CMAS penetration-induced cracking behavior in the ceramic top coat of APS TBCs

Ceramics International 45 (2019) 14366–14375

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CMAS penetration-induced cracking behavior in the ceramic top coat of APS TBCs

T

Zhenwei Caia,b, Jishen Jiangc, Weizhe Wanga,b,∗, Yingzheng Liua,b, Zhaomin Caoa,b a

Key Laboratory of Power Machinery and Engineering, School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China Gas Turbine Research Institute, Shanghai Jiao Tong University, Shanghai, 200240, China c Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai, 519082, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: CMAS penetrated APS TBCs Cracking behavior in TC CMAS penetration depth Microstructure shape Horizontal cracks

The penetration of calcium-magnesium-alumino-silicate (CMAS) is one of the most vital factors inducing the failure of air plasma sprayed thermal barrier coatings (APS TBCs). In present study, a two-dimensional periodical model considering the microstructures in ceramic top coat (TC) is built to study the cracking behavior in the TC of APS TBCs penetrated by CMAS during the cooling process. The CMAS penetration process is considered by filling the microstructures with the same shape of CMAS. The results show that CMAS penetration into the microstructures of the TC changed the stress distribution around the microstructures and induced a mixed crack type here. A microstructure with a relatively sharper geometry will experience a more severe stress state when penetrated by CMAS. The material discontinuity due to CMAS penetration also causes a slightly higher stress level around the microstructure at the CMAS deposit/TC interface, the CMAS penetrated layer and TC/BC interface. Thus, the horizontal cracks are easier to initiate from the microstructures with sharper geometry in these three regions.

1. Introduction Air plasma sprayed thermal barrier coatings (APS TBCs) are widely used in gas turbines as a critical thermal insulation component. Environmental calcium-magnesium-alumino-silicate (CMAS) is molten at high temperature, adheres to the surface of ceramic top coat (TC), and further penetrates into the TC microstructure, changing its material properties significantly. This kind of transformation always leads to an obvious reduction in the life of thermal barrier coatings [1–4]. Molten CMAS glass in the microstructure can form a relatively stiff glaze upon cooling [4,6–9], which can give rise to the growth of an effective elastic modulus in the TC, reduce TBC strain tolerance during turbine heatingcooling cycles, and induce premature cracking in the TC compared to TBCs without CMAS penetration. This study therefore investigates the effect of CMAS penetration on the cracking behavior around the TC microstructures and provides some insight into the APS TBC process. Numerous studies have investigated the effect of CMAS penetration on cracking behavior in the TC. Extensive examination of the columnar structure of electron-beam physical vapor deposition (EB-PVD) TBCs [5,8,10,11,13,14] reveals that type I cracks initiate regularly at the edges of columns in EB-PVD TBCs. For lamellar ceramic APS TBCs, the

process generates pores, voids, and microcracks in the TC [16–19], and these microstructures significantly affect the stress state and cracking behavior of APS TBCs [20–28]. Studies considering the microstructures in the TC observed a higher stress level at the tips of microstructures than those that did not consider them [20–25]. This stress concentration is due to the geometric restraint of the microstructural tip, and readily initiates cracks in these microstructural defects [20]. The geometric restraints of these microstructures are mainly determined by the microstructure shape, microstructure spacing, and microstructure angle [21,24]. These influential factors change the state of the stress concentration, the stress level in the area between two adjacent microstructural defects, and the direction of crack initiation, increasing the possibility of crack initiation [26,27]. For example, Wang et al. [21] simplified the microstructure shape as ellipses to numerically compare the cracking behavior in the TC with microstructure angles from 0° to 90°, and the results indicated that the stress concentration formed much more easily at the tips of horizontal microstructures (0°) and promoted crack initiation. The above-mentioned studies demonstrated that microstructures in the TC significant affect the stress state and cracking behavior. Compared to this effect, the microstructure in the TC with consideration of CMAS attack could cause the premature failure of APS

∗ Corresponding author. Key Laboratory of Power Machinery and Engineering, School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail address: [email protected] (W. Wang).

https://doi.org/10.1016/j.ceramint.2019.04.152 Received 10 March 2019; Received in revised form 13 April 2019; Accepted 17 April 2019 Available online 20 April 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

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Fig. 1. Scanning electron micrographs of thermal barrier coatings: (a) APS TBCs with CMAS [15], (b) APS TBCs without CMAS [15], (c) Delamination at three different locations in the CMAS-penetrated aero-turbine components reported by Krämer et al. [5].

TBCs because CMAS penetration into the microstructures is likely to change microstructural features such as microstructure shape, especially in the cooling process [17]. A number of experimental tests illustrated that CMAS penetration indeed accelerates crack propagation in the TC [5,12,15]. Yang et al. [15] compared the crack distribution at the cross section in APS TBCs with (Fig. 1(a)) and without (Fig. 1(b)) CMAS attack. As seen from the figures, the existence of CMAS promotes the propagation of horizontal cracks. Krämer et al. [5] observed three kinds of delamination in the APS TBCs subjected to CMAS penetration (Fig. 1(c)) in the component test: (i) close TC/BC interface, (ii) close the CMAS penetrated layer, and (iii) close TC/CMAS deposit interface. Mack et al. [12] reproduced these delamination behaviors through a fundamental test, and they demonstrated that the existence of CMAS in the microstructure accelerated crack initiation and that CMAS penetration depth had a significant effect on delamination. Although these experiments fully demonstrated the influence of CMAS penetration, phenomenological illustrations of the results cannot reveal crack evolution due to the CMAS effect. An investigation of this effect would be helpful in determining the microscopic regulation of APS TBCs during the process. However, few studies have sought to clarify the mechanism of the crack behavior around the microstructures of the TC under CMAS penetration. Therefore, understanding the effect of CMAS penetration on crack behavior is necessary for the design, processing, and application of APS TBCs. In this respect, with the development of finite element modeling techniques, many methods have been introduced to simulate crack initiation and propagation behavior in APS TBCs including the virtual crack closured technique (VCCT), cohesive zone model (CZM) and extended finite element method (XFEM). Wang et al. [39] compared the three computational methods and found that VCCT and CZM were commonly applied to simulate the interfacial fracture like TC/BC interface cracking, while XFEM was beneficial to calculate the arbitrary crack growth in the ceramic coatings without predefining any crack paths. Furthermore, the computational cost by applying XFEM was not high due to the low requirement for the mesh quality [34]. In this study, the major objective is to study the crack initiation and propagation behavior in TC nor the interfacial fracture, thus, XFEM

is selected as simulation method. The present study numerically examines the cracking behavior in the TC of APS TBCs penetrated by CMAS during the cooling process. In this process, CMAS is treated as a solid state. The CMAS penetration process is considered by filling the microstructures with the same shape of CMAS. With this modeling method, the influence of CMAS penetration is first studied by comparing the different stress states around the microstructure with and without CMAS penetration. Furthermore, the influence of different CMAS penetration depths on the stress distribution in the TC are investigated by changing the number of the microstructures filled with CMAS. The influence of the microstructure shape on the TC stress level is also studied. Finally, the cracking behavior induced by CMAS penetration is modelled using the extended finite element method (XFEM), and the delamination modes in the APS TBCs are discussed.

2. Numerical model 2.1. Model basis for finite element analysis APS TBCs have various microstructures, such as pores, voids, and micro-cracks due to the thermal spraying process. During this process, the latter splat covers the former splat, and microstructures among different splats are created because the adjacent splats do not fully overlap. Different splats have different melting conditions that result in different shrinking volumes after they impinge on the former splats. Therefore, the microstructures in the TC will exhibit different shapes and distributions, as shown in Fig. 2(a). During aircraft engine operation in an ashy environment, CMAS is gradually deposited on the TBC surface, as shown in Fig. 2(b). When the temperature of the hot gas from the combustion increases to the melting point of the CMAS (generally above 1200 °C), the solid CMAS deposit transforms into a liquid state and then gradually penetrates the TC through the open microstructure on the TBC surface, as shown in Fig. 2(c). The TC material reacts with the molten CMAS at high temperature, however, the creep effect of TBC is ignored due to a lack of the creep data about the

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Fig. 2. The penetration process of CMAS into APS TBC.

reaction product in the present study. In the cooling process of the gas turbine, the TBC temperature drops considerably, and then the penetrated CMAS solidifies again, which leads to a severe stress state in the TC. In this paper, we only study the mechanical behavior in the APS TBC penetrated by CMAS during the cooling process. Thus, several assumptions have been made as following: (1) In the present study, the phase transformation of TC material due to the reaction between CMAS and TC material is not considered during the cooling process. Actually, the thermal expansion mismatch between CMAS and TC material is the major factor leading to the crack initiation and propagation in TC compared to the influence of phase transformation during cooling process [5,8]. This part has been discussed in detail in the present paper. (2) The CMAS is assumed as a solid state during the whole cooling process. In the present study, the time of the temperature of TC exceeding 1200 °C is relatively short compared to the cooling process, thus only the material properties of CMAS in solid state is considered.

2.2. Model description and material parameters As shown in Fig. 3(a), a plane-strain model incorporating the microstructures in APS TBCs is used in this study. The TBC system consists of three layers: the thickness of TC layer HTC = 200 μ m, the thickness of BC layer the thickness of substrate HBC = 100 μ m, HSUB = 2000 μ m. HBC and HSUB are considered in the FE calculation but not displayed in this figure. HCD is the thickness of CMAS deposit adhering the top surface of TBC, and HCD = 20 μ m is selected for the simulation [8,29], HCP is the depth of the CMAS penetration zone induced by filling the microstructures of the TC with CMAS. The initial value of HCP is set as 50 μ m to study the differences in the stress distribution around the microstructure with and without CMAS penetration, then HCP is subsequently changed from 0 μ m to 100 μ m to study the influence of CMAS penetration depth on the stress distribution within TC. The microstructures in the TC are simplified as ellipses, and only horizontal microstructures which are parallel to the x axis are considered in this model. The major axis of the ellipses is a, and the minor axis is b, and an initial microstructure shape: a = 0.5 μ m, b = 4 μ m is selected. More microstructure shapes are considered in Section 3. The porosity of the TC is set as 10%. The number of

Fig. 3. Schematic view of the finite element model incorporating the (a) Horizontal microstructure of APS TBCs, (b) Mesh around the tip of microstructure, and (c) Thermal boundary conditions. 14368

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microstructures (ellipses) N depends on the shape of the microstructures, and N is calculated as 34 based on the initial microstructure shape. The microstructure shape and the selected porosity of the TC in this study can be observed in most APS TBCs [18,19]. A half-period boundary condition is accepted in this study. The left boundary condition of the model is symmetric, while the right one is periodic. Furthermore, the left boundary is prohibited to move in the x direction, and the right boundary is restrained by applying the multi-point constraint (MPC) method [29]. The bottom edge of the mode cannot move in the y direction, while the top edge of CMAS deposit is free. Finite element analysis was conducted employing the commercial software ABAQUS 6.13 [38]. The meshes of the areas around the microstructures are refined to improve the calculation accuracy, as shown in Fig. 3(b). In this study, a homogenous temperature field is applied on the whole TBC model, and the temperature varies as cooling time increases, as shown in Fig. 3(b). The entire cooling time is set as 600 s. The FE calculation starts from a stress-free state at 1250 °C and then cools down to room temperature, 20 °C. The material of TC layer, BC layer and substrate are 8wt.%Y2O3 stabilized ZrO2 (8YSZ), NiCoCrAlY, and Hastelloy-X respectively. TC is treated as linear elastic material, while the plasticity of the BC and substrate is considered to more accurately estimate the stress at the TC/BC interface. The normal material properties of the APS TBCs are listed in Table 1 [29]. The CMAS is assumed as a solid state and its material properties are also listed in Table 1 [8].

displacement, respectively. Fracture toughness is also an important parameter to describe cracking behavior. When the failure occurs, the strain energy release rate G increases to Gc , which is named as the fracture toughness. As is shown in Fig. 4, the value of Gc is equal to the triangular area surrounded by the curve and x, y-axis. The critical energy release rates can be expressed as: For mode I:

Gnc =

1 σ0 δf 2

(3)

For mode II:

Gsc =

1 τ0 θf 2

(4)

However, when considering the mixed mode loading condition, the damage is a function of multi-axis stress/strain. The mixed mode failure can be exhibited by Ref. [33]:

Gn G + sc = 1 Gnc Gs

In this study, XFEM is used to model crack initiation and propagation behavior. In XFEM, the displacement is calculated as [34]:

uXFEM (x ) = 2.3. TC crack modeling method

∑ S∈N

A traction-separation law (TSL) has been widely employed to describe the fracture or damage behavior of material in previous studies. In this method, cracks initiate in “fracture process zones”, and the stiffness of the material decreases due to the accumulated damage. For the numerical studies using XFEM enrichment elements [30,31], traction-separation laws have been employed as a damage model. Fig. 4 displays the typical traction-separation responses of a bilinear tractionseparation law selected in this study, it contains two kinds of mode: mode I and mode II. Constitutive model of model I can be described as [32,33]:

δ ≤ δ0 Kδ ⎧ σ = (1 − D) Kδ , δ0 ≤ δ ≤ δf ⎨ δ ≥ δf , 0 ⎩

(5)

⎧ ⎨ ⎩

Ni (x ) uS + [sgn(x ) aS ]S ∈ NH +

Ntip ⎫ ⎡ ∑ Fα (x ) b α⎤ S ⎥ ⎢ α=1 ⎦S∈Ntip ⎬ ⎣ ⎭

(6) where Ni (x ) is modal shape function, us is the degree of freedom (DOF) for non-enriched nodes, aS and bSα are enriched DOFs applied to model discontinuity, sgn(x) is a Heaviside function that represents the jump in displacement across the crack surfaces, NH is the nodes from the elements separated by a crack, Ntip is the nodes of the crack tip element, and Fα (x ) is an asymptotic crack tip enrichment function. When using XFEM in ABAQUS, the enrichment elements should be set at these dangerous areas, and the degradation and eventual failure in an enriched element are governed by the linear traction-separation model, as mentioned above. In this study, a criterion governed by maximum principal stress is introduced to predict the crack initiation:

(1)

⎧ 〈σmax 〉 ⎫ = 1 0 ⎨ ⎩ σmax ⎬ ⎭

and

0

δ ≤ δ0 ⎧ ⎪ δf (δ − δ0) D = δ (δ − δ ) , δ0 ≤ δ ≤ δf ⎨ f 0 ⎪ 1 δ ≥ δf , ⎩

(7)

0 σmax

(2)

where σ and δ are the traction stress and displacement respectively, δ0 and δf are the critical opening displacement and the displacement when facture occurs, K is the initial stiffness, D is damage where 0 ≤ D ≤ 1. In this constitutive model, damage is initiated when the stress reaches σ0 , and the stiffness of the material starts to drop to (1-D) K as the damage accumulates. When the damage D reaches 1, failure occurs and the stress decreases to 0. The traction-separation response of mode II shown in Fig. 4 exhibits the same tendency, in which τ0 , θ0 , and θf are the corresponding critical stress, the opening displacement, and the failure Table 1 Material properties of TBCs, CMAS [8,29]. Layer

E (GPa)

ν

ρ (kg/m3)

K(Wm−1K−1)

CMAS TC BC Substrate

84 11.7 71.9 150

0.25 0.2 0.35 0.3

2540 5650 7320 8220

1.78 1.6 11.1 25

α × 10−6 (°C−1) 8.1 10.04 17.65 16.6

c× 10−6 (Jkg−1K−1) 875 445 764 524

is the critical maximum principal stress. 〈⋅〉 is the Macaulay where bracket to ensures that a crack can't initiate at compressive stress state. The damage starts to accumulate when this stress ratio increases to 1. Before final fracture occurring, opening displacement at the crack tip depends on the fracture toughness. In this study, XFEM in ABAQUS is applied to model the crack in TC induced by CMAS penetration. Generally, the critical strength and fracture toughness of TC are influenced by several factors, e.g., the material composition, microstructures, and air spraying process, etc. These factors make the fracture parameters differs a lot at different samples. In previous studies [35,36], the value of the strength of the TC ranged from 30 to 200 MPa, thus the critical strength in this study is set as 120 MPa. A typical fracture toughness of 20 J/m2 is also selected for the FE calculation [37]. A systematic study of the fracture parameters will be carried in future work. 3. Results and discussions 3.1. Stress analysis in the TC The influence of CMAS penetration on the stress distribution in the TC during the cooling process is first studied in the case with a

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Fig. 4. Schematic of the (a) Mode I and (b) Mode II bilinear traction-separation laws.

Fig. 5. (a) Distribution of shear stress σ12 , stress in the y-axis direction σ22 , and max in-plane principal stress σMPS around the microstructure with and without CMAS at different cooling times, (b) Magnification of zone Ⅰ with CMAS and zone Ⅱ without CMAS shown in (a).

penetration depth of HCP=100 μm and a microstructure shape of a = 0.5 μ m, b = 4 μ m. Fig. 5(a) displays the distribution of shear stress σ12 , stress in the y-axis direction σ22 , and max in-plane principal stress σMPS around the microstructure with and without CMAS at different cooling times. Due to the bilateral symmetry of the model, only the left half is considered for analysis. In addition, the stress in the x-axis direction σ11 is not analyzed here because it does not contribute to the horizontal crack initiation. As shown in Fig. 5(a), the penetration of CMAS induces a considerable increase in σ12 around the microstructure compared to the results without CMAS, especially in the zone near the tip of the microstructures: zone I with CMAS and zone II without CMAS, as shown in detail in Fig. 5(b). This is due to the thermal mismatch between the TC and CMAS in the microstructure, and the effect of this mismatch grows considerably as the temperature drops during the cooling process. The distribution of σ22 around the microstructure also

changes for this reason. As shown in Fig. 5(b), the location of the concentration of tensile stress transfers from the tip of the microstructure to the upper and lower sides around the tip when CMAS is considered. In addition, the maximum value of the tensile stress with CMAS is also higher than that without CMAS. As a result, σMPS , which takes the effects of both shear stress and tensile stress into account, exhibits a similar distribution around the microstructure as σ12 and σ22 when penetrated by CMAS. The maximum value of σMPS is observed at the microstructure edge around the tip. Based on the maximum principal criterion introduced in section 2.3, crack initiation seems more likely to occur at the edge of the microstructure with CMAS because of the more severe stress state there. Even the stress around the microstructure exhibits an almost upand-down symmetrical distribution, as shown in Fig. 5, and further comparison of the stress along the upper and lower edges of the

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Fig. 6. The σMPS distribution along path 1 and path 2 at different cooling times.

microstructure reveals that the maximum σMPS is located at the upper edge due to the BCs. As shown in Fig. 6(a), paths 1 and 2 are selected along the upper edge of the microstructure with and without CMAS, and the σMPS distribution along path 1 and path 2 is plotted at different cooling times in Fig. 6(b) and (c). X represents the projection of distance from the point to the tip of the microstructure in the x-axis direction. The value of the maximum σMPS along both paths increases with the cooling time, but the location of maximum σMPS remains unchanged throughout the process. As shown in Fig. 6(b), the maximum σMPS along path 1 is located at a point 0.08 μm away from the tip of the microstructure in the x-axis direction, while the maximum σMPS along path 2 is located at the tip of the microstructure, as shown in Fig. 6(c). The maximum σMPS along paths 1 and 2 at room temperature is 223 MPa and 176 MPa, respectively. This indicates that the CMAS penetration induced a more severe stress state around the microstructure under the given microstructure shape. To further explain the more severe stress state in the TC induced by CMAS penetration, a mechanism diagram of the deformation around the microstructure is displayed in Fig. 7. Before the cooling process, the TC is in a no-stress state. During the cooling process, the sudden drop in the thermal expansion of the TC leads to its volume shrinking extensively. For the microstructure without CMAS, shrinking in the x- and y-axis directions is not uniform, causing a lower b/a ratio compared to the initial microstructure shape, which leads to high tensile stress at the tip of the microstructure. The triggered crack initiation here should be purely type I. However, as CMAS has lower thermal expansion and a higher modulus compared to the TC, for the microstructure with CMAS, the shrinking deformation is hampered by the stiff CMAS in it. This results in increased shear stress and tensile stress near the tip of the microstructure and a mixed crack type here. The influence of CMAS penetration on the stress in the whole TC

Fig. 8. The maximum σMPS around each microstructure with 0 to N cracks.

with microstructures is further studied. Fig. 8 displays the maximum σMPS around each microstructure from 0 to N. N is given as 34, and half of the microstructures have been penetrated by CMAS in this case. Comparing the stress levels between the CMAS-penetrated and nonpenetrated zones of the TC reveals that the penetration of CMAS results in a more severe stress state around the microstructure under the given microstructure shape. As shown in Fig. 8, the most severe stress state arises around the microstructures near the CMAS penetrated interface. This is due to the material discontinuity between the CMAS-penetrated and non-penetrated zones, and it causes a thermal mismatch at the

Fig. 7. Mechanism diagram of deformation around the microstructure with and without CMAS in the cooling process. 14371

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Fig. 9. The maximum σMPS around the two microstructures with or without CMAS near the CMAS-penetrated interface at CMAS penetration depths of 0 μ m, 50 μ m, 100 μ m, and 200 μ m.

penetrated interface. The material discontinuity also causes a slightly higher stress level around the microstructure at the CMAS deposit/TC interface and TC/BC interface. These three locations have been validated in experimental studies as the most dangerous regions in which to develop delamination [5], especially at the CMAS-penetrated interface. Thus, further study should focus on the microstructure near this region. In general, the characteristics of the material discontinuity depend on the thickness of the two materials, which affects the thermal mismatch stress level at the interface. Thus, the effect of CMAS penetration depth on the stress state in the TC should be further studied. Fig. 9 shows the maximum σMPS around the two microstructures with and without CMAS near the CMAS-penetrated interface at CMAS penetration depths of 0 μ m, 50 μ m, 100 μ m, and 200 μ m. As shown in Fig. 9, maximum σMPS around the microstructures with CMAS decreases with as the CMAS penetration depth increases. This is attributed to the continuous filling of CMAS into the microstructures, and the solidified CMAS deposits in the microstructures would compensate for the thermal mismatch strain between the TC and BC upon cooling and would thus mediate the thermal mismatch stress within the TC. For the microstructure without CMAS, the introduction of CMAS first causes a sudden rise of σMPS and then drops gradually as the CMAS penetration depth increases for the same reason as for the microstructure with CMAS. This trend reveals that crack initiation or delamination could appear at the early phase of CMAS penetration because of the more severe stress state at a lower CMAS penetration depth. 3.2. The influence of microstructure shape on TC stress distribution As discussed above, the microstructures in APS TBCs have many different shapes due to the thermal spraying process. It has been confirmed that microstructures with different shapes induce different degrees of stress concentration, resulting in different likelihoods of crack initiation. It is therefore necessary to study the influence of microstructure shape on the stress distribution in TC penetrated by CMAS. As shown in Fig. 10, the microstructure shape is controlled by the b/a ratio, also called the shape coefficient. We set the minor axis to a = 0.5 μ m and the major axis to b = 0.5, 1, 2, 3, 4, 5, and 6 μ m. Fig. 11(a) displays the σMPS distribution around the microstructure with CMAS at different shape coefficients under a CMAS penetration depth of 100 μ m. A bigger area of the stress concentration zone can be observed as the shape coefficient increases, and stress level around the tip of microstructure becomes higher at the same time. Fig. 11(b) shows the σMPS distribution along path 1. It can be seen that the maximum σMPS

Fig. 10. Schematic of microstructures with different shapes.

increases considerably, from 70 MPa to 250 MPa, with the shape coefficient ranging from 1 to 12, and the location of the maximum σMPS moves closer to the exact tip of the microstructure at the same time. It can thus be easily understood that a higher shape coefficient means sharper geometry at the tip of the microstructure, which would lead to a higher stress level there. For comparison, the σMPS distribution around the microstructure without CMAS at a different b/a ratio under a CMAS penetration depth of 100 μ m is displayed in Fig. 12(a). Because of the non-CMAS state in the microstructure, the area of the stress concentration shrinks as the shape coefficient increases, which differs from what is shown in Fig. 11(a). However, the maximum σMPS along path 2 still increases slightly as the shape coefficient increases, as shown in Fig. 12(b). Comparing the maximum σMPS along paths 1 and 2 under different shape coefficients, it can be seen that when the b/a ratio is < 6, the maximum σMPS along path 1 is smaller than that along path 2, which means that the crack initiation is more likely to occur in the microstructure without CMAS. When the b/a ratio is ≥ 6, the maximum σMPS along path 1 is bigger than that along path 2, which means that the crack initiation is more likely to occur in the microstructure with CMAS. In conclusion, there is a critical value for the shape coefficient at which only a microstructure with a relatively sharper geometry would experience a more severe stress state when penetrated by CMAS. 3.3. TC crack behavior The above discussions concern TC stress analysis and only reveal the possible locations where cracks may initiate. Crack initiation and propagation behavior can be further studied using XFEM. In this section, the cases with CMAS penetration depth of 100 μ m under different microstructure shapes are considered, and enrichment elements are assigned in three areas of the TC: the microstructure near the CMAS deposit/BC interface, the microstructures near the CMAS-penetrated interface, and the microstructure near the TC/BC. The results show that cracks only appear around the microstructure filled with CMAS near the CMAS-penetrated interface due to the most severe stress state here. Fig. 13 displays the crack length upon the cooling process around the CMAS-penetrated microstructure in this region. The contours in Fig. 13 indicate that there are two cracks initiate at the upper and lower edges of the microstructure. The crack at the upper edge is the major crack, which initiates at the location with maximum σMPS and develops into a longer crack during the cooling process. In comparison, the crack at the lower edge may be negligible due to its short length. As shown in the curve in Fig. 13, the crack starts to initiate around 460 s and propagates

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Fig. 11. (a) σMPS distribution around the microstructure with CMAS at different shape coefficients under a CMAS penetration depth of 100 μ m, (b) σMPS distribution along path 1.

Fig. 12. (a) σMPS distribution around the microstructure without CMAS at different shape coefficients under a CMAS penetration depth of 100 μ m, (b) σMPS distribution along path 2.

Fig. 13. Crack length during the cooling process around the CMAS-filled microstructure near the CMAS-penetrated interface.

to 0.2 μ m at room temperature. This crack experiences rapid growth in a very short time. Crack propagation may be revealed to be more dangerous if more thermal cycles are considered. Because of the significant effect of the microstructure shape on the stress within TC, the influence of the microstructure shape on TC crack behavior is also discussed here. Fig. 14 shows the crack lengths under different shape coefficients at room temperature. Consistent with the

Fig. 14. Crack lengths under different shape coefficients of the microstructure at room temperature.

findings of the stress analysis, the cracks are more likely to initiate at the microstructure with a b/a ratio of ≥ 6. As the shape coefficient increases, the crack propagates to a longer length and exhibits a higher stress level. The crack length reaches to 1.3 μ m at the microstructure with a b/a ratio of 12. It can be deduced that the microstructures with sharper geometry are much more serious in the TC. Thus, more

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Fig. 15. Schematic showing the delamination modes in APS TBCs with CMAS penetration.

attention should be given to how to reduce the sharp microstructures in the APS TBC process. Further, the cracks developed from these microstructures could be found to trigger delamination or spallation if the vertical cracks are considered. The above analysis reveals the CMAS-induced cracking behavior in the TC. However, compared to the cracks or delamination observed in other experiments [5,12,15], the crack in this study only initiates around the microstructures at the CMAS-penetrated interface, and the final length of the crack is relatively shorter because only one thermal cycle and only horizontal microstructures are considered in the model. To further explain the CMAS-induced failure observed in Fig. 2(c) [5], a synoptic prediction of the crack formations and coalescences considering the microstructures in the TC is displayed in Fig. 14. Different shapes, spacing, and angles of the microstructures are considered with CMAS penetration, as shown in Fig. 15(a). During the cooling process, cracks initiate at both of the horizontal and vertical CMAS-penetrated microstructures with relatively sharper geometry, especially around the microstructures at the interface of the CMAS deposit/TC, the CMAS penetrated layer, and the TC/BC. At the late period of cooling, horizontal cracks propagate to coalesce with adjacent horizontal or vertical cracks to induce three considerable spallation of TC from the substrate, as shown in Fig. 15(c). This spalling finally causes the failure of APS TBCs. 4. Conclusions To study the fracture mechanism in the TC of APS TBCs induced by CMAS penetration, a numerical model considering the CMAS penetration in the microstructures of the TC was built to investigate the stress state and cracking behavior in the TC upon cooling. The effect of different CMAS penetration depths on the stress distribution in the TC and the influence of the microstructure shape on the TC stress level were discussed. The cracking behavior induced by CMAS penetration was investigated by using the XFEM, and the delamination modes in the APS TBCs were further studied. The results indicated the following. 1. The material discontinuity due to CMAS penetration caused a slightly higher stress level around the microstructure at the CMAS deposit/TC interface, the CMAS penetrated layer and the TC/BC interface. The stress concentration zone transferred from the tip of the microstructure to the upper and lower sides around the tip when the CMAS was considered. The CMAS penetration also induced a mixed crack type around the microstructures. 2. The maximum σMPS around the microstructures with CMAS decreased as the CMAS penetration depth increased. Crack initiation or delamination could occur at the early phase of CMAS penetration because of the more severe stress state at a lower CMAS penetration depth.

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