An innovative model coupling TGO growth and crack propagation for the failure assessment of lamellar structured thermal barrier coatings

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An innovative model coupling TGO growth and crack propagation for the failure assessment of lamellar structured thermal barrier coatings Zhi-Yuan Weia, Hong-Neng Caia,∗, Guo-Hui Menga, Adnan Tahira, Wei-Wei Zhangb,∗∗ a State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province, 710049, PR China b School of Materials Science and Engineering, Chang'an University, Xi'an, Shaanxi Province, 710064, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Thermal barrier coatings (TBCs) Lamellar or layered structure Thermally grown oxide Crack propagation Delamination and failure

The failure of plasma-sprayed thermal barrier coating (TBC) is often caused by the coating spallation due to crack propagation. In this study, a new model with stacking lamellae is developed based on the cross-section micrograph to explore crack propagation behavior within the ceramic top coat (TC) during isothermal cycling. The dynamic growth process of thermally grown oxide (TGO) is simulated via material properties change step by step. The stress profiles in the lamellar model are first evaluated, and the pore and lamellar interface crack effects on the stress state are further explored. Then, the successive crack growth, linkage, and ultimate coating spallation process is simulated. The results show that the stress intensity in TC enhances with thermal cycling. Large stress concentration always occurs near the pore and lamellar interface crack, which can result in the incipient crack growth. Moreover, the lamellar interface crack also changes the stress distribution within the TC and at the TC/bond coat interface. The multiple crack propagation upon temperature cycling is explored, and the possible coalescence mechanism is proposed. The lamellar crack steadily propagates at the early stage. The crack length sharply increases before the occurrence of coating spallation. The simulated coat spalling path is in line with the experimental result. Therefore, the new lamellar model developed in this work is beneficial to further reveal coating failure mechanism and predict coating lifetime.

1. Introduction The thermal efficiency of an aircraft engine can be improved by raising the operating temperature. Nevertheless, the increase in the operating temperature will certainly result in a higher temperature on the surface of hot components in the engine. A ceramic layer, namely thermal barrier coating (TBC), is often prepared on the blade surface to decrease its surface temperature and increase the thermal efficiency of engine [1–4]. The TBC system is usually composed of three layers: ceramic top coat (TC), bond coat (BC) and substrate (SUB). The BC layer can enhance the adhesive strength between the ceramic layer and substrate and raise the oxidation resistance of the substrate. A thermally grown oxide (TGO) layer usually forms between the bond coat and ceramic layer due to the bond coat oxidation at elevated temperature. Atmospheric plasma spraying (APS) becomes one of the most popular manners to prepare the TBC due to its flexibility and low cost [5,6]. The APS coating possesses a typical lamellar structure feature with only about one-third lamellar interface bonding rate [7,8]. Accordingly, a lot

∗

of inherent cracks corresponding to the non-bonded interface between lamellae exist within the ceramic coating [9,10]. Such structure characteristic makes the coating exhibit a high thermal barrier effect and low fracture toughness. The delamination and spallation of coating often happen during thermal service. To improve the resistance of APS coating to failure, lots of efforts have been made such as new structure design [11,12], development of new material [13,14], and optimized spraying process [15,16]. In addition, the introduction of short ceramic fiber in TBCs can also extend their thermal cyclic lifetime [17–20]. For APS coating, except for the inherent cracks between lamellae, many vertical cracks and pores also exist within individual lamella [21]. These cracks link up with each other, which leads to an intricate crack network. Under thermal and mechanical loading, the cracks mainly propagate along the lamellar interface and also have a trans-lamellar propagation due to the existence of vertical crack [22]. The coating spallation usually occurs owing to crack propagation and subsequent coalescence. Therefore, clarifying the crack propagation behavior and their coalescence mechanism are crucial for understanding the failure

Corresponding author. Corresponding author. School of Materials Science and Engineering, Chang'an University, Xi'an, Shaanxi, 710064, PR China. E-mail addresses: [email protected] (H.-N. Cai), [email protected] (W.-W. Zhang).

∗∗

https://doi.org/10.1016/j.ceramint.2019.09.120 Received 30 July 2019; Received in revised form 9 September 2019; Accepted 13 September 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.2019.09.120

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of TBCs and predicting the lifetime. Since the APS coating system is a multi-layer structure, the crack propagation behavior within the ceramic layer is often affected by many factors such as TGO growth [23,24] and creep deformation [25], BC yield strength [26], TC/BC interface morphology [27] and roughness [28], and ceramic sintering [29,30]. In addition, the inherent crack network within the APS coating also increases the difficulty to understand the crack growth behavior and link-up mechanism. In order to ascertain crack behavior and coating failure mechanism, considerable works have been made such as sintering mechanism study [31–33], TGO displacement instability assessment [34,35], phase change exploring [36], analyzing the effects of constituent material properties [37,38] and interface morphology [39,40]. Due to the lamellar structure feature and the existence of multiple defects in APS coating, to build a real lamellar model of TBCs in three-dimensional space is very difficult. Hence, lots of simplified models [41,42] are adopted to investigate the stress states and crack behavior within the coating during temperature cycling. On the whole, these models can be classified into five categories. The first one is the spherically symmetric model [43–45]. Evans et al. [46] developed the spherically symmetric theory model according to two kinds of TGO growth mechanisms to assess TGO growth stress, and they explored the stress change within the TBCs and the creep effect on the stress states during temperature cycling. The second one is the idealized cosine model, which is the most popular one at present [47–50]. Bednarz et al. [51] systematically studied the influences of constituent material properties on the variation of stress states during cyclic thermal loading using a standard cosine model. The third one is the real interface model [52–55]. Zhu et al. [56] examined the stress distribution and crack growth behavior within the TBCs induced by the oxide growth using a finite element (FE) model with real TGO shape and proposed two different failure mechanisms. The fourth one is the porous model [57–59]. Wang et al. [60] developed a three-dimensional porous model based on the sample of TBCs and investigated the evolution process of crack growth and damage failure in TBCs under external tensile loading. The fifth one is the idealized lamellar model [61–63]. Ranjbar-far et al. [62] developed a layered model using the c ++ custom program and investigated the crack growth behavior under different TGO thicknesses and interface morphologies. However, the shape and bonding status of lamellae in their model are far from the real morphology of coating. Although different models had been developed for assessing the stress profiles and crack behaviors within the TBCs, none of the models can consider the real lamella morphology and interface bonding status between lamellae. The interface bonding rate between flattened particles directly determines the thermal-mechanical performances and durability of coating [8]. For plasma sprayed coating, the cracks within the ceramic layer often grow along the lamellar interface and also have the trans-lamella propagation. To further understand the crack behavior within the APS coating, the successive propagation and coalescence of multi-crack during thermal service need to be explained. Consequently, it is essential to develop a new model to explore the growth behavior of the lamellar interface crack, which is beneficial to further understand the coating failure mechanisms. In this paper, a new FE model with the lamellar structured feature is developed to explore the stress state and crack growth behavior upon temperature cycling. The real TC/BC interface profile extracted from the cross-section micrograph is incorporated into the model. During thermal cycling, dynamic TGO growth is simulated via material property change step by step. The evolutions of residual stress state within the lamellar ceramic layer are examined in detail. The influences of pore and inherent crack on the stress distribution are also explored using different models. The successive crack propagation, link-up, and coating spallation process in the lamellar structured model is simulated, and crack coalescence mechanisms are investigated in depth.

Fig. 1. Microstructure feature of atmospheric plasma-sprayed YSZ coating showing the typical defects such as large pore, inter-lamella crack, and intralamella crack.

2. Finite element model 2.1. Geometry construction In APS coating, the flattened particles stack with each other, and the substantial non-bonded interfaces between lamellae act as the inherent cracks. Besides, the vertical crack also occurs in every lamella after ceramic deposition. The occurrence of the pore is also inevitable, which is determined by plasma spraying process. These three typical defects have been demonstrated in Fig. 1. The thickness of lamella is directly associated with the spraying parameters. A larger spraying distance and powder size lead to an increase in the lamellar thickness [8,63]. In general, the thickness of a single lamella is less than 2 μm [8]. The gap between crack surfaces is very small and usually sub-micrometer scale. Some cracks with a large gap can be observed based on the scanning electron microscope (SEM) micrograph. However, lots of small cracks are difficult to be observed. Therefore, the bond status between lamellae after deposition is very hard to be found out. Li et al. [7] discovered that the average interface bonding ratio between flattened particles is about 32% for the Al2O3 coating by plasma spraying process using the electro-coppering. The relatively large pores and cracks can be well visualized (see Fig. 2(a)), and the bonded and non-bonded interfaces between lamellae can be deduced based on the SEM micrograph. After that, Wang et al. [64] founded that the mean bonding rate between lamellae for the yttria-stabilized zirconia (YSZ) coating is also about 32% using the impregnation of alumina. However, for the APS YSZ coating after impregnating Al2O3, the contrast between YSZ and Al2O3 is not very obvious. Fortunately, these coatings prepared by the plasma spraying method have similar microstructure feature and lamellar interface bonding rate. Consequently, the typical SEM image of a plasma-sprayed Al2O3 coating after electroplating copper is used for building the lamellar FE model. The basic diagram of bonded and non-bonded interfaces are plotted in Fig. 2(b), which is based on the SEM micrograph shown in Fig. 2(a). As the lamellar FE model is created for the first time, most vertical cracks are temporarily neglected to decrease the difficulty of model construction and save the computation time. The corresponding geometry model is established using the commercial software “ABAQUS” [65]. When TGO thickness is relatively small, the coating spallation always occurs within the ceramic layer close to the TC/BC interface. With the increase of TGO thickness, the cracking path shifts to the interface from the inner of ceramic [66,67]. If the whole ceramic layer is created using the stacking lamellae, the computation including crack propagation and TGO growth during thermal cycling is almost impossible to be realized. Therefore, only these ceramic regions close to the TC/BC interface are established as lamellar structure according to the real SEM micrograph. The total thickness of the lamellar ceramic layer is about 45 μm, which can satisfy the need for modeling the crack growth and coating spallation. In the current model, the thickness of 2

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Fig. 2. Cross-section morphology of copper-electroplated Al2O3 coating (a) [7], non-bonded lamellar interface distribution extracted from the real morphology shown in Fig.2a (b), established physical model with stacked lamellae (c), finite element mesh grid showing the bonded interface between lamellae (d), magnified view of geometry in two regions and the corresponding grid feature (e).

the entire ceramic top coat is 250 μm. To build model easily and save computation cost, the ceramic parts above the lamellar region are considered as an isotropic and homogenous material. The thicknesses of bond coat and substrate are 150 μm and 3 mm, respectively. The real TC/BC interface profile traced from the cross-section microstructure morphology (see Fig. 2(a)) is adopted to restore the residual stress state within the TC layer as realistic as possible. The initial TGO thickness is about 0.3 μm, which is usually prepared by pre-oxidation treatment prior to thermal shock [66]. The physical geometry model, including the lamellar ceramic regions, is presented in Fig. 2(c). The whole FE model is meshed using the quadrilateral element with generalized plane strain. The number of elements has reached to 350000. The lamellar regions are discretized by smaller mesh size. Herein, the virtual crack closure technique (VCCT) [68] is employed to calculate the strain energy release rate (SERR) and simulate crack growth. This method requires the element size before and after the crack tip to be equivalent as possible. The mesh grids involving the lamellar regions have been shown in Fig. 2(d). The typical element size within the lamellar region is about 0.045 μm. The bonding nodes between lamellae have been presented by the highlighted red node sets, which are corresponding to the bonded interface in Fig. 2(b). Besides, some local regions near the TC/BC interface are also refined using a smaller element size to obtain more accurate stress value, and the typical grid size is about 0.25 μm. Apart from the regions mentioned above, other regions are discretized using a relatively coarse grid, and the element size in the regions far from the TC/BC interface is larger. To model crack growth in the crossed lamellar interface such as region A in Fig. 2(c), a special treatment, putting a very small pore at the crossed position, is adopted. These small pores do not affect overall stress distribution. The enlarged views of geometry and mesh in the region A have been demonstrated in Fig. 2(e). Those separate nodes along the lamellar interface are corresponding to the non-bonded lamellar interface. As TGO growth is simulated by material property change step by step here, the BC region close to the TGO/BC interface is divided into 100 layers when the model is built, which has been shown in Fig. 2(c). The enlarged drawing of region B is also presented in Fig. 2(e). These layers posses the bond coat properties before thermal

cycling. After every cycle, the corresponding layer will be converted into TGO. At high temperature, the TGO layer is allowed to simultaneously grow along the directions parallel and perpendicular to the TC/ BC interface. The detail of dynamic TGO growth is described in section 2.5. 2.2. Material parameter The APS TBC system is a composite multilayer structure. The properties of constituent materials are always dependent on temperature. The ceramic top coat is prepared using a hollow spherical 8 wt% yttria-stabilized zirconia powder (8YSZ). The MCrAlY bond coat is prepared by cold spraying using a commercial Ni23Co20Cr8.5Al4.0Ta0.6Y in a spherical shape. The Nickel-based superalloy Inconel 738 is used for the substrate. The detail descriptions on the spraying condition can be found in the reference [66]. Since the top layer is a brittle ceramic material, the VCCT method is employed to simulate the crack growth. The TC layer is regraded as an elastic material. At high temperature, the sintering can change the microstructure of APS coating and lead to a decrease in porosity and the healing of some small cracks [69,70]. So, it causes an increase in stiffness of ceramic coating, which will increase the driving force (strain energy release rate) of the crack extension [71]. In this study, we mainly focus on the effect of TGO growth on the propagation behavior of crack within the ceramic coating during thermal cycling. So, the sintering effects on crack behavior are temporarily ignored. Although the substrate is a metallic layer, the creep and plastic deformation behaviors at high temperature almost don't affect the stress states within the ceramic layer or near the TC/BC interface [72]. Therefore, the substrate layer is also considered as elastic material. The relevant elastic parameters and coefficient of thermal expansion (CTE) for all layers have been listed in Table 1 [73,74]. Since the plastic deformation of bond coat largely affect the stress distribution and cracking behavior in TC, it is regarded as elastic-plastic material. The yield strength dependent on temperature for BC is demonstrated in Table 2 [51]. At high temperature, TGO growth can induce large growth stress. If TGO is considered as an elastic material, large growth stress far greater than experiment value will be 3

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Table 1 Material data used for all layers [73,74]. T (°C)

E (GPa)

ν

α × 10-6 (°C

TC

-1

)

E (GPa)

ν

α × 10-6 (°C

0.27 0.27 0.27 0.27 0.27

5.1 – – – 9.8

0.30 0.30 0.30 0.30 0.30

– 12.6 13.6 15.4 16.3

-1

)

TGO

25 200 400 800 1000

17.5 – – – 12.4

0.20 0.20 0.20 0.20 0.20

9.68 – 9.70 – 10.34

BC

378 371 361 336 311 SUB

25 200 400 800 1000

218 209 199 162 118

0.30 0.30 0.30 0.30 0.30

10.3 11.3 12.5 14.3 16.0

210 200 187 156 138

Fig. 3. Cyclic temperature loading applied for calculations.

typical temperature cycle comprises three stages: a heating phase in 300 s, a holding phase with 7200 s, and a cooling phase in 300 s. TGO growth is allowed to occur at high temperature.

Table 2 BC yield strength reliant on temperature [51]. σybc (MPa)

T (°C)

868 807 562 321 265 117 66 38

20 500 600 700 750 850 950 1050

2.5. TGO growth design TGO growth is allowed to appear at high temperature of thermal cycling. When the Al from the bond coat chemically reacts with the O element from the air or zirconia, the new oxides will form. Most of the new oxides are created at the TGO/BC interface. However, a small fraction of new oxides will form at the boundary of TGO grains [35]. The new oxides from the TGO/BC interface lead to TGO thickening, while those from the internal grain boundary will cause TGO lengthening. Although the number of new oxides created at the grain boundary is very small, they play a critical role in the failure of TBCs. As the TGO layer is constrained by adjacent layers, its growth will induce large stress, namely TGO growth stress. When the Al ions react with O ions, the volume expansion will occur as the volume of Al2O3 is greater than Al. In this work, the volume expansion induced by chemical element reaction is assumed to be determined by the PillingBedworth (P–B) value [76]. However, if TGO growth stress is directly calculated through the P–B value, the obtained stress level is far greater than the experiment value. That is because the P–B theory supposes that the diffusion of metallic element at the interface does not happen. However, the real oxidation process is always accompanied by element diffusion. After diffusion, there are lots of atomic vacancy in the bond coat, which will offset a fraction of expansion stress. Therefore, a modified volume expansion strain will be used. Herein, the strain induced by volume expansion is denoted by εv and chosen as 0.0043. Rhines et al. [77] had pointed out that inconsistent deformation between film and substrate would occur only when the new oxides grew along the direction parallel to the interface. Once an incongruous deformation happens, the growth stress will be induced. Since the new oxides increase with the oxidation time, the lateral growth strain continuously enlarges. Clarke et al. [78] proposed the lateral growth strain rate theory of oxide and believed that the TGO lateral strain rate is proportional to the thickening rate, which can be expressed as: . . εl = Dox h (1)

generated. In order to control the growth stress into a reasonable level, TGO is allowed to have a high-temperature yield property [34]. Herein, the plastic deformation of TGO occurs at high temperature with a yield strength σytgo . With the decrease in temperature, the yield strength dramatically increases. When the system temperature is less than 900 °C, the TGO layer will exhibit elastic behavior. The yield strength linearly changes among all temperature ranges. In this work, TGO yield strength σytgo at high temperature is 1 GPa for all calculations [74]. The mises plastic flow law is used for the bond coat and TGO. The creep behavior for all layers is temporarily ignored, which doesn't affect the overall trend of stress state and energy change during thermal cycling [75]. 2.3. Constraint boundary The model is regarded as a representative volume element (RVE). The left side is constrained in the x-direction. A periodic boundary condition is exerted on the right side of the model using the equation constraint, which will allow these nodes lying the boundary to move along the x-direction with the same displacement. At the same time, the movement of these nodes along the y-direction will be not limited. Additionally, those nodes lying on the bottom of the model are not allowed to move in the y-direction to avoid a rigid-body motion. 2.4. Temperature loading

where ε˙l presents the strain rate of TGO growth parallel to the TC/BC interface, h˙ denotes the thickening rate of TGO perpendicular to the TC/BC interface, and Dox is a factor. In this paper, the parameter Dox is set as 0.00785 μm-1 [79]. Note that the total lateral strain εlg in TGO is composed of two components: the volume expansion strain εv induced by element chemical reaction, and the lateral strain εl brought by the new oxide formed at the grain boundary in TGO. The εv value is dominated by the P–B value, and the εl value is determined by Clarke’ theory. However, the total thickening strain εtg in TGO only comprises the volume

When the sample of TBCs is subjected to a furnace isothermal cycling test, the temperature within the sample can be regraded as equivalent everywhere at a certain point in time. Thus, the FE model will experience a homogeneous cyclic temperature loading (see Fig. 3). The whole model is regarded as initially stress-free before thermal shock [40]. First, the model undergoes a cooling phase. The stress states after the initial cooling phase can approximately match the residual stress after coat deposition. Then, multiple cycles are exerted on the model. Finally, the system is reheated to the high temperature. Here, a 4

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expansion strain εv. At high temperature, the growth kinetics of metallic oxide usually meets a parabolic relationship. However, its oxidation process is more complicated than metal as the alloy oxide growth is affected by the microelement. The coating on the alloy substrate surface also influences oxide growth. In general, the oxide thickness of alloy material with the oxidation time satisfies the following equation:

h = At n + h 0

change process from bond coat to TGO can be materialized using the user subroutine “USDFLD” in Abaqus. A solution dependent variable (SDV) will be used to dominate the manner of the material property change. If the SDV value is zero, the properties of the corresponding layer are still bond coat properties, which means that this layer is still bond coat. When the SDV value become one, the corresponding layer is fully converted into TGO and remain unchanged during the subsequent thermal cycling. If a value in the range from zero to one is found, it suggests that the relevant layer is being turned into TGO, and the properties of this layer will be linearly changed from bond coat to TGO. For example, if the model undergoes the heating phase of the first cycle, the SDV values of all thickening layer are zero, which means that all layers are still bond coat properties at this moment. When the model is in the holding phase of the first cycle, the SDV value of the TGO1st layer begins to increase but the value of other layers are still zero, which indicates the first thickening layer is being changed into TGO from the bond coat. When the model begins to enter into the cooling stage of the first cycle, the TGO1st layer is fully turned into the TGO layer. At this moment, the SDV value of other layers is still zero. After the first cycle, the TGO1st layer becomes into TGO from bond coat while other layers are still bond coat. When the system is in the cooling stage of the first cycle or the heating stage of the second cycle, only the SDV value of the TGO1st layer is one whereas the values of other layers are zero. If the model enters into the holding stage of the second cycle, the SDV value of the TGO2nd layer starts to increase, the value of the TGO1st layer is still one, and the values of other layers are zero. When the system begins to get into the cooling phase of the second cycle, the SDV values of the TGO1st and TGO2nd layer are one while the values are zero for other layers, which suggests that the TGO1st and TGO2nd layer have been completely converted into TGO while other thickening layers are still bond coat. In the same way, after 100 cycles, the SDV values of all thickening layers become one. In other words, all thickening layers become TGO after 100 cycles. When a thickening layer is being changed into TGO from the bond coat, the corresponding thickening growth strain εtg and lateral growth strain εlg will be imposed using the user subroutine “UEXPAN” in Abaqus. Fig. 4(b) has showed that the evolution of growth strains with oxidation time in the 20th thickening layer. It can be found that the thickening strain εtg linearly increases to 0.0043 from 0 when the TGO20th layer is being converted. At the same time, the lateral strain εlg also linearly increases to the corresponding value achieved by the following equation.

(2)

where h, h0, A, and n are the total thickness of oxide film, initial oxide thickness, oxidation factor, and oxidation exponent, respectively. Herein, the relationship between total TGO thickness and time under different oxidation temperature is achieved by experiments and expressed as:

h = (Aox . e−EA / RT . (t + t 0))nox

(3)

where EA denotes the oxidation energy, R presents the ideal gas constant. T and t0 are the oxidation temperature and time corresponding to initial TGO thickness. The relevant parameters EA, Aox, and nox have been calculated according to the experimental curve, and their values are 179190 J mol-1, 254.6 μm2 s-1, and 0.5, respectively [80]. In this study, t0 is equal to 6000 s by Equation (3) as the initial TGO thickness is 0.3 μm. In the literature [26,34,50], TGO growth is always simulated by the element swelling. However, when TGO grows to a relatively large thickness, the element distortion may occur. In this study, a dynamic growth manner is adopted, which can make TGO layer grow without thickness limitation. The basic map of TGO dynamic growth with temperature cycling has been shown in Fig. 4(a). Before thermal cycling, the initial TGO layer is on the bond coat surface. With the proceeding of thermal cycling, the bond coat is constantly oxidated through a chemical reaction. Here, 100 thermal cycles are chosen to investigate crack growth behavior within the ceramic layer. In order to simulate the dynamic TGO growth process, the BC parts close to the initial TGO layer are divided into 100 geometric layers before temperature cycling. The thickness of each layer decreases with the oxidation time, which is based on Equ. (3). To facilitate the description, these layers are referred to as the TGO thickening layer (see Fig. 2(e)), and the first thickening layer is called as TGO1st. Likewise, the tenth and hundredth thickening layer are TGO10th and TGO100th, respectively. Before thermal cycling, all thickening layer is the bond coat properties. When the system experiences the first cycle, the properties of TGO1st will be linearly converted into TGO properties from bond coat properties. After the first cycle, the TGO1st layer has been fully turned into TGO and then keep TGO properties. By the same token, when the TBC system is subjected to the hundredth cycle, the TGO100th layer will be changed into TGO from the bond coat. After 100 cycles, all TGO thickening layers are turned into TGO from the bond coat. The material

εlg = Dox h + ε v

(4)

εtg

After 20 thermal cycles, the thickening growth strain will remain unchanged while the lateral growth strain εlg will vary with oxidation time based on Equ. (4). After all thermal cycles, the thickening and lateral strain are uniform through TGO thickness.

Fig. 4. Schematic map of the dynamic growth simulation of TGO with temperature cycling (a) and the variation of oxidation growth strain in the 20th thickening layer with total time (b). 5

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3. Crack growth modeling tool

the lamellar interface, which can be expressed as:

In this study, crack growth along the lamellar interface is materialized using a node release technique referred to as “Debond” in Abaqus. Since this technique is based on the linear elastic fracture mechanism (LEFM), it is well fit for simulating the cracking of brittle material. It requires the user to define a crack growth path in advance. When the fracture parameter at the crack tip meets the critical value, the node pair at the crack tip is debonded. Herein, the VCCT criterion is employed to achieve the SERR at the crack tip and determine when the nodes at the crack tip are released. The SERR is the needed energy to create a new crack with the ΔA area, which is first proposed by Irwin et al. [81]. Lots of methods such as the global virtual crack extension technique, the local virtual crack extension technique, and the virtual crack closure technique can be used to obtain the energy at the crack tip. Compared with other methods, the VCCT is more convenient and efficient due to the only need of the nodal force at the crack tip and nodal displacement behind the crack tip. Moreover, the VCCT is also insensitive to the FE mesh grid and can get a considerably accurate result by the lower order element. Rybicki et al. [68] first proposed the modified crack closure integral (MCCI) used for two-dimensional problems, and afterward, the MCCI method is renamed as VCCT. This method supposed that the open displacements behind the virtual and realistic crack tip are equivalent. So, it only requires the nodal force at the crack tip and the nodal displacement behind the crack tip. For any FE software, the nodal force and displacement are the basic variables. The SERR components GI and GII can be easily achieved using the VCCT method. The schematic drawing of the VCCT for the first-order element with four nodes is shown in Fig. 5. The SERRs can be calculated by the following formulas.

Gequiv

GI =

Fv,1,2 Δv Fv,1,2 (v3 − v4 ) = 2BΔa 2BΔa

(5)

G II =

Fu,1,2 Δu Fu,1,2 (u3 − u4 ) = 2BΔa 2BΔa

(6)

G =⎛ I ⎞ G ⎝ IC ⎠ ⎜

Gequivc

⎟

am

G + ⎛ II ⎞ G ⎝ IIC ⎠ ⎜

an

⎟

(7)

where the parameter Gequiv is the equivalent strain energy. The components GIC and GIIC correspond to the fracture toughness under two different fracture loadings. The parameter am and an are the exponents and often set as 1.0 [56,74]. The fracture toughness for the APS coating is chosen as 15 J m-2 [82], and they are assumed to be equivalent for two fracture modes due to the lack of adequate data [56]. 4. Result and discussion 4.1. Stress states in the lamellar structured coating The investigations of stress profile in TBCs are prerequisite to explore crack propagation behavior and coating delamination mechanism. In this study, a new lamellar model, which is different from other ideal or porous models, is developed for analyzing the coating failure. Therefore, it is essential to examine the stress state within the TC and near the TC/BC interface before the propagation of interface crack between lamellae. The normal stress σ22 perpendicular to the coating surface mainly induces a mode I fracture, whereas the shear stress σ12 parallel to the coating surface is more likely to result in a mode II fracture. So, the states of stress σ22 and σ12 during temperature cycling will be quite concerned. During the holding phase of the cycle, TGO growth happens, which will bring large growth stress. The TGO thickness also continuously increases with temperature cycling. The in-plane growth stress of TGO is mainly attributed to its deformation due to the constrained lengthening. Since the TC/BC interface is not a flat surface, TGO deformation also will lead to the occurrence of local tensile and shear stresses in the TGO and adjacent layers. To visualize the stress states in TBCs during thermal shock, the contours of stress σ22 at room temperature after different thermal cycles have been demonstrated in Fig. 6(a). For the TC layer, after one cycle (N = 1), the tensile stress σ22 mainly appeared at the peak of the TC/TGO interface. Since the TC/BC interface morphology is irregular, most of valley regions are under the compression state, while some regions experience slight tension, which is different from the model with a sinusoidal interface [51,74]. Thus stress distribution can be easily explained. At the early phase of temperature cycling, the TGO layer is so thin that it does not resist the effect from the BC layer. The CTE for the bond coat is greater than that of the ceramic layer. So, the TC valley will be subjected to the compressive force from the bond coat due to the rapid shrinkage during the cooling phase. Except for the peak, the tensile stresses also occur near the crack in TC and boundary of the pore. That is because large stress concentration always occurs at the crack tip and corner of the unsmooth boundary. However, it is noted that the tensile stress near the crack and pore are not very large after one cycle (N = 1). Therefore, the crack propagation along the lamellar interface is not expected at the early thermal cycle. With the proceeding of temperature cycling (N = 20), the tensile stresses at the crack tip constantly increase. All the TC valleys are under the compression state. That is because that TGO deformation always leads to the downward displacement of the valley center and upward displacement of the peak. Especially for the TBC model with pre-cracks, the TGO deformation becomes more obvious. Thus deformation can stretch the TC layer adjacent to TGO in the ydirection, which induces the tensile stress at the TC valley. On the other hand, the thicker TGO can also offset a fraction of compressive force from the bond coat shrinkage. When the system undergoes more cycles (N = 40), the stress states in TC keep unchanged except for the increase in magnitude. The stress intensity is also large enough to make the inherent crack between lamellae propagate. However, in this section, only stress states are focused, and crack growth is not allowed to

where Fu,1,2 and Fv,1,2 are the force components at the crack tips along the x and y direction, respectively. The ui and vi are the nodal displacement components behind the crack tips along x and y-direction, respectively. The parameter Δa is the characteristic element length. The parameter B is the thickness along the z-direction and 1.0 for the twodimensional model. As the crack growth in TBCs is often together controlled by fracture mode I and mode II during thermal cycling, a power law for mixed fracture criterion [40] is employed for modeling the crack growth along

Fig. 5. Schematic illustration of the virtual crack closure technique (VCCT) suitable for the quadrilateral element with four nodes. 6

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Fig. 6. The distribution contour of the normal stress σ22 (a) and shear stress σ12 (b) at room temperature in TBCs after subjected to different cycles (N = 1 presents the first temperature cycle).

coat is always greater than that of TC and TGO. Thus, the tensile stress will occur at the TGO/BC peak due to the rapid shrinkage of BC during the cooling phase, which also means that the crack is more likely to nucleate at the peak of the TGO/BC interface. Many results [51,83–85] also exhibited the cracks forming at the TGO/BC interface, which was in agreement with the possible cracking path predicted by simulation in this work. Since the focuses are concentrated on the cracks between lamellae in this study, the crack growth along the TC/TGO/BC interface is temporarily ignored. The crack propagations in the plasma-sprayed coating are often controlled by the mixed fracture mode. Therefore, it is necessary to examine the states of shear stress σ12 in the current model. The contours of stress σ12 at room temperature after different thermal cycles have been shown in Fig. 6(b). It can be seen that the shear stress magnitude is very small after one cycle (N = 1), which suggests mode II at the early phase of thermal cycling has little influence on the coating failure. With the proceeding of thermal cycling (N = 20), the shear stresses at the crack tip and TC valley become more intense. When the model experiences sixty cycles (N = 60), the shear stress intensity at the TC valley reaches 227 MPa, which is double than that corresponding to a lower cycle (N = 20). Also, the stress intensity at the lamellar crack tip is four times of lower cycle (N = 20). With the further increase in the cycle (N = 80), the shear stress is also enhanced. However, the speed of stress increase shows an obvious decrease, which is similar to normal

happen. Consequently, the stress intensity at the crack tip will constantly increase with thermal cycling, and the crack surface also has a larger opening displacement. In section 4.3, the crack growth behavior and coalescence mechanism will be explored in detail. If the number of thermal cycles is further increased (N = 60), the stress distribution will remain invariant. The stress magnitude at the valley in TC increases to 525 MPa, which is greater than the value of 332 MPa corresponding to a lower thermal cycle (N = 20). Certainly, the tensile stress at the lamellar crack tip is also further increased. When the cycle reaches eighty times (N = 80), the tensile stresses in TC are further enhanced. Moreover, the TGO thickness also increases compared with that corresponding to a lower cycle (N = 20). However, the rate of stress increase with cycles begins to decrease due to the parabolic growth of TGO thickness obeying Equ. (3). After one hundred cycles (N = 100), the tensile stress at the TC valley has reached 617 MPa. Large stress concentration appears at the lamellar crack tip, and the tensile stress intensity also comes up to 496 MPa. Based on the above analyses, crack growth in the lamellar structured model is possible to be observed when the system is subjected to some thermal cycles. Moreover, the crack coalescence and coating spallation may also be found after more cycles. For the BC layer, in the cooling process, the peak of the TGO/BC interface is always subjected to tensile stress, while the valley constantly undergoes compressive stress. Moreover, the stress characteristic does not change with thermal cycling. This is because the CTE of the bond 7

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Fig. 7. Variation of the residual stresses at point A in TC as a function of temperature cycle (a) and the stress magnitude (at room temperature) at point B in BC after different cycles (Note that the position of point B continuously migrates with thermal cycling due to the dynamic TGO growth).

irregularity of the interface. With the continuation of thermal cycling, the normal stress at the valley becomes tensile due to the TGO thickening and lateral growth. In contrast, the peaks undergo compressive stress (N = 10). When the system experiences more cycles (N = 50), the stress distribution along the TC/TGO remains unchanged, but the stress magnitude constantly increases. After more thermal cycles (N = 100), only stress intensity is enhanced. It is noted that the stress distributions on both sides of the peak or valley are not symmetrical due to the complex interface morphology, which is different from the model with a sinusoidal interface [37,41,51]. From Fig. 8(b), it can be observed that the stress states along the TGO/BC interface are not sensitive to thermal cycles. After cooling, the peak of the TGO/BC interface is always subjected to tensile stress while the valley of the interface is under the compressive status. That is because the CTE of the bond coat is much greater than that of TC and TGO. During the cooling, the rapid shrinkage from the bond coat will induce the tensile stress at the peak of the TGO/BC interface. With the proceeding of thermal cycling (N = 50), the stress intensity continues to increase. After more cycles (N = 100), the stress magnitude only has a very slight increase, which is mainly ascribed to the plastic yield of the bond coat. To further reveal the reason why the valley of the TC/TGO interface is subjected to the tensile stress after cooling, the changes in the morphology and amplitude of the TC/TGO interface are investigated, and the relevant results have been shown in Fig. 9. It is quite evident that the center of the valley moves down and the peak has an upward displacement after 100 temperature cycles (see Fig. 9(a)), which is in consistent with the result in the literature [26]. To quantitatively describe interface deformation before and after thermal cycling, the changes in the interface amplitude within the region A and B are extracted and shown in Fig. 9(b). It can be seen that the interface amplitude changes increase with the advancement of thermal cycling. The trends are in line with that observed in the literature [75]. The amplitude increase is mainly due to the interface deformation induced by

stress. When the system experiences one hundred cycles (N = 100), the TGO thickness is far greater than its initial thickness. The shear stress intensity in TC is very large, which is comparable to that of the tensile stress. Therefore, after several cycles, the fracture mode II begins to contribute to the crack growth and coating delamination, which also confirms that the coating failure during thermal shock is together controlled by the fracture mode I and mode II. The variations of the tensile and shear stress with temperature cycles in TC are also quantitatively investigated, and the related results have been shown in Fig. 7(a). The monitored point A is set at the valley in Fig. 6(a). It can be found that the tensile and shear stress intensities continuously enhance with temperature cycling. The maximum always occurs at the end of the cooling phase except for at the early thermal cycles. The increase in the stress magnitude is mainly ascribed to the lateral growth of TGO at the holding phase. The rate of stress increase constantly reduces with temperature cycling, which is because the TGO growth obeys a parabolic rule. The evolutions of stress intensity at point B in the bond coat with thermal cycling are presented in Fig. 7(b). Currently, it is noted that the TGO/BC interface dynamically moves down with temperature cycling. That is because that the TGO growth is dynamically simulated via material change step by step. So, the position of point B also dynamically changes with cycles. It can be observed that the stress intensity in BC constantly increases with thermal cycles at the early stage of thermal loading. However, after some cycles, the stress variations begin to get into a steady stage. That is mainly ascribed to the plastic yield deformation of the bond coat. To quantitatively study the evolutions of the stress at the TC/TGO/ BC interface, the normal stress σ22 states at room temperature at the interface under different thermal cycles are demonstrated in Fig. 8. From Fig. 8(a), it can be found that the stress states at the TC/TGO interface after one cycle (N = 1) are similar to that corresponding to the initial cooling (N = 0). The peak of the TC/TGO interface is subjected to slight tension. Most of the valleys are under the compressive status. However, some valleys also experience a slight tension due to the

Fig. 8. Distribution of the normal stress σ22 (at room temperature) at the TC/TGO interface (a) and the TGO/BC interface (b) after different cycles (Note that the TGO/BC interface continuously migrates with thermal cycling due to the dynamic TGO growth). 8

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affected by the TGO deformation. But if the model experiences a gradient thermal cyclic loading, these cracks between lamellae away from the TC/TGO interface maybe also propagate along the lamellar interface due to a higher modulus induced by the ceramic sintering. Therefore, the coat delamination under the inhomogeneous temperature loading usually occurs within the ceramic layer above the TC/BC interface. For the shear stress, the influences of pore and lamellar crack on stress state are similar to normal stress σ22. The large pore close to the TC/TGO interface change the local stress profiles near the interface, which is shown in Fig. 10(d). From Fig. 10(d) and (e), it can be found that large stress concentration also appears near the pore and lamellar crack, and the stress at the crack tip becomes more intense. The stress intensities near the pore and crack far from the TC/TGO interface are decreased in current thermal loading conditions. These trends are similar to normal stress, which also suggests the shear stress in the lamellar structured model plays a more important role in the failure of TBCs compared with other models. Moreover, for the normal and shear stresses, the large pore and lamellar crack in TC have little influences on the stress states in the bond coat. To quantitatively explore the effects of the large pore and lamellar crack on the stress profiles at the interface, the normal stress states at room temperature along the interface after 100 cycles for three different models are demonstrated in Fig. 11. For the TC/TGO interface (see Fig. 11(a)), the porous and intact model have the same stress profile along the interface except for some specific positions where the large pore is very close the TC/TGO interface. At these positions, the stress magnitudes have an obvious difference. Therefore, only those pores close to the TC/TGO interface have a relatively large influence on the stress intensity at the interface, although the stress concentration near the pores in TC may induce the crack nucleation. Additionally, at some positions, the stress magnitude for the porous model is less than that for the intact model, which means that the large pores can release the stress in TC. However, the normal stress states in the lamellar model developed in this work are distinctly different from the intact and porous models. At some positions, larger stress magnitudes appear at the TC/TGO interface in the lamellar model, while the stress intensity is less than that of the intact and porous models at other positions. That is ascribed to the complex interface morphology. The lamellar cracks in TC can release the stress in TC through the opening of crack surfaces. Moreover, the lamellar cracks close to the TC/TGO interface can also change the local tension and compression states along the interface. But the stress distribution and intensity along the TGO/BC interface are almost not affected by the pores and lamellar interface cracks in TC (see Fig. 11(b)). Consequently, the lamellar model built in this study can reflect the stress states within the ceramic and at the TC/BC interface more realistically.

Fig. 9. Morphology of the TC/TGO interface before and after temperature cycling (a) and the change in the interface amplitude (in the region A and B shown in Fig. 9a) as a function of temperature cycling (b).

the lateral growth of TGO at high temperature. The relevant reasons had also been given in the literature [75,86]. All in all, the above results indicate that the tensile and shear stress intensities in TC constantly enhance with thermal cycling, which is a prerequisite for making crack nucleate and propagates. Moreover, large stress concentration occurs near the cracks and pores, which is more likely to induce the crack growth along the lamellar interface at the early phase of thermal cycling compared with other non-lamellar models. 4.2. Roles of large pore and lamellar interface crack The lamellar model developed in this work comprises a lot of pores and lamellar interface cracks, which are different from other porous or sinusoidal models. Therefore, it is essential to explore the influences of pore and lamellar crack on the stress profile in TBCs to further understand the possible crack growth and coating failure mechanisms. Herein, three different models are employed to investigate the roles of pore and lamellar interface crack. The first one is the undamaged model without any defects in TC, which is referred to as the intact model. The second one is the imperfect model only with the large pores. The last one is the lamellar structured model developed in this work. After one hundred cycles (N = 100), the stress profiles of the normal stress σ22 and shear stress σ12 at room temperature for these three models are shown in Fig. 10. It can be found that a remarkable stress concentration occurs at the edge of pore compared Fig. 10(a) with (c). The tensile stress intensity at the edge of pore close to the TC/TGO interface is larger, which is due to the effect from the TGO deformation. Moreover, the existence of large pore also changes the stress distribution in TBCs. Especially when the pores are very close to the TC/TGO interface, the stress states along the interface are more likely to be affected by these large pores. If the pores are far from the TC/TGO interface, its effect on the stress fields will be sharply weakened in current conditions. However, if the system is being subjected to an inhomogeneous temperature loading, these pores away from the interface will be able to prevent heat flow or change the flow direction. Fig. 10(e) shows a larger stress concentration appears at the tip of the lamellar interface crack compared with Fig. 10(a). Thus stress intensity can lead to crack growth during thermal shock. Furthermore, the stress intensity at the crack tip is larger if the lamellar crack is closer to the TC/TGO interface. That is because these cracks close to the TC/TGO interface is easier to be

4.3. Crack growth and link-up in the lamellar structured coating The stress results in the above sections have shown that the stress intensity in TC constantly increases with temperature cycling. After several cycles, all the tensile and shear stress magnitude reach a very large value, which is sufficient to make crack propagate. Especially, large stress concentration always occurs at the lamellar crack tip. Therefore, during temperature cycling, crack propagation and subsequent coalescence may be expected in the lamellar model developed in this work. To further understand the coating failure, the successive crack growth along the lamellar interface has been explored based on the lamellar structured model, and the relevant results are shown in Fig. 12. The coating delamination induced by multiple cracks coalescence has also been found in the current model. Based on the stress results mentioned above, after one cycle (N = 1), the stress intensity in TC at room temperature is very small, which is not sufficient to evoke the crack growth. In Fig. 12(a), it can be seen that the stress concentration at the tip of crack 1 is more obvious 9

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Fig. 10. The distribution contour of the normal stress σ22 at room temperature (after 100 cycles) in the intact, porous, and lamellar model are demonstrated in Fig. 10(a), (c), and (e), respectively, and the corresponding shear stress σ12 distribution under the same conditions are shown in Fig. 10(b), (d), and (f).

propagate toward the left boundary of the model, and its growth is mainly dominated by mode I. The SERRs of other cracks also further increase with temperature cycling. The total SERR value for crack 2 is about 9.3 J m-2, which gets close to the critical value. After sixty cycles (N = 60), the crack 2 begins to grow under mode II. All the lamellar crack surfaces have a larger opening displacement. Also, crack 1 also continues to propagate toward the left boundary. Simultaneously, the total SERR value for crack 3 also reaches 13.1 J m2 , which means that the crack 3 will happen to propagate if the TBC system undergoes more cycles. When the model is subjected to the seventieth cycle (N = 70), crack 3 has started to propagate along the lamellar interface. Also, the lengths of crack 1 and 2 are further increased. At this point, the SERR components GI and GII at the left tip of crack 4 are about 7.37 and 3.94 J m-2, respectively. The total SERR value at its right tip has also reached 12.8 J m-2, which is very close to the fracture toughness of coating. The strain energy at the right tip of crack 5 also accumulates to a certain extent. So, after more cycles, crack 4 and 5 may happen to propagate. When the model experiences seventy-nine cycles (N = 79), the crack 3 meets the neighboring pore,

than other lamellar cracks. Although the SERR component GII has reached 4.9 J m-2 at the right tip, it is far less than the fracture toughness of ceramic coating. Therefore, crack growth is not observed at the beginning phase of thermal cycling. When the system experiences more cycles (N = 10), the stress intensity at the lamellar crack tip increases with thermal cycling. So, the corresponding SERRs also enhance with the increase in the cycles, which is displayed in Fig. 12(b). The strain energies at all crack tips are constantly accumulated. At the right tip of crack 1, the SERR component GII comes up to 11.2 J m-2, which is a value close to the fracture toughness of coating. Therefore, the growth of crack 1 may be found during the following cycles. As predicted, the crack 1 begins to propagate toward the right boundary of the model under mode II after more cycles. When the model is subjected to twenty cycles (N = 20), the right tip of crack 1 has linked with the pore. At the same time, the strain energy at other crack tip is further accumulated. The total SERR values at the tip of crack 2 and 3 are about 3.8 and 3.9 J m-2, respectively. Moreover, the SERR component GI has also reached 4.6 J m-2 at the left tip of crack 1. When the number of thermal cycles attains forty times (N = 40), the left tip of crack 1 begins to

Fig. 11. Distribution of the normal stress σ22 (at room temperature after 100 cycles) in the intact, porous, and lamellar model: (a) at the TC/TGO interface and (b) at the TGO/BC interface. 10

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Fig. 12. Successive Process of the crack growth, link-up, and coating delamination process (a–h), the cross-section morphology after coating delamination observed in experiments (i), the variation of the relative total crack length along the delamination path with temperature cycling (j).

spallation path predicted by simulations. After coating spallation, only a very small fraction of ceramic is attached on the surface of the bond coat. To further explore the crack propagation behavior, the relationship between the delamination length and thermal cycles along the spallation path is plotted and shown in Fig. 12(j). It is very evident that the cracks do not propagate at the beginning phase of thermal cycling and then grow very slowly after several cycles. When the system experiences more cycles, the speed of crack growth begins to increase. Before the occurrence of complete coating spallation, the crack length rapidly increases within a very small amount of thermal cycles. When the through crack forms due to the complex crack growth and coalescence, the ultimate delamination and spallation begins to occur, which is in consistent with the experimental results [87–89]. In brief, during thermal shock, the coating failure is a very complex process, and it is not caused by a single crack growth but multiple cracks growth and coalescence. The growth and linkage of multiple cracks in the current lamellar model are materialized using a fracture mechanics method, and the crack propagation behavior during thermal cycling is assessed. The ultimate coating spallation is observed and agrees with the experimental results shown in Fig. 12(i).

and the crack 2 and 5 link up with the adjacent cracks to form the longer crack 8 and 6, respectively. The left tip of crack 1 is further extended, which is close to the adjacent pore. At the moment, crack 4 also happens to grow. The crack 7 also propagate along the lamellar interface. It is evident that the stresses below the propagatable cracks are released. Additionally, the stress intensities above these cracks also become very small due to crack growth. When the model undergoes the eightieth cycle (N = 80), a through crack begins to form, and the coating delamination is observed. First, the crack 4 continues to grow and links up with the crack 6 to form a larger crack. With the proceeding of cooling, the large crack continues to propagate toward the right boundary of the model and has a linkage with the crack 8 to form the crack 10. Then, the left tip of crack1 merges with the adjacent pore, which creates the new crack 9 due to the coalescence of the crack 1, pore, and crack 3. When the cooling continues, the large crack 9 and crack 10 happen to merge to form the through crack, which connects the left and right boundary, which leads to the ultimate coating delamination and spallation. The results from the furnace cyclic tests also suggested the coating spallation appears within the TC close to the TC/BC interface when the TGO thickness is relatively thin [67]. The microstructure morphology after coating spallation is demonstrated in Fig. 12(i), which is in line with the 11

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5. Summary and conclusion

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In this study, a novel lamellar structured model for APS coating is developed to explore the crack growth behavior and coalescence mechanisms upon temperature cycling. The dynamic growth process of TGO at high temperature is simulated via material properties change step by step with cycles. The crack propagation along the lamellar interface in the ceramic layer is materialized using the “Debond” technique combined with a mixed-mode fracture criterion. The virtual crack closure technology (VCCT) method is employed to achieve the strain energy release rate (SERR) components GI and GII. The stress profiles in the lamellar model during thermal cycling are first evaluated, and the effects of pore and lamellar interface crack on the stress state are further explored. Then, the successive crack growth, coalescence, and coating spallation are simulated based the new model with stacking lamellae. The main conclusions include: (1) The stress intensities in the ceramic layer continuously increase with temperature cycling, which is prerequisite to cause crack growth and coating delamination. (2) Although the pore and lamellar interface crack can release the stress within the ceramic layer, large stress concentration always appears near them, which results in the incipient crack nucleation and propagation. The lamellar interface crack can change the stress state within the TC and at the TC/TGO interface to some extent. (3) The coating failure is a complex process induced by multiple crack propagation and coalescence. During temperature cycling, the successive crack growth, linkage, and final coating delamination are expected, and the simulated coating spallation path is in line with the experimental result. (4) At the early phase of thermal cycling, the crack grows in a very slow speed. Before the ultimate coating spallation, the crack length rapidly increases within a small number of thermal cycles. The possible crack combination mechanisms are revealed based on the lamellar model. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 51671159), the National Basic Research Program of China (No. 2012CB625100), the Fundamental Research Funds for the Central Universities, and the National Program for Support of Topnotch Young Professionals. References [1] N.P. Padture, Advanced structural ceramics in aerospace propulsion, Nat. Mater. 15 (2016) 804–809. [2] V. Kumar, B. Kandasubramanian, Processing and design methodologies for advanced and novel thermal barrier coatings for engineering applications, Particuology 27 (2016) 1–28. [3] V. Kumar, K. Balasubramanian, Progress update on failure mechanisms of advanced thermal barrier coatings: a review, Prog. Org. Coat. 90 (2016) 54–82. [4] G.R. Li, L.S. Wang, G.J. Yang, A novel composite-layered coating enabling selfenhancing thermal barrier performance, Scr. Mater. 163 (2019) 142–147. [5] P.K. Wright, A.G. Evans, Mechanisms governing the performance of thermal barrier coatings, Curr. Opin. Solid St. M. 4 (1999) 255–265. [6] A.G. Evans, D.R. Mumm, J.W. Hutchinson, G.H. Meier, F.S. Pettit, Mechanisms controlling the durability of thermal barrier coatings, Prog. Mater. Sci. 46 (2001) 505–553. [7] A. Ohmori, C.J. Li, Quantitative characterization of the structure of plasma-sprayed Al2O3 coating by using copper electroplating, Thin Solid Films 201 (1991) 241–252. [8] C.J. Li, A. Ohmori, Relationships between the microstructure and properties of thermally sprayed deposits, J. Therm. Spray Technol. 11 (2002) 365–374. [9] C.J. Li, Y. Li, G.J. Yang, C.X. Li, A novel plasma-sprayed durable thermal barrier coating with a well-bonded YSZ interlayer between porous YSZ and bond Coat, J. Therm. Spray Technol. 21 (2012) 383–390. [10] G.R. Li, L.S. Wang, G.J. Yang, Achieving self-enhanced thermal barrier performance through a novel hybrid-layered coating design, Mater. Des. 167 (2019) 107647. [11] C.J. Li, Y. Li, G.J. Yang, C.X. Li, Evolution of lamellar interface cracks during isothermal cyclic test of plasma-sprayed 8YSZ coating with a columnar-structured YSZ

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