1. Introduction
Thermal barrier coatings (TBCs), an oxide ceramic layer for the protection of a substrate material, are widely used for the thermal, oxidation and hot corrosion protection of high-temperature components in gas turbines [
1]. The coatings provide insulation to metallic structures, thus, delaying the thermally-induced failure that governs the component durability and life [
2,
3]. However, as the thrust–weight ratio of engines become higher, the temperature of gas turbines for military aircraft engines has reached 1700 °C. The operating temperature of traditional YSZ coatings is generally lower than 1200 °C, which cannot meet the requirements of future military aircraft engines [
4,
5]. Therefore, the method to reduce the thermal conductivity of YSZ coatings became a hot topic in recent years. The thermal conductivity of YSZ coatings is closely related to the microstructure; therefore, it is necessary to study the microstructure of the TBCs in order to reduce its thermal conductivity.
Numerous works have investigated the relationship between the microstructures and thermal conductivity. Pores and cracks are the most important factors affecting the thermal conductivity. Moreover, there have been many studies on the effect of pores and cracks that focus on thermal conductivity. Chi and coworkers used image analysis (IA) data to simulate the effect of porosity on the thermal diffusivity; it turns out a very fast increase in the thermal diffusivity within the first 15 h of service. It might be due to the crack-like pores that filled with air through this process and to the thermal diffusivity of air (2.2 × 10
−5 m
2·s
−1) which is roughly two orders of magnitude higher than the air thermal diffusivity of typical YSZ porous TBCs (3–5 × 10
−7 m
2·s
−1) [
6]. Chi et al. [
7] compared coatings with different microstructures prepared with different feedstocks and different spraying processes, then analyzed structure–thermal conductivity images during thermal cycling. The results revealed that more interface, higher porosity and more interlamellar pores can reduce the thermal conductivity of TBCs. Increasing the length and width of the interlamellar pores at high temperatures can reduce the tendency of the coating to sinter, thereby lowering the thermal conductivity of TBCs. However, no quantitative relationship was provided between the microstructure and thermal conductivity.
Wei and coworkers quantified the influence of pore radius and crack length on effective thermal conductivity. It is found that the longest crack has the greatest effect on thermal conductivity [
8]. Clyne and Golosnoy established equations of pores to predict thermal conductivity of TBCs using Eshelby-based and contact-based analytical models respectively [
9,
10]. When the Eshelby-based model is used in materials with high porosity, the calculated results are found to be higher than the experimental results because the Eshelby-based analytical model depends upon the assumption that only the tetragonal phase is present. Contact-based analysis models have been adopted to predict the microstructure changes during sintering. However, the establishment of these models is based on the analysis of SEM images, leading to the establishment of an equation that is roughly similar to the experimental value rather than based on the actual microstructure and resulting in the limitations of model application. To research the relationship between interface and thermal conductivity, the model of heat conduction established by McPherson [
11], the model of object oriented finite (OFF) established by Wang et al. [
12] and the mathematical formula that can calculate the influence of the interface on thermal conductivity established by Wei and his colleagues [
13] all made explanations for low thermal conductivity of the coatings with the lamellae. They think that the lamellar interspaces are equivalent to the pores parallel to the interface and that the width of the pores is equivalent to the average free path of the gas molecules, which limits the conduction of heat flow. In these studies, the influence of the splat interface on the coating performance was quantified and the influence coefficient was calculated to account for 25%–70% of the total influence, but the establishment of these model is also based on SEM microstructure observations followed by simulation calculations, which fail to calculate based on the true microstructure the influence coefficients of the grain boundaries, interface and monoclinic separately.
Therefore, we tried to establish a finite element (FE) model based on the microstructure of electron backscatter diffraction (EBSD) analysis because more information, such as grain size and phase composition, can be easily obtained by EBSD compared with SEM. Hence, it is more accurate to establish the FE model based on EBSD images when we consider the influence of multiple factors on the thermal conductivity. The effect coefficient of grain boundaries, interfaces and monoclinic phase on thermal conductivity are directly calculated; additionally, it provides a reference for how to guide the spraying process to lower the thermal conductivity of the coatings.
2. Materials and Methods
Commercially-available ZrO
2-3% mol Y
2O
3 nanopowder and micropowder were used. Metco A-2000 APS equipment was used to deposit the coatings onto aluminum substrates (Guan Yu special Alloy products Co. Ltd., Shanghai, China, 128 mm × 84 mm × 2 mm). Two specimens, designated as M
1 and M
2, were sprayed with nanopowder. A third specimen, designated as M
3, was sprayed with micropowder. The spray gun parameters are listed in
Table 1.
Microstructure of the YSZ coating is characterized by SEM (Magellan 400, FEI, Hillsboro, OR, USA) equipped with an EBSD detector. EBSD provides the conditions for the analysis of crystal microdomain orientation and crystal structure while preserving the conventional features of SEM. Through EBSD image analysis of a certain sample area, the size, distribution, orientation and grain boundary distribution of the crystal grains and the phase contained in the area can be obtained.
In this study, 25 EBSD images were selected for each YSZ coating, and an FE mesh model that is consistent with the true microstructure is generated. The FE meshes of the M
1, M
2 and M
3 coatings with microstructures are illustrated in next part. The thermal conductivities of the YSZ coatings are obtained through a steady-state heat transfer analysis, while the thermal conductivity of ceramics in the direction of the temperature gradient can be computed with Fourier’s equation:
where
h is the thickness of ceramic,
is the width, λ
m represents the thermal conductivity for the bulk material, Γ is the integral path of the heat flux density and ∇
T is the temperature gradient.
The thermal conductivity of the tetragonal phase, the grain boundaries and the splat interface are 2.65, 1.54 and 0.03 W/m·K, respectively [
14]. Rhagavan et al. revealed that the thermal conductivity of pure monoclinic zirconia with 98% density was 3.6 W/m·K [
15]. Thus, the thermal conductivity of monoclinic phase in our model is also set to be 3.6 W/m·K. The thermal conductivity of each content is shown in
Table 2.
4. Conclusions
The FE model was established based on EBSD analysis, which could offer more microstructure information. At the same time, an ideal interface model was introduced. The computational results are in agreement with the experimental findings, and the calculation error is lower than 10%. Using this model can simulate the effect of each microstructure on thermal conductivity more accurately.
The splat interface and grain boundaries play a critical role in the reduction of thermal conductivity, and the influence coefficient of the interface on thermal conductivity is much larger than that of the grain boundary. Therefore, it is necessary to take the splat interface into consideration when simulating the influence of microstructures on thermal conductivity. Moreover, when studying methods for reducing the thermal conductivity of coatings, the introduction of splat interfaces is a worthwhile consideration.