Experimental and Numerical Study of the Thermo-Mechanical Behavior of Plasma-Sprayed Gadolinium and Yitria Zirconate-Based Thermal Barrier Coatings

Advanced Ceramics Progress: Vol. 7, No. 4, (Autumn 2021) 36-51

Materials and Energy Research Center MERC Contents lists available at ACERP Advanced Ceramics Progress Journal Homepage:www.acerp.ir Original Research Article Experimental and Numerical Study of the Thermo-Mechanical Behavior of Plasma-Sprayed Gadolinium and Yitria Zirconate-Based Thermal Barrier Coatings N. Nayebpashaee a, , E. Etemadi b, B. Mohammad Sadeghi c, S. H. Seyedein d a Assistant Professor, Department of Metallurgy and Mechanical Engineering, Technology and Engineering Research Center, Standard Research Institute (SRI), Karaj, Alborz, Iran b PhD Candidate, Faculty of Materials Science and Engineering, Malek Ashtar University, Tehran, Tehran, Iran c Assistant Professor, School of Metallurgy and Materials Engineering, Iran University of Science and Technology, Tehran, Tehran, Iran d Professor, School of Metallurgy and Materials Engineering, Iran University of Science and Technology, Tehran, Tehran, Iran  Corresponding Author Email: n.nayebpashaee@standard.ac.ir (N. Nayebpashaee) URL: https://www.acerp.ir/article_144395.html ARTICLE INFO ABSTRACT Article History: Received 01 January 2022 Received in revised form 02 February 2022 Accepted 06 February 2022 The current study aims to analyze the thermal and residual stress distributions in both duplex and functionally-graded thermal barrier coatings (TBCs) of yttria-stabilized zirconia (YSZ) and gadolinium zirconate (GZ) during a realistic heating regime. To this end, finite element model was employed to model the effects of thermal loading on the thermomechanical response and stress distribution. In addition, three different YSZ-based TBC systems, one duplex, and two FG-TBCs were fabricated using the APS method. The coatings were characterized based on SEM/EDS, map analysis, and XRD. The residual stress, elastic modulus, microhardness, and fracture toughness of the coatings were determined using nanoindentation method. The obtained results revealed that the microstructure, porosity, and chemical composition changed gradually due to the functionally-graded coating. Examination of the surface of the samples after the application of thermal shock showed that the separation of the layers occurred more frequently in the cases of two-layer coatings than in the graded ones. The contours of the heat flux and nodal temperatures confirmed that most of the damaging thermal residual stresses were concentrated in the ceramic top coat, thus resulting in less damage and life-shortening of the substrate. The magnitude of the residual stress in the FG-TBC was lower than that in the duplex TBC, and the stress distribution was more uniform, hence improvement in the performance and extention of the life of the thermal barrier system. According to the findings, the YSZ-based TBC outperformed the gadolinium zirconate-based TBC in terms of thermal shock resistance and residual stress. Keywords: Functionally Graded Thermal Barrier Coating (FGTBC) Thermal Shock Residual Stress Nano-Indentation Finite Element Method https://doi.org/10.30501/ACP.2022.322563.1078 1. INTRODUCTION Tolerance of higher temperatures in different parts of internal combustion engines has always been an important concern in aerospace and turbine industries. Thermal Barrier Coatings (TBCs) are regarded as important elements in the durability of hot section components. They function as the insulating components such as turbine blades, combustor cans, ducting and nozzle guide vanes operating at elevated temperature. In addition, they make an increase in the operating temperature of gas turbines possible [1-5]. The typical TBC is composed of three layers namely Bond Coat (BC), Top Coat (TC), and Thermally Grown Oxide (TGO). The BC is made of MCrAlY (with M=Ni and/or Co), and the TC often consists of a thermal barrier layer based on Yttria-Stabilized Zirconia (YSZ) [1-3]. At high temperatures, oxygen is transferred from the TC to the BC through micro cracks and interconnected pinholes within the TC. During the operation, aluminum in the BC diffuses and reacts with oxygen from the combustion gases. As a result, an oxidized scale of alumina (Al2O3) is formed on the BC called the TGO layer which is primarily related to the oxidation of the BC. The major disadvantages of YSZ are the limited operational temperature resulting from the phase transformation, sintering induced volume shrinkage, and low corrosion resistance. To overcome these drawbacks, the necessity of searching for new alternative materials is highlighted more than ever [1,6-8]. Zirconate-based TBCs are expected to be appropriate candidates for future applications in high-temperature components due to their low thermal conductivity, high stability, and high sintering resistance at high temperatures [1,8]. Gadolinium Zirconate (Gd2Zr2O7 or GZ) is another candidate material that is a new and promising alternative ceramic coating material to YSZ that enjoys several major advantages such as higher thermal stability at elevated temperatures and lower thermal conductivity (1.3 W/mK-1 at 1100 °C), and better hot corrosion resistance than those of YSZ (1.8 W/mK-1 at 1100 °C), thus potentially allowing better thermal insulation [9,10]. Some problems may arise in the case of plasma-sprayed TBC such as spallation caused by the TGOs with different thickness values and morphologies as well as cracking in long-term services due to their poor bond strength and high residual stresses. Functionally Graded Thermal Barrier Coatings (FG-TBCs) with a gradual compositional variation from the TCto the BC were proposed to overcome these limitations. The microstructural grading of FG-TBCs could help reduce the mismatch in thermomechanical properties. In addition, using FG-TBCs may improve other properties such as adhesion, corrosion, and oxidation [4,5,11]. Evaluating and measuring the residual stresses is of high importance in industry in determining the lifetime of the components. The measurement techniques for residual stress in the coatings can be divided into two groups of destructive and non-destructive methods. The non-destructive methods measure some parameters that are related to the stress. X-ray or neutron diffraction are referred to as the non-destructive methods, and the hole-drilling and layer removal method are regarded as the destructive ones. Nanoindentation is an indentation method for testing the hardness and other related mechanical properties of materials. It is also used to estimate the residual stress in thin films and coatings [12-15]. According to the literature, several experimental, analytical, and numerical studies have been conducted on the residual stress, crack evolution, failure mechanism, splatting impact, TGO and layer thickness, and thermal shock resistance of the TBCs [7,8,16-20]. For instance, Z. Valefi and M. Saremi [7] evaluated the effects of plasma spray parameters, atomizing gas, and substrate preheat temperature on the microstructure and phase composition of YSZ coatings produced through the SPPS process. According to their findings, upon increasing the power of plasma, using hydrogen as the precursor atomizing gas, and increasing the substrate preheat temperature, the amount of non-pyrolyzed precursor in the coatings would decrease [7]. S. M. Yunus et al. [17] compared the thermal resistance of a the plasma sprayed multilayer (GZ/YSZ) TBC with that of the single-layer YSZ coating and found that the single-layer YSZ system performed 12 % better than the multilayer TBC system at 1250 °C [17]. N. Nayebpashaee et al. [19] simulated the residual stress distribution and fracture mode of the TBCs based on the micromechanical approach FE with and without considering the presence of two-phase TGO. Their obtained results showed acceptable agreement between the simulated and experimental failure and crack growth modes. J. Song et al. [21] evaluated the effect of the non-uniform growth of the TGO on the stress evolution and interfacial crack initiation using the finite element method. They concluded that the non-uniform growth of the TGO would increase the magnitude of the residual stress in the TC layers, thus leading to early initiation of interfacial cracks [21]. The current study aimed to investigate the thermal and residual stress distribution in duplex TBC and functionally graded YSZ and GZ-TBCs during a realistic heating regime including heating, operating time, and final cooling. Despite the common applications of functionally graded strategies in surface engineering, very few studies have been conducted on the numerical aspects of functionally graded TBCs with novel zirconate (GZ) composition as the top ceramic layer TBCs in the literature. In addition, limited studies have focused on the thermal shock behavior of the TBC containing GZ as the TC so far. 2. MATERIALS AND METHODS Yitria Zirconate-based TBC is usually applied in experimental studies. The used powders for bond and top coats were prepared according to the instructions given in Table 1. Prior to spraying, the starting powders were heat-treated at 100 °C for two hours to remove moisture. To obtain better substrate roughness and a clean surface, the Inconel (substrate) was blasted with silicon carbide particles with a mesh count of 25 in. at the optimum pressure of four bars, followed by smooth grinding, degreasing, and acid pickling. Table 2 lists the plasma spray parameters used for TBC coating. X-Ray Diffraction (XRD) analysis was carried out to evaluate the materials formed on the top surface of the coating and characterize the coating surface after cooling the sprayed sample using a Siemens D 500 instrument. A thermal cycle was taken into account at the dwell time of 300 seconds and temperature of 1300 °C to perform the thermal shock. The samples were heated to the target temperature of 1300 °C in an electric furnace with air and then cooled to 25 °C using an air blast unit. The thermal shocks with the oxidation time (cause of TGO formation) were repeated 45 times. Finally, to reveal the microstructure of the multiple shocked coatings in SEM studies, the samples were mounted, ground, and polished. The coating componenets were identified using OM, SEM/EDS, and mapping analysis. TABLE 1. Specifications of powders used in plasma spraying Layer Composition Powder Morphology Size (µm) Top coat ZrO2-8 wt % Y2O3 Metco 204 –NS Spherical 40-75 Bond coat Ni-22Cr-10Al-1Y AMDRY 962 Spherical 11-106 TABLE 2. Operating parameter of plasma spraying Inconel 738 used in this research NiCrAlY (Amdry962) 75 NiCrAlY + 25 YSZ 50 NiCrAlY + 50 YSZ 25 NiCrAlY + 75 YSZ YSZ (metco204Ns) Unit Parameter 450 450 500 500 500 A Arc current intensity 50 50 55 55 55 V Voltage 85 85 80 80 80 SCFH* Carrier gas flow rate (Argon) 15 15 15 15 15 SCFH Carrier gas flow rate (Hydrogen) 30 30 30 30 30 SCFH Powder carrier gas flow rate (Argon) 15 15 20 20 25 lb/hr Powder feed rate 12 10 10 8 8 cm Spray distance 2 2 2 2 2 mm Injection diameter water water water water water - Cooling circulation system *Standard Cubic Feet per Hour 2.1. Evaluation of Residual Stress by Nano Indentation Method In this study, the residual stress was measured through nanoindentation method as well as indentation fracture technique. When using this technique to indent the surface of a brittle material with moderate force, it often produces a permanent impression with radially aligned cracks at the corner of the indent [12,22]. In order to calculate the residual stress, first, the mechanical properties of the coating such as Young's modulus, microhardness, and fracture toughness should be calculated. The calculation method is based on the methods presented in the previous study [23]. According to the load-depth curve, the hardness H and reduced modulus Er are defined by Equations 1 and 2 [23]: H=P_max/A_c (1) E_r=√π/2β S/√(A_c ) (2) where Pmax is the maximum load, Ac the contact area, S=dP⁄dh the contact stiffness at initial unloading, and b a constant that depends on the geometry of the indenter. The reduced modulus Er is defined through Equation (3) [23] as: 1/E_r = (1- ϑ_i^2)/E_i + (1- ϑ_s^2)/E_s (3) where E and Ei are the elastic modului of the specimen and indenter, respectively, and ʋ and υi are the Poisson’s ratios of the specimen and indenter, respectively [23]. The Poisson's ratios of the TBC and diamond indenter are 0.2 and 0.07, respectively, and the valse of Ei for the diamond is 1141 GPa [24]. For Berkovich diamond indenter, we have A_c=24.49 h_c^2≈24.5 h_c^2 where hc is the contact depth. Hence, Equation (1) will be as H=P_max/(24.5 h_c^2 ) . When a Vickers indenter is penetrated into the interface of two different materials, the fracture toughness for the coating/BC interface is evaluated using Equation (4) [23]: K_IC= δ(E/H)^(1⁄2) P/c^(3⁄2) (4) where δ is the geometric factor and δ=0.015 for a Vickers indenter, and c= (c1+c2+c3)/3 is the average length of three radial cracks with the lengths of c1, c2, and c3 [23]. When applying the TBC containing stress and nanoindentation perpendicular to the cross-section of the TC layer in accordance with Figure 1, the fracture toughness is measured through Equation (5) [23]: Figure 1. Schematics of Berkovich indentation perpendicular to the top coat of multiple-shocked coating K_IC=δ(E/H)_i^(1⁄2) P/c^(3⁄2) + 2/√π σc^(1⁄2) (5) Then, the ratio P/c3/2 can be obtained as [23]: P/c^(3⁄2) = (K_IC/χ_i )+(-2σ/(√π 〖 χ〗_i )) c^(1⁄2) (6) where χ_i= δ(E⁄H)_i^(1⁄2). Equation (6) is regarded as a function of c−1/2 where (-2σ/(√π 〖 χ〗_i )) and (K_IC/χ_i ) denote the slope and intercept of Equation (6), respectively [23]. To obtain a better linear equation, a series of indentation tests should be carried out. 2.2. Performing Nano Indentation Test A Triboscope system (Histron Inc. USA) was used to measure the stress in the nanoindentation method. A Berkovich diamond indenter was used for performing nanoindentation experiments. A device equipped with Atomic Force Microscopy (AFM) (NanoScope E, Digital Instruments, USA) was also used to examine the surface topography of the specimens. The values of the loading rate, pause time, and unloading rate were 5 mNs-1, 5 s, and 5 mNs-1, respectively. At room temperature, a series of forces ranging from 500 µN to 10,000 µN in increments of 1,000 µN were perpendicularly applied to the cross-section of the top layer of the multi-shocked TBC considering the YSZ. The length of the cracks was calculated using the image processing toolbox of the MATLAB software. 2.3. Finite Element Analysis This section primarily aims to determine the temperature and stress distribution in the TBC. To this end, a simulation of TBC was performed using ABAQUS software. In addition, a two-dimensional finite element model was employed to numerically simulate the temperature distribution and consequent induced residual stress in the TBC. The schematic illustration of the studied area in the TBC system used in the hot section of the gas turbines is given in Figure 2. Figure 2. TBC calculation domain As graphically shown in Figure 3, the duplex TBC system consists of both metallic and ceramic layers including an Inconel 738 substrate, a NiCoCrAlY sliding layer (BC), and GZ (YSZ) as a Top Layer (TC). The selected functionally graded TBC system used in this study is made of the following layers: an Inconel 738 substrate, a NiCoCrAlY bond (BC), 50 % BC + 50 % GZ (YSZ), and GZ (YSZ) as the top coat (Figure 3). In order to obtain accurate results, appropriate thermal and mechanical boundary conditions should be considered. The thermal cycling applied at the highest level of the thermal barrier is shown in Figure 4. The heating cycle under study involves heating from 25 °C to 1300 °C in 30 seconds. In the second stage, it sustains temperature of 1300 °C for 200 seconds and in the third stage, it is cooled down from 1300 °C to 25 °C in 30 seconds. In order to provide a suitable boundary condition for the bottom surface of the substrate, a thermal flux was used on this surface. To apply this thermal flux, the heat transfer coefficient (h) was assumed to be 25 W/m2.K [25]. As illustrated in Figure 5, in order to satisfy the mechanical boundary conditions, the point of the TBC system should be kept constant. In addition, the degree of freedom of the movement of all nodes located on the vertical surface of the TBC system should be closed in a horizontal direction to create symmetrical boundary conditions. On the contrary, the degree of freedom of their movement in the vertical direction should be kept open. Considering the dependence of the thermal and mechanical properties of the material on temperature, we gave the properties of different layers of TBC at different temperatures to the software as the inputs. Table 3 lists these thermal and mechanical properties of different layers of TBC [26-28]. In order to validate the proposed model in this study, a comparison was made between the simulation and experimental results obtained from the nanoindentation method. Figure 3. Schematic view of (a) duplex and functionally graded (b,c) coating designs Figure 4. Thermal cycle applied at the highest level of thermal barrier coating Figure 5. Assigning mechanical boundary conditions TABLE 3. Thermal and mechanical properties of different layers of the thermal barrier coating [26–28] Substrate Hastelloy-X Bond Coat NiCrAlY Top Coat GZ Top Coat YSZ TGO 〖Al〗_2 O_3 Temperature (K) Material properties 201 225 175 210 380 276 E (GPa) 180 186 170.8 205 338 673 150 147 150.8 181 - 1073 141 134 135 162 312 1473 8220 7320 6320 5400 3978 276 Ρ (Kg/m3) 673 1073 1473 0.32 0.3 0.2 0.2 0.27 276 υ 673 1073 1473 13.4 11.6 8.9 9.1 5.1 276 α (×10-6.K-1) 14.2 14 9.04 10.58 - 673 15.6 16 10.08 11.13 - 1073 15.8 20.8 10.9 8.5 9.8 1473 442 501 344 500 857 276 Cp (J.(kg.K)-1) 514 592 430 576 673 668 781 456 637 1073 831 764 460 650 1473 10.4 4.3 1.11 1.06 25.2 276 K (W/m.°C) 18.6 6.4 0.77 0.8 673 23.8 10.2 0.61 0.65 1073 27.4 11.3 0.58 0.62 1473 3. RESULTS AND DISCUSSION Figure 6a shows the optical microscopy images of the structure of YSZ-based duplex TBC composed of three sections: substrate, bond coat, and top coat. The transparent areas represent the metal phases, dark gray areas the ceramic phases, and black areas the pores in the coating. The BC shown in a lighter color is a layered structure consisting of splats approximately parallel to the substrate surface. This microstructure is one of the main features of plasma spray coatings. As observed in Figure 6a,the interface between the layers of the TC and bond coats in the duplex TBC is clearly distinguished. Figure 6b shows the optical microscopy images of the structure of YSZ-based functionally graded TBC. According to this figure, the coating is characterized by a layered structure, and each layer contains micro cracks and pores that appear in black color. From the BC to the TC layer of the FG-TBC, the portion of NiCrAlY in the layers gradually changes. This gradient distribution of layers in the FG-TBC leads to the reduction of residual stresses caused by different CTEs between the metal and ceramic phases. X-Ray Diffraction (XRD) analysis was carried out to distinguish between the phases of the initial (feedstock) powder and as-sprayed TC layer for Yttria stabilized Zirconia-based TBC, the results of which are shown in Figure 7. As observed in Figure 7a, the feedstock powder contains zirconium dioxide (ZrO2) with the dominant structure of tetragonal phase in the form of partially stabilized zirconia and stabilized (non-transformable) zirconia and lower amount of cubic and monoclinic phases. As shown in Figure 7b, plasma spraying causes a significant reduction in the intensity of monoclinic phase. The as-sprayed coating is mostly composed of tetragonal phase with only traces of the monoclinic phase, and the amount of the cubic phase decreases in terms of the feedstock. According to the equilibrium phase diagram of zirconia-yitria, the stable zirconia phase at room temperature contains 8 % of the weight of zirconia in the tetragonal phase. The non-transformable (stable) tetragonal phase is the main phase of plasma-sprayed zirconia which is formed as a result of rapid cooling of the whipped molten particles on the surface. In plasma spraying, a high proportion of Y2O3 (8 % by weight) in YSZ increases the phase temperature stability of the tetragonal ZrO2 after cooling. Plasma spraying as a rapid process often leads to the formation of transformable (semi-stable) phases in the coating. In plasma sprayed TBCs, rapid cooling leads to the formation of a transformable (semi-stable) tetragonal phase (t') instead of a non-transformable (stable) tetragonal phase (t). In other words, rapid cooling during thermal spraying preserves the yttrium distribution of the primary powder in the tetragonal phase, thus leading to preservation of the transformable (semi-stable) tetragonal phase at room temperature. When the YSZ coating is semi-stable, and its chemical composition is the same as that of the more stable phase at higher temperatures, the chemical composition of the material will be mixed at room temperature rather than just the tetragonal phase predicted at room temperature. The resulting phases will be cubic and tetragonal [29,30]. Figure 6. SEM images of the structure of (a) duplex coating and (b) functionally graded Yttria stabilized Zirconia based thermal barrier coating Figure 7. X-Ray Diffraction (XRD) analysis of a) the feedstock powder of YSZ-based top coat and b) as sprayed topcoat Thermal spraying forms semi-stable compounds sensitive to the spray parameters. Even if the samples are coated with spray parameters that are as similar as possible (same source power, similar spray distance, etc.), the differences in the properties of the initial powder should be ignored. These changes in the properties of the initial powder result in different microstructures (porosity and pore properties) in the generated coatings. Therefore, the coatings differ in their properties, hence different phases of the sprayed coating [29,31,32]. High amount of cubic and monoclonal phases, instead of the tetragonal phase, is undesirable due to their lower mechanical properties. When cooled down to room temperature, the tetragonal phase is transformed into the monoclonal phase. This transformation is accompanied by an increase in the volume, hence creation of significant stress and possibly nucleation and crack growth within the TBC that would reduce the lifecycle of the coating [29–31]. As reported, the removal and depletion of yttrium (Y) from YSZ during operation and its exposure to high temperatures (above 1200 °C) and thermal cycling would form a monoclinic phase upon cooling to room temperature. As a result, the monoclinic phase is fromed based on the Y-depleted tetragonal phase during cooling. According to the findings, the higher the concentration of stabilizing elements in the tetragonal zirconia, the lower the proportion of formed monoclinic phase [29,32]. Normally, it is expected that no peak is found for monoclinic zirconia (m-ZrO2) in the YSZ layer after spraying. However, in this study, XRD analysis confirmed the presence of small a amount of monoclinic phase in the TBC immediately after deposition (in the sprayed state), in addition to the presence of dominant non-transformable (stable) tetragonal (t-ZrO2), convertible tetragonal (semi-stable) (t'-ZrO2), and cubic phases. Apparantly, according to the spraying conditions in this study, all of the monoclinic phases in the YSZ powder cannot be removed. However, plasma spraying caused a significant reduction in the monoclonal phase in the primary powder. Figure 8 depicts the SEM structure of duplex YSZ based-coating with map analysis of the elements. According to dot mapping of the elements, while Cr, Ni, and Al are mostly concentrated in the lower BC layer, Zr and Y are concentrated only in upper TC layer. Figure 9 illustrates the SEM images of the structure of YSZ based-functionally graded coating as well as map analyses of elements. Dot mappings confirms that although Cr, Ni, and Al are mainly concentrated in lower BC layer, they are also present in the upper graded layers, hence a gradual change can be observed in Ni, Cr, and Al elements from the bond to top coats. In addition, a slight gradual distribution of Zr and Y from the top to the bond coats was observed. The results of SEM analysis revealed that microstructure, porosity, and chemical composition changed gradually through the functionally graded coating. In order to carry out finite element analysis, a mesh sensitivity analysis was taken into account to determine the number of required elements in a model, thus ensuring that the analysis results were not affected by changing the mesh size The mesh sensivity is determined based on Figure 10 which shows the temperature change as a function of element size. Figure 11 shows the contour of the stress distribution S_22 (in Pascal) for Gadolinium Zirconate-based TBC containing two-layer (duplex) thermal barrier, three-layer functionally graded thermal barrier, and five-layer functionally graded TBCs. According to Figure 11a, the maximum tensile stress and compressive stress in the duplex GZ-based TBC are about 19.42 MPa and 18.09 MPa, respectively. As observed in Figure 11b, the maximum tensile stress in the GZ-based three-layer functionally graded TBC is reduced to 11.37 MPa. The gradual change in the thermal expansion coefficients of the FGM layers leads to better adhesion among the layers and lower stress concentration. As shown in Figure 11c, the maximum tensile stress in the GZ-based five-layer functionally graded TBC is 8.53 MPa, which is the least one compared to the maximum stress level in the two-layer thermal barrier and three-layer functionally graded TBCs. The simulation results of the stress distribution in the duplex and functionally graded GZ based TBC were in good agreement with those reported in the literature [18,29,30]. In the functionally graded TBC, the less difference between thermal expansions of layers would improve the adhesive bonding of ceramic/metal interface, thus avoiding later stress concentration and lessening the risk of crack initiation and propagation [11,33,34]. The maximum tensile stress in the three-layer functionally graded TBC was reduced by 41 %, compared to that of the two-layer TBC. In addition, the maximum tensile stress in the five-layer functionally graded TBC was reduced by 25 %, compared to that of the three-layer functionally graded TBC. This shows the effect of using functionally graded TBCs on both residual stress reduction and coating lifetime extension. Figure 8. SEM image of the structure of YSZ/NiCrAlY coating with map analyses of elements Figure 9. SEM image of the structure of Yttria stabilized Zirconia based functionally graded coating with map analyses of elements Figure 10. Mesh sensitivity analysis for TBC coating analysis Figure 11. Stress distribution contours S22 (in Pascal) in Gadolinium Zirconate based thermal barrier coating a) duplex, b) three-layer FG-TBC, and c) five-layer FG-TBC Figure 12 shows the contour of the stress distribution S22 (in Pascal) for Yttria stabilized Zirconia-based TBC: duplex (YSZ/NiCrAlY), a three-layer FG-TBC (YSZ/ 50 %YSZ + 50 %NiCrAlY/NiCrAlY) and a five-layer FG-TBC (YSZ/ 75 %YSZ + 25 %NiCrAlY/ 50 %YSZ + 50 %NiCrAlY/ 25 %YSZ + 75 %NiCrAlY/ NiCrAlY). Given that the thermal expansion of the BC is greater than that of the ceramic layer, compressive strength is observed in peak regions and tensile strength in valleys. In addition, a slow transition can be observed while approaching from the peak to the valley. The simulation results revealed that after the thermal shock, the average values of the maximum stress are 29 MPa for the duplex TBC (interface of TC / bond coat), 3.15 MPa for the three-layer FG-TBC system (interface of 50 % NiCrAlY - 50 %YSZ / YSZ), and 1.8 MPa for the five-layer FG-TBC system (interface of 25 % NiCrAlY- 75 % YSZ / YSZ). Of note, the stress distribution in the five-layer FG-TBC system is uniform which affects the performance and longevity of the thermal barrier system. The reason for this phenomenon is that the coefficient of the thermal expansion changed gradually throughout the five-layer functionally graded coating. A comparison of Figures 11 and 12 confirms the higher amount of the residual stress in the Gadolinium zirconate-based TBC than that in the Yitria zirconate-based TBC. In Table 3, α_GZ<α_YSZ<α_NiCrAlY ; therefore, the difference in the thermal expansion coefficients of GZ and NiCrAlY is greater than that of YSZ and NiCrAlY, thus resulting in higher stress concentration. As observed in Figure 13, the temperature distribution contours for the Gadolinium Zirconate-based TBC are shown in the following froms: two-layer (duplex) TBC, three-layer FG-TBC, and five-layer FG-TBC. The temperature difference between the TC surface and substrate in a three-layer TBC is 35 °C which is lower than that of two-layer (duplex) TBC, i.e., 62 °C. The three-layer functionally graded TBC has a 43 % lower insulating value than that of the two-layer TBC, and the five-layer functionally graded TBC has a 17 % lower insulating value than that of the three-layer functionally graded TBC mainly because the thickness of the TC of FG-TBCs is less than that of duplex TBCs. To provide thermal insulation, the layers near the surface (high temperature side) of FG-TBC should be ceramic rich. The composition gradually changes along the TBC thickness, from the ceramic-rich near the surface to the metal-rich near the coating-metallic substrate interface. The layers near the interface are metal-rich, thus having higher fracture toughness [33,34]. Figure 14 shows the temperature distribution contours of the two-layer, three-layer, and five-layer functionally graded Yttria stabilized Zirconia-based TBCs. The simulation results revealed that the temperature dropped by 102 °C along the duplex TBC. Thermal insulation was found to be reduced by 30 % in the functionally graded YSZ/NiCrAlY coatings, compared to duplex coatings. It was previously reported that the insulation value of FGTBCs was lower than that of conventional duplex YSZ TBCs with the same total coating thickness and YSZ porosity.The five-layer FG-TBC performs even worse than its three-layer counterpart due to a thinner YSZ top layer [35]. As observed in Figure 14, heat is primarily concentrated in the upper section of the coating system, and the substrate is protected from thermal damages. In other words, heat transfer is limited to the heat resistive ceramic parts while the BC and substrate experience lower temperatures, thus allowing for higher working temperatures. TBC protects the substrate from thermal load and keeps it at relatively lower Figure 12. Stress distribution contours S22 (in Pascal) in Yittria Zirconate base thermal barrier coating a) duplex, b) three-layer FG-TBC, and c) five-layer FG-TBC Figure 13. Temperature distribution contours in Gadolinium Zirconate based: a) two layer thermal barrier coating, b) three-layer functionally graded thermal barrier coating, and c) five-layer functionally graded thermal barrier coating temperatures, thus resulting in an improved fatigue life, increased lifetime, and lower maintenance costs. A comparison of Figures 13 and 14 revealed that the YSZ system exhibited better thermal insulation ability than GZ system. In addition, GZ had lower thermal conductivity (1.3 W/mK-1 at 1100 °C) than that of YSZ (1.8 W/mK-1 at 1100 °C). Consequently, it can be anticipated that GZ can provide better thermal insulation to the metallic substrate than YSZ. However, temperature reduction in the GZ system was even lower than that in the YSZ system. At 1500 °C, the YSZ system outperformed the GZ system approximately 39 %. According to the reports, the YSZ layer is characterized by more porosity than the GZ layer. YSZ also contains higher porosity content than that of GZ that can be justified by the lower melting temperature of GZ (2570 °C) than that of YSZ (2700 °C). Therefore, the GZ splats undergo a greater degree of melting temprature than that of YSZ, thus resulting in a relatively denser coating for GZ than that for YSZ. The dependence of the porosity of heat conductivity of coatings was taken into account to explain the lower thermal reduction of Gadolinium Zirconate-base TBC than that of the YSZ system [36,37]. Through an indentation fracture mechanics approach, the micro hardness, fracture toughness, and residual stress of the multiple-shocked TBC were evaluated. Figure 15 illustrates the load-displacement curve for the maximum force of 9000 µN. Figure 14. Temperature distribution contours in Yttria stabilized Zirconia based a) two layer thermal barrier coating, b) three-layer functionally graded thermal barrier coating, and c) five-layer functionally graded thermal barrier coating Figure 15. Load–displacement curve of the stressed three-layer YSZ-based FG-TBC under the maximum load of 9000 µN in the direction perpendicular to the cross-sectional area of the top coat Figure 16. AFM images of impression by Berkovich indenter on the cross-section of the top coat layer of the stressed 3-layer YSZ-based FG-TBC under the maximum load of 8000 µN Figure 16 depicts the AFM images of a Berkovich indenter impression on a stressed FG-TBC under the maximum load of 8000 N. The relationship between the load and displacement from the initial unloading was used to calculate the Young's modulus, as shown in Equations (1)-(3). The values of the calculated hardness and Young's modulus in the TC are reported in Table 4. The size of the radial cracks was determined using image processing software. Two parameters P/C2 and C0.5 were then calculated using the mean length of radial cracks. The results are reported in Table 5 according to which, the diagram of P/C1.5 was plotted in terms of C0.5 (Figure 17). As mentioned earlier in Figure 17, (-2σ/(√π 〖 χ〗_i )) and (K_IC/χ_i ) denote the slope and intercept of Equation (6), respectively. The calculation results of the Xi, KIC, and residual stress are reported in Table 6, Table 7, and Table 8, respectively. TABLE 4. Hardness and Young’s modulus values for the top coat of stressed 3-layer YSZ- based FG-TBC P E_r E_i υ_i Υ E H 5000 178.6 1141 0.07 0.25 195.35 12.65 6000 185.8 1141 0.07 0.25 204.6 13.93 7000 211.6 1141 0.07 0.25 238.8 18.38 7500 190.5 1141 0.07 0.25 210.71 15.85 8000 111.5 1141 0.07 0.25 114.77 10.48 9000 211.7 1141 0.07 0.25 238.93 15.22 TABLE 5. The results of the calculation of the P/C1.5 and C0.5 and the mean length of the radial cracks P(µN) C_1(µm) C_2(µm) C_3(µm) C_avg(µm) C_avg(m) P/C^(1.5)(N/m^(1.5))*〖10〗^6 C^(0.5)(m^(0.5)) 5000 0.33 0.33 0.29 0.32 3.16E-07 28.15 0.00056 6000 0.38 0.38 0.42 0.39 3.93E-07 24.35 0.00063 7000 0.46 0.44 0.43 0.44 4.43E-07 23.74 0.00067 7500 0.54 0.53 0.55 0.54 5.40E-07 18.90 0.00073 8000 0.55 0.55 0.63 0.58 5.76E-07 18.30 0.00075 9000 0.54 0.58 0.62 0.58 5.80E-07 20.38 0.00076 Figure 17. Relationships of P/C1.5 versus C0.5 when indented on the top coating surface TABLE 6. Results of the calculation of the Xi Xi E/H H_avg(GPa) E_avg(GPa) α 0.059 13.91 14.42 200.53 0.016 TABLE 7. Results of the calculation of the residual stress of stressed 3-layer YSZ- based FG-TBC σ (MPa) σ (Pa) Slope 0.100861- 100861- 46287 TABLE 8. Results of the calculation of the fracture toughness of the stressed three-layer YSZ- based FG-TBC K_IC (MPa.m^(1⁄2)) Intercept X E/H H_avg (GPa) E_avg (GPa) α 3.18 53.933 0.059 13.91 14.42 200.53 0.016 As validation or model evaluation, the stresses obtained from the nanoindentation method and simulation are presented in Table 9. The presented simulation is acceptable based on the low difference in the obtained results. The results from the stress measurement through nanoindentation method indicated that the designed method could measure the stress along the coating depth without damaging the sample. TABLE 9. Comparison of the nanoindentation and simulation results of the stressed three-layer YSZ- based FG-TBC σ_xx (Nanoindentation) σ_xx (Simulation) Error percent -0.100861 (MPa) -0.098 (MPa) 2.84 4. CONCLUSION The current study aimed to investigate the thermal and residual stress distribution in the duplex and functionally graded Thermal Barrier Coatings (TBCs) of yttria-stabilized zirconia (YSZ) and gadolinium zirconate (GZ) during a realistic heating regime that includes heating, operating time, and final cooling. For this purpose, a finite element model was employed to model the effects of thermal loading on the thermomechanical response and stress distribution. In addition, three different YSZ-based TBC systems, one duplex, and two FG -TBCs, were fabricated using the APS method. The residual stress, elastic modulus, microhardness, and fracture toughness of the coating were determined using the nanoindentation stress measurement method. The FGM strategy reduced the stress values in the coating more significantly than the conventional coating. Small differences in the thermal expansion would improve the adhesive bond between different ceramic/metal interfaces and reduce the risk of crack initiation and propagation. According to the findings, the level of residual stress in the functionally graded TBC was lower than that in the duplex TBC, and the stress distribution was more uniform, hence performance improvement and longevity expansion of the thermal barrier system. The results also indicated that most of the damage and heat fluxes were concentrated and accumulates in the ceramic face layers, hence less damage and shortened substrate life. Examination of the surface of the specimens after the application of thermal shock revealed that the separation of the layers occurred more frequently in the two-layer TBCs than in the graded coatings. The results of stress measurement through the nanoindentation method showed that the developed stress measurement method could measure stress along the coating depth without damaging the specimen. It was also found that the TBC based on yttria-stabilized zirconia was slightly better than the that based on GZ in terms of thermal shock resistance and residual stress. ACKNOWLEDGEMENTS The authors would like to appreciate Iran University of Science and Technology and Standard Research Institute for their support.

Please cite this article as: Nayebpashaee, N., Etemadi, E., Mohammad Sadeghi, B., Seyedein, S. H., “Experimental and Numerical Study of the Thermo-Mechanical Behavior of Plasma-Sprayed Gadolinium and Yitria Zirconate-Based Thermal Barrier Coatings”, Advanced Ceramics Progress, Vol. 7, No. 4, (2021), 36-51. https://doi.org/10.30501/ACP.2022.322563.1078