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Dominant effect of oriented 2D pores on heat flux in lamellar structured thermal barrier coatings
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Dominant effect of oriented 2D pores on heat flux in lamellar structured thermal barrier coatings Zhi-Yuan Weia, Li-Shuang Wangb,∗, Hong-Neng Caia,∗∗, Guang-Rong Lia,c,∗∗∗, Xue-Feng Chend, Wei-Xu Zhange a
State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China School of Materials Science and Engineering, Xi'an Shiyou University, Xi'an, 710065, China c Forschungszentrum Jülich, Institute of Energy and Climate Research IEK-1: Materials and Processing, D-52425, Jülich, Germany d State Key Laboratory for Manufacturing Systems Engineering, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China e State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal barrier coatings Analytical model Thermal resistance Functional 2D pores Structural tailoring
Thermal barrier coatings (TBCs) provide thermal insulation to metallic components served at high temperatures. The oriented 2D pores are primarily responsible for the efficient prevention of heat flux. Thus, structural design of TBCs with higher thermal insulation requires clear understanding on the thermal conduction inside coatings. Up to now, previous analytical models to investigate the heat conduction were mainly based on the concept of thermal contact resistance. However, the related assumption was far away from the real coating microstructure. In this study, the intrinsic structural characteristics of plasma sprayed TBCs were firstly investigated. Subsequently, an analytical model based on the structural features was developed to understand the dominant effect of oriented 2D pores on heat flux inside the coatings. Results showed that the insulative ratio of 2D pores dominantly determine the effective prevention of heat flux. Moreover, effects of the microstructural parameters, including splat thickness, bonding ratio and unit size, on the total thermal resistance was discussed. Overall, the understanding of the dominant effect of 2D pores would make it possible to design new TBCs with high performance in future applications.
1. Introduction Thermal barrier coatings (TBCs) protect metallic materials from direct thermal exposure during their service [1–4]. Therefore, the TBCs become necessary for aircraft engines and land-based gas turbines, whose working temperature exceeds the bearable limit of the superalloy components [5–9]. Given the thermal barrier function, TBCs should have low thermal conductivity, which is determined by the materials and the structure that related to the processing methods. It is believed that plasma spraying has proven its value to prepare TBC with excellent thermal barrier performance [10–14]. For example, the thermal conductivity of plasma sprayed yttria-stabilized zirconia (PSYSZ) can be as low as 1 W⋅m−1K−1, which is only 40% with respect to the bulk YSZ [15–17].
Commonly, a plasma sprayed ceramic coating is composed of stacked splats, exhibiting a lamellar structure [10,17–24]. There is only a limited fraction of bonding interface among all splat interfaces. The quantitative evaluation in plasma sprayed Al2O3 and yttria-stabilized zirconia (YSZ) coatings showed that only a maximum of 32% bonding ratio can be reached when the substrate temperature was not specially heated to higher than ∼300 °C [25–29]. The limited bonding ratio suggested that there is a large number of inter-splat pores between layers. In addition, due to the brittle nature of ceramic materials, some intra-splat cracks are formed inside layers during the process of thermal spraying. It is reported that the inter-splat pores and intra-splat cracks are connected together [30–32]. The inter-splat pores are often perpendicular to the heat flux, whereas most of the intra-splat cracks are parallel to the heat flux. The oriented inter-splat pores can effectively
∗
Corresponding author. School of Materials Science and Engineering, Xi'an Shiyou University, Xi'an, Shaanxi, 710065, PR China. Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China. ∗∗∗ Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China. E-mail addresses: [email protected] (L.-S. Wang), [email protected] (H.-N. Cai), [email protected] (G.-R. Li). ∗∗
https://doi.org/10.1016/j.ceramint.2019.05.254 Received 12 April 2019; Received in revised form 13 May 2019; Accepted 23 May 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: Zhi-Yuan Wei, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.05.254
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prevent the direct thermal conduction, since the thermal conductivity of air is significantly lower than that of the bulk splats. As a result, the oriented 2D pores inside plasma sprayed TBCs are dominantly responsible for the 150% improvement in thermal insulation with respect to the bulk materials [15]. In addition, the unique porous structure results in enhanced strain tolerance that is necessary for durable TBCs [16,33–40]. Therefore, the plasma sprayed ceramic coatings find their widely application in TBCs. It should be noted that the case become much more complicated in real service. A main problem is that sintering leads to approximately 80% increase in thermal conductivity, suggesting that nearly 60% degradation happens in thermal insulation [41–44]. Many investigations suggested that the main cause is the significant healing of oriented 2D pores [45,46]. Therefore, the current TBCs need further structural design to achieve high performance. As a fundamental work, it is firstly necessary to understand the thermal conductive behavior through plasma sprayed TBCs. In previous reports [47,48], the thermal resistance of plasma sprayed ceramic coatings has been understood based on the basic concept of thermal contact resistance. In the thermal conduction model firstly proposed by McPherson [48], the electric contact resistance theory was introduced to the thermal conductive behavior of thermally sprayed ceramic coatings [48–50]. In this case, to simplify the mathematical calculation, there is often an assumption that the size in the through-thickness direction (splat thickness, δ) is much larger than that in the in-plane direction (the distance between bonding area, C), i.e., δ > > C, as shown in Fig. 1. However, in real coatings, an opposite phenomenon can be obviously observed, since the splat thickness is approximately 10% with respect to the in-plane size [12,32,51]. This will obviously result in discrepancy between the calculation results and the experimental data. With the development of advanced gas turbine for aircraft engine and land-based gas turbine, a further enhanced thermal insulation is required for TBCs. According to the conventional model [48], the decrease in both bonding ratio and splat thickness will increase the thermal resistance. However, this decreasing trend would actually be against the basic assumption in the conventional model, i.e. δ≫C. Given that, Clyne et al. [49] proposed an analytical model with two-flux regions. In their model [49], the thermal contact resistance dominates one flux region, whereas the inter-splat thermal conduction determines the other flux region. This suggests that the thermal flux in the in-plane direction, along with the through-thickness direction, should be taken into account. However, the dominant effect of the oriented 2D pores on the heat flux and its relationship with structural factors are not yet clear. In this study, to fully understand the thermal conductive behavior
Table 1 Plasma spraying parameters to deposit YSZ coatings and individual splats. Parameters
Individual splats
Coatings
Plasma arc voltage, V Plasma arc current, A Flow rate of primary gas (Ar), L/min Flow rate of secondary gas (H2), L/min Flow rate of powder feeding gas (N2), L/min Spray distance, mm Torch traverse speed, mm/s Preheating temperature, °C
70 600 50 7 6 110 1000 250
70 600 50 7 6 110 800 /
through the 2D-pore-rich TBCs, intrinsic characteristics of plasma sprayed ceramic coating were investigated, and an analytical model was developed. The effects of the microstructural parameters, including splat thickness, bonding ratio between splats and unit size, on the total thermal resistance were discussed. The dominant effect of oriented 2D pores on heat flux was revealed. This will give positive suggestions on the development of TBCs with higher performance through microstructure tailoring. 2. Experimental 2.1. Sample preparation and thermal exposure Commercially available hollow spherical powders (−75 to +45 μm, Metco 204B-NS, Sulzer Metco Inc., New York, USA) was used to deposit coatings by a plasma spray method (GP-80, 80 kW class, Jiujiang, China). Table 1 shows the plasma spraying parameters. All the coatings were deposited to be approximately 1 mm. In order to obtain free-standing samples, coatings were deposited on stainless steel substrates that can be removed by a hydrochloric acid solution. Substrates have dimensions of φ12.7 mm × 7 mm, in order to facilitate the measurement of thermal conductivity. Before coating deposition, the substrate was roughened by grit blast, to avoid delamination of coatings during deposition. The free-standing samples were used for two aims. First is to observe the intrinsic characteristics of plasma sprayed ceramic coating with asdeposited samples. Second is to present the dominant effect of microstructural changes on the prevention of heat flux with samples heat treated at 1300 °C, based on the consideration that the service temperature of TBCs is often above 1000 °C. A relatively low rate of 10 °C/ min were used to control the heating and cooling rates. After different durations, changes in microstructure and thermal conductivity were investigated. 2.2. Microstructural characterization and property determination Microstructure of samples before and after thermal exposure was observed by scanning electron microscopy (SEM, TESCAN MIRA3, Brno, Czech Republic). It is known that 2D pores dominantly determine the effective properties of plasma sprayed ceramic coatings [12,52,53]. As a result, change in 2D pore length was determined based on 50 SEM images at 5000 × magnification, as shown in Fig. 2. Subsequently, the length density, defined as the total length of 2D pores in unit area, were obtained. Other details on the length measurement can be found elsewhere [46]. Focused ion beam (FIB, HeliosNanoLab600i, FEI, USA) was used to obtain the cross-section of partially bonded layers, in order to remain initial state. Thermal conductivity of the samples was determined by a laser flash method with following equation:
λ = ρ⋅CP⋅α
Fig. 1. Schematics of the concept of thermal contact resistance: (a) standard heat flux [50], and (b) simplified model used in the thermally sprayed coatings [48].
(1)
where λ is thermal conductivity, ρ is coating density, CP is heat capacity, and α is thermal diffusivity of the coating. 2
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coatings are deposited by stacking of disk-shaped splats that are formed by spreading and solidifying of molten powder after impact on underlying substrate [19,29,56,57]. In the case of the brittle ceramic splats that are used in TBCs, the quenching stress further divide the diskshaped splats into several segments. Therefore, the basic unit to form the plasma sprayed ceramic coatings is the splat segment. In addition, one splat segment is partially bonded to the lower layer (Fig. 3c), leading to the formation of inter-splat pores. In brief, the plasma sprayed ceramic coatings is intrinsically formed by stacking of composited 2D layers: 2D bulk splat segments surround by the air-trapped 2D pores (inter-splat pores and intra-splat cracks). Given that, length, thickness and bonding ratio of a splat segment are the main microstructural parameters. The thickness of splat segment was obtained from the cross-section of coatings and individual splats, as shown in Fig. 3a, c. Most of the segments have a thickness of 1–4 μm. This is consistent with the morphology observed from other reports [16,30,51]. Segment length was determined from the surface morphology of coatings and individual splats, as shown in Fig. 3b, d. It is easier to distinguish some clear splat segments from the flat individual splat than from the rough coating surface. In fact, the segments appear to be irregular shapes, since the intra-splat cracks randomly extend in directions. In order to facilitate the simulation in following section, the splat segments were assumed to be cubic shape. The average length of segments can be obtained from Eq. (2), and the result is about 6–20 μm.
Fig. 2. Schematic to determine pore length in plasma sprayed TBCs.
The thermal diffusivity was determined by laser flash analyzer (Netzsch, Germany). For each state, at least three samples were used to minimize errors. The CP was measured by differential scanning calorimetry (DSC 404, Netzsch, Germany). 3. Experimental results 3.1. Intrinsic characteristics at as-deposited state Fig. 3 shows cross-section and surface of plasma sprayed YSZ coatings and an individual splat at their as-deposited states. Distinctly porous feature can be observed. This pore-rich structure contributes to the effective prevention against heat flux, just as the service environment requires for TBCs [31]. Three kinds of pores can be clearly separated: globular voids and 2D inter-splat pores and 2D intra-splat cracks, which were widely reported [16,30,52,54]. Due to its porous nature, porosity was commonly used to characterize the structure of plasma sprayed ceramic coatings [16,55]. However, the reported porosities were approximately 10%∼20% [18,54], whereas the drop in thermal conductivity of coatings was often larger than 50% with respect to the corresponding bulk materials [41–43]. This suggests that the widely used porosity cannot essentially exhibit the microstructural features of plasma sprayed TBCs. The intrinsic characteristics of plasma sprayed ceramic coatings can be captured from their forming process. The plasma sprayed ceramic
C=
A N
(2)
where C refers to the average length of a segment, A refers to the apparent area of a defined region, N refers to the amount of segments in a defined region. Fig. 4 shows cross-section of a coating prepared by FIB. The partially bonded layers can be clear observed. The bonding ratio between segments can be obtained from previous reports. It is revealed that the bonding ratio is 10%–32% for plasma sprayed ceramic coatings using a method called structural visualization [12,25–27,47,58]. In addition, the bonding ratio can also be reflected from the determined properties
Fig. 3. Morphology of plasma sprayed YSZ: (a) cross-section of a coating, (b) surface of a coating, (c) [32] cross-section of an individual splat, and (d) [32] surface of an individual splat. 3
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healed in a multi-contact form, as reported in previous study [46,67]. Fig. 7 shows changes in 2D pore density. Regarding the decrement after thermal exposure, the porosity is less than 10% [12,16], whereas the 2D pore density is larger than 50%. In addition, the stage-sensitive changes of 2D pore density appear to be similar to the thermal conductivity. Based on the above-observed results, it is clear that the 2D pores primarily determine the thermal property of plasma sprayed ceramic coatings. Actually, the 2D pores are highly related to the structural parameters of a splat segment (i.e., the length, thickness and bonding ratio). Therefore, an analytical model was developed to investigate the dominant effect of 2D pores on the prevention of heat flux. 4. Simulation method 4.1. Model development Fig. 4. Partially bonded layers of a plasma sprayed coating prepared by FIB [32].
According to the conventional model [48], the splat thickness is assumed to be much larger than the segment length. In that way, the relative thermal resistance (KU/B, a ratio of the coating resistance to the corresponding bulk resistance) can be calculated using the following equation:
that are highly dependent on bonding ratio. For example, the fracture toughness [59] and ionic conductivity [60] of plasma sprayed ceramic coatings were about 20%∼30% with respect to the corresponding bulk materials. The ranges of microstructural parameters were determined to investigate the effect of microstructure on the prevention against heat flux in following section.
KU / B =
RU πr = RB 2αδ
(3)
where RU and RB are thermal resistances of the coating unit and the bulk material, respectively, r is the radius of a bonding area, α is the bonding ratio between splats, and δ is the splat thickness. However, according to the experimental observation in this study and previous reports [30,51], the segment length is approximately 10 times larger than the splat thickness. Therefore, the assumptions of δ≪C, other than the common assumption (δ > > C) in the conventional model, would be more suitable for the thermally sprayed coatings. A new model based on the intrinsic characteristics of plasma sprayed TBCs was developed. In details, the structural model was formed by stacking of splat segments that are basic units found in coatings, as shown in Fig. 8. The assumptions are described as follows: (i) the segments have same length (C) and thickness (δ); (ii) circular bonding area is located at the bottom center of a segment; (iii) the segments are stacked on the lower layer uniformly; (iv) most of all, the value of segment thickness is assumed to be much smaller than that of the segment length (δ≪C). As a result, the thermal conduction is divided into two directions, i.e. in-plane direction and through-thickness direction, as shown in Fig. 8f. Fig. 8c, d show the top view of the representative segments and the cross-sections along the black dotted line, respectively. Thermal radiation and thermal convection in the coating are ignored in this study. The thermal conduction in the through-thickness direction occurs in the bonding region (lines in dashed blue color) of the two adjoining splats, and the thermal conduction in the in-plane direction occurs within the splat between the two near bonding regions (lines in solid red color). Due to the obvious symmetry of the structure, a periodic pattern was extracted from the structure. The top view and the corresponding cross-sectional view are shown in
3.2. Changes in thermal property and microstructure during thermal exposure Fig. 5 shows changes in thermal conductivity of plasma sprayed YSZ coatings as a function of dwell time. For comparison, some data of thermal conductivity from previous reports were also presented as normalized values [16,43,52,55,61,62]. It is found that the thermal conductivity at as-deposited state is approximately 1 W m−1K−1, whereas it increases to nearly 2 W m−1K−1 after thermal exposure. This suggests that more than 50% degradation happens after thermal exposure, as can also be found in other reports [41–44]. Another interesting phenomenon is that most of the degradation occurs at initial thermal exposure. For example, the initial 10 h completes 80% degradation of thermal conductivity in total 200 h. This is caused by the stage-sensitive sintering kinetics revealed in other reports [18,54]. Fig. 6 shows the evolution of structure during thermal exposure. It is observed that the quantity of 2D pores significantly decreases. This is caused by sintering of ceramic materials at high temperature. During thermal exposure, thermally activated matter is spontaneously transferred to decrease the free energy of the whole system, which is a common phenomenon in porous ceramic materials [63–65]. Materials transfer can proceed in several methods, e.g., grain boundary grooving [52,66], surface faceting [54]. As a result, the pore surface become roughened and subsequently lead to bridge-connection between 2D pores. Therefore, the pore in plasma sprayed ceramic coating would be
Fig. 5. Changes of thermal conductivity as a function of dwell time (a) and normalized thermal conductivity with respect to their as-deposited states (b). 4
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Fig. 6. Evolution of microstructure before (a) [68] and after thermal exposure (b).
Fig. 7. Changes of 2D pore density as a function of dwell time (a) and normalized 2D pore density with respect to their as-deposited states (b).
procedures can be described as follows:
Fig. 8e and f, respectively. The theory of electric conduction between two rods in an infinite thin plate was used to determine the in-plane thermal resistance [69]. The total resistance can be obtained from the following equations:
RIP =
RTT1 = RTT2 = RTT =
KU / B
1 2
ρ ⎡ •⎢ (3.11 − 0.027α )ln πδ ⎢ ⎣
1 2
−
α π
−
α π
+
1 2
−
α π
−
1 2
+
α π
⎤ ⎥ ⎥ ⎦
ρδ 1 πr 2 4
(i) firstly, according to the Fourier's law, the heat flux transfers into the top surface (qin), and transfers out of the bottom surface (qout) are given by equation (7) and equation (8), respectively:
(5)
−
α π
+
1 2
−
α π
1 2
−
α π
−
1 2
+
α π
⎤ ⎥+ 2 α ⎥ ⎦
qout = h (TT − TS)
(8)
(ii) secondly, adiabatic boundary conditions were used to make sure that the top-bottom heat flux is equal to the bottom-environment heat exchange. As a result, the following relationship is obtained:
R 2RTT + RIP = U = = RB RB 4πδ 2 1 2
(7)
(4)
C2
⎡ •⎢ (3.11 − 0.027α )ln ⎢ ⎣
k e (TD − TT ) H
qin =
qin = −qout
(9)
(iii) finally, effective thermal conductivity of the periodic pattern is obtained based on equation (10):
(6)
where RU is the total thermal resistance of the coating unit, RB and ρ is the thermal resistance of the bulk material, RIP is the thermal resistance along in-plane direction, RTT is the thermal resistance along throughthickness direction, r is the radius of a bonding area, α is the bonding ratio between splats, δ is the segment thickness, and C is the segment length.
ke ≈
(TD − TS) hH ΔT ′
(10)
where TD is the top surface temperature of the top coat, TS is the environmental temperature, h is the thermal convection coefficient, H is the height of model, and ΔT′ is the temperature difference between the top and the bottom surfaces.
4.2. Simulation of heat flux 5. Simulation analysis The pattern constrained by periodic boundary condition was used to simulate the heat transfer behavior. The details to introduce the periodic boundary conditions can be found in previous report [70]. The mean values of structural parameters (i.e., length, thickness and bonding ratio of a splat segment) were used based on the experimental observation in Section 3. The input data are shown in Table 2. In addition, the x-z plane is defined as the reference plane, which is perpendicular to the heat flux. Thermal conductivity was predicted by ANSYS software. The detail
5.1. Comparison between model prediction and experiment During thermal exposure, significant changes in the thermal conductivity and the 2D pore can be observed in Figs. 5 and 7, respectively. This suggests that the changes in thermal properties are essentially related with the 2D pores. Fig. 9 shows the predicted thermal conductivity affected by the change in 2D pores, and the comparison with experimental data. It is obvious that the predicted values are well 5
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Fig. 8. Model development in this study: (a) top view, (b) perspective view, (c) top view of a basic stacking pattern, (d) cross-section of A-A′ corresponding to (c), (e) a basic unit for the heat flux, and (f) cross-section of (e). Table 2 Structural and intrinsic parameters used as the input data. Parameters
Values
Thermal conductivity of bulk YSZ, W·m−1·K−1 Thermal conductivity of pores, W·m−1·K−1 Mean length of a structural unit, μm Mean thickness of a structural unit, μm Mean bonding ratio between structural units, %
2.5 0.025 13 2.5 25
consistent with the experimental values. Overall, the changing trend can be divided into two stages from the view of thermal duration: much larger changing degree (∼80%) is completed at stage I, followed by slight changing degree at stage II. In addition, the stage I covers much shorter time (less than 10 h) with respect to the stage II (hundreds of hours). In brief, the correlation between the thermal property and the 2D pores further confirms the intrinsic characteristic obtained in this study. This is consistent with other reports on mechanical properties [53,54,71].
Fig. 9. Comparison in thermal conductivity between predicted and experimental values.
perpendicular to the heat flux would effectively prevent the heat transfer [12,53]. The underlying reason is that the thermal conductivity of air is dramatically smaller than that of the bulk materials. Fig. 10
5.2. Dominant effect of 2D pores on the heat flux Owing to the extremely large thermal resistance, the pores 6
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Fig. 10. Effect of aspect ratio on heat flux: (a) changes in aspect ratio of 2D pores during thermal exposure, (b) [12] aspect ratio of 10, and (c) [72] aspect ratio of 40.
5.3. Effect of structural parameters on the relative thermal resistance
shows the changes in aspect ratio of 2D pores during thermal exposure and its effect on heat flux. At as-deposited state, the aspect ratio is approximately 30–40, whereas it decreases to 10 by and large. Given the changes in the 2D pore length density (Fig. 6), the change in aspect ratio is mainly caused by healing of 2D pores. It is obvious that a greater temperature drop is caused by the 2D pore with a higher aspect ratio. That's why distinct degradation in thermal insulation of TBCs happens during service. The underlying mechanism is highly associated with the 2D distribution of heat flux caused by the unique structure. At the center of a pore, the heat flux would go through the air zone with a very low thermal conductivity. However, at the tips of a pore, the heat flux would change the original path, since it is much easier to go across the pore through neighboring bonding area. Therefore, only the center area can effectively prevent the heat flux. This phenomenon can also be found in other reports [49,73]. In this study, the ratio of effective area to prevent heat flux with respect to the total area is called insulative ratio. Based on the following equation [12], the insulative ratio of 2D pores can be determined. │qx│ < │qy│
5.3.1. Effect of segment length on the relative thermal resistance Fig. 12 shows the effect of unit size (C) on the relative thermal resistance for both the conventional model [48] and the model developed in this study. Regarding the changing trends in these two models, a common phenomenon is that the relative thermal resistances are increased as a function of unit size (C). However, the increase trends are different. In the case of the conventional model, a nearly linear relationship was found between the relative thermal resistance and the unit size (C). In fact, the relative thermal resistance in Eq. (3) can be changed to the following equation. Eq. (12) clearly suggests the linear relationship between the relative thermal resistance and unit size (C).
KU / B =
πα C 2αδ
(12)
where C is the unit size, α is the bonding ratio between splats, and δ is the splat thickness. In the case of the model proposed in this study, it is obvious that the increase of the relative thermal resistance is nonlinear. To further explore the nonlinear relationship, the respective contribution of the inplane and the through-thickness directions are shown in Fig. 12b. According to Eq. (5), if n × n units are combined together to form one large unit, the RTT of the large unit is as small as 1/n2 of that of the small unit. However, the n × n small units are in parallel. Therefore, the total thermal resistance in the through-thickness direction is not changed. This is consistent with Fig. 12b that the contribution of the through-thickness direction to the relative thermal resistance remained at a constant in spite of the change of unit size. According to Eq. (4), the thermal resistance of a unit in the in-plane direction is independent of unit size. Since the n × n small units in parallel change to one large unit, the total thermal resistance of the coating increases with n × n i.e. n2. This quadratic dependency contributes to a more significant increase than the linear increase dependency. For example, Fig. 13 shows the effect of unit size (changing from L to 2L) on the thermal resistance at different directions. Under a same volume, the length and sectional area of heat flux along through thickness remain unchanged. Therefore, the RTT is unaffected by the unit size. However, with the increase of the unit size, the heat flux would be decrease in an inverse-square law. This is the reason that the RIP would be quadratic dependent on the unit size.
(11)
where qx is the x-component of the heat flux, and qy is the y-component of the heat flux. Fig. 11 shows the insulative ratio before and after thermal exposure. It is obvious that thermal exposure results in significant decrease in insulative ratio. Similar phenomenon can also be found in other reports [12,74]. This suggests that the decrease in insulative ratio of 2D pores is the dominant factor responsible for the degradation in thermal insulation.
5.3.2. Effect of bonding ratio on the relative thermal resistance Fig. 14 shows the effect of bonding ratio (α) on the relative thermal resistance for both the conventional model [48] and the model in this study. Both of these two models presented a nonlinear relationship between the relative thermal resistance and bonding ratio. However, it is obvious that a much larger relative thermal resistance and a much more significant increase dependency on the decrease of bonding ratio
Fig. 11. Insulative ratio before and after thermal exposure. 7
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Fig. 12. Effect of unit size (C) on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red downtriangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 15. Schematics to show the effect of bonding ratio on the thermal resistance.
It is found that the thermal resistance in through-thickness direction is inversely proportional to the bonding ratio α. It presented a much more significant dependency on bonding ratio than that of the conventional model. As a result, the increase of the relative thermal resistance caused by the decrease of bonding ratio for the novel model is more significant with respect to that of the conventional model.
Fig. 13. Schematics to show the effect of unit size on the thermal resistance.
for the model proposed in this study. In the case of the conventional model, according to Eq. (3), the relative thermal resistance can be changed into,
KU / B =
πC 2 αδ
5.3.3. Effect of splat thickness on the relative thermal resistance Fig. 16 shows the effect of splat thickness on the relative thermal resistance for both the conventional model [48] and the model in this study. Nonlinear relationships between the relative thermal resistance and splat thickness were found for both cases. Moreover, the relative thermal resistance of the model proposed in this study was much larger with respect to that of the conventional model. In the case of the conventional model, according to Eq. (3), it is found that the relative thermal resistance is inversely proportional to splat thickness. In the case of the model proposed in this study, respective contribution of both the in-plane and the through-thickness directions are shown in Fig. 16b, in order to further explore the nonlinear relationship between the relative thermal resistance and splat thickness. According to Eq. (5), the relative thermal resistance in the throughthickness direction can be given by,
(13)
It is obvious that the relative thermal resistance is inversely proportional to α . When the bonding ratio decreased from 40% to 10%, the relative thermal resistance increased by one time. In the case of the model proposed in this study, to further understand the nonlinear relationship between the relative thermal resistance and bonding ratio, the respective contribution of the in-plane and the through-thickness directions are shown in Fig. 14b. According to Eq. (4), the thermal resistance of a unit in the in-plane direction presented a complicated dependency on the splat bonding ratio. It can be found from Fig. 15 that the thermal conduction route length increases with the decrease in bonding region size. Since the bonding region size is proportional to α , the decrease in bonding ratio contributes to the increase in the relative thermal resistance. According to Eq. (5), the thermal resistance in through-thickness direction can be changed into,
RTT
4ρδ = αC 2
RTT 2 = RB α
(14)
(15)
It is found that the relative thermal resistance in the throughFig. 14. Effect of bonding ratio on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red downtriangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
8
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Fig. 16. Effect of splat thickness (δ) on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red down-triangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
thermal insulation in plasma sprayed TBCs. Therefore, the structural design on TBCs with high thermal barrier performance can be mainly concentrated on the 2D pores. The novel model proposed in this study is based on the assumption of δ < < C, whereas the conventional model is based on a opposite assumption, i.e. δ > > C [48]. Since the segment length C is approximately several ten times of splat thickness δ [30,31,54,67], the novel model would be more suitable for the microstructure of thermally sprayed ceramic coatings. The overall dependent tendency of the relative thermal resistance on the microstructural parameters, including bonding ratio, unit size and splat thickness, is similar for these two models. However, the detailed dependency is quite different. On the one hand, the relative thermal resistance of the novel model is much larger compared to that of the conventional model. On the other hand, the increase dependencies of the relative thermal resistance with the change of unit size, bonding ratio and splat thickness for the novel model is much more significant with respect to those of the conventional model. Towards the higher performances of advanced TBCs [6], the novel model can provide some positive suggestions. With the increase of the unit size and the decrease of bonding ratio and splat thickness, the novel model would be more effective compared to the conventional model, since the assumption of δ≪C for the novel model becomes more appropriate than the assumption of δ≫C for the conventional model. Given that, it may be quite powerful to increase the thermal resistance of the coatings by increasing their segment length, and by decreasing their bonding ratio and splat thickness. On the other hand, the insulative ratio intrinsically determine the effective prevention against heat flux. However, the conventional plasma sprayed ceramic coatings often exhibit an insulative ratio of approximately 10–30 [12,16,75,76]. Therefore, in future work, it would be meaningful to design the 2D pores with a larger insulative ratio. Actually, plasma sprayed nanostructured coatings are potential to achieve this goal [77–81]. However, the problem is how to form some larger 2D pores oriented perpendicular to heat flux. Therefore, some processing innovation is still highly necessary.
thickness direction is independent on splat thickness. According to Eq. (4), the relative thermal resistance in the in-plane direction can be given by,
RIP r2 ⎡ ⎢ (3.11 − 0.027α )ln = RB 4αδ 2 ⎢ ⎣
1 2 1 2
−
α π
−
α π
+
1 2
−
1 2
−
α π
+
α π
⎤ ⎥ ⎥ ⎦
(16)
It is found that the relative thermal resistance in the in-plane direction is inversely proportional to δ2. It presented a much more significant dependency on the splat thickness than that of the conventional model. As a result, the increase of the relative thermal resistance with the decrease of splat thickness for the novel model is more significant with respect to the conventional model, as shown in Fig. 17. 6. Outlook of the microstructure design It should be mentioned that both 2D and 3D pores can be found in the plasma sprayed TBCs. However, the 2D pores dominate the thermal insulation based on this study and previous reports [41–44]. On the one hand, at as-deposited state, the reported porosities characterized by 3D pores are often less than 20% [18,54], while the drop in thermal conductivity was significantly larger than 50% compared to the corresponding bulk materials [41–43]. On the other hand, the change in porosity after thermal exposure is less than 10% [12,16], whereas the 2D pore density is larger than 50%, as shown in Fig. 7. Given the fact that more than 50% degradation of thermal insulation happens after thermal exposure, as can be found in Fig. 5 and other reports [41–44], it is reasonable to conclude that the 2D pores dominantly determine the
7. Conclusions To understand the thermal conductive behavior in TBCs, an analytical model was developed based on the intrinsic characteristics of plasma sprayed ceramic coatings. It is found that the thermal conductivity is highly associated with the 2D composited stacking structure: bulk splats and air-trapped pores. Sintering induced healing of 2D pores are the main cause for the degradation of thermal insulation during thermal exposure. The underlying mechanism is the decrease in insulative ratio of 2D pores. Effects of the microstructural parameters, including splat thickness, splat/splat bonding ratio and splat length, on the total thermal resistance were discussed. Compared with the conventional models, the overall dependent tendencies of the relative thermal resistance on the microstructural parameters are similar. However, the detailed dependency is quite different. Both the value and the increase dependency of the relative thermal resistance with the
Fig. 17. Schematics to show the effect of splat thickness on the thermal resistance. 9
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changes of microstructural parameters for the model developed in this study is much more significant with respect to those of the conventional model. With the increase of unit size and the decrease in both splat bond ratio and splat thickness, the new model would be more effective compared to the conventional model due to its more appropriate assumption of δ < < C. In brief, the understanding of the dominant effect of 2D pores on prevention against heat flux would make it possible to design new TBCs with high performance in future applications.
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Dominant effect of oriented 2D pores on heat flux in lamellar structured thermal barrier coatings Zhi-Yuan Weia, Li-Shuang Wangb,∗, Hong-Neng Caia,∗∗, Guang-Rong Lia,c,∗∗∗, Xue-Feng Chend, Wei-Xu Zhange a
State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China School of Materials Science and Engineering, Xi'an Shiyou University, Xi'an, 710065, China c Forschungszentrum Jülich, Institute of Energy and Climate Research IEK-1: Materials and Processing, D-52425, Jülich, Germany d State Key Laboratory for Manufacturing Systems Engineering, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China e State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal barrier coatings Analytical model Thermal resistance Functional 2D pores Structural tailoring
Thermal barrier coatings (TBCs) provide thermal insulation to metallic components served at high temperatures. The oriented 2D pores are primarily responsible for the efficient prevention of heat flux. Thus, structural design of TBCs with higher thermal insulation requires clear understanding on the thermal conduction inside coatings. Up to now, previous analytical models to investigate the heat conduction were mainly based on the concept of thermal contact resistance. However, the related assumption was far away from the real coating microstructure. In this study, the intrinsic structural characteristics of plasma sprayed TBCs were firstly investigated. Subsequently, an analytical model based on the structural features was developed to understand the dominant effect of oriented 2D pores on heat flux inside the coatings. Results showed that the insulative ratio of 2D pores dominantly determine the effective prevention of heat flux. Moreover, effects of the microstructural parameters, including splat thickness, bonding ratio and unit size, on the total thermal resistance was discussed. Overall, the understanding of the dominant effect of 2D pores would make it possible to design new TBCs with high performance in future applications.
1. Introduction Thermal barrier coatings (TBCs) protect metallic materials from direct thermal exposure during their service [1–4]. Therefore, the TBCs become necessary for aircraft engines and land-based gas turbines, whose working temperature exceeds the bearable limit of the superalloy components [5–9]. Given the thermal barrier function, TBCs should have low thermal conductivity, which is determined by the materials and the structure that related to the processing methods. It is believed that plasma spraying has proven its value to prepare TBC with excellent thermal barrier performance [10–14]. For example, the thermal conductivity of plasma sprayed yttria-stabilized zirconia (PSYSZ) can be as low as 1 W⋅m−1K−1, which is only 40% with respect to the bulk YSZ [15–17].
Commonly, a plasma sprayed ceramic coating is composed of stacked splats, exhibiting a lamellar structure [10,17–24]. There is only a limited fraction of bonding interface among all splat interfaces. The quantitative evaluation in plasma sprayed Al2O3 and yttria-stabilized zirconia (YSZ) coatings showed that only a maximum of 32% bonding ratio can be reached when the substrate temperature was not specially heated to higher than ∼300 °C [25–29]. The limited bonding ratio suggested that there is a large number of inter-splat pores between layers. In addition, due to the brittle nature of ceramic materials, some intra-splat cracks are formed inside layers during the process of thermal spraying. It is reported that the inter-splat pores and intra-splat cracks are connected together [30–32]. The inter-splat pores are often perpendicular to the heat flux, whereas most of the intra-splat cracks are parallel to the heat flux. The oriented inter-splat pores can effectively
∗
Corresponding author. School of Materials Science and Engineering, Xi'an Shiyou University, Xi'an, Shaanxi, 710065, PR China. Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China. ∗∗∗ Corresponding author. State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China. E-mail addresses: [email protected] (L.-S. Wang), [email protected] (H.-N. Cai), [email protected] (G.-R. Li). ∗∗
https://doi.org/10.1016/j.ceramint.2019.05.254 Received 12 April 2019; Received in revised form 13 May 2019; Accepted 23 May 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: Zhi-Yuan Wei, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.05.254
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prevent the direct thermal conduction, since the thermal conductivity of air is significantly lower than that of the bulk splats. As a result, the oriented 2D pores inside plasma sprayed TBCs are dominantly responsible for the 150% improvement in thermal insulation with respect to the bulk materials [15]. In addition, the unique porous structure results in enhanced strain tolerance that is necessary for durable TBCs [16,33–40]. Therefore, the plasma sprayed ceramic coatings find their widely application in TBCs. It should be noted that the case become much more complicated in real service. A main problem is that sintering leads to approximately 80% increase in thermal conductivity, suggesting that nearly 60% degradation happens in thermal insulation [41–44]. Many investigations suggested that the main cause is the significant healing of oriented 2D pores [45,46]. Therefore, the current TBCs need further structural design to achieve high performance. As a fundamental work, it is firstly necessary to understand the thermal conductive behavior through plasma sprayed TBCs. In previous reports [47,48], the thermal resistance of plasma sprayed ceramic coatings has been understood based on the basic concept of thermal contact resistance. In the thermal conduction model firstly proposed by McPherson [48], the electric contact resistance theory was introduced to the thermal conductive behavior of thermally sprayed ceramic coatings [48–50]. In this case, to simplify the mathematical calculation, there is often an assumption that the size in the through-thickness direction (splat thickness, δ) is much larger than that in the in-plane direction (the distance between bonding area, C), i.e., δ > > C, as shown in Fig. 1. However, in real coatings, an opposite phenomenon can be obviously observed, since the splat thickness is approximately 10% with respect to the in-plane size [12,32,51]. This will obviously result in discrepancy between the calculation results and the experimental data. With the development of advanced gas turbine for aircraft engine and land-based gas turbine, a further enhanced thermal insulation is required for TBCs. According to the conventional model [48], the decrease in both bonding ratio and splat thickness will increase the thermal resistance. However, this decreasing trend would actually be against the basic assumption in the conventional model, i.e. δ≫C. Given that, Clyne et al. [49] proposed an analytical model with two-flux regions. In their model [49], the thermal contact resistance dominates one flux region, whereas the inter-splat thermal conduction determines the other flux region. This suggests that the thermal flux in the in-plane direction, along with the through-thickness direction, should be taken into account. However, the dominant effect of the oriented 2D pores on the heat flux and its relationship with structural factors are not yet clear. In this study, to fully understand the thermal conductive behavior
Table 1 Plasma spraying parameters to deposit YSZ coatings and individual splats. Parameters
Individual splats
Coatings
Plasma arc voltage, V Plasma arc current, A Flow rate of primary gas (Ar), L/min Flow rate of secondary gas (H2), L/min Flow rate of powder feeding gas (N2), L/min Spray distance, mm Torch traverse speed, mm/s Preheating temperature, °C
70 600 50 7 6 110 1000 250
70 600 50 7 6 110 800 /
through the 2D-pore-rich TBCs, intrinsic characteristics of plasma sprayed ceramic coating were investigated, and an analytical model was developed. The effects of the microstructural parameters, including splat thickness, bonding ratio between splats and unit size, on the total thermal resistance were discussed. The dominant effect of oriented 2D pores on heat flux was revealed. This will give positive suggestions on the development of TBCs with higher performance through microstructure tailoring. 2. Experimental 2.1. Sample preparation and thermal exposure Commercially available hollow spherical powders (−75 to +45 μm, Metco 204B-NS, Sulzer Metco Inc., New York, USA) was used to deposit coatings by a plasma spray method (GP-80, 80 kW class, Jiujiang, China). Table 1 shows the plasma spraying parameters. All the coatings were deposited to be approximately 1 mm. In order to obtain free-standing samples, coatings were deposited on stainless steel substrates that can be removed by a hydrochloric acid solution. Substrates have dimensions of φ12.7 mm × 7 mm, in order to facilitate the measurement of thermal conductivity. Before coating deposition, the substrate was roughened by grit blast, to avoid delamination of coatings during deposition. The free-standing samples were used for two aims. First is to observe the intrinsic characteristics of plasma sprayed ceramic coating with asdeposited samples. Second is to present the dominant effect of microstructural changes on the prevention of heat flux with samples heat treated at 1300 °C, based on the consideration that the service temperature of TBCs is often above 1000 °C. A relatively low rate of 10 °C/ min were used to control the heating and cooling rates. After different durations, changes in microstructure and thermal conductivity were investigated. 2.2. Microstructural characterization and property determination Microstructure of samples before and after thermal exposure was observed by scanning electron microscopy (SEM, TESCAN MIRA3, Brno, Czech Republic). It is known that 2D pores dominantly determine the effective properties of plasma sprayed ceramic coatings [12,52,53]. As a result, change in 2D pore length was determined based on 50 SEM images at 5000 × magnification, as shown in Fig. 2. Subsequently, the length density, defined as the total length of 2D pores in unit area, were obtained. Other details on the length measurement can be found elsewhere [46]. Focused ion beam (FIB, HeliosNanoLab600i, FEI, USA) was used to obtain the cross-section of partially bonded layers, in order to remain initial state. Thermal conductivity of the samples was determined by a laser flash method with following equation:
λ = ρ⋅CP⋅α
Fig. 1. Schematics of the concept of thermal contact resistance: (a) standard heat flux [50], and (b) simplified model used in the thermally sprayed coatings [48].
(1)
where λ is thermal conductivity, ρ is coating density, CP is heat capacity, and α is thermal diffusivity of the coating. 2
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coatings are deposited by stacking of disk-shaped splats that are formed by spreading and solidifying of molten powder after impact on underlying substrate [19,29,56,57]. In the case of the brittle ceramic splats that are used in TBCs, the quenching stress further divide the diskshaped splats into several segments. Therefore, the basic unit to form the plasma sprayed ceramic coatings is the splat segment. In addition, one splat segment is partially bonded to the lower layer (Fig. 3c), leading to the formation of inter-splat pores. In brief, the plasma sprayed ceramic coatings is intrinsically formed by stacking of composited 2D layers: 2D bulk splat segments surround by the air-trapped 2D pores (inter-splat pores and intra-splat cracks). Given that, length, thickness and bonding ratio of a splat segment are the main microstructural parameters. The thickness of splat segment was obtained from the cross-section of coatings and individual splats, as shown in Fig. 3a, c. Most of the segments have a thickness of 1–4 μm. This is consistent with the morphology observed from other reports [16,30,51]. Segment length was determined from the surface morphology of coatings and individual splats, as shown in Fig. 3b, d. It is easier to distinguish some clear splat segments from the flat individual splat than from the rough coating surface. In fact, the segments appear to be irregular shapes, since the intra-splat cracks randomly extend in directions. In order to facilitate the simulation in following section, the splat segments were assumed to be cubic shape. The average length of segments can be obtained from Eq. (2), and the result is about 6–20 μm.
Fig. 2. Schematic to determine pore length in plasma sprayed TBCs.
The thermal diffusivity was determined by laser flash analyzer (Netzsch, Germany). For each state, at least three samples were used to minimize errors. The CP was measured by differential scanning calorimetry (DSC 404, Netzsch, Germany). 3. Experimental results 3.1. Intrinsic characteristics at as-deposited state Fig. 3 shows cross-section and surface of plasma sprayed YSZ coatings and an individual splat at their as-deposited states. Distinctly porous feature can be observed. This pore-rich structure contributes to the effective prevention against heat flux, just as the service environment requires for TBCs [31]. Three kinds of pores can be clearly separated: globular voids and 2D inter-splat pores and 2D intra-splat cracks, which were widely reported [16,30,52,54]. Due to its porous nature, porosity was commonly used to characterize the structure of plasma sprayed ceramic coatings [16,55]. However, the reported porosities were approximately 10%∼20% [18,54], whereas the drop in thermal conductivity of coatings was often larger than 50% with respect to the corresponding bulk materials [41–43]. This suggests that the widely used porosity cannot essentially exhibit the microstructural features of plasma sprayed TBCs. The intrinsic characteristics of plasma sprayed ceramic coatings can be captured from their forming process. The plasma sprayed ceramic
C=
A N
(2)
where C refers to the average length of a segment, A refers to the apparent area of a defined region, N refers to the amount of segments in a defined region. Fig. 4 shows cross-section of a coating prepared by FIB. The partially bonded layers can be clear observed. The bonding ratio between segments can be obtained from previous reports. It is revealed that the bonding ratio is 10%–32% for plasma sprayed ceramic coatings using a method called structural visualization [12,25–27,47,58]. In addition, the bonding ratio can also be reflected from the determined properties
Fig. 3. Morphology of plasma sprayed YSZ: (a) cross-section of a coating, (b) surface of a coating, (c) [32] cross-section of an individual splat, and (d) [32] surface of an individual splat. 3
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healed in a multi-contact form, as reported in previous study [46,67]. Fig. 7 shows changes in 2D pore density. Regarding the decrement after thermal exposure, the porosity is less than 10% [12,16], whereas the 2D pore density is larger than 50%. In addition, the stage-sensitive changes of 2D pore density appear to be similar to the thermal conductivity. Based on the above-observed results, it is clear that the 2D pores primarily determine the thermal property of plasma sprayed ceramic coatings. Actually, the 2D pores are highly related to the structural parameters of a splat segment (i.e., the length, thickness and bonding ratio). Therefore, an analytical model was developed to investigate the dominant effect of 2D pores on the prevention of heat flux. 4. Simulation method 4.1. Model development Fig. 4. Partially bonded layers of a plasma sprayed coating prepared by FIB [32].
According to the conventional model [48], the splat thickness is assumed to be much larger than the segment length. In that way, the relative thermal resistance (KU/B, a ratio of the coating resistance to the corresponding bulk resistance) can be calculated using the following equation:
that are highly dependent on bonding ratio. For example, the fracture toughness [59] and ionic conductivity [60] of plasma sprayed ceramic coatings were about 20%∼30% with respect to the corresponding bulk materials. The ranges of microstructural parameters were determined to investigate the effect of microstructure on the prevention against heat flux in following section.
KU / B =
RU πr = RB 2αδ
(3)
where RU and RB are thermal resistances of the coating unit and the bulk material, respectively, r is the radius of a bonding area, α is the bonding ratio between splats, and δ is the splat thickness. However, according to the experimental observation in this study and previous reports [30,51], the segment length is approximately 10 times larger than the splat thickness. Therefore, the assumptions of δ≪C, other than the common assumption (δ > > C) in the conventional model, would be more suitable for the thermally sprayed coatings. A new model based on the intrinsic characteristics of plasma sprayed TBCs was developed. In details, the structural model was formed by stacking of splat segments that are basic units found in coatings, as shown in Fig. 8. The assumptions are described as follows: (i) the segments have same length (C) and thickness (δ); (ii) circular bonding area is located at the bottom center of a segment; (iii) the segments are stacked on the lower layer uniformly; (iv) most of all, the value of segment thickness is assumed to be much smaller than that of the segment length (δ≪C). As a result, the thermal conduction is divided into two directions, i.e. in-plane direction and through-thickness direction, as shown in Fig. 8f. Fig. 8c, d show the top view of the representative segments and the cross-sections along the black dotted line, respectively. Thermal radiation and thermal convection in the coating are ignored in this study. The thermal conduction in the through-thickness direction occurs in the bonding region (lines in dashed blue color) of the two adjoining splats, and the thermal conduction in the in-plane direction occurs within the splat between the two near bonding regions (lines in solid red color). Due to the obvious symmetry of the structure, a periodic pattern was extracted from the structure. The top view and the corresponding cross-sectional view are shown in
3.2. Changes in thermal property and microstructure during thermal exposure Fig. 5 shows changes in thermal conductivity of plasma sprayed YSZ coatings as a function of dwell time. For comparison, some data of thermal conductivity from previous reports were also presented as normalized values [16,43,52,55,61,62]. It is found that the thermal conductivity at as-deposited state is approximately 1 W m−1K−1, whereas it increases to nearly 2 W m−1K−1 after thermal exposure. This suggests that more than 50% degradation happens after thermal exposure, as can also be found in other reports [41–44]. Another interesting phenomenon is that most of the degradation occurs at initial thermal exposure. For example, the initial 10 h completes 80% degradation of thermal conductivity in total 200 h. This is caused by the stage-sensitive sintering kinetics revealed in other reports [18,54]. Fig. 6 shows the evolution of structure during thermal exposure. It is observed that the quantity of 2D pores significantly decreases. This is caused by sintering of ceramic materials at high temperature. During thermal exposure, thermally activated matter is spontaneously transferred to decrease the free energy of the whole system, which is a common phenomenon in porous ceramic materials [63–65]. Materials transfer can proceed in several methods, e.g., grain boundary grooving [52,66], surface faceting [54]. As a result, the pore surface become roughened and subsequently lead to bridge-connection between 2D pores. Therefore, the pore in plasma sprayed ceramic coating would be
Fig. 5. Changes of thermal conductivity as a function of dwell time (a) and normalized thermal conductivity with respect to their as-deposited states (b). 4
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Fig. 6. Evolution of microstructure before (a) [68] and after thermal exposure (b).
Fig. 7. Changes of 2D pore density as a function of dwell time (a) and normalized 2D pore density with respect to their as-deposited states (b).
procedures can be described as follows:
Fig. 8e and f, respectively. The theory of electric conduction between two rods in an infinite thin plate was used to determine the in-plane thermal resistance [69]. The total resistance can be obtained from the following equations:
RIP =
RTT1 = RTT2 = RTT =
KU / B
1 2
ρ ⎡ •⎢ (3.11 − 0.027α )ln πδ ⎢ ⎣
1 2
−
α π
−
α π
+
1 2
−
α π
−
1 2
+
α π
⎤ ⎥ ⎥ ⎦
ρδ 1 πr 2 4
(i) firstly, according to the Fourier's law, the heat flux transfers into the top surface (qin), and transfers out of the bottom surface (qout) are given by equation (7) and equation (8), respectively:
(5)
−
α π
+
1 2
−
α π
1 2
−
α π
−
1 2
+
α π
⎤ ⎥+ 2 α ⎥ ⎦
qout = h (TT − TS)
(8)
(ii) secondly, adiabatic boundary conditions were used to make sure that the top-bottom heat flux is equal to the bottom-environment heat exchange. As a result, the following relationship is obtained:
R 2RTT + RIP = U = = RB RB 4πδ 2 1 2
(7)
(4)
C2
⎡ •⎢ (3.11 − 0.027α )ln ⎢ ⎣
k e (TD − TT ) H
qin =
qin = −qout
(9)
(iii) finally, effective thermal conductivity of the periodic pattern is obtained based on equation (10):
(6)
where RU is the total thermal resistance of the coating unit, RB and ρ is the thermal resistance of the bulk material, RIP is the thermal resistance along in-plane direction, RTT is the thermal resistance along throughthickness direction, r is the radius of a bonding area, α is the bonding ratio between splats, δ is the segment thickness, and C is the segment length.
ke ≈
(TD − TS) hH ΔT ′
(10)
where TD is the top surface temperature of the top coat, TS is the environmental temperature, h is the thermal convection coefficient, H is the height of model, and ΔT′ is the temperature difference between the top and the bottom surfaces.
4.2. Simulation of heat flux 5. Simulation analysis The pattern constrained by periodic boundary condition was used to simulate the heat transfer behavior. The details to introduce the periodic boundary conditions can be found in previous report [70]. The mean values of structural parameters (i.e., length, thickness and bonding ratio of a splat segment) were used based on the experimental observation in Section 3. The input data are shown in Table 2. In addition, the x-z plane is defined as the reference plane, which is perpendicular to the heat flux. Thermal conductivity was predicted by ANSYS software. The detail
5.1. Comparison between model prediction and experiment During thermal exposure, significant changes in the thermal conductivity and the 2D pore can be observed in Figs. 5 and 7, respectively. This suggests that the changes in thermal properties are essentially related with the 2D pores. Fig. 9 shows the predicted thermal conductivity affected by the change in 2D pores, and the comparison with experimental data. It is obvious that the predicted values are well 5
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Fig. 8. Model development in this study: (a) top view, (b) perspective view, (c) top view of a basic stacking pattern, (d) cross-section of A-A′ corresponding to (c), (e) a basic unit for the heat flux, and (f) cross-section of (e). Table 2 Structural and intrinsic parameters used as the input data. Parameters
Values
Thermal conductivity of bulk YSZ, W·m−1·K−1 Thermal conductivity of pores, W·m−1·K−1 Mean length of a structural unit, μm Mean thickness of a structural unit, μm Mean bonding ratio between structural units, %
2.5 0.025 13 2.5 25
consistent with the experimental values. Overall, the changing trend can be divided into two stages from the view of thermal duration: much larger changing degree (∼80%) is completed at stage I, followed by slight changing degree at stage II. In addition, the stage I covers much shorter time (less than 10 h) with respect to the stage II (hundreds of hours). In brief, the correlation between the thermal property and the 2D pores further confirms the intrinsic characteristic obtained in this study. This is consistent with other reports on mechanical properties [53,54,71].
Fig. 9. Comparison in thermal conductivity between predicted and experimental values.
perpendicular to the heat flux would effectively prevent the heat transfer [12,53]. The underlying reason is that the thermal conductivity of air is dramatically smaller than that of the bulk materials. Fig. 10
5.2. Dominant effect of 2D pores on the heat flux Owing to the extremely large thermal resistance, the pores 6
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Fig. 10. Effect of aspect ratio on heat flux: (a) changes in aspect ratio of 2D pores during thermal exposure, (b) [12] aspect ratio of 10, and (c) [72] aspect ratio of 40.
5.3. Effect of structural parameters on the relative thermal resistance
shows the changes in aspect ratio of 2D pores during thermal exposure and its effect on heat flux. At as-deposited state, the aspect ratio is approximately 30–40, whereas it decreases to 10 by and large. Given the changes in the 2D pore length density (Fig. 6), the change in aspect ratio is mainly caused by healing of 2D pores. It is obvious that a greater temperature drop is caused by the 2D pore with a higher aspect ratio. That's why distinct degradation in thermal insulation of TBCs happens during service. The underlying mechanism is highly associated with the 2D distribution of heat flux caused by the unique structure. At the center of a pore, the heat flux would go through the air zone with a very low thermal conductivity. However, at the tips of a pore, the heat flux would change the original path, since it is much easier to go across the pore through neighboring bonding area. Therefore, only the center area can effectively prevent the heat flux. This phenomenon can also be found in other reports [49,73]. In this study, the ratio of effective area to prevent heat flux with respect to the total area is called insulative ratio. Based on the following equation [12], the insulative ratio of 2D pores can be determined. │qx│ < │qy│
5.3.1. Effect of segment length on the relative thermal resistance Fig. 12 shows the effect of unit size (C) on the relative thermal resistance for both the conventional model [48] and the model developed in this study. Regarding the changing trends in these two models, a common phenomenon is that the relative thermal resistances are increased as a function of unit size (C). However, the increase trends are different. In the case of the conventional model, a nearly linear relationship was found between the relative thermal resistance and the unit size (C). In fact, the relative thermal resistance in Eq. (3) can be changed to the following equation. Eq. (12) clearly suggests the linear relationship between the relative thermal resistance and unit size (C).
KU / B =
πα C 2αδ
(12)
where C is the unit size, α is the bonding ratio between splats, and δ is the splat thickness. In the case of the model proposed in this study, it is obvious that the increase of the relative thermal resistance is nonlinear. To further explore the nonlinear relationship, the respective contribution of the inplane and the through-thickness directions are shown in Fig. 12b. According to Eq. (5), if n × n units are combined together to form one large unit, the RTT of the large unit is as small as 1/n2 of that of the small unit. However, the n × n small units are in parallel. Therefore, the total thermal resistance in the through-thickness direction is not changed. This is consistent with Fig. 12b that the contribution of the through-thickness direction to the relative thermal resistance remained at a constant in spite of the change of unit size. According to Eq. (4), the thermal resistance of a unit in the in-plane direction is independent of unit size. Since the n × n small units in parallel change to one large unit, the total thermal resistance of the coating increases with n × n i.e. n2. This quadratic dependency contributes to a more significant increase than the linear increase dependency. For example, Fig. 13 shows the effect of unit size (changing from L to 2L) on the thermal resistance at different directions. Under a same volume, the length and sectional area of heat flux along through thickness remain unchanged. Therefore, the RTT is unaffected by the unit size. However, with the increase of the unit size, the heat flux would be decrease in an inverse-square law. This is the reason that the RIP would be quadratic dependent on the unit size.
(11)
where qx is the x-component of the heat flux, and qy is the y-component of the heat flux. Fig. 11 shows the insulative ratio before and after thermal exposure. It is obvious that thermal exposure results in significant decrease in insulative ratio. Similar phenomenon can also be found in other reports [12,74]. This suggests that the decrease in insulative ratio of 2D pores is the dominant factor responsible for the degradation in thermal insulation.
5.3.2. Effect of bonding ratio on the relative thermal resistance Fig. 14 shows the effect of bonding ratio (α) on the relative thermal resistance for both the conventional model [48] and the model in this study. Both of these two models presented a nonlinear relationship between the relative thermal resistance and bonding ratio. However, it is obvious that a much larger relative thermal resistance and a much more significant increase dependency on the decrease of bonding ratio
Fig. 11. Insulative ratio before and after thermal exposure. 7
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Fig. 12. Effect of unit size (C) on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red downtriangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 15. Schematics to show the effect of bonding ratio on the thermal resistance.
It is found that the thermal resistance in through-thickness direction is inversely proportional to the bonding ratio α. It presented a much more significant dependency on bonding ratio than that of the conventional model. As a result, the increase of the relative thermal resistance caused by the decrease of bonding ratio for the novel model is more significant with respect to that of the conventional model.
Fig. 13. Schematics to show the effect of unit size on the thermal resistance.
for the model proposed in this study. In the case of the conventional model, according to Eq. (3), the relative thermal resistance can be changed into,
KU / B =
πC 2 αδ
5.3.3. Effect of splat thickness on the relative thermal resistance Fig. 16 shows the effect of splat thickness on the relative thermal resistance for both the conventional model [48] and the model in this study. Nonlinear relationships between the relative thermal resistance and splat thickness were found for both cases. Moreover, the relative thermal resistance of the model proposed in this study was much larger with respect to that of the conventional model. In the case of the conventional model, according to Eq. (3), it is found that the relative thermal resistance is inversely proportional to splat thickness. In the case of the model proposed in this study, respective contribution of both the in-plane and the through-thickness directions are shown in Fig. 16b, in order to further explore the nonlinear relationship between the relative thermal resistance and splat thickness. According to Eq. (5), the relative thermal resistance in the throughthickness direction can be given by,
(13)
It is obvious that the relative thermal resistance is inversely proportional to α . When the bonding ratio decreased from 40% to 10%, the relative thermal resistance increased by one time. In the case of the model proposed in this study, to further understand the nonlinear relationship between the relative thermal resistance and bonding ratio, the respective contribution of the in-plane and the through-thickness directions are shown in Fig. 14b. According to Eq. (4), the thermal resistance of a unit in the in-plane direction presented a complicated dependency on the splat bonding ratio. It can be found from Fig. 15 that the thermal conduction route length increases with the decrease in bonding region size. Since the bonding region size is proportional to α , the decrease in bonding ratio contributes to the increase in the relative thermal resistance. According to Eq. (5), the thermal resistance in through-thickness direction can be changed into,
RTT
4ρδ = αC 2
RTT 2 = RB α
(14)
(15)
It is found that the relative thermal resistance in the throughFig. 14. Effect of bonding ratio on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red downtriangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
8
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Fig. 16. Effect of splat thickness (δ) on the relative thermal resistance: (a) total KU/B derived from the conventional model (empty circle) and the model developed in this study (black square), (b) total KU/B (black square) and the respective contribution from 2RTT (blue up-triangle) and RIP (red down-triangle). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
thermal insulation in plasma sprayed TBCs. Therefore, the structural design on TBCs with high thermal barrier performance can be mainly concentrated on the 2D pores. The novel model proposed in this study is based on the assumption of δ < < C, whereas the conventional model is based on a opposite assumption, i.e. δ > > C [48]. Since the segment length C is approximately several ten times of splat thickness δ [30,31,54,67], the novel model would be more suitable for the microstructure of thermally sprayed ceramic coatings. The overall dependent tendency of the relative thermal resistance on the microstructural parameters, including bonding ratio, unit size and splat thickness, is similar for these two models. However, the detailed dependency is quite different. On the one hand, the relative thermal resistance of the novel model is much larger compared to that of the conventional model. On the other hand, the increase dependencies of the relative thermal resistance with the change of unit size, bonding ratio and splat thickness for the novel model is much more significant with respect to those of the conventional model. Towards the higher performances of advanced TBCs [6], the novel model can provide some positive suggestions. With the increase of the unit size and the decrease of bonding ratio and splat thickness, the novel model would be more effective compared to the conventional model, since the assumption of δ≪C for the novel model becomes more appropriate than the assumption of δ≫C for the conventional model. Given that, it may be quite powerful to increase the thermal resistance of the coatings by increasing their segment length, and by decreasing their bonding ratio and splat thickness. On the other hand, the insulative ratio intrinsically determine the effective prevention against heat flux. However, the conventional plasma sprayed ceramic coatings often exhibit an insulative ratio of approximately 10–30 [12,16,75,76]. Therefore, in future work, it would be meaningful to design the 2D pores with a larger insulative ratio. Actually, plasma sprayed nanostructured coatings are potential to achieve this goal [77–81]. However, the problem is how to form some larger 2D pores oriented perpendicular to heat flux. Therefore, some processing innovation is still highly necessary.
thickness direction is independent on splat thickness. According to Eq. (4), the relative thermal resistance in the in-plane direction can be given by,
RIP r2 ⎡ ⎢ (3.11 − 0.027α )ln = RB 4αδ 2 ⎢ ⎣
1 2 1 2
−
α π
−
α π
+
1 2
−
1 2
−
α π
+
α π
⎤ ⎥ ⎥ ⎦
(16)
It is found that the relative thermal resistance in the in-plane direction is inversely proportional to δ2. It presented a much more significant dependency on the splat thickness than that of the conventional model. As a result, the increase of the relative thermal resistance with the decrease of splat thickness for the novel model is more significant with respect to the conventional model, as shown in Fig. 17. 6. Outlook of the microstructure design It should be mentioned that both 2D and 3D pores can be found in the plasma sprayed TBCs. However, the 2D pores dominate the thermal insulation based on this study and previous reports [41–44]. On the one hand, at as-deposited state, the reported porosities characterized by 3D pores are often less than 20% [18,54], while the drop in thermal conductivity was significantly larger than 50% compared to the corresponding bulk materials [41–43]. On the other hand, the change in porosity after thermal exposure is less than 10% [12,16], whereas the 2D pore density is larger than 50%, as shown in Fig. 7. Given the fact that more than 50% degradation of thermal insulation happens after thermal exposure, as can be found in Fig. 5 and other reports [41–44], it is reasonable to conclude that the 2D pores dominantly determine the
7. Conclusions To understand the thermal conductive behavior in TBCs, an analytical model was developed based on the intrinsic characteristics of plasma sprayed ceramic coatings. It is found that the thermal conductivity is highly associated with the 2D composited stacking structure: bulk splats and air-trapped pores. Sintering induced healing of 2D pores are the main cause for the degradation of thermal insulation during thermal exposure. The underlying mechanism is the decrease in insulative ratio of 2D pores. Effects of the microstructural parameters, including splat thickness, splat/splat bonding ratio and splat length, on the total thermal resistance were discussed. Compared with the conventional models, the overall dependent tendencies of the relative thermal resistance on the microstructural parameters are similar. However, the detailed dependency is quite different. Both the value and the increase dependency of the relative thermal resistance with the
Fig. 17. Schematics to show the effect of splat thickness on the thermal resistance. 9
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changes of microstructural parameters for the model developed in this study is much more significant with respect to those of the conventional model. With the increase of unit size and the decrease in both splat bond ratio and splat thickness, the new model would be more effective compared to the conventional model due to its more appropriate assumption of δ < < C. In brief, the understanding of the dominant effect of 2D pores on prevention against heat flux would make it possible to design new TBCs with high performance in future applications.
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