Abstract
Numerical-based finite element investigation has been conducted to explain the effect of bond coat thickness on stress distribution in traditional and nanostructured yttria-stabilized zirconia (YSZ)-based thermal barrier coatings (TBC). Stress components have been determined to quantitatively analyze the mechanical response of both kinds of coatings under the thermal shock effect. It has been found that maximum radial tensile and compressive stresses that exist at thermally grown oxide (TGO)/bond coat interface and within TGO respectively decrease with an increase in bond coat thickness. Effect of bond coat thickness on axial tensile stresses is not significant. However, axial compressive stresses that exist at the edge of the specimen near bond coat/substrate interface decrease appreciably with the increase in bond coat thickness. Residual stress profile as a function of bond coat thickness is further explained for comparative analysis of both coatings to draw some useful conclusions helpful in failure studies of TBCs.
Introduction
Thermal barrier coatings (TBCs) are commonly used as protective coatings for hot-section metal components in gas turbines which allow increase in gas inlet temperature and thus improve performance and thermal efficiency of turbine engines [1–4]. Thermal insulation capability and high temperature stability are the key performance parameters of TBCs. TBCs have typical multilayer configuration with a top layer of zirconia, a film of aluminum oxide developed at high temperature, a metallic bond coat (BC) layer from which the oxide grows, and the metallic super alloy substrate [5]. The BC serves to protect the substrates from oxidative and corrosive attacks and plays an important role in improving the bonding between ceramic topcoat and substrate. BC as an intermediate layer also reduces the thermal expansion mismatch stresses arising from metal substrate and ceramic coating. The ceramic topcoat typically composed of yttria-stabilized zirconia (YSZ) has a lower thermal conductivity than the metallic substrate and thus act as a shield against heat damage. Enhanced jet engine efficiencies necessitated significant increase in combustion temperatures and operating pressures. These requirements have proved to be a big driving force to improve the TBC technology, such as novel compositions, production techniques and improvement in microstructure, and physical and mechanical properties of TBCs [1]. Nanostructured yttria-stabilized zirconia coatings (nano-YSZ) due to their potential superior mechanical and physical properties over traditional coatings have received wide interest in the last decade [6–11]. Moreover, in the nanostructured YSZ, a refined clustered morphology with a particle size below 1 μm increases the strain accommodation ability [12, 13].
BC is an essential component of a TBC system. Chemical composition of BC and its thickness are major performance parameters and are important for the TBC life assessment. Previous investigations on BC mainly cover its oxidation behavior [14–18], effect of surface morphology [19, 20] and thermo-mechanical behavior of different BCs [21–24]. Stress state in the TBC systems is critical for the assessment of failure mechanism and to estimate the thermal life of the TBCs. Very limited data are available on variation in stress state as a function of BC thickness specifically with nanostructured YSZ topcoat in comparison with traditional YSZ coatings.
In the present study an investigation on the mechanical response of the traditional and nanostructured TBCs under thermal load effect has been carried out with varying BC thickness. Study has been carried out by using finite element method using commercial code ANSYS and results of radial, axial and shears stress distribution in traditional and nanostructure YSZ coatings are presented for comparative analysis.
Numerical approach and model description
Geometric model, FEM mesh and materials parameters
A circular round-shaped specimen was considered. An axisymmetric case was taken into account in the radial and through thickness directions allowing the problem to be reduced to a two-dimensional case for easy computation as schematically shown in Figure 1.
Schematic illustration of geometric model.
The model included four layers: top coat 200 µm, TGO 5 µm, BC 100~200 µm (varying parameter) and substrate with thickness of 2 mm. Finite element solution was employed to simulate the coupled and highly non-linear thermo-mechanical phenomena that occurred during the cooling of multilayer TBC system from elevated temperature. 2-D coupled field element PLANE223 was used that has eight nodes with up to four degrees of freedom per node. Due to the regular shape of the sample, mapped grid was selected for mesh construction for easy computation. Geometry was consisting of approximately 20,000–25,000 elements depending on the BC thickness. Due to oxide thin layer, the TGO and its neighboring regions were finely meshed to enhance the sensitivity of the model to the rigorous changes in stress state in this region. The analysis model had four layers: Ni-based superalloy substrate, NiCrAlY bond-coating, Al2O3 thermally grown oxide (TGO) and ceramic top coat. Thermal and mechanical performance parameters of the materials used in the analysis were acquired from literature and are given in Table 1 [1, 25–27].
| Material | Temperature (˚C) | Young’s modulus (GPa) | Poisson’s ratio | Thermal expansion coefficient (×10-6˚C-1) | Thermal conductivity (Wm-1˚C-1) |
| Traditional YSZ | 20 | 48 | 0.1 | 9 | 1.956 |
| (Top coat) | 200 | 47 | 0.1 | 9.2 | 1.834 |
| 400 | 44 | 0.1 | 9.6 | 1.736 | |
| 600 | 40 | 0.11 | 10.1 | 1.627 | |
| 800 | 34 | 0.11 | 10.8 | 1.634 | |
| 1000 | 26 | 0.12 | 11.7 | 1.681 | |
| 1100 | 22 | 0.12 | 12.2 | 1.7 | |
| Nano-structured | 100 | 60 | 0.23 | 10.7 | 1.11 |
| YSZ | 300 | 58 | 0.23 | 11.1 | 1.06 |
| (Top coat) | 500 | 44 | 0.24 | 11.2 | 0.02 |
| 700 | 38 | 0.24 | 11.3 | 1.0 | |
| 900 | 36 | 0.25 | 11.4 | 0.99 | |
| 1000 | 34 | 0.25 | 11.5 | 1.01 | |
| 1100 | 32 | 0.25 | 11.6 | 1.12 |
Boundary conditions
Symmetric boundary conditions were taken in account due to axisymmetric configuration of the model. All layers were assumed homogeneous and isotropic. Thermal load was applied through a drop in the temperature from an a assumed stress free state at 1050°C to room temperature (25°C) in 300 seconds time. Heat convection was imposed on the top and side of the sample while bottom of the specimen was assumed thermally insulated. Phase transformation and creep mechanisms were assumed inactive during the simulation. Peak radial, axial and shear stresses were determined with both type of ceramic top coats and results were compared with few useful findings.
Results and discussion
In-plane stresses
Figure 2 shows variation in tensile radial stress as a function of BC thickness in nanostructured and traditional YSZ coatings. It shows that radial tensile stress in nanostructured YSZ coating is slightly higher than in traditional YSZ coating with an almost constant difference in all thickness cases considered in this study.
Radial tensile stress in traditional and nanostructured YSZ coatings as a function of bond coat thickness.
From Figure 2, the results show an inverse relationship between the peak radial tensile stress and BC thickness. The stress drops approximately 95 MPa by an increase in BC thickness from 100 μm to 200 μm.
The variation in residual compression stresses in both traditional and nanostructured TBCs for the considered BC thickness range is shown in Figure 3. It shows that radial compressive stress that exists in the TGO also drops with the increase in BC thickness. However, this drop is not very significant and maximum difference in stress for the increase in BC thickness from 100 μm to 200 μm is not more than 25 MPa. Since the energy density in the TBC system play an important role in controlling its durability [28, 29], based on stress values calculated from FE analysis, total elastic strain energy per unit area in the TGO is calculated for TBC structural integrity assessment. The resultant elastic strain energy for both kinds of coatings over the all BC thicknesses (100–200 μm) is in the range of 118 J/m2 to 120 J/m2. Since there is no significant variation in compressive stress and in elastic store energy due to BC thickness, it can be anticipated that thermal stress variation caused by increase in BC thickness will not have considerable effect on failure of TBCs. This is the case when there is no any external mechanical load applied on the TBC system. However, if the external load is applied as reported by Kwon et al. [30], the thin BC may enhance contact damage and thus transmits the damage to the substrate, whereas the thick BC limits the damage to BC. Radial stress distribution for two BC thicknesses, 100 μm and 200 μm for both TBCs, is shown in Figure 4. It can be seen from Figure 4 that the stress distribution in both TBCs for different BC thicknesses is almost same with a difference in peak stress values in both tension and compression which have been explained in Figures 2 and 3. Figure 4 shows that the tensile radial stress exists at the BC/TGO interface near the edge of the specimen. This stress particularly in the thin BC TBCs may propagate any pre-existing defect at the interface to increase its extent and eventually may results in TBCs failure [31]. Since both radial compressive and tensile stresses drop with the increase in BC thickness, it can be inferred that thick metallic BC are more durable than thin BCs. Moreover, it has also been reported that the nanostructured zirconia coating has larger adhesion strength than traditional zirconia coating [32]. Therefore, with the almost similar stress state in traditional and nanostructured YSZ coatings, nanostructured coatings are expected to be more long-lived as compared to traditional coating with the thick BCs.
Radial compressive stress in traditional and nanostructured YSZ coatings as a function of bond coat thickness.
Contour plot of radial stress (σxx) distribution in (left) traditional and (right) nanostructured YSZ coatings at 100 μm (a, b) and 200 μm (c, d) bond coat thicknesses.
Out-of-plane stresses
Peak axial tensile and compressive stresses in nanostructured and traditional TBCs as a function of BC thickness are shown in Figures 5 and 6.
Axial tensile stresses in traditional and nanostructured YSZ coatings as a function of bond coat thickness.
Axial compressive stresses in traditional and nanostructured YSZ coatings as a function of bond coat thickness.
Figure 5 shows that increasing the BC thickness has very little effect on axial tensile stresses in bond kinds of TBCs. However, these stresses in traditional YSZ coating have dropped linearly with the increase in BC thickness. Whereas a little variation in stress value of nanostructured TBC is observed that has slightly increased after 160 μm thick BC.
Axial compressive stresses also drop with BC thickness as shown in Figure 6. The maximum drop of stress is approximately 90 MPa. Moreover, this stress in nanostructured TBCs is lower than in traditional YSZ coatings.
Stress state in axial direction is further elaborated with the contour plots of axial stresses for 100 μm and 200 μm BC thickness cases presented in Figure 7. Figure 7 shows that maximum tensile axial stress in all cases exists in the BC which is slightly shifted to the bottom of substrate in 200 μm BC nanostructure YSZ coating case. Moreover, maximum axial compressive stresses in 100 μm BC traditional coating and 100 μm and 200 μm BCs nanostructure coatings exist close to the BC/substrate interface near the edge of the specimen. However, maximum axial stress in 200 μm BC traditional coating case lies near the BC/TGO interface close to the edge of the sample. Axial stresses existing close to the interface near the edge of the specimen may also be important especially if some oxide network is present at BC/substrate interface. The oxides formed at BC/substrate interface are generally of spinel type [33, 34] which give the interface poor mechanical properties and thus any stress state in this vicinity may also be an important consideration for the assessment of TBC life.
Contour plot of axial stress (σyy) distribution in (left) traditional and (right) nanostructured YSZ coatings at 100 μm (a, b) and 200 μm (c, d) bond coat thicknesses.
Shear stresses
This stress state is important as initiation of an interface separation is contingent upon the existence of a shear stress at the interface [35]. The variation in shear stress in traditional and nanostructured coating for varying BC thickness is presented in Figure 8. Figure shows that shear stress increases with the increase in BC thickness in both coating systems. However, the shear stress value in nanostructured coating is higher than traditional coating with a relatively constant difference. Shear stress pattern in both coating systems for 100 μm and 200 μm BC thickness cases is shown in Figure 9. As shown in the figure, the maximum shear stress in all coating systems exists at BC/TGO interface. However, the minimum value of shear stress in nanostructured coating lies at topcoat/TGO interface different from traditional YSZ coating which exist in BC near the edge of the specimen. TGO bonded to its substrate sustain large in-plane residual stresses (in this study ~3.5 GPa) that are transferred to the TGO via shear stresses on the interface near their edges, and these edge zones play a significant role in TGO delamination [36] and failure of TBCs. Thus, the stress concentration observed at the metallic BC/TGO interface may play an important role on decohesion of the layers leading to instability and failure of TBCs.
Shear stresses in traditional and nanostructured YSZ coatings as a function of BC thickness.
Contour plot of shear stress (σxy) distribution in (left) traditional and (right) nanostructured YSZ coatings at 100 μm (a, b) and 200 μm (c, d) bond coat thicknesses.
Conclusion
In the present paper, effect of BC thickness on stress response of traditional and nanostructured YSZ coatings has been analyzed under thermal load effect. In-plane and out-of-plane tensile and compressive stresses decrease with the BC thickness. However, variation in in-plane compressive and out-of-plane tensile stresses is very small. Drop in radial tensile and axial compressive stresses is considerable and is almost same in value in MPa (100 MPa) as increase in BC thickness in micrometers (100 μm). Radial tensile stresses in nanostructured YSZ coating are very close to the traditional YSZ coating, whereas axial compressive stresses in nanostructured coating are lower than traditional YSZ coatings. Different from radial and axial stresses, peak shear stresses increase with BC thickness and are slightly higher in nanostructured YSZ coating than in traditional YSZ coating. In summary, most of the stresses in nanostructured YSZ coating are either lower or very close to the traditional YSZ coating. In view of associated stress state data, it can be suggested that nanostructured YSZ coatings with thick BC are more durable against thermal loads than traditional YSZ coatings.
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