coatings
Article Thermal Stress Analysis of Environmental Barrier Coatings Considering Interfacial Roughness
Guangwu Fang 1,* , Jiacheng Ren 1, Jian Shi 2, Xiguang Gao 3 and Yingdong Song 3
1 School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243002, China; [email protected] 2 Laboratory of Strength, AECC Sichuan Gas Turbine Establishment, Chengdu 610500, China; [email protected] 3 Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; [email protected] (X.G.); [email protected] (Y.S.) * Correspondence: [email protected]
Received: 10 August 2020; Accepted: 22 September 2020; Published: 30 September 2020
Abstract: A numerical analysis of the effect of roughness interface on the thermal stress in the environmental barrier coatings for ceramic matrix composites was performed. Based on the concept of representative volume elements, a micromechanical finite element model of the coated composites was established. The rough interfaces between the coating layers were described using sine curves. The cooling process after preparation and the typical service conditions for the CMCs component were simulated, respectively. The results show that the rough interface has little effect on the temperature distribution along the depth direction for the studied T/EBC coatings for SiC/SiC composites. The stress concentration occurs at the rough EBC/BC interface, which is prone to cause delamination cracking. Under typical service conditions, the high temperature can eliminate part of the thermal residual stress. Meanwhile, the thermal gradient will cause large thermal stress in the TBC layer and the stress will result in surface cracks. The stress concentrations appear at the peaks and valleys of rough interfaces. The variation range of thermal stress increases with the roughness amplitude and decreases with the wavelength.
Keywords: rough interface; ceramic matrix composite; environmental barrier coating; thermal stress; crack; finite element method
1. Introduction Ceramic matrix composites (CMCs), such as SiC/SiC composites, have the advantages of high specific strength and stiffness, oxidation resistance, as well as excellent mechanical properties at high temperatures. Therefore, it is one of the most potential materials for the hot section components of an aero-engine [1–5]. Under the service conditions of an aero-engine, CMCs components suffer high-temperature, gas erosion, and complex stress state. To prevent environmental degradation of CMCs, similar to the thermal barrier coatings (TBCs) deposited on superalloy components, the environmental barrier coatings (EBCs) were developed to protect the surface of CMCs components [6,7]. Coatings play an important role to prolong the life of hot section components and increase the efficiency of the turbine by enabling higher combustion temperatures in an aero-engine. To figure out the failure mechanism, most research attempts to investigate the damage initiation and related influencing factors by stress analysis. Marcin [8] analyzed the thermal stress distribution in the YSZ/NiCoCrAlY coating system on a nickel-base superalloy using the finite element method. He also
Coatings 2020, 10, 947; doi:10.3390/coatings10100947 www.mdpi.com/journal/coatings Coatings 2020, 10, 947 2 of 12 considered the effect of delamination cracks on stress distribution. Wang et al. [9,10] calculated the thermal residual stress inside a La2Zr2O7/8YSZ coating system deposited on the surface of the superalloy (GH4169) using the birth and death element technology. They simulated the thermal stress under the typical service conditions for the turbine and discussed the mechanism of crack initiation and propagation. Yu et al. [11] used the finite element method to simulate the effect of the thickness of thermally grown oxides (TGO) on the stress distribution in TBCs. Abir et al. [12] established an analytical method for thermal residual stress in functionally graded coatings and discussed the influence of layers’ properties on the distribution of thermal residual stress. Their results showed that the thermal expansion mismatch between the components and the stress concentration caused by the microstructure (such as the uneven interface between the layers) are the main sources of the damage. Therefore, a lot of studies [13–15] had been carried out to analyze the failure mechanism by simulating the effect of rough interface on stress distribution in the different coated systems. Most of the mentioned studies focused on the coatings deposited on superalloy substrates. As the application of CMCs grows, coatings for CMCs have attracted more and more attention [16,17]. Lee et al. [18] qualitatively analyzed the thermal residual stress of a Si/mullite/BSAS coating deposited on SiC/SiC composites. Zhang et al. [19] prepared a SiC/mullite/Yb2SiO5 coating on the surface of SiC/SiC composites and investigated the relations between the properties and microstructures of the coating. However, there are still few modeling studies on the coatings of CMCs comparing to the coating systems for superalloy. Abdul-Aziz et al. [20] developed a finite element model for the residual stress of Si/mullite/BSAS coating on SiC/SiC composites was analyzed by the finite element method. Heveran et al. [21] carried out a finite element simulation of residual stresses in various coating systems for SiC/SiC composites. It should be noted that the interface between each coating layer is simplified as a flat interface in all the mentioned models. In general, the material system of coatings for CMCs is significantly different from that of conventional superalloys [22]. Since the damage mechanism of EBCs is directly related to the material system and the rough interface between coating layers is an important damage source, an appropriate model for EBCs should take the specific material system and rough interface into account. In the present work, the residual stress and thermal stress inside the latest generation coating system were simulated and analyzed, and the influence of rough interface on the stress distribution was analyzed.
2. Modeling Methodology
2.1. Coating System and Material Propperties At present, the EBCs material system has been developed through four generations. The fourth one, namely the T/EBC system [23], usually consists of the following parts: (1) The surface layer is a thermal barrier coating (TBC), which is mainly composed of ceramic materials with low thermal conductivity, such as La2Zr2O7 and Gd2Zr2O7. It works as a thermal barrier; (2) Under the TBC is an EBC layer which is usually composed of the rare earth silicate with excellent water oxygen corrosion resistance and phase stability, such as ReSiO5 and Re2Si2O7. This layer mainly provides protections from environmental degradations such as oxidation and corrosion. (3) Between the EBC and substrate is a bonding layer (BC) which should have good thermal expansion matching and chemical compatibility with EBC and CMCs. The Si layer is the most popular one. This T/EBC coating system is chosen as the investigative object here. The coating consists of three layers: La2Zr2O7 is used for TBC, Yb2Si2O7 for EBC, and Si for BC. The coatings are usually deposited by air plasma spray (APS) process and usually contain a lot of pores. Thus, their properties may be very different from those of the dense materials. Referring to the literatures [10,19,21,24], the thermal-mechanical properties of the coating layers were listed in Table1. The plain-woven SiC/SiC composites were selected as the CMCs substrate. This material system has a relatively mature preparation process. And their mechanical properties had been investigated by many experimental and numerical studies. This paper focuses on the stress analysis of the coatings, Coatings 2020, 10, 947 3 of 12
so the CMCs substrate was simplified as an orthotropic homogeneous material. The thermal-mechanical Coatingsproperties 2020,listed 10, x FOR in TablePEER 2REVIEW were taken from the literature [ 25]. Since a two-dimensional analysis model3 of 12 is established in this paper, only the properties in the 1–2 plane, as shown in Figure1, were necessary. The plain-woven SiC/SiC composites were selected as the CMCs substrate. This material system has a relativelyTable mature 1. Thermal-mechanical preparation process. properties And their of the mechanical constituents properties in composites had coating. been investigated by many experimental and numerical studies. This paper focuses on the stress analysis of the Constituents E/GPa v k/(W m 1 K 1) α/( 10 6K 1) coatings, so the CMCs substrate was simplified as an orthotropic· − · − homogeneous× − − material. The thermal-mechanicalTBC properties (La2Zr2O7 ) listed in 63 Table 2 0.25 were taken 0.87 from the literature 4.25 [25]. Since a two- dimensional analysisEBC model (Yb2Si 2isO established7) 150 in this paper, 0.28 only the 3.5 properties in the 5.5 1–2 plane, as shown BC (Si) 97 0.21 14.23 3.5 in Figure 1, were necessary.
TableTable 2. 2. ThermalThermal-mechanical-mechanical properties properties of of 2D 2D woven woven SiC/SiC SiC/SiC composites. composites.
1 1 1 1 6 1 6 1 E1/GPa E2/GPa v12 G12/GPa k1/(W m−1 K−1 ) k2/(W m −1K −1) α1/( 10 K−6 −)1 α2/( 10 −K6 −1) E1/GPa E2/GPa v12 G12/GPa k1/(W·m· − ·K· −) k2/(W·m· − ··K − ) α1×/(×10− K− ) α2/(×10× − K− ) 238.37238.37 81.40 81.40 0.20 0.20 96.92 96.92 12.1 12.1 8.838.83 4.364.36 3.803.80
FigureFigure 1. 1. MicrostructureMicrostructure of of 2D 2D woven woven SiC/SiC SiC/SiC composites. composites.
2.2.2.2. Model Model Geometry Geometry and and Boundary Boundary Conditions Conditions PreviousPrevious studies studies [19 [19,,21]21] had had shown shown that that the the damages damages inside inside the the coatings coatings are are mainly mainly caused caused by by twotwo factors: factors: i i)) the the mismatch mismatch of of thermal thermal expansion expansion between between layers; layers; ii) ii) the the stress stress concentration concentration caused caused byby the the rough rough interface interface between between layers. layers. It It is is necessary necessary to to establish establish a a micro micro model model considering considering the the rough rough interface.interface. A A two two-dimensional-dimensional model model was was usually usually used used to to analyze analyze t thehe micro micro stress stress inside inside multilayer multilayer coatings.coatings. To To simplify simplify the the model, model, sinusoidal, sinusoidal, triangular, triangular, ellipse, ellipse, and and other other geometric geometric curves curves were were often often usedused to to characterize characterize the the roughness roughness of of the the interface. interface. Here, Here, the the sinusoidal sinusoidal curve curve was was used used to to model model the the interfacesinterfaces insid insidee the the T/EBCs T/EBCs system. system. An An RVE RVE model model with with a a length length of of one one wavelength wavelength was was established. established. TheThe relationship relationship between between roughness and sinusoidal function is shown in EquationEquation (1) [[26].26]. ( Ra = 2 2A RAa π (1) RSm =πλ (1) RSm λ where Ra and Rsm refer to the amplitude and spacing parameters of roughness for the studied interfaces. wTheyhere canRa beand obtained Rsm refer through to the measurement. amplitude and The spacing definitions parameters of surface of roughness roughness forparameters the studied and interfaces.related information They can can be be obtained found in the through literature measurement. [27]. A and λ Therefer definitions to the amplitude of surface and wavelength roughness parametersof the sine function,and related respectively. information can be found in the literature [27]. A and λ refer to the amplitude and wavelengthParticularly, of the the thickness sine function, of TBC, respectively. EBC, and BC layers is 100 µm, and the thickness of the CMCs substrateParticularly, is 1000 µthem. thickness The geometric of TBC, model EBC, of and an BC RVE layers is shown is 100 in μm, Figure and2 .the thickness of the CMCs substrateAs shown is 1000 in μm. Figure The2 ,geometric the following model mechanical of an RVE boundary is shown conditions in Figure were2. applied to the analysis model.As The shown bottom in Figure boundary 2, the of the following CMCs substrate mechanical was boundaryfixed in the conditionsy-direction. were The displacement applied to the in analysisx-direction model. was fixed The at bottom a selected boundary point on of the the bottom CMCs surface. substrate The was periodic fixed boundary in the y- conditiondirection. (PBC) The displacementof Equation (2) in was x-direction applied to was the leftfixed and at right a selected boundary point of the on coated the bottom system. surface. The periodic boundary condition (PBC) of Equation (2) was applied to the left and right boundary of the coated ( ux(λ, y) ux(0, y) = εxλ system. − (2) uy(λ, y) uy(0, y) = 0 uxλ, y− u x 0, y ε xλ (2) uyyλ, y u 0, y 0 where ux and uy are displacements in the x- and y-directions, respectively. εx is the average strain in the x-direction of RVE. In this paper, the equation interaction in ABAQUS was used to carry out the PBC. A piece of Python code was written for this end.
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where ux and uy are displacements in the x- and y-directions, respectively. εx is the average strain in the x-direction of RVE. In this paper, the equation interaction in ABAQUS was used to carry out the PBC.Coatings A piece2020, 10 of, x PythonFOR PEER code REVIEW was written for this end. 4 of 12
Coatings 2020, 10, x FOR PEER REVIEW 4 of 12
FigureFigure 2. 2.Geometric Geometric modelmodel andand mechanicalmechanical boundary boundary conditions conditions of of CMCs CMCs coatings. coatings.
2.3.2.3. SimulationSimulation ProcedureProcedureFigure 2. Geometric model and mechanical boundary conditions of CMCs coatings. As mentioned, the preparation process of EBCs is usually completed at a high temperature. 2.3.As Simulation mentioned, Procedure the preparation process of EBCs is usually completed at a high temperature. Consequently,Consequently, the the thermal thermal residual residual stress stress was was introduced introduced in in the the coatings coatings which which should should be be paid paid As mentioned, the preparation process of EBCs is usually completed at a high temperature. attentionattention to. to. OnOn thethe otherother hand,hand, CMCsCMCs componentscomponents areare mainlymainly usedused underunder high high temperaturetemperature such such as as combustionConsequently, liner and the turbine thermal blades residual in aero-engine. stress was introduced Therefore, in this the paper coatings attempted which should to investigate be paid the combustionattention liner to. On and the turbineother hand, blades CMCs in componentsaero-engine. are Therefore, mainly used this under paper high attempted temperatu reto such investigate as thermal stress induced under the processing and operating conditions as shown in Figure3. the thermalcombustion stress liner induced and turbine under blades the processing in aero-engine. and Therefore,operating thisconditions paper attempted as shown to in investigate Figure 3 . the thermal stress induced under the processing and operating conditions as shown in Figure 3. (1)(1) BeforeBefore thethe EBCsEBCs waswas depositeddeposited onon thethe surfacesurface ofof CMCsCMCs atat 10001000◦ °CC,, allall thetheconstituents constituents werewere assumed(1)assumed Before toto the bebe stressEBCsstress was free;free; deposited on the surface of CMCs at 1000 °C , all the constituents were (2)(2) AfterAfterassumed thethe preparation to be stress thefree; coated system system was was cooled cooled down down to to 0 0°C◦C,, thermal thermal residual residual stress stress is is(2)introduced; introduced; After the preparation the coated system was cooled down to 0 °C , thermal residual stress is introduced; (3)(3) AtAt last,last, the the coated coated system system was was analyzed analyzed under under a typical a typical operating operating condition. condition. The topThe surfacetop surface was (3) At last, the coated system was analyzed under a typical operating condition. The top surface heatedwas heated by 1700 by C1700 high-temperature °C high-temperature gas; the convectivegas; the convective heat transfer heat coe transferfficient iscoefficient 8000 W/(m is2 8000C). was heated◦ by 1700 °C high-temperature gas; the convective heat transfer coefficient is 8000 ·◦ W/(m2·°C ). While the bottom surface of CMCs was cooled by 500 °C air, and the convective heat WhileW/(m the2 bottom·°C ). While surface the bottom of CMCs surface was of CMCs cooled was by cooled 500 ◦C by air, 500 and °C air, the and convective the convective heat heat transfer 2 2 coetransferfficient coefficient is 8000 W is/(m 8000C). W/(m ·2°C ). transfer coefficient is 8000·◦ W/(m ·°C ).
Figure 3. Temperature field of during the simulation process for CMCs coatings. Figure 3. Temperature field of during the simulation process for CMCs coatings.
Figure 3. Temperature field of during the simulation process for CMCs coatings.
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2.4. Numerical Implementation In the present work, the numerical procedure was performed using the commercial software ABAQUS 6.14. The two-dimensional geometry model mentioned earlier was generated using a piece of Python code which can control the interfacial roughness conveniently by several pre-defined parameters. The 4-node plane stress thermally coupled element (CPS4T) has been applied in the FE model as the heat conduction need to considered. A refined mesh through the coating layers was established while the mesh of CMCs substrate is coarse to save computing resources. In particular, the element size in coating layers is ~1 µm. Two coupled temp-displacement steps were defined to simulate the studied procedure. Notably, a predefined temperature field were set at the initial step besides of the mechanical boundary conditions. For step 1, the temperature type boundary conditions were applied to cool the system. For step 2, the surface film conditions in interaction module were defined at both the top and bottom surface to simulate the operation thermal conditions. During the post-processing, the stress distributions along interface or depth were extracted using the path command as shown in Figure3.
3. Results and Discussions According to Equation (1), the amplitude and wavelength of the sinusoidal interface in RVE are corresponding to the amplitude and spacing characteristic of interface roughness, respectively. Therefore, the thermal stresses in RVEs with different wavelengths and amplitudes were simulated to analyze the effect of interface roughness on the stress distribution. According to the literature, the sinusoidal amplitude and wavelength were chosen in the range of 5~20 and 100~400 µm, respectively.
3.1. The Effect of Rough Interface on Thermal Residual Stress Figure4 shows the simulated residual stress of the coated system (roughness parameter λ = 200 µm, A = 10 µm) when it is cooled from 1000 to 0 ◦C. Due to the mismatch of thermal expansion between the different constituents of coatings and CMCs substrate. As seen, large thermal residual stress is caused during the preparation process. For all coating layers, the thermal residual stress along the longitudinal direction (S11) is larger than the other components. This is because there is no constraint in the through-thickness direction. But each layer is constrained by each other in the longitudinal direction as the PBC applied to the coated system. For the coefficients of thermal expansion of each layer, as shown in Tables1 and2, it can be found that: EBC > CMCs > TBC > BC. Thus, the residual tensile stress occurs in the EBC layer while compressive stress occurs in the BC layer. For the thermal residual stress, the maximum tensile stress is 294 MPa and the maximum compressive stress is 443 MPa. As proved, the vertical crack in the EBC layer caused by thermal residual tensile stress (S11) is one of the most common damage modes during the cooling process. Besides, large shear stress (S12) and through-thickness stress (S22) are caused at the EBC/BC interface due to the significant difference of thermal expansion coefficients between the EBC layer and the BC layer. The EBC/BC interface is prone to delamination failure under thermal residual stress. The experimental research [19] found similar phenomena in a Si/mullite/Yb2SiO5 coating system deposited on SiC/SiC composites. No crack in the Si coating (BC layer) was found, while considerable microcracks were found in mullite (EBC layer) and Yb2SiO5 (TBC layer). Additionally, the cracking inside the mullite coating was the most serious. It can also be seen from the figure that the rough interface would cause stress concentration at the peak and valley areas. The maximum tensile stress in the EBC layer and the maximum compressive stress in the BC layer appear at the areas near the peak or valley of the sinusoidal interfaces. At the same time, the through-thickness stress (S22) and shear stress (S12) of each layer also reach the maximum values near the peak or valley. The extreme values of S22 and S12 in the entire coated system appear at the interface between the EBC layer and the BC layer. To figure out the effect of rough interface on the distribution of thermal residual stress, the preparation processes of the coating system with different rough interfaces were simulated. Coatings 2020, 10, 947 6 of 12
Firstly, the longitudinal residual stress S11 along the depth was extracted and compared. The distributions of S11 along two different paths, at the peak and valley of the sinusoidal curve, were plotted in Figure5. As seen, the magnitudes of thermal residual stress in the TBC layer and CMCs substrate are at a comparatively low level. While large thermal residual stress occurs in the EBC layer and BC layer. Comparing Figure5a,b, it can be found that the distribution of thermal residual stress along the depth direction at the valley and trough is very different. Taking EBC as an example, S11 increases with the depth at the peak and decreases at the valley. In theory, the average stress of each layer is almost the same for coatings with different interfacial roughness. However, the fluctuation ranges of stress increase with the amplitude of the sinusoidal interface. Comparing Figure5c,d, it is found that the fluctuation range of S11 in coating layers decreases with the wavelength of the sinusoidal interfaceCoatings for the2020, same 10, x FOR amplitude. PEER REVIEW 6 of 12
Coatings 2020, 10, xFigure FOR PEER 4. The REVIEW contours of thermal residual stress in coated CMCs after processing. 7 of 12 Figure 4. The contours of thermal residual stress in coated CMCs after processing. To figure out the effect of rough interface on the distribution of thermal residual stress, the preparation600 processes of the coating system with different600 rough interfaces were simulated. Firstly, (a) =200m, A= 5m (b) =200m, A= 5m =200m, A=10m =200m, A=10m the longitudinal400 residual stress S11 along the depth was extracted400 and compared. The distributions =200m, A=15m =200m, A=15m of S11 along two different paths, at =200 them, peak A=20 mand valley of the sinusoidal curve, were =200 plottedm, A=20 inm Figure 5. As seen,200 the magnitudes of thermal residual stress in the200 TBC layer and CMCs substrate are at a
comparatively0 low level. While large thermal residual stress0 occurs in the EBC layer and BC layer. Comparing Figure 5a,b, it can be found that the distribution of thermal residual stress along the depth -200 -200
Stress, S11 (MPa)
directionStress, S11 (MPa) at the valley and trough is very different. Taking EBC as an example, S11 increases with the depth at-400 the peak and decreases at the valley. In theory, the-400 average stress of each layer is almost the same for coatingsTBC withEBC differentBC interfacialCMCs roughness. However,TBC the EBC fluctuationBC rangesCMCs of stress -600 -600 increase with0 the amplitude100 200 of the sinusoidal300 400 interface. Comparing0 100Figure 5200c,d, it is300 found that400 the Depth along peak (m) Depth along valley (m) fluctuation range of S11 in coating layers decreases with the wavelength of the sinusoidal interface for the same amplitude.
600 600 (c) =100m, A=10m (d) =100m, A=10m =200m, A=10m 400 =200m, A=10m 400 =300m, A=10m =300m, A=10m =400m, A=10m =400m, A=10m 200 200
0 0
-200 -200
Stress, S11 (MPa) Stress, S11 (MPa)
-400 -400 TBC EBC BC CMCs TBC EBC BC CMCs -600 -600 0 100 200 300 400 0 100 200 300 400 Depth along peak (m) Depth along valley (m)
Figure 5. Variation of thermal residual stress S11 in CMCs coatings along the depth direction: the effect of amplitude at (a) peak path and (b) valley path; the effect of wavelength at (c) peak path and (d) valleyFigure path. 5. Variation of thermal residual stress S11 in CMCs coatings along the depth direction: the effect of amplitude at (a) peak path and (b) valley path; the effect of wavelength at (c) peak path and (d) valley path. As discussed in Figure 4, stress concentration was caused near the EBC/BC interface which is the prone area of delamination damage. The variations of normal stress along the longitudinal direction at the EBC/BC interface with different interfacial roughness were plotted in Figure 6. As seen, the maximum normal stress at the EBC/BC interface appears in the middle for the sinusoidal interface. Figure 6a shows the effect of the amplitude of interface roughness on the stress distribution. For the same wavelength, the fluctuation ranges of normal thermal residual stress at the EBC/BC interface increases with the amplitude. The maximum normal residual stress increases from 10 MPa for A = 5 μm to 130 MPa for A = 20 μm, and the minimum normal residual stress increases from 0.2 MPa for A = 5 μm to 22 MPa for A = 20 μm. Figure 6b shows the effect of wavelength of interface roughness on stress distribution. For the same amplitude, the fluctuation ranges of normal thermal residual stress decrease with the wavelength. When A = 10 μm, the maximum normal thermal residual stress decreases from 90 MPa for λ = 100 μm to 10 MPa for λ = 400 μm. Meanwhile, the minimum normal residual stress decreases from 30 MPa for λ = 100 μm to 2 MPa for λ = 400 μm. It can be seen that the roughness of the interface has a significant effect on the normal thermal residual stress at the EBC/BC interface.
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As discussed in Figure4, stress concentration was caused near the EBC /BC interface which is the prone area of delamination damage. The variations of normal stress along the longitudinal direction at the EBC/BC interface with different interfacial roughness were plotted in Figure6. As seen, the maximum normal stress at the EBC/BC interface appears in the middle for the sinusoidal interface. Figure6a shows the e ffect of the amplitude of interface roughness on the stress distribution. For the same wavelength, the fluctuation ranges of normal thermal residual stress at the EBC/BC interface increases with the amplitude. The maximum normal residual stress increases from 10 MPa for A = 5 µm to 130 MPa for A = 20 µm, and the minimum normal residual stress increases from 0.2 MPa for A = 5 µm to 22 MPa for A = 20 µm. Figure6b shows the e ffect of wavelength of interface roughness on stress distribution. For the same amplitude, the fluctuation ranges of normal thermal residual stress decrease with the wavelength. When A = 10 µm, the maximum normal thermal residual stress decreases from 90 MPa for λ = 100 µm to 10 MPa for λ = 400 µm. Meanwhile, the minimum normal residual stress decreasesCoatings 20 from20, 10, 30x FOR MPa PEER for REVIEWλ = 100 µm to 2 MPa for λ = 400 µm. It can be seen that the roughness8 of 12 the interface has a significant effect on the normal thermal residual stress at the EBC/BC interface.
160 160 (a) =200m, A= 5m (b) =100m, A=10m =200m, A=10m =200m, A=10m =200m, A=15m =300m, A=10m 120 120 =200m, A=20m =400m, A=10m
80 80
Normal stress (MPa) 40 Normal stress (MPa) 40
0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized location Normalized location
Figure 6. Variations of normal thermal residual stress along the EBC/BC interface of CMCs coatings with different (a) amplitude; (b) wavelength. Figure 6. Variations of normal thermal residual stress along the EBC/BC interface of CMCs coatings with different (a) amplitude; (b) wavelength. The variation of tangential thermal residual stress along the longitudinal direction at the EBC/BC interface with different roughness is plotted in Figure7. It can be seen that for the sinusoidal interface, The variation of tangential thermal residual stress along the longitudinal direction at the EBC/BC the maximum and minimum tangential residual stress of the EBC/BC interface appears at the end interface with different roughness is plotted in Figure 7. It can be seen that for the sinusoidal interface, and middle of wavelength, respectively. The absolute values of maximum and minimum tangential the maximum and minimum tangential residual stress of the EBC/BC interface appears at the end stress are approximately equal. Figure7a shows the e ffect of the amplitude of the rough interface and middle of wavelength, respectively. The absolute values of maximum and minimum tangential on the stress distribution. For the same wavelength λ = 200 µm, the fluctuation ranges of tangential stress are approximately equal. Figure 7a shows the effect of the amplitude of the rough interface on thermal residual stress at the EBC/BC interface increases with the amplitude of roughness. The range the stress distribution. For the same wavelength λ = 200 μm, the fluctuation ranges of tangential of tangential thermal residual stress increases from 70 MPa for A = 5 µm to 250 MPa for A = 20 µm. thermal residual stress at the EBC/BC interface increases± with the amplitude± of roughness. The range Figure7b shows the e ffect of the wavelength of the rough interface on stress distribution. With the same of tangential thermal residual stress increases from ± 70 MPa for A = 5 μm to ± 250 MPa for A = 20 amplitude, the fluctuation ranges of tangential thermal residual stress decrease with the wavelength. μm. Figure 7b shows the effect of the wavelength of the rough interface on stress distribution. With When A = 10 µm, the maximum tangential thermal residual stress range decreases from 240 MPa for the same amplitude, the fluctuation ranges of tangential thermal residual stress decrease± with the λ = 100 µm to 90 MPa for λ = 400 µm. It can be seen that the rough interface has a significant effect wavelength. ±When A = 10 μm, the maximum tangential thermal residual stress range decreases from on the tangential thermal residual stress at the EBC/BC interface. ± 240 MPa for λ = 100 μm to ± 90 MPa for λ = 400 μm. It can be seen that the rough interface has a 3.2.significant The Effect effect of Rough on the Interface tangential On Thermal thermal Stress residual under stress Service at the Conditions EBC/BC interface. The CMCs components are usually designed to service under a large thermal gradient. 300 300 Here, the thermal(a) stress distribution =200m, A= 5m of the coated system under(b) a thermal =100m, A=10 gradientm is simulated. =200m, A=10m =200m, A=10m 200 200 Under the given simulation =200 conditions,m, A=15m the variation of temperature with =300 depthm, A=10 inm the coated system =200m, A=20m =400m, A=10m was obtained.100 It can be seen from Figure8 that the temperature100 at the top surface of the TBC layer reaches above 1500 ◦C, and the temperature at the bottom of the TBC layer drops to less than 1200 ◦C. 0 0 The temperature at EBC/BC interface drops to less than 1100 ◦C and the temperature at the top surface of CMCs decreases-100 slightly. It can be seen that the TBC layer-100 works well as a thermal barrier. Figure8a,b
Tangential stress (MPa) Tangential stress (MPa) -200 -200
-300 -300 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized location Normalized location
Figure 7. Variations of tangential thermal residual stress along the EBC/BC interface of CMCs coatings with different (a) amplitude; (b) wavelength.
3.2. The Effect of Rough Interface On Thermal Stress under Service Conditions The CMCs components are usually designed to service under a large thermal gradient. Here, the thermal stress distribution of the coated system under a thermal gradient is simulated. Under the given simulation conditions, the variation of temperature with depth in the coated system was obtained. It can be seen from Figure 8 that the temperature at the top surface of the TBC layer reaches above 1500 °C , and the temperature at the bottom of the TBC layer drops to less than 1200 °C . The temperature at EBC/BC interface drops to less than 1100 °C and the temperature at the top surface of CMCs decreases slightly. It can be seen that the TBC layer works well as a thermal barrier. Figure 8a,b also compare the effects of roughness amplitude and wavelength on temperature variation. It
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160 160 (a) =200m, A= 5m (b) =100m, A=10m =200m, A=10m =200m, A=10m =200m, A=15m =300m, A=10m 120 120 =200m, A=20m =400m, A=10m
80 80
Normal stress (MPa) 40 Normal stress (MPa) 40
0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized location Normalized location
Figure 6. Variations of normal thermal residual stress along the EBC/BC interface of CMCs coatings with different (a) amplitude; (b) wavelength.
The variation of tangential thermal residual stress along the longitudinal direction at the EBC/BC interface with different roughness is plotted in Figure 7. It can be seen that for the sinusoidal interface, the maximum and minimum tangential residual stress of the EBC/BC interface appears at the end and middle of wavelength, respectively. The absolute values of maximum and minimum tangential stress are approximately equal. Figure 7a shows the effect of the amplitude of the rough interface on the stress distribution. For the same wavelength λ = 200 μm, the fluctuation ranges of tangential thermal residual stress at the EBC/BC interface increases with the amplitude of roughness. The range of tangential thermal residual stress increases from ± 70 MPa for A = 5 μm to ± 250 MPa for A = 20 μm. Figure 7b shows the effect of the wavelength of the rough interface on stress distribution. With the same amplitude, the fluctuation ranges of tangential thermal residual stress decrease with the Coatings 2020, 10, 947 8 of 12 wavelength. When A = 10 μm, the maximum tangential thermal residual stress range decreases from ± 240 MPa for λ = 100 μm to ± 90 MPa for λ = 400 μm. It can be seen that the rough interface has a alsosignificant compare effect the e ffonects the of tangential roughness thermal amplitude residual and wavelengthstress at the onEBC/BC temperature interface. variation. It can be seen that the interfacial roughness has little effect on the temperature distribution which can be ignored.
300 300 (a) =200m, A= 5m (b) =100m, A=10m =200m, A=10m =200m, A=10m 200 200 =200m, A=15m =300m, A=10m =200m, A=20m =400m, A=10m 100 100
0 0
-100 -100
Tangential stress (MPa) Tangential stress (MPa) -200 -200
-300 -300 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Coatings 2020, 10, x FOR PEER REVIEW 9 of 12 Normalized location Normalized location can beFigure seen 7. thatVariations the interfacial of tangential roughness thermal residualhas little stress effect along on thethe EBC temperature/BC interface distribution of CMCs coatings which can be ignored.with diff erent (a) amplitude; (b) wavelength. Figure 7. Variations of tangential thermal residual stress along the EBC/BC interface of CMCs coatings
with different0 (a) amplitude; (b) wavelength. 0 (a) (b) TBC TBC 3.2. The Effect100 of Rough Interface On Thermal Stress under 100Service Conditions
EBC EBC
Them) CMCs components are usually designed to servicem) under a large thermal gradient. Here, the
200 200 thermal stress distribution of the coated system under a thermal gradient is simulated. Under the
Depth( BC Depth( BC given simulation conditions, =200m, A= the5m variation of temperature with depth in the coated system was 300 300 =100 m, A=10 m obtained. It can be seen from=200m, A=10Figurem 8 that the temperature at the top surface =200m, A=10 of mthe TBC layer reaches =200m, A=15m CMCs =300m, A=10m CMCs =200m, A=20m =400m, A=10m above 1500400 °C , and the temperature at the bottom of the400 TBC layer drops to less than 1200 °C . The 1000 1100 1200 1300 1400 1500 1600 1000 1100 1200 1300 1400 1500 1600 temperature at EBC/BCTemperature( interfaceºC) drops to less than 1100 °C and the Temperature(temperatureºC) at the top surface of CMCs decreases slightly. It can be seen that the TBC layer works well as a thermal barrier. Figure Figure 8. Variation of temperature versus depth of CMCs coatings under service conditions with 8a,b also compare the effects of roughness amplitude and wavelength on temperature variation. It different (a) amplitude; (b) wavelength.
Figure 8. Variation of temperature versus depth of CMCs coatings under service conditions with Figuredifferent9 shows (a) amplitude the predicted; (b) wavelength stress profile. of CMCs coating (roughness parameter λ = 200 µm, A = 10 µm) under typical service conditions. Compared with the thermal residual stress shown in FigureFigure4, it can 9 shows be seen the that predicted the thermal stress residual profile stressof CMCs of each coating layer (roughness has been eliminated parameter toλ = a 200 certain μm, extentA = 10 due μm to) under the service typical condition service conditions. of high temperature. Compared The with maximum the thermal stress residual along thestress longitudinal shown in directionFigure 4, (S11)it can is be 133 seen MPa that and the the thermal minimum residual is 231 stress MPa, of which each layer is greatly has been reduced eliminated compared to witha certain the − thermalextent due residual to the stressservice caused condition during of high processing. temperature. The positions The max ofimum the maximumstress along tensile the longitudinal stress and compressivedirection (S11) stress is 133 are MPa almost and the the same minimum as those is of−231 the MPa, thermal which residual is greatly stress. reduced The biggest compared difference with isthe that thermal the distribution residual stress of thermal caused stressduring in processing. the TBC layer The ispositions more uneven, of the maximum and the obvious tensile stressstress concentrationand compressive appears stress on are its asurface.lmost the This same is because as those the of TBC the layer thermal bears residual a large stress. thermal The gradient, biggest whichdifference leads is to that a large the distribution thermal stress. of thermal The concentration stress in the of TBC thermal layer stressis more on uneven, the coating and surfacethe obvious will leadstress to concentration a large number appears of surface on its cracks, surface. which This is isconsistent because with the TBC the results layer bears observed a large in relevant thermal experimentalgradient, which studies leads [28 to]. a large thermal stress. The concentration of thermal stress on the coating surfaceFigure will 10 lead shows to a thelarge variation number of of Mises surface stress cracks, along which the length is consistent direction with of the TBCresults surface observed under in typicalrelevant service experimental conditions studies of CMCs [28]. coating. It can be seen that the minimum Mises stress occurs at the valley while the maximum stress occurs at the peak. Figure 10a shows the influence of the amplitude of surface roughness on the thermal stress distribution. For the same wavelength, the larger the amplitude is, the larger magnitude and range the Mises stress are. The maximum Mises stress on TBC surface increases from 190 MPa for A = 5 µm to 280 MPa at A = 20 µm when λ = 200 µm. Figure 10b shows the effect of wavelength of surface roughness on thermal stress distribution. As seen, the higher the wavelength is, the smaller the stress level and range of Mises stress on the surface of the coating is for the same amplitude.
Figure 9. The thermal stress contours of CMCs coating under typical service conditions.
Figure 10 shows the variation of Mises stress along the length direction of the TBC surface under typical service conditions of CMCs coating. It can be seen that the minimum Mises stress occurs at the valley while the maximum stress occurs at the peak. Figure 10a shows the influence of the amplitude of surface roughness on the thermal stress distribution. For the same wavelength, the larger the amplitude is, the larger magnitude and range the Mises stress are. The maximum Mises stress on TBC surface increases from 190 MPa for A = 5 μm to 280 MPa at A = 20 μm when λ = 200 μm.
Coatings 2020, 10, x FOR PEER REVIEW 9 of 12 can be seen that the interfacial roughness has little effect on the temperature distribution which can be ignored.
0 0 (a) (b) TBC TBC
100 100
EBC EBC
m) m)
200 200
Depth( BC Depth( BC =200m, A= 5m 300 300 =100 m, A=10 m =200m, A=10m =200m, A=10m =200m, A=15m CMCs =300m, A=10m CMCs =200m, A=20m =400m, A=10m 400 400 1000 1100 1200 1300 1400 1500 1600 1000 1100 1200 1300 1400 1500 1600 Temperature(ºC) Temperature(ºC)
Figure 8. Variation of temperature versus depth of CMCs coatings under service conditions with different (a) amplitude; (b) wavelength.
Figure 9 shows the predicted stress profile of CMCs coating (roughness parameter λ = 200 μm, A = 10 μm) under typical service conditions. Compared with the thermal residual stress shown in Figure 4, it can be seen that the thermal residual stress of each layer has been eliminated to a certain extent due to the service condition of high temperature. The maximum stress along the longitudinal direction (S11) is 133 MPa and the minimum is −231 MPa, which is greatly reduced compared with the thermal residual stress caused during processing. The positions of the maximum tensile stress and compressive stress are almost the same as those of the thermal residual stress. The biggest difference is that the distribution of thermal stress in the TBC layer is more uneven, and the obvious stress concentration appears on its surface. This is because the TBC layer bears a large thermal gradient, which leads to a large thermal stress. The concentration of thermal stress on the coating surfaceCoatings 2020 will, 10 lead, 947 to a large number of surface cracks, which is consistent with the results observed9 of in 12 relevant experimental studies [28].
Coatings 2020, 10, x FOR PEER REVIEW 10 of 12
Figure 10b shows the effect of wavelength of surface roughness on thermal stress distribution. As seen, the higher the wavelength is, the smaller the stress level and range of Mises stress on the surface of the coating is for the same amplitude. FiFiguregure 9. TheThe thermal thermal stress stress contours contours of of CMCs CMCs coating under typical service conditions.
300 300 Figure 10(a) shows the variation=200m, A= 5m of Mises stress along the length(b) direction =100of them, A=10 TBCm surface under typical service conditions =200 of m,CMCs A=10m coating. It can be seen that the minimum =200 Misesm, A=10m stress occurs at =200m, A=15m =300m, A=10m the valley while the maximum =200m, A=20 stressm occurs at the peak. Figure 10a shows =400m, the A=10 influencem of the 200 200 amplitude of surface roughness on the thermal stress distribution. For the same wavelength, the larger the amplitude is, the larger magnitude and range the Mises stress are. The maximum Mises 100 100 stress onMises stress (MPa) TBC surface increases from 190 MPa for A = 5 μm toMises stress (MPa) 280 MPa at A = 20 μm when λ = 200 μm.
0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized location Normalized location
Figure 10. Mises stress along the length of the surface of CMCs coatings with different (a) amplitude; Figure 10. Mises stress along the length of the surface of CMCs coatings with different (a) amplitude; (b) wavelength. (b) wavelength. 3.3. Analysis of Possible Failure Mode 3.3. Analysis of Possible Failure Mode The stress distribution plays an important role in determining the failure mode. As calculated, it can beThe recognized stress distribution that the residualplays an tensile important stress role was in induceddetermining in the the EBC failure layer mode. while As the calculated, residual compressiveit can be recogniz stress wased that induced the residual in the BC tensile layer stress during was the induced processing in the of coatings.EBC layer This while means the aresidual large stresscompressive mismatch stress will was be inducedinduced betweenin the BC theselayer twoduring adjacent the processing coating layers.of coatings Moreover,. This means the rough a large interfacestress mismatch will enlarge will the be mismatch. induced between As shown these in Figure two adjacent11a, the delaminationcoating layers. cracks Moreover, would probablythe rough initiateinterface at location will enlargeA, B andthe mismatch.C. Whether As delamination shown in Figure will occur11a, the or delamination not is determined crack bys would the interfacial probably strengthinitiate ofat thelocation related A,interface. B and C. Whether And where delamination the delamination will occur will or initiate not is can determined be captured by bythe theinterfacial stress concentrations.strength of the These related dangerous interface. regions And where are caused the delamination by the microstructure, will initiate i.e., can the be roughcaptured interface by the here.stress It can concentrations. be seen that the These probability dangerous of delamination regions are between caused by EBC the and microstructure, BC layers will increasei.e., the withrough theinterface interfacial here. roughness. It can be Similarly,seen that thethe delaminationprobability of between delamination EBC and between BC layers EBC prefer and BC to initiatelayers will at theincrease transition with between the interfacial raised and roughness. depression Similarly, areas. the delamination between EBC and BC layers preferUnder to initiate the typical at the service transition conditions between with raised large and temperature depression gradient, areas. the distribution of thermal stress isUnder quite the diff typicalerent to service the residual conditions stress. with As large discussed, temperature the thermal gradient, residual the distribution stress in the of Tthermal/EBC coatingstress is system quite different can be eliminated to the residual to some stress. extent. As discussed, However, the large thermal stress residual concentrations stress in would the T/EBC be inducedcoating atsystem coating can surface be eliminated at the same to some time. extent. Indeed, However, the most large regions stress of concentrations TBC layer were would under be compressioninduced at but coating uneven surface stress at distribution the same timewere. caused Indeed, by the the most coarse regions surface. of The TBC compressive layer were stress under cancompression also cause crackbut uneven initiations stress as distribution shown in Figure were caused11b. The by most the coarse dangerous surface. regions The compressive were denoted stress as Dcan, E and alsoF causein the crack figure. initiations Cracks as will shown initiate in atFigure these 11b regions. The most when dangerous the maximum regions stress were reaches denoted the as strengthD, E and of theF in TBC the figure. layer. The Cracks cracking will initiate direction atwill these be regions determined when by the the maximum local stress stress state. reaches It should the strength of the TBC layer. The cracking direction will be determined by the local stress state. It should be noted that the crack patterns may be very different as the stress state will vary with the location as the surface is uneven.
Figure 11. Analysis of possible failure mode for the investigated coatings induced by (a) thermal residual stress and (b) operating thermal stress.
Coatings 2020, 10, x FOR PEER REVIEW 10 of 12
Figure 10b shows the effect of wavelength of surface roughness on thermal stress distribution. As seen, the higher the wavelength is, the smaller the stress level and range of Mises stress on the surface of the coating is for the same amplitude.
300 300 (a) =200m, A= 5m (b) =100m, A=10m =200m, A=10m =200m, A=10m =200m, A=15m =300m, A=10m =200m, A=20m =400m, A=10m 200 200
100 100
Mises stress (MPa) Mises stress (MPa)
0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized location Normalized location
Figure 10. Mises stress along the length of the surface of CMCs coatings with different (a) amplitude; (b) wavelength.
3.3. Analysis of Possible Failure Mode The stress distribution plays an important role in determining the failure mode. As calculated, it can be recognized that the residual tensile stress was induced in the EBC layer while the residual compressive stress was induced in the BC layer during the processing of coatings. This means a large stress mismatch will be induced between these two adjacent coating layers. Moreover, the rough interface will enlarge the mismatch. As shown in Figure 11a, the delamination cracks would probably initiate at location A, B and C. Whether delamination will occur or not is determined by the interfacial strength of the related interface. And where the delamination will initiate can be captured by the stress concentrations. These dangerous regions are caused by the microstructure, i.e., the rough interface here. It can be seen that the probability of delamination between EBC and BC layers will increase with the interfacial roughness. Similarly, the delamination between EBC and BC layers prefer to initiate at the transition between raised and depression areas. Under the typical service conditions with large temperature gradient, the distribution of thermal stress is quite different to the residual stress. As discussed, the thermal residual stress in the T/EBC coating system can be eliminated to some extent. However, large stress concentrations would be induced at coating surface at the same time. Indeed, the most regions of TBC layer were under compression but uneven stress distribution were caused by the coarse surface. The compressive stress can also cause crack initiations as shown in Figure 11b. The most dangerous regions were denoted as Coatings 2020, 10, 947 10 of 12 D, E and F in the figure. Cracks will initiate at these regions when the maximum stress reaches the strength of the TBC layer. The cracking direction will be determined by the local stress state. It should bebe noted noted that that the the crack crack patterns may be veryvery didifferentfferent asas thethe stress stress state state will will vary vary with with the the location location as asthe the surface surface is is uneven. uneven.
FigureFigure 11. 11. AnalysisAnalysis of of possible possible failure failure mode mode for for the the investigated investigated coatings coatings induced induced by by (a (a) ) thermal thermal residualresidual stress stress and and ( (bb)) operating operating thermal thermal stress stress..
4. Conclusions The residual stress distribution in the EBCs, induced by thermal expansion mismatch, is found to vary with the rough interface as well as in-depth. For the T/EBC coating system deposited on SiC/SiC composite, the rough interface does not alter the temperature distribution with the depth. The stress profile indicates that the stress in the coatings is affected by the rough interface. The results are as follows:
During the processing, considerable thermal residual stress is induced in coatings. Large in-plane • and through-thickness residual stress may cause vertical cracks in the EBC layer and delamination cracks at the interface between the EBC and BC layer. The rough interface plays an important role in the distribution of thermal residual stress. Stress concentration occurs near the peak and valley of the rough interface. The range of stress variation increases with the amplitude while decreases with the wavelength. Under the typical service conditions for SiC/SiC composites, the thermal residual stress in the • T/EBC coating system can be eliminated to some extent. However, large thermal stress may be induced at the surface layer of TBC due to the thermal gradient. This stress tends to cause surface cracks. Thus, the surface roughness has a significant impact on the thermal stress distribution. The magnitude and range of thermal stress increase with the roughness level.
Author Contributions: Conceptualization, G.F. and J.R.; methodology, G.F. and X.G.; software, J.R.; validation, G.F. and J.S.; writing—original draft preparation, G.F.; writing—review and editing, Y.S.; visualization, J.S.; project administration, X.G.; funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Science and Technology Major Project, Grant No. 2017- IV-0005-0042; the Natural Science Foundation of universities in Anhui, Grant No. KJ2018A0057; Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology, Grant No. CEPE2018006; and the National Natural Science Foundation of China, Grant No. 11972183. Conflicts of Interest: The authors declare no conflict of interest.
References
1. Xu, Y.; Ren, S.; Zhang, W.; Wu, Z.; Gong, W.; Li, H. Study of thermal buckling behavior of plain woven C/SiC composite plate using digital image correlation technique and finite element simulation. Thin Wall Struct. 2018, 131, 385–392. [CrossRef] 2. Li, J.; Martin, E.; Leguillon, D.; Dupin, C. A finite fracture model for the analysis of multi-cracking in woven ceramic matrix composites. Compos. Part B Eng. 2018, 139, 75–83. [CrossRef] Coatings 2020, 10, 947 11 of 12
3. Dong, X.; Shin, Y.C. Predictions of thermal conductivity and degradation of irradiated SiC/SiC composites by materials-genome-based multiscale modeling. J. Nucl. Mater. 2018, 512, 268–275. [CrossRef] 4. Fang, G.; Li, L.; Gao, X.; Song, Y. Finite Element Analysis of the Crack Deflection in Fiber Reinforced Ceramic Matrix Composites with Multilayer Interphase Using Virtual Crack Closure Technique. Appl. Compos. Mater. 2020, 27, 307–320. 5. Song, Y.; Gao, X.; Sun, Z. Progress on Fatigue Hysteresis Mechanisms and Models of Aero-engine Ceramic Matrix Composites. J. Nanjing Univ. Aeronaut. Astronaut. 2019, 51, 417–426. 6. Xu, J.; Sarin, V.K.; Dixit, S.; Basu, S.N. Stability of interfaces in hybrid EBC/TBC coatings for Si-based ceramics in corrosive environments. Int. J. Refract. Met. Hard Mater. 2015, 49, 339–349. [CrossRef] 7. Lee, K.; Roode, M.; Kashyap, T. Environmental Barrier Coatings for Ceramic Matrix Composites-an Overview; GRC-E-DAA-TN38835; NASA: Washington, DC, USA, 2017. 8. Białas, M. Finite element analysis of stress distribution in thermal barrier coatings. Surf. Coat. Technol. 2008, 202, 6002–6010. [CrossRef] 9. Wang, L.; Wang, Y.; Sun, X.G.; He, J.Q.; Pan, Z.Y.; Wang, C.H. Finite element simulation of residual stress
of double-ceramic-layer La2Zr2O7/8YSZ thermal barrier coatings using birth and death element technique. Comput. Mater. Sci. 2012, 53, 117–127. [CrossRef] 10. Wang, L.; Wang, Y.; Zhang, W.Q.; Sun, X.G.; He, J.Q.; Pan, Z.Y.; Wang, C.H. Finite element simulation of stress
distribution and development in 8YSZ and double-ceramic-layer La2Zr2O7/8YSZ thermal barrier coatings during thermal shock. Appl. Surf. Sci. 2012, 258, 3540–3551. 11. Yu, Q.M.; Cen, L.; Wang, Y. Numerical study of residual stress and crack nucleation in thermal barrier coating system with plane model. Ceram. Int. 2018, 44, 5116–5123. [CrossRef] 12. Bhattacharyya, A.; Maurice, D. Residual stresses in functionally graded thermal barrier coatings. Mech. Mater. 2019, 129, 50–56. [CrossRef] 13. Nayebpashaee, N.; Seyedein, S.H.; Aboutalebi, M.R.; Sarpoolaky, H.; Hadavi, S.M.M. Finite element simulation of residual stress and failure mechanism in plasma sprayed thermal barrier coatings using actual microstructure as the representative volume. Surf. Coat. Technol. 2016, 291, 103–114. [CrossRef] 14. Rezvani Rad, M.; Farrahi, G.H.; Azadi, M.; Ghodrati, M. Stress analysis of thermal barrier coating system subjected to out-of-phase thermo-mechanical loadings considering roughness and porosity effect. Surf. Coat. Technol. 2015, 262, 77–86. [CrossRef] 15. Moridi, A.; Azadi, M.; Farrahi, G.H. Thermo-mechanical stress analysis of thermal barrier coating system considering thickness and roughness effects. Surf. Coat. Technol. 2014, 243, 91–99. [CrossRef] 16. Al Nasiri, N.; Patra, N.; Pezoldt, M.; Colas, J.; Lee, W.E. Investigation of a single-layer EBC deposited on SiC/SiC CMCs: Processing and corrosion behaviour in high-temperature steam. J. Eur. Ceram. Soc. 2019, 39, 2703–2711. [CrossRef] 17. Appleby, M.P.; Zhu, D.; Morscher, G.N. Mechanical properties and real-time damage evaluations of environmental barrier coated SiC/SiC CMCs subjected to tensile loading under thermal gradients. Surf. Coat. Technol. 2015, 284, 318–326. [CrossRef] 18. Lee, K.N.; Eldridge, J.I.; Robinson, R.C. Residual Stresses and Their Effects on the Durability of Environmental Barrier Coatings for SiC Ceramics. J. Am. Ceram. Soc. 2005, 88, 3483–3488. [CrossRef]
19. Zhang, X.; Zhou, K.; Liu, M.; Deng, C.; Niu, S.; Xu, S. Preparation of Si/Mullite/Yb2SiO5 Environment Barrier Coating (EBC) by Plasma Spray-Physical Vapor Deposition (PS-PVD). J. Inorg. Mater. 2018, 33, 325–330. 20. Abdul-Aziz, A.; Bhatt, R.T. Modeling of thermal residual stress in environmental barrier coated fiber reinforced ceramic matrix composites. J. Compos. Mater. 2012, 46, 1211–1218. [CrossRef] 21. Heveran, C.M.; Xu, J.; Sarin, V.K.; Basu, S.N. Simulation of stresses in TBC–EBC coating systems for ceramic components in gas turbines. Surf. Coat. Technol. 2013, 235, 354–360. [CrossRef] 22. Song, Y.; Zhuan, X.; Wang, T.J.; Chen, X. Thermal Stress in Fabrication of Thermal Barrier Coatings. J. Therm. Stresses 2014, 37, 1390–1415. [CrossRef] 23. Lee, K.N.; Fox, D.S.; Bansal, N.P. Rare earth silicate environmental barrier coatings for SiC/SiC composites
and Si3N4 ceramics. J. Eur. Ceram. Soc. 2005, 25, 1705–1715. [CrossRef] 24. Robertson, A.L.; Solá, F.; Zhu, D.; Salem, J.; White, K.W. Microscale fracture mechanisms of HfO2-Si environmental barrier coatings. J. Eur. Ceram. Soc. 2019, 39, 2409–2418. [CrossRef] 25. Shen, X.; Qiao, Y.; Dong, S.; Liu, X.; Gong, L. Thermal Load Test Method and Numerical Calculation for Ceramic Matrix Composite Turbine Guide Vane. Appl. Compos. Mater. 2019, 26, 553–573. [CrossRef] Coatings 2020, 10, 947 12 of 12
26. Eriksson, R.; Sjöström, S.; Brodin, H.; Johansson, S.; Östergren, L.; Li, X.-H. TBC bond coat–top coat interface roughness: Influence on fatigue life and modelling aspects. Surf. Coat. Technol. 2013, 236, 230–238. [CrossRef] 27. Gadelmawla, E.S.; Koura, M.M.; Maksoud, T.M.A.; Elewa, I.M.; Soliman, H.H. Roughness parameters. J. Mater. Process. Technol. 2002, 123, 133–145. [CrossRef] 28. Zhu, D.; Nemeth, N.N. Environmental Barrier Coating Fracture, Fatigue and High-Heat-Flux Durability Modeling and Stochastic Progressive Damage Simulation; GRC-E-DAA-TN48415; NASA: Washington, DC, USA, 2017.
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