Microcrack propagation induced by dynamic infiltration of calcium-magnesium-alumino-silicate in columnar structures for thermal barrier coatings

Columnar-structured thermal barrier coating systems (TBCs) possess a strain tolerant columnar microstructure wherein the gaps between the columns are filled with high-porosity oxides. At high temperatures, columnar-structured TBCs may be eroded via contact with a significant amount of calcium-magnesium-alumina-silicate (CMAS). A numerical model is proposed to estimate the temperature and stress fields of the microcracks induced by the CMAS infiltration. The energy release rate is evaluated to understand the influence of CMAS on the microcracks in the columnar microstructure. The effects of CMAS on the microcrack propagation are discussed in detail by using the extended finite element method. The results demonstrate that both the stress and energy release rate near the microcrack were found to dramatically increase when the CMAS reached the microcrack. Moreover, increasing the time of CMAS infiltration could destroy the thermal insulation provided by the top coat and considerably increase the energy release rate. The present analysis reveals that the vertical cracks are easily to initiate from the microstructure column and coalesce with adjacent horizontal and vertical pores, thereby resulting in premature failure of TBCs via delamination.


Introduction
Thermal barrier coating systems (TBCs) have been extensively applied in the field of aerospace engineering for use in gas turbines and aero-engine components. These systems can prevent the failure of a turbine component upon undergoing high temperature oxidation processes for an extended period. TBCs mainly consists of a ceramic top coat (TC) that provides a layer of insulation, an underlying superalloy engine component in conjunction with two other layers between the substrate, and a bond coat (BC) layer, traditionally made of a NiCrAlY or NiCoCrAlY, and serve to reduce the oxidation and hot corrosion between the TC and substrate [1,2]. Upon thermal exposure, a thermally grown oxide (TGO) layer forms between the TC and BC layers. During the continuous high-temperature exposure experienced by operating gas-turbine engines, oxygen diffuses from the atmosphere into the internal layers, reacting with aluminum to form oxides (-Al 2 O 3 ) at the TGO/BC interface.
The advanced material currently in use as the ceramic TC layer is approximately 7-8 wt% yttria stabilized zirconia (7YSZ). This material performs excellently as a result of its low thermal conductivity and high coefficient of thermal expansion [3]. YSZ is particularly resistant to hot corrosion because it possesses a relatively high melting point. The two major states arts of manufacturing for ceramic TC are laminar and columnar structure. The atmospheric plasma spray (APS), which is based on the former manufacturing method, exhibits the layer parallel to the interface. On the other hand, electron beam-physical vapor deposition (EB-PVD) is known as high strain tolerance owing to the specific columnar microstructure. Beside EB-PVD, suspension plasma spraying (SPS) and plasma sprayphysical vapor deposition (PS-PVD) are alternative methods for the columnar structure [4].
In this paper, we have focused only on the columnar structured coating, which possesses a strain-tolerant columnar grain microstructure and intercolumnar porosity. This columnar structure can be derivative to the TC layer of EB-PVD [5], SPS [6], and PS-PVD [7] TBCs.
The voids between the columnar grains may not only provide strain tolerance, but also reduce the thermal conductivity of this layer, which is beneficial for its use in high temperature environments [8,9].
The high temperature and harsh environmental conditions that gas turbines are operated in lead to the deposit of calcium-magnesium-alumino-silicate (CMAS) impurities, sand, runway debris, volcanic ash, air pollution, and fly ash into these turbines. A reasonable method of CMAS infiltration was described in earlier paper [10]. As a result of the eruption of the Eyjafjallajökull volcano in Iceland, aircraft engine manufacturers have paid a significant amount of attention to safety regulations regarding volcanic ash [11,12]. When CMAS adheres to the surface of the TC layer at high temperature, it rapidly penetrates into the gaps of the columnar microstructure. In brief, the CMAS may affect TBCs that are deposited by EB-PVD, PS-PVD, or APS, prompting a decrease in strain tolerance and the premature failure of the multilayered coating system [13]. Consequently, delamination and spallation would be induced via cracking. Therefore, it is essential to understand the failure mechanism of CMAS penetration into a TBCs. Several previous studies [14][15][16][17] have investigated CMAS-induced damage to TBCs. In a numerical study of CMAS, Chen [18] indicated that the thermal and elastic properties of CMAS greatly influence the energy release rate that may result in interfacial delamination. Su and Yi [19] concluded that a decrease of the in-plane modulus increases the strain energy release rate. The effect of interfacial crack geometric and material properties on the driving force in the coating system has been investigated by some researches [20][21][22][23]. The localized spallation of TBCs during of thermal exposure is been investigated by Zhang et al. [24]. The bending fracture behavior of freestanding coating has been studied by Mao et al. [25]. Jiang et al. [26,27] experimentally studied the influence of bending tests on TBCs. Recently, the transient thermal stress induced by CMAS has been studied by Chang et al. [28].
However, few researchers have investigated the crack propagation behavior induced by dynamic CMAS infiltration under thermal loading in the columnar-structured coating.
Understanding the influence of dynamic CMAS infiltration on crack propagation can predict failure mechanism and service life, thereby providing the optimum design of the columnarstructured coating. Using finite element method, two major techniques are applied to simulate the interfacial crack dynamic behavior including the virtual crack closed technique (VCCT) [29] based upon energy release rates (J-integral) and the cohesive zone model (CZM) [30] based upon the traction-separation law. The path of crack propagation should be predefined in both of VCCT and CZM. This limitation is suitable for interfacial crack or simple model.
However, it is difficult to determine the propagation path in complicated structures. The extended finite element method (XFEM) [31] as a useful technique can simulate the dynamic crack behavior. The propagation path is not necessary to define in simulation and complicated environment can be considered such as pores and inclusions. Recently, based on XFEM, Cai et al. [32] investigated the crack propagation induced by CMAS penetration during cooling stage. Nevertheless, the failure mechanism of the columnar-structured coating induced by CMAS has not yet been investigated owing to the complexities of dynamic CMAS infiltration and microstructure in the columnar-structured coating.
The two major objectives are studied in this article to understand the influence of CMAS dynamic infiltration on the microstructure of the columnar-structured TBCs. First, the temperature and stress fields around microcrack induced by CMAS dynamic infiltration are evaluated. The influence of CMAS properties (heat conductivity and thermal expansion coefficient), temperature gradient, and density of microcrack are investigated in this study.
Second, the microcrack propagation behavior in YSZ column induced by dynamic CMAS infiltration is studied using the XFEM and the failure modes in columnar-structured coatings are discussed in detail.

Numerical modeling
The numerical analysis is performed using the commercial finite element program ABAQUS 6.14 [33]. The finite element models are constructed using a mesh with almost 45,000 elements, most of which are generalized plain strain elements. A mesh located near the microcrack tip and the YSZ/CMAS/high-porosity oxidation interface is applied to capture the singularity, and the mesh sensitivity is used to preserve the convergence of the calculations. The energy release rate is calculated based on the J-integral and the dynamic crack growth is calculated based on the XFEM. The transient temperature field during three thermal cycles is first simulated by a heat transfer procedure. To evaluate the corresponding thermal stress field, the temperature field is transported as a predefined field into the static procedure.

Finite element model
Based on experiment observation, several columnar microstructures in TC layer are shown in Fig. 1. The column structures deposited by EB-PVD, SPS, and PS-PVD TBCs are shown in Fig. (1a), Fig. (1b), and Fig. (1c), respectively. The columns of EB-PVD infiltrated by CMAS and crack propagation through several columns in infiltrated areas are shown in Fig. (1d). A plane-strain model of the microstructure of the columnar-structured coating is shown in Fig. 2. This unit-cell numerical model includes 11 YSZ columns, which are initially straight and parallel to one another, and possess a column width of h and a gap width of d between the columns. The column width used in this study is h = 9 m and the high-porosity oxidation gap width is d = 1 m because the porosity of the TC is about 10% [43][44][45]. The TGO layer is neglected in this study. HTC, HBC, and HSUB are the thicknesses of the TC, BC, and substrate, respectively. HCMAS0 is the height of deposition on the surface of the TBC (i.e., on top of the TC), and HCMAS is the depth of the CMAS infiltration induced by the infiltration of CMAS into the column gaps of the columnar-structured TBCs. The depth of the substrate is set to HSUB = 300 mm, and the layer thicknesses are HTC = HBC = 100 μm [4,26] and HCMAS0 = 20 μm [14]. To determine the influence of a crack by dynamic CMAS infiltration, a microcrack of length 2a with an angle of inclination  with respect to the x-axis with a depth of HCRACK, which is measured from the CMAS0/TC interface to the crack center, was preassigned in the YSZ #6 column, as shown in Fig. 2.

Material parameters
In this study, the material properties of the TBC, including the Young's modulus, Poisson's ratio, coefficient of thermal expansion, the mass density, heat conductivity, and specific heat capacity demonstrate a linear elastic behavior. The material properties of all layers are listed in Table 1, including the hypothetical elastic and thermal characteristics of the highly porous oxides. The coefficient of thermal expansion and heat conductivity of the CMAS at high temperatures are listed in the following section. It should be noted that the selected temperature-dependent highly porous oxides are assumed to possess a relatively small Young's modulus and heat transfer coefficient.

Thermal loading and boundary conditions
The half-period geometric model used in this study is assumed to behave symmetrically on the left-edge and periodically on the right-edge of the system, as shown in Fig. 2. The left edge of this model is not permitted to move in the x-direction and the right edge may move freely. However, the parallel displacements of all the nodes on the right edge are assumed to be consistent with one another (via the multi-point constraint method). The top edge of the CMAS is free from any constraints. To ignore the bending moment of this model, the bottom edge is fixed in the vertical direction. The crack surface is assumed to be traction-free and thermally insulated from the heat flow.

CMAS penetration
The gaps between the columns are initially filled with highly porous oxides. The subsequently deposited CMAS is drawn via capillary action into the open spaces between the columns. Naraparajuer et al. [34] experimentally determined the resistance towards CMAS infiltration using two real volcanic ashes and one synthetized CMAS powder. They provided an effective method to prevent infiltration by chemically reacting the molten glass to form a crystallized phase. Based on the experimental results presented in Ref. [34], the CMAS powder data is fitted to achieve a smooth curve, as shown in Fig The infiltration rate, CMAS0 H & , is provided by: The infiltration rate indicated in Eq. (2)

Microcrack propagation induced by CMAS penetration
To study the dynamic damage process, VCCT and CZM methods are usually be implemented. However, the crack propagation path induced by the dynamic CMAS infiltration could not be predicted. Herein, XFEM is selected as modeling the microcrack propagation. The displacement in XFEM can be defined as [35] ( ) ( ) ( ) u  Fig. 5 with D being the damage parameter which can be expressed as [37]: where  is the separation, 0  is the critical opening separation and f  is the final failure separation. During the elastic behavior period, the linear curve with material stiffness k describes the mechanical behavior of the enriched region for the YSZ column #6 as shown in

Temperature field
During the high temperature holding stage, the temperature distribution between the 800 o C and 1350 o C materials is shown in Fig. 6. Note that the thermal conductivity of the TC increased. In addition, the magnitude of the heat flux of a perpendicular crack is almost the same as that experienced without cracking because a perpendicular crack does not block the flow of heat. Fig. 10 shows the heat flux distribution of TC layer for different thermal cycles.
The zone I represents the CMAS penetrated zone and zone II represents the CMAS nonpenetrated zone. The CMAS penetration depth gradually increases with the infiltration time.
In conclusion, the temperature and heat flux fields are considerably affected by both the inclination angles of the microcracks and the infiltration depth of CMAS.

Stress field
The stresses affected by the infiltration of CMAS may be classified into three types [27]. and the stresses are stable and maintained at a high value. Fig. 11 shows the maximum principal stress distribution for different thermal cycles when a microcrack is embedded in column #6 (HCRACK = 60 μm) and the inclination angle of the microcrack is 60 0 . It is interesting to see that the stress field of a microcrack has not been influenced by CMAS infiltration at t = 9000 s (type I) during the first thermal cycle (Fig. (11a)). When the infiltration time increases up to t = 24000 s (type II) during the second thermal cycle, the CMAS starts to reach the microcrack leading to a higher local stress around the tip-B as shown in Fig. 11(b). As the infiltration time increases up to t = 39000 s (type III) during the third thermal cycle, both the two crack tips of microcrack are covered by CMAS infiltration resulting in a significant increase in local stress around two crack tips as shown in Fig. (11c). angles are depicted in Fig. 12 and Fig. 13, respectively, where a microcrack is embedded in column #6 (HCRACK = 60 μm). As expected, the stresses increase during heating and decrease during cooling. The stresses experience a dramatically turbulent phenomenon when the CMAS begins to reach the microcrack during the second thermal cycle. Fig. 12 shows that the microcrack seems to behave as an open-mode fracture when the inclination angle of the microcrack is 30, 60 or 90°. Fig. 13 shows that the microcrack behaves as a sliding-mode fracture when the inclination angle of the microcrack is either 30 or 60°. It is interesting to note that the magnitude of the sliding-mode stress around tip-A at 0 30  = is larger than that at 0 60  = during the second thermal cycle in Fig. 13(a). However, the magnitude of the sliding-mode stress around tip-B at 0 30  = is smaller than that at 0 60  = during the second thermal cycle, as shown in Fig. 13(b), and this occurs due to differing distances between the crack tip and CMAS. Fig. 13(b) shows that the sliding-mode stress around tip-B at an inclination angle of 60° is bigger than that at 30°. This is because the distance between tip-B and the CMAS at 60° is smaller than that between tip-B and the CMAS at 30°. Conversely, the distance between tip-A and the CMAS at 60° is larger than that between tip-A and the CMAS at 30°. Therefore, the CMAS would reach tip-B at a 60-degree inclination angle more Finally, in order to consider multiple microcracks in the YSZ columns, the effect of the microcrack density on the energy release rate is depicted in Fig. 17. Three different cases were considered for different amounts of microcracks (NCRACK): NCRACK = 1 for a crack located at column #6, NCRACK = 3 for cracks located at columns #3, #6, and #9, and NCRACK = 5 for cracks located at columns #2, #4 #6, #8, and #10. The numerical results indicate that the energy release rate of NCRACK = 1 is larger than that of both NCRACK = 3 and NCRACK = 5. This is because the energy release rate is concentrated at the tip of a single microcrack in this case.
The possibility of microcrack propagation can therefore be greatly reduced by increasing the density of the cracks, which is consistent with the findings of previous studies for the density of the cracks [15,16].

Microcrack propagation induced by CMAS infiltration
There exists a great possibility for the microcrack propagation induced by dynamic CMAS infiltration. In this section, the microcrack propagation induced by dynamic CAMS infiltration is investigated using XFEM. In the following discussion, the microcrack is embedded in column #6 (HCRACK = 60 μm), the inclination angle of the microcrack is either 60° or 30° and the enrichment elements are assigned in column #6 of YSZ. Fig. 18 indicates the normalized crack growth under dynamic CMAS infiltration while Fig. 19 displays the process of microcrack propagation with time. When the inclination angle of the microcrack is 60°, the microcrack in column #6 of YSZ is unable to grow, herein the crack growth is almost zero during the heating and holding stage in the first thermal cycle as displayed in Fig. 18(a). Note that the normalized crack growth is defined as the crack growth divided by the height of TC (HTC). It can be seen that the stress around the microcrack still maintains a small value since CMAS did not reach the microcrack as shown in Fig. 19 (a).
During the cooling stage in the first thermal cycle, the tip-B starts to propagate when the maximum principal stress and fracture toughness reach their critical values. Fig. 19(b) displays that the microcrack starts to propagate around 14800 s (cooling stage during the first thermal cycle) at tip-B. As mentioned in the previous section, tip-B will propagate first since the distance between tip-B and the CMAS at 60° is smaller than the distance between tip-A and the CMAS at 60°. When the infiltration time increases up to 18000 s (holding stage during the second thermal cycle), the tip-A also starts to propagate because both the maximum principal stress and fracture toughness exceed their critical values as shown in Fig.   19(c). Both the tip-A and tip-B continue to propagate as the infiltration time increases up to 29650 s (holding stage during the second thermal cycle) as shown in Fig. 19(d). The crack growth result shows that the crack propagates slowly during the holding stage in the second thermal cycle as indicated in Fig. 18(a). Subsequently, the column structure encounters a severely damaged pattern during the cooling stage. At this moment, the crack starts to propagate quickly during the cooling stage in the second thermal cycle owing to a large thermal mismatch between CMAS and column structure. As shown in Fig. 19(e), a significant increase in thermal mismatch accelerates the driving force to microcrack propagation along the YSZ column around 29900 s (cooling stage in the second cycle). As we mentioned above, the large degradation of the strain tolerance and delamination occurs in this situation. Fig. 18(a) shows that the crack growth experiences a big jump in the black flame at this moment. As shown in Fig. 19(f), the tip-A slowly propagates downward when the CMAS infiltration rate decreases owing to an increase in viscous drag as the penetration depth increases around 44900 s (cooling stage in the third thermal cycle). It could speculate that the tip-A will propagate downward and extend to the interface YSZ/BC when the YSZ is entirely infiltrated by CMAS. The crack propagation pattern of the 30° inclination angle of the microcrack is provided in Fig. 19(g). This result is consistent with the above finding of the energy release rate analysis indicating that the energy release rate value of 30° is much smaller than the energy release rate value of 60° as shown in Fig. 14. Referring to Fig. 18, the normalized crack growth of the 30° inclination angle at tip-B only reaches 0.022, which is much smaller than the normalized crack growth of 0.55 for the 60° inclination angle of the microcrack. During the cooling stage (t = 14800s, 29900s, 44900s) as shown in thermal loading history (Fig. 3), the stress significantly decreases to zero in room temperature and hence it is not obvious to see the green part indicating the CMAS infiltration in Figs. 19b,19e,19f and 19g. Fig. 20 shows the comparison of failure behaviors between finite element method and experiment method. Note that the obtained crack propagation behavior based on our proposed numerical model yields an excellent agreement with those provided in experiment [17].  Fig. 12.

Conclusions
This study investigates the effect of CMAS infiltration on microcracks embedded in the  experimental method [17]