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Section 3. Materials Science
DOI: http://dx.doi.org/10.20534/ESR-17-5.6-10-15
Ilinkova Tatiana Aleksandrovna, Kazan National Research and Technical University Kazan Aviation Institute, Professor Kazan Chemical and Technological Institute (BSc)Honors Belarusian Polytechnic Institute (Minsk) MSc. Research Institute of Engines of Minaviaprom (Moscow) PhD.
E-mail: [email protected] Agbanwu David Onu, Undergraduate student
Kazan National Research and technical university-Kazan Aviation Institute
MEASUREMENT OF THE COEFFICIENT OF THERMAL CONDUCTIVITY AND FINITE ELEMENT ANALYSIS OF THE STRESS AND DEFORMATION OF THERMAL BARRIER COATINGS
Abstract: Thermal barrier coatings (TBCs) are widely used on different components of gas turbine engines especially in the combustion chamber where so much thermal energy is expended. During thermal cycling, stresses develop and this directly affects the durability of the coatings. In this study, an experimental procedure was followed in finding the 1, coefficient of thermal conductivity of the TBC-an important parameter in calculating the values of stresses, deformations and the temperature field along the thickness of the TBC coating, the finite element method (FEM) implemented in the ANSYS application package, was used. Keywords: thermal, barrier coating, base material, zirconia, ceramic, cycling, stress, substrate.
1. Introduction
Thermal barrier coatings (TBCs) used in the combustion chamber of gas turbine engine and other hot components increase engine efficiency and performance [2; 3]. The schematic diagram of a typical TBC system is shown in Fig 2. The durability and performance of thermal barrier coatings is affected by several structural factors such as porosity in the ceramic and stress developed in the TBC system especially during thermal cycling in the engine. Let us consider the
nature of thermal stresses in the ceramic layer. In most cases, the destruction of the coating can occur for three reasons.
1. Due to high interfacial tangential stress, a, by shear mechanism.
2. Due to high normal stresses, by detachment mechanism.
3. Due to high compressive stresses a, by the mechanism of longitudinal bending [4; 5; 6].
Figure 1. Geometry of the model. The radial direction is denoted by 'y', the normal direction is 'x'
When the coated sample is heated from room temperature Ta to the operating temperature Tp 1523 K, due to the difference in the coefficients of thermal expansion, a stress aa arises, which is expressed by the relation:
EK (aM -aK )(Tp-TJ
where:
1 -Mk
(1)
Ek - Young's modulus of the ceramic;
aj a^ - average coefficient of thermal expansion of metallic layer and ceramics in the temperature interval of T - Tj
p - Poisson's ratio of the ceramic.
The outer layers of the ceramic layer tend to stretch, while the inner layers, which are colder, is hardly compressed. As a result, biaxial compressive and radial tensile stresses develop. Under the action of these stresses, the ceramic layer tends to bend and separate from the substrate, thereby causing destruction of the ceramic layer [7].
As observed from formula (1), the more the thermal stresses as a result of rapid heating, the larger the temperature gradient over the thickness of the ceramic coating.
The finite element method (FEM), implemented in the ANSYS application package, was used to calculate the values of stress and deformations in the layers "ceramic coating — sublayer — base".
2. Materials and methods
The thermal barrier coating used in the simulation consist of three layers. The outer ceramic layer of yttria-stabilized zirconia (YSZ), which has a low thermal conductivity. Under the ceramic layer is a heat-resistant layer (substrate), which protects the base metal from oxidation and contributes to increasing the strength ofadhesion of the ceramic layer to the substrate. The three layers of the TBC including the base material are assumed to be homogeneous. Thermal and elastic-plastic properties of the substrate and ceramic materials (temperature, young's modulus, thermal expansion coefficient, thermal conductivity and Poisson's ratio) were considered in the analysis. The coefficient of thermal conductivity of the YSZ coating used were obtained in the experiment described in (2.1). The material properties such as the strength and density, which may vary during thermal cycling, have been neglected in this study. Their values as a function of temperature are given in Tables 1 to 3 [14; 15; 16].
The analysis was carried out with the temperature on the ceramic surface at 1523 K. These results in the highest temperature gradient in the radial direction and, accordingly, the maximum stresses appear in the system. However, in a short while, these stresses relax, due to deformation of the sublayer.
Figure 2. Layers of a thermal barrier coating (TBC) Table 1. Characteristics of the base material (Ni-Cr-W-Mo)
Temperature 293 K 873 K 1073 K 1173 K 1273 K
E (Pa) 1.95*10 11 1.66*10 11 1.41*10 11 1.3*10 11 1.20*10 11
0.3 0.3 0.3 0.3 0.3
a x 10-6 (1/K) 11.0 14.01 15.8 16.3 21.1
X (W/mK) 10.9 21.4 24.3 25.1 26.9
Thickness, mm 2.0
Table 2. Characteristics of the substrate (Ni-Cr-Al)
Temperature 473 K 873 K 1073 K 1173 K 1273 K
E (Pa) 1.9*10 11
0.3
a x 10-6 (1/K) 13.3 14.6 15.7 16.3 18.9
X (W/mK) 13 14 14.3 14.5 15
Thickness, mm 0.1
Table 3. Characteristics of the material of the ceramic layer (YSZ).
Temperature 473 K 873 K 1073 K 1173 K 1273 K 1373 K
E (Pa) 3.2*10 10
0.27
a x 10-6 (1/K) 9 10.2 11 11.4 11.8 12.1
Thickness, mm 0.3
2.1 Calculation of the thermal protection efficiency of the Thermal Barrier Coating of optimum thicknesses
It is important to know the measure of thermal protection of the thermal barrier coating in the thickness range 260-460 ^m (A range in which no damage is observed in the test). An important
physical parameter of the thermal barrier coating is the coefficient of its thermal conductivity, X, which is necessary in calculating the temperature and heat stress within the coatings. The coefficient of thermal conductivities of the ceramic layer with varying cycles as seen in table 4 obtained from the experiment is described below.
Figure 3. View of the experimental setup
Figure 4. Schematic Diagram of the experimental setup; 1 - sample; 2 - sample clamp; 3 - burner; 4 - air compressor; 5 - fixed cooling nozzle; 6 - movable cooling nozzle; 7 - pyrometer; 8 - swivel mechanism; 9 - gearmotor; 10 - thermocouple; 11 - propane and oxygen; 12 - timer; 13 - electronic unit; 14 - potentiometer; 15 - solenoid valve; 16 - control valves
It is important to note that, in the experiment, the coefficient ofthermal conductivity was not calculated over the entire thickness of the sample (the base material-substrate-ceramic), but its value directly in substrate and ceramic layer. Since the thickness of the base material in this case is not included in the calculation of the thermal conductivity coefficient, on the basis of the results obtained, it is pos-
sible to calculate the value for any thicknesses and configurations of the wall of the base material. Continuous recording of temperature on the surface of the coating and the reverse side of the samples during the thermocycling tests allowed the creation of a data bank on the basis of which calculation and numerical modeling of the thermal state of the TBC was performed.
It is necessary to calculate the coefficient ofthermal conductivity in a one-dimensional setting in view of the large values of the specific heat flux produced by the propane-butane and oxygen flame on one side and the inflow ofa cooling air j et on the other. Based on the use ofa two-layer wall (ceramic- substrate) under the condition of an ideal thermal contact ofthe layers, the absence of internal heat sources in the materials, we write for the thermal conductivity coefficient of the ceramic layer thus:
\=q Sc/(Th - Tc - S qAs)
Where q is the specific heat flux through the wall of the ceramic and substrate S and S are the thickness of the ceramic and substrate
c s
respectively Th and Tc are the temperatures of the wall surfaces when heated from the side of hot gas and cooling air respectively as measured in the experiment
\ and! is the coefficient of thermal conductivity of the ceramic and the substrate respectively.
In formula (1), the actual pass through heat flux q is measured by an internal heat flux gauge via an embedded thermocouple [1]. The values of the average thermal conductivity of the ceramic layer is seen table 4.
Table 4.
Number of cycles (min) \ (W/M K)
0 0.865
100 0.89
200 0.90
500 0.91
1000 0.89
3. Results and Discussions
As the duration of the thermal alternating heat load (heating and cooling) increases, a nonmonotonic change in the TBC is usually observed, which can be associated with structural changes in the coating [1]. Overall, there is an increase in the conductivity of the ceramic except when it was exposed to 1000 cycles of heating and cooling, there was a decrease the coefficient of thermal conductivity from 0.91 to 0.89 (W/m K). This is because at the 1000th minute, the ceramic has experienced the most sintering and densification [17].
Sample of TBC before experiment 200x Sample after 400 cycles 200x
Sample after 1000 cycles 200x Figure 5. Structural changes within the ceramic layer with varying cycles
Figure 6. The numerical model of thermal stresses arising in the coating with the greatest temperature gradient
Figure 7. A numerical model of deformations arising in
Using the data in Tables 1-3, we obtained that the tensile
stress of about 188-190 MPa is acting in the ceramic layer (fig. 6). With subsequent cooling, due to the difference in the coefficient of thermal expansion of the substrate and the ceramic layer, compressive stresses will appear in the latter. This stress is localized near the sub layer. Under the influence of this stress, the ceramic coating is cracked, but it will not lose adhesion to the sublayer and the substrate, the bonding metal coating is very plastic and the stresses
a coating at the time of the greatest temperature gradient
arising in it quickly relax within a few seconds [12]. They will intensively increase when the coating temperature becomes lower than 1073 K. The occurrence of thermal stresses causes deformation. The greatest deformations predominate in the sublayer, closer to the edge of the ceramic (Fig. 7). This is explained by the fact that usually in the coating there are small residual stresses, which depend on the thickness of the coating and on the stress difference in the upper layers and the lower layers of the coating adjacent to the sublayer [13].
c)
Figure 8.The temperature field over the cross section of the sample with varying thickness (260 ^m, 300 nm and 460 ^m respectively) of the ceramic layer
The results indicate that with an increase in the thickness of the ceramic layer from 260 ^m to 460 ^m, the temperature at the boundary with the sublayer is reduced by 100 degrees. In this case, the intensity of the temperature decrease along the thickness of the
Table 5. Temperature change along the thickness of the TBC
ceramic layer is approximately the same for different thicknesses and is 0.45-0.57 K/^m. The results of the analysis are further summarized in table 5.
Thickness of ceramic layer, 8 (^m) Temperature on the surface of the ceramic layer K Temperature of the ceramic layer on the boundary with the sublayer, K AT along the thickness of the ceramic layer, K AT/8
260 1523 1382 138 0.53
300 1523 1348 172 0.57
460 1523 1313 207 0.45
4. Conclusion
In general, there was an increase in the coefficient of thermal conductivity of the ceramic layer from 0.865 to 0.91. There was a decrease at the 1000th minute of thermal cycling due to ceramic densification and sintering.
The finite element analysis was carried out to study stress buildup and deformation in a thermal barrier coating under thermal cycling. The thickness, plastic-elastic and the thermal properties of the layers were considered during the analysis. The stress and deformation test were carried out in order to understand the durability properties of TBCs.
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