also
T HE thermal barrier coatings (TBCs) are multi-layer
material systems which can be applied to the
combustion chamber of diesel engines. This may increase
Widjaja et al. [9] presented FE analysis for the development
of residual stresses during spraying of zirconia-based
thermal barrier coatings. It was assumed a flat interfaces
the thermal efficiency, improve the fatigue life, reduce some
hypothesis between dissimilar materials, in order to simplify
emissions such as hydrocarbons and save the fuel
the approach.
consumption [1-4]. A typical TBC system consists of the
The time-dependent model of CMSX-4 was studied by
substrate, metallic bond coat (BC), mostly made of Ni-Cr-
Schubert et al. [10]. The development of cracks at the
Al-Y, a thermally grown oxide (TGO) formed as a result of BC/TGO interface has been simulated using cohesive zone
BC oxidation, and ceramic top coat (TC), mostly Yttrium elements. The effect of curvature and height of the interface
stabilized Zirconium (YSZ) with composition ZrO2- asperity on stresses formation during the service was
8%Y2O3. These layers were applied by Air Plasma Spraying examined by Hsueh and Fuller [11]. A numerical simulation
(APS) to substrates [5]. of crack development within APS TBC systems was
performed by Bialas [6] by modeling the TGO thickening
Manuscript received March 06, 2011; revised April 05, 2011. This work and creep deformation of all system constituents and using
is supported in part by the Irankhodro Powertrain Company (IPCo.) under two dimensional periodic unit cell to examine the effect of
project number of 450008. interfacial asperity on stress distribution and subsequent
A. Moridi is MSc student at Material Life Estimation and Improvement
Laboratory, School of Mechanical Engineering, Sharif University of
delamination of APS TBC.
Technology, Tehran, Iran (e-mail: moridi@mech.sharif.ir). By considering a homogenous type for the temperature
M. Azadi is PhD candidate at Material Life Estimation and Improvement distribution, Sfar et al. [12] modeled the BC/TC interface
Laboratory, School of Mechanical Engineering, Sharif University of roughness, the volume growth of the oxide layer, the cyclic
Technology, Tehran, Iran (e-mail: azadi@mech.sharif.ir).
G.H. Farrahi is Professor at School of Mechanical Engineering, Sharif loading and the creep relaxation to predict their effects on
University of Technology, Tehran, Iran (Corresponding author: phone: 98- the stress distribution. Liu et al. [13] performed
21-66165533; fax: 98-21-66000021; e-mail: farrahi@sharif.edu).

ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2011 Vol III
WCE 2011, July 6 - 8, 2011, London, U.K.

experimental and numerical life prediction of thermally for modeling. The thermal and mechanical loadings and
cycled thermal barrier coatings by considering different boundary conditions are shown in Figs. 3 and 4.
thicknesses for top coat. A new step in the objective to The FE model is shown in Fig. 4 where multi point
continue the development of the TBCs performance was constraint condition is considered in the bottom face.
presented by Ranjbar-Far et al. [14]. In their study, the finite Symmetric condition is applied for the top face, thermal
element code ABAQUS was used by considering a non- load is applied for the right face and mechanical load is
homogenous temperature model to study the thermo- applied to the bottom face. The transient de-coupled
mechanical behavior of the thermal barrier coatings system. temperature-displacement analysis is used in present
The results show that the oxide formed on rough TC/BC investigation. Finer mesh is used at interface layers where
interface during service has an intrinsically different excessive gradient of temperature and stress may occur.
morphology and different growth rate compared to those The TBC system is composed of A356 substrate, Ni-Cr-
formed when considering a homogenous temperature. Al-Y bond-coat and ceramic top-coat (ZrO2-8%Y2O3). For
In the present paper, the interface roughness effect on material properties, the cyclic hardening characteristic is
stress distribution of A356.0 with TBC system is performed expressed by the isotropic hardening law. The non-linear
under thermo-mechanical loadings. As a result, thermo- kinematic hardening component describes Bauschinger
mechanical stress distributions for different roughness with effect by explaining the translation of the yield surface in
various amplitudes and wave lengths and also mutual stress space through the back-stress. This law is defined as a
roughness influence of substrate/BC and BC/TC interfaces supplement combination of a linear term and a relaxation
(in phase and out of phase) are presented. term, which presents the non-linearity. The material
properties are listed in Table 1 and for complementary data,
II. FE SIMULATION refer to [7,14,15,16].
The load cycle is composed of thermal and mechanical
Many efforts have been done to numerically investigate
cycling in synchronized out-of-phase (OP) triangular waves.
stress development in TBC systems. The interface between
The temperature varying from 100 to 250 oC in 10 minutes,
a plasma sprayed TC and BC, has a complex shape due to
is applied on right face of the specimen as shown in Fig. 3.
manufacturing process. In spite of this, often times a two
The mechanical strain amplitude varying ±0.5 percent, is
dimensional unit cell symbolizing a single asperity has been
applied on bottom face of the specimen as shown in Fig. 3.
used to be representative for the entire surface area of stress
field [6]. This is because of long calculation times and The OP thermo-mechanical loading is shown in Fig. 4. The
difficulties of generating a suitable mesh in the realistic mentioned loading simulates cylinder heads at the most
simulation. In a 2D approach, the interface shape can be severe engine condition [5]. For models considering the
simplified as sinusoidal, semicircle, semi-ellipsoid, with absence of crack propagation, the influence of the thermal
different amplitude and wave length. In order that the cyclic loading on stress distribution is not important [7],
modeled segments of the TBC system behave as if it were a therefore, a single cycle is considered.
part of a much greater medium, a combination of symmetry
boundary condition and periodic boundary condition must
be applied.
Although in the most published works [6,7,12,14], only
the roughness of BC/TC is studied but both interfaces are
considered in this paper as an innovation. This is because of
a type of failure observed in thermal shock test (Fig. 1).
This thermal shock test has been performed on 3 different
thicknesses of TC. This experiment was carried out by
repeating flame heating of the specimens to a specific
temperature and abruptly quenching at water. Failure
analysis shows that coating layers including both BC and
Fig. 1. Specimens after separation of coating layers from substrate in
TC were separated from the base material. However, on one thermal shock test
of the specimens with thinner TC thickness, some parts of
BC layer was still remained. This can be a good reason to
consider the roughness of substrate/BC interface in the
model and to study the stress distribution there. Interface
profile between substrate/BC and BC/TC has a random
nature, as it is shown in Fig. 2.
In addition, due to the considered temperature condition
which is below 250 oC, the TGO cannot be formed [7] and
thus, TGO layer is not taken into account.
In order to improve the modeling of the multilayer
system, a micrograph of the cross section and surface profile
of the substrate/BC and BC/TC interface, extracted by
image processing, were employed (Fig. 2). As mentioned,
single asperity is used instead of the entire roughness profile
Fig. 2. Surface profile of the coated specimen

ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2011 Vol III
WCE 2011, July 6 - 8, 2011, London, U.K.

TABLE I
MATERIAL PROPERTIES OF SUBSTRATE, BC AND TC LAYERS

Material Property Base Material BC Layer TC Layer

72 183
at 25 oC at 25 oC
Young modulus (GPa) 17.5
[17] [7]
at different at 25 oC
58 152
temperatures [7]
at 260 oC at 400 oC
[17] [7]
20.6 10.3
at 50 oC at 100 oC
9.68
[18] [7]
Expansion coefficient at 25 oC
22.2 11.3
(1/C) [X 10-6] [7]
at 200 oC at 200 oC
at different 9.70
[18] [7]
temperatures at 200 oC
23.0 12.5
[7]
Fig. 3. Thermal and mechanical loadings applied to the specimen at 400 oC at 400 oC
[18] [7]
Poison's ratio 0.33 [17] 0.30 [7] 0.20 [7]
Conductivity (W/mK) 190.0 [18] 10.8 [5] 0.9 [5]
Specific heat (J/kgK) 963 [17] 450 [5] 505 [5]
Density (kg/m3) 2685 [17] 7380 [5] 3610 [5]

Substrate/BC Interface, in BC Layer

400 Substrate/BC Interface, in Substrate Layer
BC/TC Interface, in BC Layer
300 BC/TC Interface, in TC Layer
Stress in y-direction (MPa)

200

100

-100

-200

-300
0 0.005 0.01 0.015 0.02 0.025 0.03
Distance (mm)
Fig. 5. Thermo-mechanical stresses in y-direction versus the distance of the
profile, for in-phase roughness, wave length = 60 (micron) and amplitude =
15 (micron)
Fig. 4. FE model of the specimen with meshed TBC system
In Fig. 6, the IP and OP positioning of interface waves
III. RESULTS AND DISCUSSION roughness are compared for a defined wave length and
Thermo-mechanical stresses in y-direction which is amplitude. At the BC/TC interface, the stress for both OP
through the coating thickness and along the interfaces of and IP roughness is similar. However, at the substrate/BC
substrate/BC and BC/TC are shown in figures for different interface, the maximum tensile stress in y-direction is
wave lengths and amplitude of semi-ellipsoid profile of the considerably lower in OP positioning of interface waves.
interfaces. Normal stresses lead to more probable mode I Although tensile stress in OP positioning of waves is less
fracture; furthermore delamination of TBC is due to the than IP, but the tensile zone of peaks in substrate/BC and
effect of normal stress in y-direction, thus only this BC/TC merge in the middle of BC layer. This can provide a
component of stress is studied. Moreover, in-phase (IP) and suitable condition for crack propagation.
out-of-phase (OP) types for substrate/BC and BC/TC The amplitude and wave length effects on the stress
interfaces waves are considered for comparison purpose. distribution in BC layer are shown in Figs. 7-10. For wave
Fig. 5 shows the stress level in BC, TBC and substrate. length effect, in order to make a better comparison, the
Values of yield strength for TBC vary from 10 to 100 MPa normalized distance of the profile is used, where the
while for BC is equal to 270 MPa [7,14]. According to the distance is divided by the wave length,.
layers yield strength, the BC stress, both in substrate/BC and Figs. 7 and 8 show the influence of the interface
BC/TC is much higher than its yield value. Thus, that can be amplitude on stress distribution. The maximum tensile stress
a reason for crack initiation that results the separation of BC at the peak in substrate/BC interface rises from 357 to 518
layer from the base material and also from TC which can be MPa when the roughness amplitude changes from 15 to 45
considered as a failure mechanism in TBC system. This is micron. Simultaneously, the compressive stress region
confirmed by observation in thermal shock test. In the increases and extends. These results are in good agreement
BC/TC interface, at TC side, the stress value is very low and with those given by Bialas [6] and Hsueh et al. [11].
has a compressive nature in most of distances. Thus for Stresses in the BC/TC interface are less than those of
other cases only the stress distribution in BC layer, both in substrate/BC and do not change considerably by varying
substrate/BC and BC/TC is considered. amplitude.

ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2011 Vol III
WCE 2011, July 6 - 8, 2011, London, U.K.

Figs. 9 and 10 show the influence of wave length 600

Wave length=60, Amplitude=15, BC/TC Interface, in BC Layer

magnitude on stress distribution. The maximum tensile 500

Wave length=60, Amplitude=30, BC/TC Interface, in BC Layer
Wave length=60, Amplitude=45, BC/TC Interface, in BC Layer
stress at the peak falls from 518 to 419 MPa when the wave

Stress in y-direction (MPa)

400
length magnitude changes from 60 to 120 micron.
300
By the results in Figs. 11-16, it is obvious that the peak
regions of the asperities are subjected to tensile stresses, 200

making possible crack propagation at the asperity interface. 100

However, due to very high compressive stresses in the 0

valley, cracks are not able to propagate into the valley -100

region. As another result, for higher roughness amplitude -200

and lower wave length magnitude, the region of -300
compressive stresses becomes wider and the region of 0 0.005 0.01 0.015 0.02 0.025 0.03
Distance (mm)
tensile stresses becomes smaller leading to a larger TBC
Fig. 8. Thermo-mechanical stresses in y-direction versus the distance of the
lifetime.
profile, at BC/TC interface, for in-phase roughness, in BC layer, different
amplitude and wave length = 60 (micron)

IP Roughness, Substrate/BC Interface, in BC Layer

Wave length=60, Amplitude=45, BC/TC Interface, in BC Layer
400 OP Roughness, Substrate/BC Interface, in BC Layer 600
IP Roughness, BC/TC Interface, in BC Layer Wave length=90, Amplitude=45, BC/TC Interface, in BC Layer
300 OP Roughness, BC/TC Interface, in BC Layer
Stress in y-direction (MPa)

Wave length=120, Amplitude=45, BC/TC Interface, in BC Layer

S tress in y-directio n (M P a)
400
200

200
100

0 0

-100
-200
-200

-400
-300
0 0.005 0.01 0.015 0.02 0.025 0.03
Distance (mm) -600
Fig. 6. Thermo-mechanical stresses in y-direction versus the distance of the 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
profile, for in-phase and out-of-phase roughness, in BC layer, wave length Normalized Distance
= 60 and amplitude = 15 (micron) Fig. 9. Thermo-mechanical stresses in y-direction versus the distance of the
profile, at substrate/BC interface, for in-phase roughness, in BC layer,
Wave length=60, Amplitude=15, Substrate/BC Interface, in BC Layer
600 different wave length and amplitude = 45 (micron)
Wave length=60, Amplitude=30, Substrate/BC Interface, in BC Layer
500
Wave length=60, Amplitude=45, Substrate/BC Interface, in BC Layer
Stress in y-direction (MPa)

Wave length=60, Amplitude=45, Substrate/BC Interface, in BC Layer

400 600
Wave length=90, Amplitude=45, Substrate/BC Interface, in BC Layer
300
Wave length=120, Amplitude=45, Substrate/BC Interface, in BC Layer
Stress in y-direction (MPa)

200 400

100
200
0

-100
0
-200

-300
0 0.005 0.01 0.015 0.02 0.025 0.03
-200
Distance (mm)
Fig. 7. Thermo-mechanical stresses in y-direction versus the distance of the -400
profile, at substrate/BC interface, for in-phase roughness, in BC layer,
different amplitude and wave length = 60 (micron)
-600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized Distance
Fig. 10. Thermo-mechanical stresses in y-direction versus the distance of
the profile, at BC/TC interface, for in-phase roughness, in BC layer,
different wave length and amplitude = 45 (micron)

ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2011 Vol III
WCE 2011, July 6 - 8, 2011, London, U.K.

Fig. 11. Thermo-mechanical stress contour in y-direction, for in-phase

roughness, wave length = 60 (micron) and amplitude = 15 (micron) Fig. 15. Thermo-mechanical stress contour in y-direction, for in-phase
roughness, wave length = 90 (micron) and amplitude = 45 (micron)

Fig. 12. Thermo-mechanical stress contour in y-direction, for out-of-phase Fig. 16. Thermo-mechanical stress contour in y-direction, for in-phase
roughness, wave length = 60 (micron) and amplitude = 15 (micron) roughness, wave length = 120 (micron) and amplitude = 45 (micron)

IV. CONCLUSION
The main object of this work is to improve the
understanding of the stress development in TBC system.
Mutual influence of waves positioning (in phase or out of
phase) along with the variations of wave length and
amplitude, improve the comprehension of the stress
distribution. Cracking and spalling are vital TBCS failure
modes both dependent on the nature and magnitude of
stresses with respect to the relative yield strengths. Note that
the yield strength represents the threshold stress of forming
Fig. 13. Thermo-mechanical stress contour in y-direction, for in-phase micro-cracks.
roughness, wave length = 60 (micron) and amplitude = 30 (micron)
This study puts in evidence that the value of stress in
substrate/BC interface is mostly higher than those of BC/TC
layer. So separation of the TBC system from substrate, in
cylinder heads application, is more probable than separation
of BC and TC, which is more probable in gas turbines
application.
Moreover the magnitude of stress increases when the
roughness amplitude enhances and wave length shortens.
This increasing in stress level leads to cracking in tensile
region but high compressive stresses in the valley do not
allow cracks propagate into the valley region. Cracks tend to
propagate towards tensile zones. OP positioning of
Fig. 14. Thermo-mechanical stress contour in y-direction, for in-phase interfaces enhance a suitable path for crack propagation due
roughness, wave length = 60 (micron) and amplitude = 45 (micron)
to a tensile zone in the middle of the BC layer.

ACKNOWLEDGMENT
Related to thermal shock test, the authors thank
Irankhodro Powertrain Company (IPCo.) for the financial
support (Project No. 450008).

ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2011 Vol III
WCE 2011, July 6 - 8, 2011, London, U.K.

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ISBN: 978-988-19251-5-2 WCE 2011

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)