Optimization Design and Performance Verification of the CeYSZ/Al2O3 Double Ceramic Layer Thermal Barrier Coatings Structure Parameters

Abstract

Double ceramic layer thermal barrier coatings (DLC-TBCs) are favored for combining the benefits of top and bottom ceramic materials. The thickness ratio of the top and bottom ceramic layers significantly impacts the performance of the DLC-TBCs. In the design process, it is generally desired to balance its thermal insulation properties with a long service life. Therefore, this study establishes a multi-objective parameter optimization design method based on NSGA-II to optimize the thickness of the CeYSZ/Al₂O₃ DCL-TBCs. Experimental verification of the coating performance was conducted based on the optimization results. Firstly, based on theoretical and numerical models, a quantitative analysis was conducted on the effects of the thickness of each material in the CeYSZ/Al₂O₃ DCL-TBCs system on thermal insulation and thermal stress. Space parameters were obtained using optimal Latin hypercube sampling, and a radial basis function (RBF) neural network surrogate model was constructed based on the numerical calculation results. Sensitivity analysis was employed to evaluate the impact of the total thickness of the TBCs and the thickness of the Al₂O₃ ceramic layer on the objective function. Finally, NSGA-II was utilized for optimization. The obtained Pareto optimal solution set was validated, showing that the performance of the CeYSZ 190 μm/Al₂O₃ 120 μm DLC-TBCs satisfied the requirements. Therefore, TBCs of different thicknesses were sprayed and subjected to thermal insulation and thermal shock experiments. The results demonstrated that the optimized TBCs significantly improved service life without compromising thermal insulation, providing a new approach for the subsequent design of DLC-TBCs structures.

Introduction

With advancements in the aerospace industry, aero-engines, as the core components of aircraft, are being developed to achieve higher bypass ratios and thrust-to-weight ratios. As engine performance improves, the operating temperatures of hot-end components have also risen. Therefore, before fabricating sensors on the engine surface, an insulating layer is essential to provide electrical insulation for the sensors (Ref 1, 2-3). Thermal barrier coatings (TBCs), primarily made of YSZ, serve as effective insulators compared to the substrate material, reducing substrate temperature and being widely used on engine blades (Ref 4, 5, 6-7). Consequently, TBCs composite materials have garnered significant attention. DCL-TBCs retain the performance of the bottom ceramic layer while taking advantage of the properties of the top ceramic layer (Ref 8, 9-10). In a study by Zhao et al. (Ref 11), a DCL-TBCs structure composed of CeYSZ/Al₂O₃ was proposed, demonstrating that a coating with CeYSZ as the bottom layer and Al₂O₃ as the top layer offers superior insulation, meeting the resistance requirements for thin-film sensors. Key indicators for evaluating and improving DCL-TBCs performance include thermal shock resistance, thermal cycling life, and insulation efficiency.

The thermal conductivity and coefficient of thermal expansion of TBCs materials, the matching of expansion coefficients between the substrate and coating, as well as surface roughness and coating thickness, all influence TBCs performance (Ref 8, 12, 13-14). Many researchers have studied how to enhance DCL-TBCs performance by selectively modifying ceramic materials through doping. This has led to materials with higher melting points, lower thermal conductivity, and higher expansion coefficients. Schmitt et al. (Ref 15) optimized composite TBCs designs to improve erosion resistance and durability, using air plasma spraying (APS) technology to develop composites with low conductivity phases, such as rare-earth oxides, and simulating particle impact stress distribution via finite element analysis (FEA). Zhuang et al. (Ref 16) focused on designing and optimizing self-healing MgO coatings applied through plasma spraying. By analyzing stress and heat transfer mechanisms, they optimized coating thickness, material composition, and self-healing agent content to extend coating lifespan and reduce crack formation caused by stress concentration.

When higher performance requirements are imposed on DCL-TBCs, structural parameters play a critical role, even without altering material properties (Ref 17). Xu et al. (Ref 18) investigated the effects of geometric and material parameters, such as the thickness and modulus of the top coat and bond coat, as well as delamination behavior at the TBCs interface. They derived the interfacial crack driving force as a function of the Young’s modulus and thickness of the top and bond coats. Han et al. (Ref 19) examined the influence of two structural parameters on the thermal insulation of DCL-TBCs: the thickness of the top coat (TC) layer and the total thickness of the TC and intermediate coat (IC) layers. Using finite element methods, they identified an optimal thickness distribution for the double ceramic layers. Dai et al. (Ref 19), through thermal cycling experiments, showed that the cyclic life of DCL coatings depends on the thickness ratio of LZ and YSZ layers, with YSZ layers between 150-200 μm yielding longer lifespans than single-layer YSZ coatings. When the YSZ layer is less than 100 μm, DCL coatings fail within the LZ layer near the YSZ-LZ interface. Zahra et al. (Ref 19) designed and optimized thick TBC structures to balance high insulation performance and durability by introducing gradient layers. Chen et al. (Ref 20) proposed a rapid multi-objective optimization method using a constrained backpropagation neural network (BPNN) combined with the constrained non-dominated sorting genetic algorithm (NSGA-II), which minimizes residual stress in the ceramic layer and reduces effective thermal conductivity across various DCL-TBC systems (Ref 21, 22-23).

Therefore, it is essential to enhance the lifespan and thermal insulation performance of the CeYSZ/Al₂O₃ DCL-TBCs proposed by Zhao et al. (Ref 11) through thoughtful ceramic layer structural design. This study conducted research and optimization design on the thicknesses of the CeYSZ ceramic bottom layer and Al₂O₃ ceramic top layer within the TBCs system based on the aforementioned DCL-TBCs model. Subsequently, an RBF neural network surrogate model was established using optimal Latin hypercube sampling and numerical calculation results, followed by parameter sensitivity analysis. The NSGA-II algorithm was then employed for parameter optimization based on the surrogate model. Finally, experimental comparisons were conducted between the designed TBCs structure and the structure proposed by Zhao et al. (Ref 11), confirming superior performance of the optimized DCL-TBCs design.

Optimization Method

Calculation and Analysis of High Temperature Thermal Stress

As shown in the Fig 1(a), the DCL-TBC model proposed by Zhao et al. (Ref 11). features a CeYSZ ceramic base layer with a higher thermal expansion coefficient and superior corrosion resistance, while the Al₂O₃ ceramic top layer is employed to enhance the insulating properties of the TBCs structure, meeting the electrical insulation requirements for in-situ sensor fabrication on the TBCs surface. Therefore, through multi-objective structural parameter optimization, this study aims to improve the service life of the TBCs by selecting the appropriate thicknesses for the Al₂O₃ and CeYSZ ceramic layers. This optimization is performed without altering the original material properties, such as thermal expansion coefficient, thermal conductivity, and electrical conductivity, while also ensuring the necessary insulation for sensor fabrication.

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Fig. 1

TBCs film structure bending diagram

Thermal mismatch due to differing coefficients of thermal expansion (CTE) between materials is a critical factor influencing the service life of TBCs operating in high-temperature environments. Thermal stresses arise from the thermal expansion mismatch between layers, affecting each layer's deformation. As depicted in Fig 1(b), when subjected to temperature changes, unconstrained differential contraction occurs between the metal substrate and ceramic layer, resulting in different levels of strain in each material. To prevent delamination between the layers, uniform tensile and compressive stresses are applied to the metal and ceramic layers, respectively, ensuring displacement compatibility while maintaining a net zero force (Ref 24, 25). The composite structure of ceramic and metal undergoes bending to balance the moments caused by asymmetric stresses applied in the previous step.

In this context, a coating with thickness $t_i$ is sequentially bonded onto a substrate with thickness $t_s$, where subscript i denotes the layer number ranging from 1 to n. The interface between the 1 and $1-n$ layers is located at position $z=h_i$. Based on these definitions, the relationship between $h_i$ and $t_i$ can be described as follows:$$h_i=\sum _{j=1}^i{t}_j(1\le i\le n,1\le j\le n)$$

Therefore, according to Zhang et al. (Ref 26), the stress distribution in the i layer coating and the substrate can be respectively represented as:$${\sigma }_i=E_i\left[\mathrm{\Delta }\alpha \mathrm{\Delta }T+\sum _{k=1}^n\frac{E_k{t}_k}{E_s{t}_s}\left({\alpha }_k-{\alpha }_i\right)\mathrm{\Delta }T-\sum _{i=1}^n\frac{6E_i{t}_i\mathrm{\Delta }\alpha \mathrm{\Delta }T}{E_s{t}_s^2}\left(z+\frac{1}{2}{t}_s-\sum _{i=1}^n\frac{E_i{t}_i}{E_s{t}_s}\left(2h_{i-1}+t_i\right)\right)\right]$$

Accordingly, the coefficient of thermal expansions (CTEs) of the substrate and the ith layer are ${\alpha }_s$ and ${\alpha }_i$, respectively. Because of the temperature difference, $\mathrm{\Delta }T$, there are unconstrained strains in the coating and substrate. where $\mathit{Es}$ and $\mathit{Ei}$ are the elastic moduli of the substrate and the ith coating layer, respectively.

Based on the above equation, the thermal stresses experienced by each coating layer under high-temperature service conditions can be computed, enabling effective estimation of the service life of the thermal barrier coating. In material mechanics calculations, it is generally assumed that each layer’s materials are homogeneous and isotropic. Additionally, creep and plastic deformation mechanisms are often disregarded. Many classical material mechanics formulas and theories are based on these assumptions to simplify analysis and computation. In most cases, the effects of creep and plastic deformation can be ignored because materials typically exhibit elastic behavior within their normal operating range.

The material calculation parameters in this study are shown in Table 1 above (Ref 5, 27, 28). Taking the CeYSZ 200 μm/Al₂O₃ 200 μm thermal barrier coating as an example in Fig 2(c), the stress distribution of the thermal barrier coating system is analyzed. At high temperatures, the thermal barrier coating system experiences internal stresses in both the x and y directions. Given that the longitudinal thickness of the thermal barrier coating is significantly smaller than its lateral dimensions, the thermal mismatch stresses along the x-axis are a critical focus of this study. Therefore, the thermal stress at different joints of the thermal barrier coating under different ceramic layer thicknesses is plotted, as shown in Fig 2(c)

Table 1. Parameters of materials

Materials	T, °C	E, GPa	α/10−6/°C	υ	λ, W/m K
Substrate	1000	149	15.6	0.3	23.8
NiCoCrAlY	1000	174	16	0.3	12
CeYSZ	1000	40	12	0.11	0.32
Al2O3	1000	30	9.6	0.26	5.8

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Fig. 2

(a) Temperature distribution gradient in TBCs (b) Influence of ceramic layer thickness on temperature distribution

In the x-direction, compressive stresses are observed in the ceramic layer, CeYSZ 200 μm/Al₂O₃ 200 μm thermal barrier coating with a maximum compressive stress value of 788.17 MPa. The edge of the ceramic layer, influenced by boundary conditions, also experiences compressive stresses approaching the oxidation layer. Furthermore, with an increase in the thickness of the Al₂O₃ ceramic layer, the maximum thermal stress in the thermal barrier coating also increases, potentially raising the likelihood of coating failure.

Calculation and Analysis of Thermal Insulations

The TBCs is a critical metric for evaluating their effectiveness. A well-performing TBCs must ensure that the metal substrate maintains a lower temperature to protect it from high-temperature degradation. According to principles of heat transfer, the thickness and distribution of ceramic layers in TBCs influence the temperature distribution within the coating, thereby affecting the overall thermal insulation performance of the system. The insulation performance of the coating reflects its ability to protect turbine blades against gas turbine hot gas corrosion, fulfilling the primary design requirements of thermal barrier coatings

To simulate and test the thermal insulation performance of coatings with different thickness ratios at 1100 °C, the insulation effectiveness is typically evaluated through the temperature distribution across the entire coating. In the thermal insulation analysis, the front surface temperature is set at 1100 °C, and the overall backside heat transfer coefficient is set at 900 W/(m²·°C). By calculating the temperature distribution within each ceramic layer and the temperature drop achievable by each layer, it is possible to analyze the impact of different thickness ratios of ceramic layers on the overall thermal insulation effectiveness of the double-layer thermal barrier coating system.

According to Fourier's law, the heat transfer equation is expressed as (Ref 23, 24):$$\frac{\partial T}{\partial t}=\frac{\lambda }{\rho c}\frac{{\partial }^{2}T}{\partial y^2}$$where c and ρ are the specific heat capacity and density, T is the transient temperature, t is time, and λ is the thermal conductivity.

As illustrated in Fig 2(a), the temperature distribution within the double ceramic thermal barrier coating and substrate at various coating thickness ratios is depicted, along with the temperature profile from the thermal barrier coating to the substrate. The temperature distribution across the entire system shows a gradual decrease from the surface of the model to the bottom of the substrate, with the most significant temperature drop occurring within the CeYSZ ceramic layer. As the thickness of the intermediate CeYSZ ceramic layer increases, the overall temperature of the substrate gradually decreases. This is due to the fact that the thermal conductivity of CeYSZ is significantly lower than that of Al₂O₃, thereby affecting the overall thermal insulation performance of the double ceramic thermal barrier coating system. The temperature profiles at various nodes for different ceramic layer thickness ratios are shown in Fig 2(b). From these curves, it can be observed that the temperature difference between nodes represents the thermal insulation provided by the bond layer. The CeYSZ layer plays a major role in thermal insulation within the TBC, whereas the thermal insulation effect of the Al₂O₃ layer and the bond layer is relatively limited. Based on this analysis, it is evident that adjusting the thickness ratio of the two ceramic layers in the double ceramic coating can alter the overall thermal insulation performance of the coating.

Optimization Objectives and Constraints

Considering the impact of stress due to different thermal expansion coefficients of the materials in TBCs during use, the reliability of the TBCs and thin-film sensor composite system is compromised, making it prone to delamination at high temperatures. However, according to the calculation results, the most significant changes in thermal stress at high temperatures occur between the Al₂O₃ ceramic layer and the CeYSZ ceramic layer, and between the bond coat and the metal substrate. The stress variation between the CeYSZ layer and the bond coat is relatively small due to the closer match in thermal expansion coefficients and other parameters. Therefore, three optimization objectives are set for this study: The temperature T of the alloy substrate when the surface of the thermal barrier coating is subjected to 1100 °C.Thermal stress in the bond coat and the thermal stress in the Al₂O₃ layer.

In multi-objective optimization problems, multiple competing or conflicting objectives are typically involved. Therefore, resolving conflicts in multi-objective optimization requires finding a set of feasible solutions, known as Pareto optimal solutions (Ref 29). For example, in this study, increasing the total thickness of the TBCs improves the thermal insulation performance of the DCL-TBCs system, but simultaneously increases the internal thermal stress of the TBCs, affecting its high-temperature service life. Additionally, based on the structure proposed in Zhao et al’s. (Ref 11) paper, In order to meet the insulation requirements of sensors machined on metal-based blade surfaces, we conducted experiments that confirmed when the thickness of the Al₂O₃ layer exceeds 100 μm, the resistance value can meet the requirement of 10⁵ Ω. The thickness of the TBC applied to different components varies, and the thickness of the TBC applied to the surface of the turbine blade is usually not more than 500 μm (Ref 30, 31).

Therefore, the constraint conditions in this study are set as the total thickness of the TBCs (TH) and the thickness of the Al₂O₃ layer (TA). The specific parameters are as follows in Table 2.

Table 2. Optimization objectives and constraints

Optimization objective	Optimization direction	Design variable	Value range
T	Min	TA	400um > TA > 100um
σ1	Min	TH	500um > TH > 100um
σ3	Min

Optimization Process

Figure 3(a) shows the flowchart of the optimization process. To optimize the design parameters with accuracy using as few samples as possible, the Design of Experiments (DOE) method is employed to conduct parameter experiments and construct empirical formulas and approximate models. First, within the constrained parameter range, optimal Latin hypercube sampling is used to uniformly select sampling points. Sixty sample points are selected in the parameter space, with 40 points used as the training set to construct the surrogate model, and 20 points used as the test set to evaluate the fitting accuracy of the surrogate model.

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Fig. 3

(a) DLC-TBCs multi-objective parameter optimization process (b) Parameter optimization RBF neural network agent model

DOE represents the response values of only a limited number of sample points and cannot capture the results for all design parameters. Therefore, constructing a surrogate model can fit an approximate model of the original objective function, accelerating the parameter optimization process. This approach effectively reduces computational cost and time consumption (Ref 32).

Common surrogate models include Radial Basis Function (RBF) neural networks, Kriging models, BP neural networks and Gaussian processes. Kriging primarily relies on interpolation but is vulnerable to noisy data and has limited ability to generalize. Similarly, Gaussian processes, which build upon Kriging, inherit some of these weaknesses. BP neural networks are suitable for complex pattern recognition and classification tasks. However, they are prone to overfitting, especially when data is insufficient, making them unsuitable in the context of this study, where the dataset is limited. In contrast, RBF neural networks excel at capturing complex nonlinear relationships between input and output variables, making them the preferred choice for the surrogate model in this study. The RBF neural network used in this study is an artificial neural network model composed of an input layer, a radial basis function layer, and an output layer (Ref 33, 34). It is characterized by its ability to perform tasks such as function approximation, classification, and clustering, and it exhibits strong capabilities in handling nonlinear problems. In Fig. 3(b), the surrogate model is an RBF neural network, which is a three-layer feedforward neural network consisting of an input layer, a hidden layer, and an output layer. The input layer comprises the design variable vectors of the sample points, which are transformed nonlinearly to obtain the hidden layer. The hidden layer contains several neurons, and the transformation function of these neurons is the radial basis function.

Typically, the radial basis function is chosen to be a Gaussian function, which is expressed as:$${\phi }_j\left(x\right)=\text{exp}\left(-,\frac{\Vert x-c_j\Vert }{2{{\delta }_j}^2}\right)j=\text{1,2},...,m$$

In this context, let x be the input sample point design variable vector, $c_j$ be the center of the radial basis function, $∥·∥$ be the Euclidean distance between the input vector and the center vector, ${\delta }_j$ be the width of the radial basis function, and m be the number of hidden layer neurons. The output layer is a linear combination of radial basis functions and weight coefficients, expressed as:$$y_i=\sum _{j=1}^m{\omega }_{\mathit{ij}}{\phi }_j\left(x\right)i=\text{1,2},...,n$$

In this context, ${\phi }_j$ represents the response values, ${\omega }_{\mathit{ij}}$ denotes the weight coefficients of the radial basis functions, and n is the number of response values.

Therefore, based on the CAE simulation results of the selected sampling points, a radial basis function neural network surrogate model is constructed and its accuracy is evaluated. The evaluation parameter is R². If R² meets the engineering requirement of 0.9, the next step of optimization is continued. If the accuracy is not achieved, more sampling points need to be added until the fitting accuracy meets the requirement.

Next, parameter sensitivity analysis is conducted to identify which parameters have the greatest impact on multiple optimization objectives. This helps the optimization algorithm to better select parameter settings and more quickly find the optimal solution. Finally, the NSGA-II algorithm is used to perform parameter optimization on the surrogate model, and the obtained optimization results are compared and validated (Ref 35). If the performance of the optimization results is inferior to that of the original DCL-TBCs, the optimization process is repeated. Otherwise, the optimization results are output, completing the optimization.

With the broader application of multi-objective parameter optimization in various fields, NSGA-II has improved upon the classic NSGA. It has made changes in algorithm selection, non-dominated sorting, and individual selection to enhance the efficiency and performance of solving multi-objective optimization problems. Additionally, NSGA-II introduces an elite preservation strategy, retaining a portion of the Pareto optimal solutions from each generation and directly passing them to the next generation to ensure population diversity and convergence. The algorithm parameters used in this study are shown in the Table 3 below.

Table 3. Parameters of NSGA-II genetic algorithm

Parameters	Value
Population size	100
Maximal algebra	200
Cross fraction	0.9
Mutation fraction	0.1

Optimization Results Analysis

Parameter Correlation Analysis

In the optimization design of DCL-TBCs, thermal insulation and thermal stress are conflicting objectives. Therefore, it is often difficult to achieve optimal results for all objectives simultaneously. Consequently, a compromise must be made between the different optimization goals to obtain a relatively optimal solution set that balances all the requirements.

The Pearson correlation coefficient is a statistical measure used to evaluate the strength and direction of the linear relationship between two continuous variables. Its value ranges between − 1 and 1. In this study, the Pearson correlation coefficient is used to assess the correlation between design variables and optimization objectives. The expression is as follows:$$p_{\mathit{xy}}=\frac{{\sum }_{i=1}^n\left(X_i,-,\overline{X}\right)\left(Y_i,-,\overline{Y}\right)}{\sqrt{\sum _{i=1}^n{\left(X_i,-,\overline{X}\right)}^2}\sqrt{\sum _{i=1}^n{\left(Y_i,-,\overline{Y}\right)}^2}}$$

Let X = [x₁, x₂, …, x_n] and Y = [y₁, y₂, …, y_n] be any two sets of data, and let $\overline{X}$ and $\overline{Y}$ be the means of X and Y, respectively, with n representing the sample size. The Pearson correlation coefficient ranges from − 1 to 1. p_xy greater than zero indicates a positive correlation between the variables, while a value less than zero indicates a negative correlation. The closer the absolute value is to 1, the stronger the correlation.

Figure 4(a) presents the results of the correlation analysis between the optimization objectives and the design variables. Based on the parameter correlation analysis, it is evident that the total thickness of the TBCs and the thickness of the Al₂O₃ ceramic layer are positively correlated with the thermal stress in the bond coat. This means that as the total thickness increases, the thermal stress in the bond coat also increases. Regarding the stress in the Al₂O₃ layer, the total thickness of the TBCs is positively correlated, while the thickness of the Al₂O₃ ceramic layer is negatively correlated. Therefore, to minimize ${\sigma }_3$, the total thickness of the TBCs should be reduced, and the thickness of the Al₂O₃ ceramic layer should be increased.

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Fig. 4

(a) Correlation between optimization objectives and design variables (b) Regression analysis for the surrogate model (c) Computational Pareto frontier

In terms of thermal insulation performance, the total thickness of the TBC is negatively correlated, whereas the thickness of the Al₂O₃ ceramic layer is positively correlated. This implies that a thicker TBCs results in better thermal insulation, while a thicker Al₂O₃ ceramic layer leads to poorer thermal insulation (Table 4).

Table 4. Optimization trend of design variables

	T	σ1	σ3
TH	Min	Max	Max
TA	Max	Max	Min

Regression Analysis of the Surrogate Model

The primary function of the surrogate model is to approximate the true objective function. Therefore, it is crucial to ensure that the surrogate model can accurately fit the real data. Evaluating the fitting accuracy of the surrogate model verifies whether the model can precisely predict the behavior of the true objective function. If the fitting accuracy of the surrogate model is low, the optimization algorithm might be misled, potentially failing to find the optimal solution or resulting in a slower convergence rate. Hence, ensuring the fitting accuracy of the surrogate model is key to improving the efficiency of the optimization algorithm. After constructing the surrogate model, it is necessary to evaluate its fitting accuracy. The accuracy of a surrogate model is typically evaluated using four metrics, with the coefficient of determination (R²) being one of the key measures. In this case, R² was chosen for assessment. A surrogate model is considered to have sufficient fitting accuracy for a given response when the R² value for that response is greater than 0.9. The formula for R² is as follows:$$R^2=1-\frac{{\sum }_{i=1}^n{\left(f_i,\left(x\right),-,{\widehat{f}}_i,\left(x\right)\right)}^2}{{\sum }_{i=1}^n{\left(f_i,\left(x\right),-,\overline{f},\left(x\right)\right)}^2}$$where $f_i\left(x\right)$ represents the actual values of the response, ${\widehat{f}}_i\left(x\right)$ denotes the approximate values calculated by the surrogate model, ${\overline{f}}_i\left(x\right)$ is the mean of $f_i\left(x\right)$, and n is the number of test points.

The analysis results are shown in the Fig. 4(c), indicating that the predicted results are in good agreement with the CAE calculation results. Table 5 displays the R² values of the RBF neural network surrogate model for the three objective functions. It can be seen that all R² values are greater than 0.9, meeting the standards for engineering applications. Therefore, it is considered that parameter optimization based on this surrogate model has sufficient reliability.

Table 5. Optimization trend of design variables

Parameters	Value
T	0.9869
σ1	0.9983
σ3	0.9978

Pareto Front

Using the NSGA-II method, the parameter optimization of the TBCs structure was completed, resulting in a total of 20,000 solutions. The final set of solutions that align with the optimization trend is shown in Fig. 4(c). From the figure, it can be observed that a stable Pareto front emerged after iteration, representing the trade-offs between the conflicting objective functions. Clearly, optimizing one objective function inevitably compromises the performance of another objective function (Ref 27).

To comprehensively evaluate the Pareto optimal solutions and determine the most favorable one, this study aims to meet engineering requirements by ensuring that the back temperature of the DLC-TBCs remains below 620 K. Consequently, the selection of optimized Pareto solutions is constrained by the requirement that the thickness of the TBC must exceed 310 µm. The DLC-TBCs system is a composite consisting of different metals and ceramics with significantly varying mechanical properties. During service, alternating heating and cooling cycles induce differential expansion and contraction in the materials, leading to thermal mismatch stress. A sharp increase in thermal mismatch stress can cause cracking of the TBC, and premature failure of the DLC-TBCs is a critical factor affecting the safety of aircraft engines. Therefore, when selecting a Pareto optimal solution, it is crucial to maintain low values for both the thermal stress in the bond coat and the stress in the Al₂O₃ layer. Based on these objectives, the study ultimately selects a ceramic layer total thickness of 310 µm, with the Al₂O₃ layer thickness being 120 µm.

Thermal Barrier Coating Testing Experiment

Preparation of Thermal Barrier Coatings by Atmospheric Plasma Spraying

In this experiment, GH2747 nickel-based superalloy was used as the substrate, with its specific composition shown in the Table 6 below. The aforementioned thermal barrier coatings were prepared on the surface using APS. The ceramic layer powder consisted of 20 wt% CeYSZ + 80 wt.% (8 wt.% Y₂O₃/ZrO₂) micron-sized powder, hereinafter referred to as CeYSZ (supplied by Beijing Sans Spry New Materials Co., Ltd.), with particle sizes ranging from 20 to 70 µm. The Al₂O₃ micron-sized powder (supplied by Beijing Sans Spry New Materials Co., Ltd.) had particle sizes ranging from 40 µm to 80 µm. GH2747 Ni-based superalloys (manufactured by Central Iron & Steel Research Institute, Φ30 mm × 5 mm) were used as substrates.

Table 6. Parameters of plasma spraying

Plasma parameters	CoNiCrAlY	CeYSZ	Al2O3
Current (A)	580	850	900
Argon gas flow (SCFH)	100	80	80
Hydrogen gas flow (SCFH)	15	45	55
Carrier gas flow (SCFH)	12	10	10
Powder feed rate (r/min)	2	4	3
Spraying distance (mm)	75	75	75

In this study, different configurations of DLC-TBC were prepared for subsequent experimental analysis: CeYSZ 200 µm/Al₂O₃ 200 µm as mentioned in Zhao et al.'s (Ref 11) paper, and the optimized configuration of CeYSZ 190 µm/Al₂O₃ 120 µm from this study. Before spraying, the substrate was ultrasonically cleaned with acetone to eliminate surface contaminants. Sandblasting was then applied using quartz sand at a pressure of 0.5 MPa to increase surface roughness, improving mechanical adhesion between the coating and substrate. The process was repeated uniformly until the surface became rough and non-reflective. To minimize the temperature gradient between the substrate and coating, the substrate was preheated, as large temperature differences can cause thermal stress, leading to cracking or spalling of the coating. The bond layer of the thermal barrier coating, made from CoNiCrAlY, was applied with a thickness of 70 μm.

Cross-sectional EDS Analysis of TBCs

The cross-sectional EDS analysis of the four types of TBCs is shown in Fig. 5. The figure indicates that the coatings are well bonded, with distinct bond coat and ceramic layer structures. The thickness and clear interfaces of each coating layer can be observed, demonstrating that the thermal barrier coating structure used in this test is dense and has good mechanical bonding. Due to factors such as gas volatilization and coating techniques during the preparation process, there is usually a certain degree of porosity in the coatings. The distribution of elements between the layers has also been determined: O and Y are present in all ceramic layers, Zr and Ce are only present in the CeYSZ ceramic layer, Ni, Co, and Cr are mainly distributed in the bond coat, and Al is found in both the Al₂O₃ ceramic layer and the bond coat.

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Fig. 5

TBCs section EDS (a) 190 µm CeYSZ/120 µm Al₂O₃ (b) 200 µm CeYSZ/200 µm Al₂O₃

Thermal Insulation Test

In the thermal insulation test, the combustion flame jet formed by oxygen and propane was used to simulate the internal combustion environment of an engine, heating the samples coated with TBCs (Ref 28). The thermal insulation of the TBCs was calculated based on the temperature difference between the back and front surfaces of the sample. The front surface temperature of the sample was controlled by adjusting the distance between the flame jet and the sample surface. When the front surface temperature of the sample was set to 1100 ± 10 °C, the coating surface was allowed to reach this temperature range and then maintained for 12-15 min.

When the temperature on the display panel of the temperature tester showed only minor fluctuations, it was considered to have reached a thermal equilibrium state. The average temperature difference between the front and back surfaces was calculated using the temperatures measured by standard thermocouples. This value was then compared with the average temperature difference of an uncoated sample to determine the thermal insulation temperature of the thermal barrier coating system (Ref 26). The test system is shown in Fig. 6(a) and (b). As can be seen from the test results in Fig. 6(c) and (d), the thermal barrier coating can play a certain role in heat insulation and protect the matrix, and the thermal insulation effect of different thickness thermal barrier coatings is different. Among them, the back temperature of 190 µm CeYSZ/120 µm Al₂O₃ is 48.09% of the flame temperature and the back temperature of 200 µm CeYSZ/200 µm Al₂O₃ is 47.61% of the flame temperature. The thermal insulation effect of the two thermal barrier coatings is not much different, and the thermal insulation effect of the Al₂O₃ ceramic layer is not much improved. The back temperature of the Al₂O₃ ceramic layer increased by 80um only decreased by 0.48%.

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Fig. 6

DLC-TBCs back temperature test system schematic (b) DLC-TBCs back temperature test system diagram (c) 190 µm CeYSZ/ 120 µm Al₂O₃ back temperature curve (d) 200 µm CeYSZ/ 200 µm Al₂O₃ back temperature curve

Thermal Shock Test

The thermal shock resistance of a coating refers to its ability to maintain performance after undergoing one or multiple high-low temperature cycles. This resistance mainly depends on the relationship between the induced stress and the strength of the coating. The TBCs system is a composite system composed of different metal and ceramic materials with significantly different mechanical properties (Ref 28). During service, alternating heating and cooling cycles cause various materials to expand and contract to varying degrees, generating thermal mismatch stress.

In this study, thermal shock cycling tests were conducted to determine the high-temperature lifespan of the coatings. First, the experimental temperature was set to 1100°C, and this temperature was maintained consistently inside a muffle furnace. Samples at room temperature (approximately 25°C) were placed in the furnace and heated for about 20 min until they reached 1100°C. The samples were then immediately removed and rapidly quenched in water at 25°C for 90 s. After water quenching, the samples were dried in an oven for 10 minutes. This procedure was repeated for 5, 10, 20, and 30 cycles. The surface morphology of the samples after different numbers of cycles was observed and characterized to determine whether the coating had failed.

During the thermal shock test, the surface of the 200 µm CeYSZ/200 µm Al₂O₃ coating showed the most significant changes. Due to the edge effect of the substrate, delamination first appeared at the edges of the substrate coating. Starting from the 8th thermal shock cycle, the Al₂O₃ ceramic layer began to peel off the surface of the 200 µm CeYSZ/200 µm Al₂O₃ coating. As the experiment progressed, this phenomenon became more pronounced. However, the substrate surface still retained a protective Al₂O₃ coating until the completion of 19 thermal shock cycles, at which point the CeYSZ layer was completely exposed.

In contrast, the 190 µm CeYSZ/120 µm Al₂O₃ coating experienced partial delamination of the Al₂O₃ ceramic layer, covering about 20% of the area. After the 24th cycle, the 200 µm CeYSZ/200 µm Al₂O₃ thermal barrier coating had almost completely failed, with most of the substrate exposed. The 190 µm CeYSZ/120 µm Al₂O₃ coating retained only a small portion of the Al₂O₃ ceramic layer. By the end of the 30th thermal shock cycle, the substrate of the 200 µm CeYSZ/200 µm Al₂O₃ thermal barrier coating was fully exposed, indicating complete failure. Although the Al₂O₃ ceramic layer of the 190 µm CeYSZ/120 µm Al₂O₃ coating had completely delaminated, the CeYSZ ceramic layer remained intactFrom Fig. 7(b), it is observed that after the completion of the 30th thermal shock experiment, the 190 µm CeYSZ/120 µm Al₂O₃ coating exhibited good adhesion between the CeYSZ ceramic layer and the bond coat, with the CeYSZ layer showing minor cracks. In contrast, as shown in Fig. 7(c), the 200 µm CeYSZ/200 µm Al₂O₃ coating displayed numerous cracks within the CeYSZ layer, and the thickness was reduced due to spalling.

[See PDF for image]

Fig. 7

(a)Fracture surfaces of thermally cycled samples (b) Cross-sectional BSE image of the 190 µm CeYSZ/120 µm Al₂O₃ coating after 30 thermal shock experiments (c) Cross-sectional BSE image of the 200 µm CeYSZ/200 µm Al₂O₃ coating after 30 thermal shock experiments.

Conclusion

This paper proposes a design method for DLC-TBCs, selecting the thickness of the ceramic layer as the design variable. A total of 60 sample cases were generated and subjected to simulation calculations. Correlation analysis between the design variables and objective functions was then conducted. The NSGA-II algorithm based on the RBF neural network surrogate model was used for optimization. Finally, TBCs with different ceramic layer thicknesses were prepared and their performance was compared. The following conclusions were obtained:

1. The regression analysis results show that the R² values for all three objective functions are greater than 0.9, indicating that the relationship between the design variables and objective functions fitted by the RBF neural network surrogate model is highly accurate. This suggests that using the surrogate model for parameter optimization is a feasible method.

2. According to the sensitivity analysis, to enhance the thermal insulation performance of DLC-TBCs, the total thickness of the ceramic layer should be increased, along with the proportion of the CeYSZ layer. Additionally, to reduce the stress in the ceramic layer, the total thickness of the TBC should be minimized. Therefore, parameter optimization resulted in a total ceramic layer thickness of 310 µm, with an Al₂O₃ layer thickness of 120 µm.

3. The original thickness of CeYSZ 200 µm/Al₂O₃ 200 µm and the optimized thickness of CeYSZ 190 µm/Al₂O₃ 120 µm DLC-TBCs were prepared. Through back temperature and thermal shock tests, it was demonstrated that the optimized ceramic layer structure sacrifices very little in thermal insulation performance while significantly improving the lifespan of the TBCs. This also confirms that the NSGA-II algorithm can provide new insights for the design of DLC-TBCs.

Acknowledgments

No acknowledgments to declare.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Publisher's Note

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