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Effect of TGO creep on top-coat cracking induced by cyclic displacement instability in a thermal barrier coating system
Surface & Coatings Technology 254 (2014) 410–417
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Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat
Effect of TGO creep on top-coat cracking induced by cyclic displacement instability in a thermal barrier coating system Luochuan Su, Weixu Zhang, Yongle Sun, T.J. Wang ⁎ State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
a r t i c l e
i n f o
Article history: Received 7 January 2014 Accepted in revised form 28 June 2014 Available online 4 July 2014 Keywords: Thermal barrier coating system Top-coat crack TGO creep Displacement instability Thermal cycling
a b s t r a c t The displacement instability of the thermally grown oxide (TGO) under thermal cycling is a fundamental source of cracking within the ceramic top-coat (TC) in a thermal barrier coating system. The effect of TGO creep on TC cracking induced by cyclic instability is numerically investigated in this work. Temperature-dependent elastic– plastic properties of each coating layer are considered in a finite element analysis. A power law is adopted to model the creep behavior of TGO and bond-coat (BC), and TGO growth at high temperature with the consideration of both lateral and through-thickness growth strains is simulated. The numerical results show that during thermal cycling TGO displacement instability occurs in the zone having a geometric imperfection and the accumulation of TGO displacements (downward at the center and upward around the periphery) is evident. The tensile stress (perpendicular to the TGO/TC interface) in TC mainly arises above the center of the instability zone and causes a mode I crack, whereas the shear stress is predominant around the periphery of the instability zone and causes a mode II crack. Both the tensile and shear stresses can be reduced by TGO creep which restrains the morphology distortion of the instability zone during thermal cycling. Furthermore, TGO creep can significantly decrease the energy release rate of TC cracking no matter whether the crack is located in the tensile-stress dominating zone or the shear-stress dominating zone. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Thermal barrier coating systems (TBCs) are widely used in gas turbines to protect the hot-section components (e.g. turbine blades) against extreme temperature. A typical TBC system consists of the following four layers: (i) a ceramic top-coat (TC) layer for thermal insulation, (ii) a bond-coat (BC) layer for performance improvement, (iii) a superalloy substrate to bear mechanical loads and (iv) a thermally grown oxide (TGO) layer formed between TC and BC in service, as schematically shown in Fig. 1. There are many damage mechanisms for materials and structures [1–4]. The delamination and spallation ofTC layer, which mainly result from the converging of microcracks within the TC, are major failure modes of TBCs. Experimental observations have confirmed that the displacement instability of TGO subjected to thermal cycling is a key factor that induces the cracks within the TC layer in electron beam physical vapor deposited (EB-PVD) TBCs [5–9]. The instability usually appears as a downward displacement of TGO toward the BC layer, as shown in Fig. 1. Previous studies have shown that the occurrence of the displacement instability is related to specific conditions. During thermal cycling, the TGO layer is subjected to in-plane compression due to the thermal expansion misfit among different ⁎ Corresponding author. E-mail address: [email protected] (T.J. Wang).
http://dx.doi.org/10.1016/j.surfcoat.2014.06.052 0257-8972/© 2014 Elsevier B.V. All rights reserved.
coating layers upon temperature variation and the TGO growth at high temperature, and when the compressive stress is large enough, the TGO layer begins to displace downward into the BC which is more susceptible to plastic deformation due to its relatively low yield strength. Five prerequisites have been indentified for the instability [6]: (1) the cyclic thermal load; (2) the thermal expansion misfit between the TGO layer and the substrate, which can induce a large inplane compression in the TGO layer upon cooling; (3) the permanent deformation of BC and TGO layers; (4) the TGO growth strain resulting from the formation of new oxides at high temperature; and (5) an initial morphology imperfection at the BC/TGO interface, which is required to initiate instability. The extension of this displacement instability leads to a large tensile stress perpendicular to the interface within the TC above the center of the instability zone, i.e., σ22 along axis-2 in Fig. 1. As a result, the initial microcracks nucleate preferentially there. These microcracks within the TC are a prerequisite for the ultimate failure of TBCs (see Fig. 1) [5,8,10]. Meanwhile, these microcracks would, in turn, promote the extending of TGO instability [11]. Using finite element models, Chen et al. [12] and Xu et al. [13] explored the TC cracking induced by TGO instability and found that there are three zones of crack extension accompanying the instability (see Fig. 1). In zone I, the crack is mode I and its nucleation is governed by the tensile stresses σ22; in zone II, the crack is mode II and driven by the shear stresses σ12. If the crack extends into zone III, it will become mode I again. Bhatnagar et al. [14] performed a parametric analysis and estimated the
L. Su et al. / Surface & Coatings Technology 254 (2014) 410–417
Fig. 1. Schematic of TBCs: the cracks in TC are associated with the displacement instability of TGO.
contribution of geometric and material factors (excluding TGO creep) to the crack initiation and propagation, and they also proposed a basic parametric relationship for the crack initiation within the TC. Their study shows that crack initiation and propagation are a result of the combined effects of the material and geometric factors. TGO creep is an important factor associated with thermal loading, but its effect on the TC cracking induced by TGO instability [13,14] has not been adequately studied. Extensive investigations have shown that under high temperature TGO creep is significant and can cause complex changes of the microstructures and stress state in TBCs [15–17], and thus it can influence the service life of TBCs. Baker et al. [18,19] numerically investigated the effect of TGO creep on the stress state at the TGO/TC interface with sinusoidal morphology. Later, Ding et al. [20] used more realistic material properties at high temperature to explore the effect of TGO creep on the morphology evolution of the instability zone. These works show that TGO creep is an important factor affecting the stress and deformation of the instability zone. Also, a numerical work [21] has shown that the energy release rate of the crack in TBCs is sensitive to the creep properties of materials. However, none of these previous studies considered the TGO instability induced stress state and cracks within TC. The objective of this work is to investigate the effect of TGO creep on TC cracking induced by TGO displacement instability upon thermal cycling. Firstly, a finite element model incorporating a TC crack is developed, which is based on the previous experimental observations of TGO displacement instability and crack growth [6–8,13]. The creep behavior of TGO and BC is considered and the temperature-dependent material properties are used for a physically realistic simulation. The TGO creep strength is expected to vary in different TBCs since it can be influenced by the grain size [18] and the content of the substrate material [22]. Therefore, the TGO creep property is varied in the simulation in order to investigate its effect. And then, the stresses in the tensile and shear zones within the intact TC are obtained under different TGO creep rates. Finally, the energy release rate for a TC crack under different TGO creep rates is numerically calculated. The outcome of this work may aid in the understanding of the role of material creep in the spallation and failure in TBCs. 2. Statement of the problem In the TBC system shown in Fig. 1, the cracks in the TC are normally induced by the TGO displacement instability upon thermal cycling. During thermal shock (between 25 °C and 1100 °C) and TGO growth at high temperature (1100 °C), the in-plane compressive stress in the
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TGO arises. When the compressive stress is large enough, the instability zone in Fig. 1 would be driven to extend downward, which can result in a large tensile stress σ22 within the TC above the center of the instability zone (zone I) and then an initial mode I crack would be induced in this zone. Under the tensile stress, the crack can propagate into the periphery of the instability zone (zone II), where the TGO displaces upward and the stress σ22 is compressive. However, the shear stress σ12 in this zone is significant and the crack is predominantly of mode II. Once the crack extends into the zone between the neighboring instability zones, it would become mode I again under tensile stress. Based on the investigation of the coating morphology associated with TGO instability, the instability zones and the instability-induced cracks are usually idealized as a periodic array [13,23]. Accordingly, a generalized plane strain model is developed here to study TC cracking, as shown in Fig. 1, where L is the width of the instability zone and a is the length of the crack. The strain energy release rate is an important parameter characterizing the driving force of TC cracks. When its maximum value reaches the toughness of the TC, the crack begins to extend. However, a minimum strain energy release rate would occur in the shear-stress dominating zone (zone II) during the crack extension. Once the crack passes through zone II and propagates into zone III, the strain energy release rate increases rapidly, where the crack undergoes unstable extension and abruptly coalesces with neighboring cracks [13,23]. The durability before the failure caused by the displacement-instabilityinduced cracking is determined by the onset of the unstable crack extension. Therefore, we focus on the effect of TGO creep on TC cracking before the crack coalescence and calculate the strain energy release rate on a cycle-by-cycle basis. 3. Finite element analysis 3.1. Geometric model and boundary conditions A two-dimensional finite element model is developed to incorporate the complex interface morphology and crack behavior in TBCs. The general purpose FE code ABAQUS is employed in analysis. Fig. 2 shows the geometric model wherein the substrate, BC, TGO, and TC are simplified. The thickness of each layer is listed in Table 1. With an initial thickness shown in Fig. 2 the TGO layer is thickening during high-temperature exposure and the detail of the simulation method will be described later. The configuration of the displacement instability zone is described by the curvature radii R1 = 17.8 μm and R2 = 12 μm, and the width L = 50 μm. The previous work [13] has shown that the crack propagation rate is the highest when the distance of each periodic array is W = 3L. Therefore, the width of the TBC system considered here is set to W = 150 μm. The planar crack is located in the TC at a distance b = 2.5 μm above the top interface of TGO (see Fig. 2) [13,23]. To calculate the energy release rate on a cycle-by-cycle basis, the crack length a is treated as a constant in each calculation, i.e., the crack growth process is not simulated, and different crack lengths are given in each calculation. The neglect of the crack growth does not prevent the occurrence of the interactions between the TC crack and TGO instability, so it would not lead to fundamental errors when the TGO creep effect is investigated [13]. However, if the cracking and the instability are fully coupled, there may be some other kinds of interactions, which need to be analyzed by a strong-coupling model open to future research. The periodic boundary condition [24,25] is applied at the left and right sides, and the motion in the Y direction is constrained at the bottom side. More than 24,000 four node bilinear generalized plane strain quadrilateral elements (CPEG4R) are used and a mesh sensitivity study is performed to yield adequate mesh-independent solutions. As shown in Fig. 2b, the mesh in the vicinity of the instability zone is refined with the minimum element size Δl satisfying Δl/L = 0.005. Fig. 2c shows the detailed mesh near the crack tip and the quarterpoint elements are adopted to capture the singularity. Initially, the
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Fig. 2. Details of the finite element model: (a) mesh profile and boundary conditions; (b) the refined meshes in the vicinity of the instability zone; (c) an enlarged view of the meshes near the crack-tip.
TBC system is stress-free at a temperature of 1100 °C. Then thermal cycling is exerted, and each cycle includes 10-min cooling to the ambient temperature (25 °C) and 10-min reheating to the high temperature (1100 °C) at which a 30-min holding is maintained. This sequence is repeated and 24 cycles are considered for each calculation.
Table 1 Physical and geometric parameters used in the model.⁎
TC
TGO
BC
SUB
Temperature (°C)
Young's modulus (GPa)
Poisson's ratio
Yield strength (MPa)
Thermal expansion (α × 10−6/°C)
25 200 400 800 1100 25 200 400 800 1100 25 200 400 800 1100 25 200 400 800 1100
E⊥ TC = 160.4
0.1
/
9.0 9.2 9.6 10.8 12.2 5.1 5.1 5.1 5.1 5.1 12.3 14.2 15.2 16.3 17.6 14.8 15.2 15.6 16.9 18.0
E= TC = 30.4
400 390 380 355 320 200 190 175 145 120 220 210 190 155 120
0.27
/
0.3
426 412 396 284 114 /
0.3
Layer thickness (μm) 150
3
80
2000
⁎ TC is modeled as a transversely isotropic material and E= TC is the modulus in the X direction. The Young's modulus of the TC layer is taken from [27] and other material data are taken from [33]. The layer thickness refers to ref. [6].
3.2. Material behavior Herein TGO is considered as an elastic and viscous material, BC is treated as an elastic and viscous-plastic material, and TC and the substrate are assumed to follow the linear elastic law. All the material property parameters are listed in Table 1. For EB-PVD TBCs, the TC layer exhibits transversely isotropic properties, because of its special columnar microstructure [26]. In other words, the in-plane material property is different from that in the out-of-plane direction, as shown in Table 1 [27]. For the creep behavior of TGO and BC, the following power law [14,28,29] is adopted, dεcr ΔH n ¼ A0 σ exp − RT dt
ð1Þ
where A0 is a creep constant, σ is the equivalent stress, n is the creep exponent, ΔH is the activation energy, R is the universal gas constant and T is the absolute temperature. At the cooling and heating stages during thermal cycling, the time for the temperature held in the range where creep can occur is relatively short. Thus, we only consider the creep at the high-temperature holding stage. Consequently, T is actually a constant in this case and Eq. (1) can be rewritten as dεcr n ¼ Aσ : dt
ð2Þ
For BC, ABC = 3.9 × 10− 6 and nBC = 2.5 [30]. For TGO, three different creep constants are compared: ATGO = 0 (without creep), ATGO = 7.3 × 10− 8 (small creep) and ATGO = 7.3 × 10 − 7 (large creep), in order to explore the creep effect, while the creep exponent is fixed as nTGO = 1 [31].
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At the holding stage, due to the oxidation of the BC layer, the thickness of the TGO layer will increase. As observed in experiments, TGO thickens parabolically with time [32] and the thickening rate is given by tgo h˙ ¼
kp 2htgo
;
ð3Þ
where htgo is the thickness of the TGO layer and kp is a constant with a unit of m2 s −1, the value of which should be chosen so that TGO thickens from 0.5 to 3 μm during 100 h holding at high temperature. Accompanying the thickening, the lateral growth strain εg also occurs due to the formation of new oxides on the internal grain boundary, which can be expressed as ε˙ g ¼
tgo h˙ ; d
ð4Þ
where d is a constant. The lateral growth strain εg is the main source of in-plane compressive stress in TGO. Here the simulation of TGO thermal growth is carried out using the ABAQUS user subroutine, uexpan, by imposing a growth strain at the holding stage [7]. The growth strain contains two components: thickening strain εt perpendicular to the TGO/BC interface, and the lateral strain εg parallel to the TGO/BC interface. In all calculations, the ratio of lateral strain to thickening strain in each cycle satisfies εg/εt = 0.5 with εt = 1 × 10−3 [9]. 4. Results and discussion 4.1. Stress distribution in TC layer The distribution of the stress induced by the TGO displacement instability in an intact TC is primarily analyzed. The normal stress (σ22) and shear stress (σ12) above the instability zone are emphasized since the initiation and propagation of the crack in TC are controlled by
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them. Fig. 3 shows the distribution of σ22 after 24 thermal cycles. For both cases that TGO undergoes no creep (ATGO = 0) and a large creep (ATGO = 7.3 × 10−7), σ22 is tensile above the center of the instability zone but becomes compressive around the periphery of the instability zone. In the region away from the instability zone, the stresses are close to zero. Similar results have also been reported by other researchers [13,23]. However, compared to the stress in the case that ATGO = 0, the stress magnitude is significantly reduced when TGO creep occurs (ATGO = 7.3 × 10−7). In other words, the whole TC is subjected to lower tensile or compressive stress due to the presence of TGO creep. Fig. 4a shows the stress along the prospective crack path (“X1X2” in Fig. 3) in TC under three different TGO creep rates (ATGO = 0, ATGO = 7.3 × 10−8 and ATGO = 7.3 × 10−7). It confirms that the maximum of σ22 occurs above the center of the instability zone, implying that the crack will preferentially initiate there. However, the stress magnitude reduces significantly as TGO relaxation is enhanced by increasing the creep rate constant. The evolution of the maximum of σ22 along the path “X1X2” during thermal cycling is shown in Fig. 4b. Even if TGO growth and creep are assumed to occur only at the high-temperature holding stage, they still have a significant effect on the stress state at the cooling and reheating stages. This is because the thickening and lateral growth of TGO can reduce the magnitude of the temperature change required to cause plastic yielding in the BC layer during the cooling and reheating process [34], and TGO creep can lead to permanent deformation which affects TGO geometry. These combined factors will cause TGO displacement instability in the form of a downward displacement (source of tensile stress) at the base of the instability zone and an upward displacement (source of shear stress) around the periphery of the instability zone [9]. Therefore, σ22 in Fig. 4b increases with the thermal cycles. Also, a similar occurrence can be seen in the following result of shear stress σ12. The comparison shows that, if there is no creep in TGO, the magnitude of σ22 increases rapidly at both thermal growth (holding at high temperature) and thermal shock (cooling or
Fig. 3. The stress fields σ22 in TC after 24 thermal cycles: (a) ATGO = 0 (without creep) and (b) ATGO = 7.3 × 10−7.
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Fig. 4. The distribution and history of normal stress σ22: (a) along the prospective crack path (“X1X2” in Fig. 3) after 24 thermal cycles during dwell time, and (b) evolution of the maximum tensile stress in (a) as the thermal cycles.
reheating) stages, but when the creep occurs in TGO (ATGO = 7.3 × 10−8), the stress increase with thermal cycles begins to slow down at the two stages. When TGO creep rate is further increased (i.e. ATGO = 7.3 × 10− 7 ), the stress increases only at the initial several cycles and the increasing trend is almost restrained at the following cycles, especially at the holding or thermal growth stage. Such evolutionary feature of σ22 can be attributed to the enhanced effect of creep relaxation over the stress generation by thermal loading. The shear stress (σ12) contours for different TGO creep rates are shown in Fig. 5. In general, the shear stress mainly distributes in the region near the periphery of the instability zone, where σ22 is compressive (see Fig. 3), and it is almost zero in the region above the center of instability zone where σ22 is tensile. This verifies the previous observation [12] that in the zone under tension (zone I in Fig. 1), σ22 drives the cracking, and that in the zone under compression (zone II in Fig. 1), the crack propagates due to the shear stress σ12. Furthermore, the present results enable the clarification of the TGO creep effect. Fig. 5a and b show that TGO creep can reduce the shear stress level, similar to its effect on the normal stress σ22. This effect is so significant that the magnitude of shear stress can be reduced to only tens of MPa when the creep constant increases to ATGO = 7.3 × 10−7. The shear stress distribution along the prospective crack path shown in Fig. 6a further verifies such effect. In addition, Fig. 6b shows the evolution of the maximum shear stress along the prospective crack path, from which it is clearly seen that the occurrence of creep in TGO (ATGO = 7.3 × 10− 8 and ATGO = 7.3 × 10−7) can restrain the increase of shear stress in a manner similar to that of σ22. The deformation of TGO after 24 thermal cycles is also inspected to further understand the effect of TGO creep. Fig. 7 shows the final
displacement fields in TGO after 24 thermal cycles for three different creep rates. As shown in Fig. 7a, the displacements along the thickness direction (U2) present a downward trend at the center of the instability zone but an upward trend around the periphery of the instability zone for both cases with and without considering TGO creep. This deformation characteristic is the cause of the tensile stress σ22 in zone I (Fig. 1) and shear stress σ12 in zone II [13]. When TGO undergoes creep deformation, the downward displacement tends to decrease and the larger creep rate can result in a smaller displacement. The decrease of the downward displacement will directly diminish the normal stress σ22 above the center of the instability zone and this is consistent with the stress results shown in Figs. 3 and 4. However, it presents an opposite trend for the upward displacement. One may be worried that the shear stress will increase accordingly, but in fact the shear stress decreases due to the following reasons. When there is no creep in TGO, the deformation mainly concentrates in small regions at the base and around the periphery of the instability zone. But the presence of TGO creep (ATGO = 7.3 × 10−8) can diminish the concentration and make the deformation more distributed. Furthermore, the larger creep rate (ATGO = 7.3 × 10−7) makes the deformation more uniformly distributed in the whole TGO and the local distortion becomes absent. Similarly, the creep in TGO also results in more uniform deformation in x direction (U1) and restrains the local distortion, especially around the periphery of the instability zone (Fig. 7b). It has been confirmed that the shear stress in TC can be reduced by the suppression of the local distortion around the periphery of the instability zone upon the cyclic oxidation [6,9]. Therefore, the deformation characteristic associated with the TGO creep is favorable to reduce the local tension and compression in the TC layer and then prevents the occurrence of large delamination stress in TC, which also explains the stress state shown in Figs. 3 to 6. In addition, it should be noted that similar results have been obtained by considering the other two different geometric features of the instability zone, where the curvature radii of the instability zone is R1/R2 = 2 and R1/R2 = 2.5 with R2 = 12 μm. Therefore, it can be confirmed that the TGO effect on TC stress demonstrated here is insensitive to the specific geometric parameters used. 4.2. Crack-tip strain energy release rate in TC layer In this section, we focus on the effect of TGO creep on the crack-tip strain energy release rate in the TC layer. It is assumed that there is a pre-existing crack located in the TC layer at the initial stress-free state, as shown in Fig. 2c. When the TBC system is subjected to thermal cycling, the strain energy release rate of the TC crack can be accumulated in each cycle, so it is necessary to calculate the strain energy release rate on a cycle-by-cycle basis. Herein, J-integral is adopted to calculate the strain energy release rate [35]. The typical results of the variation of strain energy release rate G with thermal cycles are shown in Fig. 8 for the crack length a = 0.3L, i.e. the crack is initially located in the tensile zone. In all the three cases for different TGO creep rates, G varies with thermal cycles. In each cycle, the maximum value of G appears at ambient temperature while the minimum value appears at the end of the heating stage. Therefore, the propagation of the crack occurs always at the cooling stage. The energy release rate G increases rapidly with the thermal cycles at both holding and cooling stages when TGO creep is absent (ATGO = 0). However, the presence of TGO creep (ATGO = 7.3 × 10−8) can slow down this increase. When the creep rate increases (ATGO = 7.3 × 10−7), the rise of G with the thermal cycles will be suppressed. Also, the same variation trend has been observed for different lengths of cracks. The variation of strain energy release rate G with the crack length after 24 thermal cycles is shown in Fig. 9. In the initial tensile-stress dominating zone, G increases as the crack length increases. However, if the crack tip locates in the shear-stress dominating zone, as shown in Fig. 6a, G decreases with the increase of crack length after it reaches a peak value. It suggests that the crack driving force is the strongest in the region where tensile stress dominates cracking. When the TGO
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Fig. 5. The shear stress σ12 in TC after 24 thermal cycles: (a) ATGO = 0 (without creep) and (b) ATGO = 7.3 × 10−7.
creep occurs, the energy release rate will be significantly decreased, irrespective of the crack location. It should also be noted that when the creep rate is large enough, the creep behavior can reduce the energy release rate to a very low level (see results when ATGO = 7.3 × 10−7 in Fig. 9) and thereby prohibit the growth of the crack. In some additional simulations, we also varied the creep constant ABC within the range measured in previous experiments. However, both stress and energy release rate are insensitive to it. This may be due to the fact that BC has a relatively low yielding strength at high temperature, which restrains its stress level and leads to a large plastic deformation. As a result, the creep deformation in BC cannot be very large to play an important role. According to the present numerical results, the crack with the maximum length is restrained in the shear-stress dominating zone, where the energy release rate is at the minimum, in agreement with a previous study [13]. However, once the crack further extends through this zone, it will propagate into the tensile-stress dominating zone again (zone III in Fig. 1), where the crack is driven by the contact wedge effect [12], which can lead to an abrupt increase in mode I energy release rate, and presents an unstable extension. As a result, crack coalescence may occur, which results in the final failure of TBCs by large scale spalling of TC which determines the system durability. Nevertheless, a prolonged service life of TBCs can be achieved by decreasing the crack driving force before the crack extends into the unstable zone. The present results show that increasing the TGO creep rate can delay the onset of the unstable extension of the crack. Regarding the problems related to crack coalescence, they are not considered here and are still an open research topic. 5. Conclusions
Fig. 6. The distribution and history of shear stress σ12: (a) along the prospective crack path (“X1X2” in Fig. 5) after 24 thermal cycles during dwell time, and (b) evolution of the maximum shear stress in (a) as the thermal cycles.
The effect of TGO creep on TC cracking induced by the cyclic displacement instability of a thermal barrier coating system is numerically investigated. A periodic unit cell finite element model is developed with the consideration of the temperature-dependent properties of each coating layer. During the thermal cycling, the high-temperature growth
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Fig. 7. The displacement contours of TGO after 24 thermal cycles: (a) U2 and (b) U1 (μm).
Fig. 8. The variation of the crack-tip energy release rate in the TC layer as thermal cycles under the crack length a = 0.3L.
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significant and it can delay the onset of an unstable crack extension which may lead to the catastrophic coalescence of neighboring cracks. Acknowledgements This work is supported by the China 973 Program (2013CB035701) and NSFC (11321062 and 11172227). References [1] [2] [3] [4] [5] [6] Fig. 9. Variation of the crack-tip energy release rate with the crack lengths for three different TGO creep rates during the dwell time after 24 thermal cycles.
[7] [8] [9] [10]
of TGO is simulated and the creep in both TGO and BC is considered. The stress and energy release rate related to the cyclic displacement instability are obtained for different TGO creep rates. The main conclusions include:
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
(1) The TGO creep can significantly reduce the stress in the TC layer upon the cyclic displacement instability. When the TGO creep rate is high, the stress increasing trend with thermal cycles can be largely restrained especially at later cycles. (2) The TGO creep can diminish the downward displacement of TGO at the center of the instability zone upon thermal cycling, which directly decreases the tensile stress in TC. However, the TGO creep can increase the upward displacement around the periphery of the instability zone. Fortunately, in such case the TGO deformation is much more uniformly distributed compared to the local distortion produced when TGO creep is absent. This deformation characteristic cuts off the source of a large shear stress in TC, especially around the periphery of the instability zone. (3) Similarly, the strain energy release rate can also be reduced by a large creep in TGO, which works in both the tensile and shear stress dominating zones. In these two zones, creep effect is
[27] [28] [29] [30] [31] [32] [33] [34] [35]
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Effect of TGO creep on top-coat cracking induced by cyclic displacement instability in a thermal barrier coating system Luochuan Su, Weixu Zhang, Yongle Sun, T.J. Wang ⁎ State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
a r t i c l e
i n f o
Article history: Received 7 January 2014 Accepted in revised form 28 June 2014 Available online 4 July 2014 Keywords: Thermal barrier coating system Top-coat crack TGO creep Displacement instability Thermal cycling
a b s t r a c t The displacement instability of the thermally grown oxide (TGO) under thermal cycling is a fundamental source of cracking within the ceramic top-coat (TC) in a thermal barrier coating system. The effect of TGO creep on TC cracking induced by cyclic instability is numerically investigated in this work. Temperature-dependent elastic– plastic properties of each coating layer are considered in a finite element analysis. A power law is adopted to model the creep behavior of TGO and bond-coat (BC), and TGO growth at high temperature with the consideration of both lateral and through-thickness growth strains is simulated. The numerical results show that during thermal cycling TGO displacement instability occurs in the zone having a geometric imperfection and the accumulation of TGO displacements (downward at the center and upward around the periphery) is evident. The tensile stress (perpendicular to the TGO/TC interface) in TC mainly arises above the center of the instability zone and causes a mode I crack, whereas the shear stress is predominant around the periphery of the instability zone and causes a mode II crack. Both the tensile and shear stresses can be reduced by TGO creep which restrains the morphology distortion of the instability zone during thermal cycling. Furthermore, TGO creep can significantly decrease the energy release rate of TC cracking no matter whether the crack is located in the tensile-stress dominating zone or the shear-stress dominating zone. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Thermal barrier coating systems (TBCs) are widely used in gas turbines to protect the hot-section components (e.g. turbine blades) against extreme temperature. A typical TBC system consists of the following four layers: (i) a ceramic top-coat (TC) layer for thermal insulation, (ii) a bond-coat (BC) layer for performance improvement, (iii) a superalloy substrate to bear mechanical loads and (iv) a thermally grown oxide (TGO) layer formed between TC and BC in service, as schematically shown in Fig. 1. There are many damage mechanisms for materials and structures [1–4]. The delamination and spallation ofTC layer, which mainly result from the converging of microcracks within the TC, are major failure modes of TBCs. Experimental observations have confirmed that the displacement instability of TGO subjected to thermal cycling is a key factor that induces the cracks within the TC layer in electron beam physical vapor deposited (EB-PVD) TBCs [5–9]. The instability usually appears as a downward displacement of TGO toward the BC layer, as shown in Fig. 1. Previous studies have shown that the occurrence of the displacement instability is related to specific conditions. During thermal cycling, the TGO layer is subjected to in-plane compression due to the thermal expansion misfit among different ⁎ Corresponding author. E-mail address: [email protected] (T.J. Wang).
http://dx.doi.org/10.1016/j.surfcoat.2014.06.052 0257-8972/© 2014 Elsevier B.V. All rights reserved.
coating layers upon temperature variation and the TGO growth at high temperature, and when the compressive stress is large enough, the TGO layer begins to displace downward into the BC which is more susceptible to plastic deformation due to its relatively low yield strength. Five prerequisites have been indentified for the instability [6]: (1) the cyclic thermal load; (2) the thermal expansion misfit between the TGO layer and the substrate, which can induce a large inplane compression in the TGO layer upon cooling; (3) the permanent deformation of BC and TGO layers; (4) the TGO growth strain resulting from the formation of new oxides at high temperature; and (5) an initial morphology imperfection at the BC/TGO interface, which is required to initiate instability. The extension of this displacement instability leads to a large tensile stress perpendicular to the interface within the TC above the center of the instability zone, i.e., σ22 along axis-2 in Fig. 1. As a result, the initial microcracks nucleate preferentially there. These microcracks within the TC are a prerequisite for the ultimate failure of TBCs (see Fig. 1) [5,8,10]. Meanwhile, these microcracks would, in turn, promote the extending of TGO instability [11]. Using finite element models, Chen et al. [12] and Xu et al. [13] explored the TC cracking induced by TGO instability and found that there are three zones of crack extension accompanying the instability (see Fig. 1). In zone I, the crack is mode I and its nucleation is governed by the tensile stresses σ22; in zone II, the crack is mode II and driven by the shear stresses σ12. If the crack extends into zone III, it will become mode I again. Bhatnagar et al. [14] performed a parametric analysis and estimated the
L. Su et al. / Surface & Coatings Technology 254 (2014) 410–417
Fig. 1. Schematic of TBCs: the cracks in TC are associated with the displacement instability of TGO.
contribution of geometric and material factors (excluding TGO creep) to the crack initiation and propagation, and they also proposed a basic parametric relationship for the crack initiation within the TC. Their study shows that crack initiation and propagation are a result of the combined effects of the material and geometric factors. TGO creep is an important factor associated with thermal loading, but its effect on the TC cracking induced by TGO instability [13,14] has not been adequately studied. Extensive investigations have shown that under high temperature TGO creep is significant and can cause complex changes of the microstructures and stress state in TBCs [15–17], and thus it can influence the service life of TBCs. Baker et al. [18,19] numerically investigated the effect of TGO creep on the stress state at the TGO/TC interface with sinusoidal morphology. Later, Ding et al. [20] used more realistic material properties at high temperature to explore the effect of TGO creep on the morphology evolution of the instability zone. These works show that TGO creep is an important factor affecting the stress and deformation of the instability zone. Also, a numerical work [21] has shown that the energy release rate of the crack in TBCs is sensitive to the creep properties of materials. However, none of these previous studies considered the TGO instability induced stress state and cracks within TC. The objective of this work is to investigate the effect of TGO creep on TC cracking induced by TGO displacement instability upon thermal cycling. Firstly, a finite element model incorporating a TC crack is developed, which is based on the previous experimental observations of TGO displacement instability and crack growth [6–8,13]. The creep behavior of TGO and BC is considered and the temperature-dependent material properties are used for a physically realistic simulation. The TGO creep strength is expected to vary in different TBCs since it can be influenced by the grain size [18] and the content of the substrate material [22]. Therefore, the TGO creep property is varied in the simulation in order to investigate its effect. And then, the stresses in the tensile and shear zones within the intact TC are obtained under different TGO creep rates. Finally, the energy release rate for a TC crack under different TGO creep rates is numerically calculated. The outcome of this work may aid in the understanding of the role of material creep in the spallation and failure in TBCs. 2. Statement of the problem In the TBC system shown in Fig. 1, the cracks in the TC are normally induced by the TGO displacement instability upon thermal cycling. During thermal shock (between 25 °C and 1100 °C) and TGO growth at high temperature (1100 °C), the in-plane compressive stress in the
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TGO arises. When the compressive stress is large enough, the instability zone in Fig. 1 would be driven to extend downward, which can result in a large tensile stress σ22 within the TC above the center of the instability zone (zone I) and then an initial mode I crack would be induced in this zone. Under the tensile stress, the crack can propagate into the periphery of the instability zone (zone II), where the TGO displaces upward and the stress σ22 is compressive. However, the shear stress σ12 in this zone is significant and the crack is predominantly of mode II. Once the crack extends into the zone between the neighboring instability zones, it would become mode I again under tensile stress. Based on the investigation of the coating morphology associated with TGO instability, the instability zones and the instability-induced cracks are usually idealized as a periodic array [13,23]. Accordingly, a generalized plane strain model is developed here to study TC cracking, as shown in Fig. 1, where L is the width of the instability zone and a is the length of the crack. The strain energy release rate is an important parameter characterizing the driving force of TC cracks. When its maximum value reaches the toughness of the TC, the crack begins to extend. However, a minimum strain energy release rate would occur in the shear-stress dominating zone (zone II) during the crack extension. Once the crack passes through zone II and propagates into zone III, the strain energy release rate increases rapidly, where the crack undergoes unstable extension and abruptly coalesces with neighboring cracks [13,23]. The durability before the failure caused by the displacement-instabilityinduced cracking is determined by the onset of the unstable crack extension. Therefore, we focus on the effect of TGO creep on TC cracking before the crack coalescence and calculate the strain energy release rate on a cycle-by-cycle basis. 3. Finite element analysis 3.1. Geometric model and boundary conditions A two-dimensional finite element model is developed to incorporate the complex interface morphology and crack behavior in TBCs. The general purpose FE code ABAQUS is employed in analysis. Fig. 2 shows the geometric model wherein the substrate, BC, TGO, and TC are simplified. The thickness of each layer is listed in Table 1. With an initial thickness shown in Fig. 2 the TGO layer is thickening during high-temperature exposure and the detail of the simulation method will be described later. The configuration of the displacement instability zone is described by the curvature radii R1 = 17.8 μm and R2 = 12 μm, and the width L = 50 μm. The previous work [13] has shown that the crack propagation rate is the highest when the distance of each periodic array is W = 3L. Therefore, the width of the TBC system considered here is set to W = 150 μm. The planar crack is located in the TC at a distance b = 2.5 μm above the top interface of TGO (see Fig. 2) [13,23]. To calculate the energy release rate on a cycle-by-cycle basis, the crack length a is treated as a constant in each calculation, i.e., the crack growth process is not simulated, and different crack lengths are given in each calculation. The neglect of the crack growth does not prevent the occurrence of the interactions between the TC crack and TGO instability, so it would not lead to fundamental errors when the TGO creep effect is investigated [13]. However, if the cracking and the instability are fully coupled, there may be some other kinds of interactions, which need to be analyzed by a strong-coupling model open to future research. The periodic boundary condition [24,25] is applied at the left and right sides, and the motion in the Y direction is constrained at the bottom side. More than 24,000 four node bilinear generalized plane strain quadrilateral elements (CPEG4R) are used and a mesh sensitivity study is performed to yield adequate mesh-independent solutions. As shown in Fig. 2b, the mesh in the vicinity of the instability zone is refined with the minimum element size Δl satisfying Δl/L = 0.005. Fig. 2c shows the detailed mesh near the crack tip and the quarterpoint elements are adopted to capture the singularity. Initially, the
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Fig. 2. Details of the finite element model: (a) mesh profile and boundary conditions; (b) the refined meshes in the vicinity of the instability zone; (c) an enlarged view of the meshes near the crack-tip.
TBC system is stress-free at a temperature of 1100 °C. Then thermal cycling is exerted, and each cycle includes 10-min cooling to the ambient temperature (25 °C) and 10-min reheating to the high temperature (1100 °C) at which a 30-min holding is maintained. This sequence is repeated and 24 cycles are considered for each calculation.
Table 1 Physical and geometric parameters used in the model.⁎
TC
TGO
BC
SUB
Temperature (°C)
Young's modulus (GPa)
Poisson's ratio
Yield strength (MPa)
Thermal expansion (α × 10−6/°C)
25 200 400 800 1100 25 200 400 800 1100 25 200 400 800 1100 25 200 400 800 1100
E⊥ TC = 160.4
0.1
/
9.0 9.2 9.6 10.8 12.2 5.1 5.1 5.1 5.1 5.1 12.3 14.2 15.2 16.3 17.6 14.8 15.2 15.6 16.9 18.0
E= TC = 30.4
400 390 380 355 320 200 190 175 145 120 220 210 190 155 120
0.27
/
0.3
426 412 396 284 114 /
0.3
Layer thickness (μm) 150
3
80
2000
⁎ TC is modeled as a transversely isotropic material and E= TC is the modulus in the X direction. The Young's modulus of the TC layer is taken from [27] and other material data are taken from [33]. The layer thickness refers to ref. [6].
3.2. Material behavior Herein TGO is considered as an elastic and viscous material, BC is treated as an elastic and viscous-plastic material, and TC and the substrate are assumed to follow the linear elastic law. All the material property parameters are listed in Table 1. For EB-PVD TBCs, the TC layer exhibits transversely isotropic properties, because of its special columnar microstructure [26]. In other words, the in-plane material property is different from that in the out-of-plane direction, as shown in Table 1 [27]. For the creep behavior of TGO and BC, the following power law [14,28,29] is adopted, dεcr ΔH n ¼ A0 σ exp − RT dt
ð1Þ
where A0 is a creep constant, σ is the equivalent stress, n is the creep exponent, ΔH is the activation energy, R is the universal gas constant and T is the absolute temperature. At the cooling and heating stages during thermal cycling, the time for the temperature held in the range where creep can occur is relatively short. Thus, we only consider the creep at the high-temperature holding stage. Consequently, T is actually a constant in this case and Eq. (1) can be rewritten as dεcr n ¼ Aσ : dt
ð2Þ
For BC, ABC = 3.9 × 10− 6 and nBC = 2.5 [30]. For TGO, three different creep constants are compared: ATGO = 0 (without creep), ATGO = 7.3 × 10− 8 (small creep) and ATGO = 7.3 × 10 − 7 (large creep), in order to explore the creep effect, while the creep exponent is fixed as nTGO = 1 [31].
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At the holding stage, due to the oxidation of the BC layer, the thickness of the TGO layer will increase. As observed in experiments, TGO thickens parabolically with time [32] and the thickening rate is given by tgo h˙ ¼
kp 2htgo
;
ð3Þ
where htgo is the thickness of the TGO layer and kp is a constant with a unit of m2 s −1, the value of which should be chosen so that TGO thickens from 0.5 to 3 μm during 100 h holding at high temperature. Accompanying the thickening, the lateral growth strain εg also occurs due to the formation of new oxides on the internal grain boundary, which can be expressed as ε˙ g ¼
tgo h˙ ; d
ð4Þ
where d is a constant. The lateral growth strain εg is the main source of in-plane compressive stress in TGO. Here the simulation of TGO thermal growth is carried out using the ABAQUS user subroutine, uexpan, by imposing a growth strain at the holding stage [7]. The growth strain contains two components: thickening strain εt perpendicular to the TGO/BC interface, and the lateral strain εg parallel to the TGO/BC interface. In all calculations, the ratio of lateral strain to thickening strain in each cycle satisfies εg/εt = 0.5 with εt = 1 × 10−3 [9]. 4. Results and discussion 4.1. Stress distribution in TC layer The distribution of the stress induced by the TGO displacement instability in an intact TC is primarily analyzed. The normal stress (σ22) and shear stress (σ12) above the instability zone are emphasized since the initiation and propagation of the crack in TC are controlled by
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them. Fig. 3 shows the distribution of σ22 after 24 thermal cycles. For both cases that TGO undergoes no creep (ATGO = 0) and a large creep (ATGO = 7.3 × 10−7), σ22 is tensile above the center of the instability zone but becomes compressive around the periphery of the instability zone. In the region away from the instability zone, the stresses are close to zero. Similar results have also been reported by other researchers [13,23]. However, compared to the stress in the case that ATGO = 0, the stress magnitude is significantly reduced when TGO creep occurs (ATGO = 7.3 × 10−7). In other words, the whole TC is subjected to lower tensile or compressive stress due to the presence of TGO creep. Fig. 4a shows the stress along the prospective crack path (“X1X2” in Fig. 3) in TC under three different TGO creep rates (ATGO = 0, ATGO = 7.3 × 10−8 and ATGO = 7.3 × 10−7). It confirms that the maximum of σ22 occurs above the center of the instability zone, implying that the crack will preferentially initiate there. However, the stress magnitude reduces significantly as TGO relaxation is enhanced by increasing the creep rate constant. The evolution of the maximum of σ22 along the path “X1X2” during thermal cycling is shown in Fig. 4b. Even if TGO growth and creep are assumed to occur only at the high-temperature holding stage, they still have a significant effect on the stress state at the cooling and reheating stages. This is because the thickening and lateral growth of TGO can reduce the magnitude of the temperature change required to cause plastic yielding in the BC layer during the cooling and reheating process [34], and TGO creep can lead to permanent deformation which affects TGO geometry. These combined factors will cause TGO displacement instability in the form of a downward displacement (source of tensile stress) at the base of the instability zone and an upward displacement (source of shear stress) around the periphery of the instability zone [9]. Therefore, σ22 in Fig. 4b increases with the thermal cycles. Also, a similar occurrence can be seen in the following result of shear stress σ12. The comparison shows that, if there is no creep in TGO, the magnitude of σ22 increases rapidly at both thermal growth (holding at high temperature) and thermal shock (cooling or
Fig. 3. The stress fields σ22 in TC after 24 thermal cycles: (a) ATGO = 0 (without creep) and (b) ATGO = 7.3 × 10−7.
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Fig. 4. The distribution and history of normal stress σ22: (a) along the prospective crack path (“X1X2” in Fig. 3) after 24 thermal cycles during dwell time, and (b) evolution of the maximum tensile stress in (a) as the thermal cycles.
reheating) stages, but when the creep occurs in TGO (ATGO = 7.3 × 10−8), the stress increase with thermal cycles begins to slow down at the two stages. When TGO creep rate is further increased (i.e. ATGO = 7.3 × 10− 7 ), the stress increases only at the initial several cycles and the increasing trend is almost restrained at the following cycles, especially at the holding or thermal growth stage. Such evolutionary feature of σ22 can be attributed to the enhanced effect of creep relaxation over the stress generation by thermal loading. The shear stress (σ12) contours for different TGO creep rates are shown in Fig. 5. In general, the shear stress mainly distributes in the region near the periphery of the instability zone, where σ22 is compressive (see Fig. 3), and it is almost zero in the region above the center of instability zone where σ22 is tensile. This verifies the previous observation [12] that in the zone under tension (zone I in Fig. 1), σ22 drives the cracking, and that in the zone under compression (zone II in Fig. 1), the crack propagates due to the shear stress σ12. Furthermore, the present results enable the clarification of the TGO creep effect. Fig. 5a and b show that TGO creep can reduce the shear stress level, similar to its effect on the normal stress σ22. This effect is so significant that the magnitude of shear stress can be reduced to only tens of MPa when the creep constant increases to ATGO = 7.3 × 10−7. The shear stress distribution along the prospective crack path shown in Fig. 6a further verifies such effect. In addition, Fig. 6b shows the evolution of the maximum shear stress along the prospective crack path, from which it is clearly seen that the occurrence of creep in TGO (ATGO = 7.3 × 10− 8 and ATGO = 7.3 × 10−7) can restrain the increase of shear stress in a manner similar to that of σ22. The deformation of TGO after 24 thermal cycles is also inspected to further understand the effect of TGO creep. Fig. 7 shows the final
displacement fields in TGO after 24 thermal cycles for three different creep rates. As shown in Fig. 7a, the displacements along the thickness direction (U2) present a downward trend at the center of the instability zone but an upward trend around the periphery of the instability zone for both cases with and without considering TGO creep. This deformation characteristic is the cause of the tensile stress σ22 in zone I (Fig. 1) and shear stress σ12 in zone II [13]. When TGO undergoes creep deformation, the downward displacement tends to decrease and the larger creep rate can result in a smaller displacement. The decrease of the downward displacement will directly diminish the normal stress σ22 above the center of the instability zone and this is consistent with the stress results shown in Figs. 3 and 4. However, it presents an opposite trend for the upward displacement. One may be worried that the shear stress will increase accordingly, but in fact the shear stress decreases due to the following reasons. When there is no creep in TGO, the deformation mainly concentrates in small regions at the base and around the periphery of the instability zone. But the presence of TGO creep (ATGO = 7.3 × 10−8) can diminish the concentration and make the deformation more distributed. Furthermore, the larger creep rate (ATGO = 7.3 × 10−7) makes the deformation more uniformly distributed in the whole TGO and the local distortion becomes absent. Similarly, the creep in TGO also results in more uniform deformation in x direction (U1) and restrains the local distortion, especially around the periphery of the instability zone (Fig. 7b). It has been confirmed that the shear stress in TC can be reduced by the suppression of the local distortion around the periphery of the instability zone upon the cyclic oxidation [6,9]. Therefore, the deformation characteristic associated with the TGO creep is favorable to reduce the local tension and compression in the TC layer and then prevents the occurrence of large delamination stress in TC, which also explains the stress state shown in Figs. 3 to 6. In addition, it should be noted that similar results have been obtained by considering the other two different geometric features of the instability zone, where the curvature radii of the instability zone is R1/R2 = 2 and R1/R2 = 2.5 with R2 = 12 μm. Therefore, it can be confirmed that the TGO effect on TC stress demonstrated here is insensitive to the specific geometric parameters used. 4.2. Crack-tip strain energy release rate in TC layer In this section, we focus on the effect of TGO creep on the crack-tip strain energy release rate in the TC layer. It is assumed that there is a pre-existing crack located in the TC layer at the initial stress-free state, as shown in Fig. 2c. When the TBC system is subjected to thermal cycling, the strain energy release rate of the TC crack can be accumulated in each cycle, so it is necessary to calculate the strain energy release rate on a cycle-by-cycle basis. Herein, J-integral is adopted to calculate the strain energy release rate [35]. The typical results of the variation of strain energy release rate G with thermal cycles are shown in Fig. 8 for the crack length a = 0.3L, i.e. the crack is initially located in the tensile zone. In all the three cases for different TGO creep rates, G varies with thermal cycles. In each cycle, the maximum value of G appears at ambient temperature while the minimum value appears at the end of the heating stage. Therefore, the propagation of the crack occurs always at the cooling stage. The energy release rate G increases rapidly with the thermal cycles at both holding and cooling stages when TGO creep is absent (ATGO = 0). However, the presence of TGO creep (ATGO = 7.3 × 10−8) can slow down this increase. When the creep rate increases (ATGO = 7.3 × 10−7), the rise of G with the thermal cycles will be suppressed. Also, the same variation trend has been observed for different lengths of cracks. The variation of strain energy release rate G with the crack length after 24 thermal cycles is shown in Fig. 9. In the initial tensile-stress dominating zone, G increases as the crack length increases. However, if the crack tip locates in the shear-stress dominating zone, as shown in Fig. 6a, G decreases with the increase of crack length after it reaches a peak value. It suggests that the crack driving force is the strongest in the region where tensile stress dominates cracking. When the TGO
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415
Fig. 5. The shear stress σ12 in TC after 24 thermal cycles: (a) ATGO = 0 (without creep) and (b) ATGO = 7.3 × 10−7.
creep occurs, the energy release rate will be significantly decreased, irrespective of the crack location. It should also be noted that when the creep rate is large enough, the creep behavior can reduce the energy release rate to a very low level (see results when ATGO = 7.3 × 10−7 in Fig. 9) and thereby prohibit the growth of the crack. In some additional simulations, we also varied the creep constant ABC within the range measured in previous experiments. However, both stress and energy release rate are insensitive to it. This may be due to the fact that BC has a relatively low yielding strength at high temperature, which restrains its stress level and leads to a large plastic deformation. As a result, the creep deformation in BC cannot be very large to play an important role. According to the present numerical results, the crack with the maximum length is restrained in the shear-stress dominating zone, where the energy release rate is at the minimum, in agreement with a previous study [13]. However, once the crack further extends through this zone, it will propagate into the tensile-stress dominating zone again (zone III in Fig. 1), where the crack is driven by the contact wedge effect [12], which can lead to an abrupt increase in mode I energy release rate, and presents an unstable extension. As a result, crack coalescence may occur, which results in the final failure of TBCs by large scale spalling of TC which determines the system durability. Nevertheless, a prolonged service life of TBCs can be achieved by decreasing the crack driving force before the crack extends into the unstable zone. The present results show that increasing the TGO creep rate can delay the onset of the unstable extension of the crack. Regarding the problems related to crack coalescence, they are not considered here and are still an open research topic. 5. Conclusions
Fig. 6. The distribution and history of shear stress σ12: (a) along the prospective crack path (“X1X2” in Fig. 5) after 24 thermal cycles during dwell time, and (b) evolution of the maximum shear stress in (a) as the thermal cycles.
The effect of TGO creep on TC cracking induced by the cyclic displacement instability of a thermal barrier coating system is numerically investigated. A periodic unit cell finite element model is developed with the consideration of the temperature-dependent properties of each coating layer. During the thermal cycling, the high-temperature growth
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Fig. 7. The displacement contours of TGO after 24 thermal cycles: (a) U2 and (b) U1 (μm).
Fig. 8. The variation of the crack-tip energy release rate in the TC layer as thermal cycles under the crack length a = 0.3L.
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significant and it can delay the onset of an unstable crack extension which may lead to the catastrophic coalescence of neighboring cracks. Acknowledgements This work is supported by the China 973 Program (2013CB035701) and NSFC (11321062 and 11172227). References [1] [2] [3] [4] [5] [6] Fig. 9. Variation of the crack-tip energy release rate with the crack lengths for three different TGO creep rates during the dwell time after 24 thermal cycles.
[7] [8] [9] [10]
of TGO is simulated and the creep in both TGO and BC is considered. The stress and energy release rate related to the cyclic displacement instability are obtained for different TGO creep rates. The main conclusions include:
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
(1) The TGO creep can significantly reduce the stress in the TC layer upon the cyclic displacement instability. When the TGO creep rate is high, the stress increasing trend with thermal cycles can be largely restrained especially at later cycles. (2) The TGO creep can diminish the downward displacement of TGO at the center of the instability zone upon thermal cycling, which directly decreases the tensile stress in TC. However, the TGO creep can increase the upward displacement around the periphery of the instability zone. Fortunately, in such case the TGO deformation is much more uniformly distributed compared to the local distortion produced when TGO creep is absent. This deformation characteristic cuts off the source of a large shear stress in TC, especially around the periphery of the instability zone. (3) Similarly, the strain energy release rate can also be reduced by a large creep in TGO, which works in both the tensile and shear stress dominating zones. In these two zones, creep effect is
[27] [28] [29] [30] [31] [32] [33] [34] [35]
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