Model construction and effect of thermally grown oxide dynamic growth on distribution of thermal barrier coatings

A physical geometric model of the dynamic growth of thermally grown oxide (TGO) was established based on an analysis of the TGO growth of 8YSZ thermal barrier coatings during thermal cycling. Finite-element simulation was used to simulate the evolution law between the coating residual stress and thermal cycling, and the linear elasticity, creep effect, and stress accumulation in each thermal cycle were studied. The interface between the top coat (TC) and the bond coat (BC) was covered with a TGO layer that grew vertically and slowly in a layer-like manner. The stress in the TGO was distributed with a “layer” zonal gradient, and the TGO/BC boundaries were distributed uniformly with a large compressive stress, which decreased the TGO layer thickening. With the longitudinal rapid random TGO growth, the boundaries were subjected to a tensile stress, and a high tensile stress concentration area developed at the boundaries. The internal stress consisted of an alternating and mixed distribution of concentrated compressive and tensile stresses. The concentration area of the maximum equivalent stress was distributed in the one-layer TGO near the TC/TGO interface. When a microcrack formed at the TGO/BC boundaries, the crack was subjected to a tensile stress of different size, with a higher tensile stress at both ends, which facilitated crack expansion. Thus, the 8YSZ thermal barrier coating was prone to crack formation and expansion at the TGO/BC boundaries and in the TGO layer near the TC/TGO boundaries.     

Finite element analysis of TGO thickness on stress distribution and evolution of 8YSZ thermal barrier coatings

According to the experimental research results of the thermally grown oxide (TGO) layered growth during the pre-oxidation process of 8 wt.% yttria-stabilized zirconia thermal barrier coating (TBC), a two-dimensional sinusoidal TC/bonding coat (BC) curve interface model of the longitudinal section of TBCs based on finite element simulation was constructed; the thickness and composition of the TGO layer relative to the TC/BC curve interfacial stress distribution and its evolution during the thermal cycling process were studied. The results show that when the TGO layer uses α-Al₂O₃ as the main oxide (black TGO), the thicker the black TGO layer, the more uniform the stress distribution of the TC/BC interface. When the TGO layer is dominated by spinel-structured Co and Cr oxides (gray TGO), the stress “band” of the TC/BC interface is destroyed; it shows the alternating phenomenon of tensile stress zone and compressive stress zone, and after the rapid random growth of TGO, the concentrated tensile stress increased by a large jump. Affected by the thickness of the prefabricated black TGO layer, there is a limit peak in the thickness of the black TGO layer, the normal stress at the TC/BC boundary is minimized, and the magnitude of the stress change is also minimized.     

Comparison of stress evolution under TGO growth simulated by two different methods in thermal barrier coatings

The growth of thermally grown oxide (TGO) is a significant factor affecting the failure mechanism of thermal barrier coatings (TBCs) during cyclic high temperature service. In this work, a complicated finite element model with two semicircles reflecting the undulation of TGO interfaces was proposed, and four representative shapes of TGO interfaces were selected. There are mainly two methods to simulate TGO growth under high temperature, and each method was achieved by implementation of user subroutines in finite element method. A total of 100 thermal cycle loads were applied to the TBCs continuously. The stress evolution in the layers of Top Ceramic Coating (TC) and Bond Coating (BC) at the end of each thermal cycle load was obtained, the influence of TGO growth on stress evolution was analyzed, the differences between two methods of TGO growth were discussed. The results show that under TGO growth simulated by the first method, the stress distribution in the y direction does not change in both TC and BC layer, and the maximum stress decreases a lot in TC layer but nearly remains the same in BC. When the growth of TGO was simulated by the second method, stress evolution is complex and undergoes up to five stages with a small undulation or convex of TGO interfaces. Stress evolution in BC layer remains as the same as in the first method. Moreover, the maximum stress increases continually in BC layer. The comparison of these two simulation method would help to study the failure of TBCs caused by TGO growth.     

Effect of material properties on residual stress distribution in thermal barrier coatings

Residual stress has a significant influence on the crack nucleation and propagation in thermal barrier coatings (TBC) system. In this work, the residual stress in the air plasma spraying (APS) TBC system during cooling process was numerically studied, and the influence of the material properties of each layer on the residual stress was investigated. The morphologies of the interface were described by a piecewise cosine function, and the amplitude for each segment gradually increases. The elasticity, plasticity and creep of top coat (TC), thermally grown oxide (TGO) layer and bond coat (BC) were considered and the elasticity and creep of the substrate layer were taken into account. The material properties of all layers vary with temperature. The results show that the material properties have complex influence on the residual stress during cooling. The effect of the material properties of TC and BC on the residual stress at the interface is relatively large, and that of TGO and substrate is relatively small. These results provide important insight into the failure mechanism of air plasma spraying thermal barrier coatings, and important guidance for the optimization of thermal barrier coating interfaces.     

Effect of TGO thickness on the thermal barrier coatings life under thermal shock and thermal cycle loading

Effect of thermally grown oxide (TGO) thickness on thermal shock resistance of thermal barrier coatings (TBCs) and also their behavior under a cyclic loading (including aging at maximum temperature) was evaluated experimentally. In order to form different thicknesses of TGO, coated samples experience isothermal loading at 1070?°C for various periods of times. Heat-treated samples were heated to 1000?°C and cooled down rapidly in water from the substrate side using a mechanical fixture. The life of samples was investigated as a function of TGO thickness. Furthermore, by performing an experiment the simultaneous effect of the TGO growth and thermal expansion mismatch– on the failure of thermal barrier coatings was evaluated. The results demonstrated that the presence of TGO with a thickness of 2–3?µm has a positive effect on the resistance against thermal shock.     

Construction of three-dimensional dynamic growth TGO (thermally grown oxide) model and stress simulation of 8YSZ thermal barrier coating

A three-dimensional cylindrical numerical simulation physical and geometric model of TBCs sinusoidal surface was established based on the ultrasonic C-scan results of 8YSZ coating after thermal cycling. The stress distribution and evolution law of the TGO/BC interface and sample center and edge affected by TGO growth were simulated by the finite-element method. The results show that the stress at the TGO/BC interfaces changes from compressive stress to tensile stress with the increase of the number of thermal cycles. The center of the interface is distributed with large radial, circumferential and axial tensile stresses, while the edge of the sample is affected by thermal mismatch, which shows that shear stresses are alternately distributed in the XZ direction. The tensile stress at the center and the shear stress at the edge are the main reasons for the failure of the core and edge flakes of the thermal barrier coating. The linear elasticity, creep effect, fatigue effect and stress accumulation effect of each layer of TBCs in each thermal cycle period are fully considered by the model, which reveals the reason why the core and edges of the thermal barrier coating are most likely to form cracks.     

Residual stress distribution along interfaces in thermal barrier coating system under thermal cycles

The residual interfacial stress plays an important role in crack initiating and propagating along the interface, which could result in delamination failure of the thermal barrier coatings (TBCs). In this study, the finite element model of air plasma spraying(APS) TBCs was established to assess the level and distribution of residual stress along top coat(TC)/thermally grown oxide (TGO) and bond coat (BC)/TGO interfaces under thermal cycles. Instead of using vertical stress S₂₂ in global coordinate system, the normal and tangential components in the local system along the interfaces, transformed from stress components S₁₁, S₂₂, and S₁₂ in the global one, were used to evaluate the way the cracks initiate and propagate along the interfaces. Firstly, the effect of the number of thermal cycles on residual stress was investigated. It was found that, for the TBCs model without TGO growth and crack, the impact of the number of thermal cycles on the stress is very insignificant and could be ignored. So the present study only chose to focus on the first thermal cycle. Then the influence of the TGO thickness and the interface amplitude on the normal and tangential residual stresses for both homogeneous and inhomogeneous temperature fields was explored. The results show that the TGO thickness, interface amplitude and temperature field affect the residual stress level and distribution, leading to different fracture mechanisms along TC/TGO and TGO/BC interfaces. Finally, the difference between the vertical stress in the global coordinate system and the normal stress in the local coordinate system was studied. Compared with vertical stress S₂₂, the stress components normal and tangential to the TC/TGO and TGO/BC interfaces are more appropriate to describing the stress distribution along the interfaces and predicting the propensity of crack initiating and propagating along the interfaces.     

Effect of TGO thickness,pores, and creep on the developed residual stresses in thermal barrier coatings under cyclic loading using SEM image-based finite element model

Thermal barrier coatings (TBC) allow the metallic internal components of gas turbine engines to operate at elevated temperatures near its melting points. Formation of thermally grown oxide (TGO) layers at the top coat (TC) and bond coat (BC) interface induces cracks in the TC that may lead to complete TBC failure due to spallation. An SEM image-based finite element (FE) model is developed using commercial finite element package ABAQUS to investigate the development of residual stresses resulting from cyclic loading of TBCs. The model includes thermo-mechanical material properties and considers the real interface between the coating layers. The model includes real pores based on an SEM image, taking advantage of image processing techniques. Effect of TC surface roughness and pores on the developed residual stresses during thermal cycling is investigated with respect to different TGO thicknesses. The analysis shows that presence of TC roughness causes stress concentration sites during heating that may force horizontal cracks to initiate and propagate with stress values that are indifferent to the TGO thickness. The pores are found to shift stress concentration regions from the TC/TGO interface to the vicinity of the pores during cooling, and that may cause horizontal cracks to start from within the TC with stresses that increase with TGO thickness. Moreover, the effect of creep for all layers on the generated residual stresses is studied. Considering creep gives lower stresses at the end of cooling, however, stress distribution remains the same with and without creep.     

Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model

Comprehensive understanding of failure mechanism of thermal barrier coatings (TBCs) is essential to develop the next generation advanced TBCs with longer lifetime. In this study, a novel numerical model coupling crack propagation and thermally grown oxide (TGO) growth is developed. The residual stresses induced in the top coat (TC) and in the TGO are calculated during thermal cycling. The stresses in the TC are used to calculate strain energy release rates (SERRs) for in-plane cracking above the valley of undulation. The overall dynamic failure process, including successive crack propagation, coalescence and spalling, is examined using extended finite element method (XFEM). The results show that the tensile stress in the TC increases continuously with an increase in an undulation amplitude. The SERRs for TC cracks accumulate with cycling, resulting in the propagation of crack toward the TC/TGO interface. The TGO cracks nucleate at the peak of the TGO/bond coat (BC) interface and propagate toward the flank region of the TC/TGO interface. Both TC cracks and TGO cracks successively propagate and finally linkup leading to coating spallation. The propagation and coalescence behavior of cracks predicted by this model are in accordance with the experiment observations. Therefore, this study proposed coating optimization methods towards advanced TBCs with prolonged thermal cyclic lifetime.     

Effect of five kinds of pores shape on thermal stress properties of thermal barrier coatings by finite element method

Thermal ablation is a very important technique to characterize the thermal properties of coating systems. On account of the concentration of thermal stress, thermal barrier coatings (TBCs) often break off from the substrate partly or completely during the thermal erosion. In this paper, the thermal erosion simulation of finite element geometric models based on the possible pore shapes were implemented, especially, the influence of pore shapes on the distribution of coating temperature, X component of stress, Y component of stress, XY-shear stress and von-Mises stress were focused on. The effects of the different porosity of square pore coatings on thermal insulation properties and thermal stresses were discussed in term of the simulation results. The simulation results indicate that different shape pores not only affect the thermal stress distribution above the contact area between the bond coating and top coating surface, but also affect the plastic deformation behavior of TBCs. The micromechanism was discussed in details in this study. The computed results verified that, the computational method can successfully predict thermal shear, crack initiation and normal failure mode of the studied TBCs. All the results are in good agreement with the corresponding experimental findings. The failure mechanism factors in this paper are of great importance to explain the failure micro-mechanism of TBCs.     

Thermomechanical simulations of the transient coupled effect of thermal cycling and oxidation on residual stresses in thermal barrier coatings

Failures in thermal barrier coatings (TBCs) are associated with the build-up of residual stresses that result from thermal cycling, growth strain, and stress relaxation associated with high temperatures. To address these highly coupled processes, three aspects were examined. The first was concerned with the effect of thermal cycling and thermal gradients on the resulting residual stress fields. The second with the dynamic growth of thermally grown oxide (TGO) layer using novel finite volume-finite element algorithms. In the third, we examined the effect of stress relaxation on the (TC/TGO) interface. We modelled these highly coupled processes using transient thermomechanical finite element simulations. The temperature profile and state of oxidation variation with time were imported as a predefined field and solved in ANSYS nonlinear platform. Our results revealed that stress relaxation of the TGO stresses at high temperatures leads to a reduction in the TC/TGO interfacial stresses. They also revealed that the use of the isotropic hardening rule limits the increase in plastic deformation of the bond coat (BC), while the use of kinematic hardening rule leads to ratcheting. Furthermore, we highlighted the importance of considering uneven growth of TGO on the resulting stress field.     

Simulation of residual stress in thick thermal barrier coating (TTBC) during thermal shock: A response surface-finite element modeling

The current study demonstrates a well-designed response surface methodology (RSM), based on the generated dataset of finite element method (FEM) to establish an integrated model for simulation of residual stress distribution in a thick thermal barrier coating (TTBC). In this study, typical TTBCs were applied on Hastelloy X Nickel-based superalloy using air plasma spray technique followed by thermal cycling. The recorded stress data of Raman spectroscopy was employed to verify the proposed FEM model. A relatively good agreement was obtained between predicted residual stresses and measured ones. Verified FEM model was used to carry out the parametric studies to evaluate the effects of such various parameters as interface amplitude, wavelength, thermally grown oxide thickness and preheating temperature on the stress distribution in the TTBC during the thermal cycling. The computed data were subsequently used for the development of RSM model. In conclusion, experimentally verified numerical data was used to construct a statistical model based on RSM and successfully used to predict the residual stress distribution field in TTBC during thermal cycling. The obtained results of hybrid FEM- RSM model were in acceptable conformity with Raman spectroscopy measurements.     

Local residual stress evolution of highly irregular thermally grown oxide layer in thermal barrier coatings

Local residual stress in thermally grown oxide (TGO) layers is the primary cause of failure of thermal barrier coating (TBC) systems, especially TBCs prepared by air plasma spray (APS) with a highly irregular TGO. Herein, the distribution of residual stress and the evolution of the irregular TGO layer in APS TBCs were investigated as a function of oxidation time. The stress was measured from cross-sectional micrographs and converted to the actual stress inside the coatings before sectioning. The TGO exhibited significant inhomogeneity at different locations. Stress conversion occurred across the TGO thickness; the layer near the yttria-stabilised zirconia (YSZ) component exhibited compressive stress, whereas that along the bond coat was under tensile stress. The evolution of the compressive stress is also discussed. These analyses may provide a better understanding of the mechanism of APS TBCs.     

Analysis of interfacial crack initiation mechanism of thermal barrier coatings in isothermal oxidation process based on interfacial stress state

In this paper, the interfacial stress state is used to analyze the interfacial crack initiation mechanism of the thermal barrier coatings (TBCs) during isothermal oxidation. The influence of thermal growth stress, initial residual stress, and creep behavior on the stress distribution is considered to have an accurate simulation result. A parameter that integrates the effects of interfacial normal and tangential stress is modified for evaluating interfacial crack initiation. It is found that, in the cooling stage, the interfacial cracks sprout at the top coat (TC)/thermally grown oxide (TGO) interface valley region and the TGO/bond coat (BC) interface peak region, which agrees with the experimental results. Furthermore, the influence of interfacial roughness on crack initiation is investigated. The result shows that different interfacial roughness affects the sprouting region of interfacial cracks and cracks within the TC layer.     

Numerical study of residual stress and crack nucleation in thermal barrier coating system with plane model

The residual stresses could cause extensive damage to thermal barrier coatings and even failure. A finite element model of thermal barrier coating system had been designed to simulate the residual stresses and then to analyze the crack nucleation behavior. The distribution of normal and tangential stress components along top coat (TC) / thermally grown oxide (TGO) and TGO / bond coat (BC) interfaces are shown in this work. It is found that the maximum tensile stress along TC/TGO interface occurs in the peak region during heating-up, and that along TGO/BC interface is also located in the peak region, but during the process of cooling-down. A parameter correlating the normal stress component with corresponding tangential one was used to evaluate the interfacial cracks, indicating that cracks will initiate at the peak-off region of TC/TGO interface in the heating-up phase, but for TGO/BC interface, cracks will initiate at the peak position in the cooling-down phase.     

Structural characteristics and high-temperature oxidation behaviour of nano-HfO2-doped thermal barrier coatings

The uneven growth of thermally grown oxides (TGOs) in thermal barrier coating systems is an important cause of cracking failure at the coating interface in high-temperature environments. The doping of rare earth elements in the bonding layer can effectively inhibit the formation of spinel oxides in the TGO and improve the high-temperature oxidation resistance of the coating. However, a single rare earth element has a limited effect on inhibiting TGO failure. In this study, a NiCoCrAlYHf coating was prepared using a supersonic flame spraying (HVOF) technique. The effects of HfO₂ doping on the high-temperature oxidation behaviour of the coatings and diffusion behaviour of metallic elements in the coatings were investigated at 1100 °C. The results showed that the nano-sized HfO₂ filled the pores between the powder particles and improved the hardness of the coating. During the high-temperature oxidation process, the oxides formed by Hf and Y had a large size and low solubility, which effectively blocked the diffusion of Al. This slowed the generation of spinel oxides, effectively inhibited the growth of the TGO, it inhibits the initiation and propagation of cracks within the coating, reduces damage to the coating from tensile and compressive stresses at the interface, and improved the high-temperature oxidation resistance of the coating.     

Influence of interface morphology on erosion failure of thermal barrier coatings

The thermal barrier coating system (TBCs) has complex structure and works in severe service environment. Erosion is one of the main factors causing the failure of TBCs. In the present study, the particle erosion process of atmospheric plasma sprayed (APS) thermal barrier coatings at elevated temperature was simulated by the finite element method. The effects of interface morphology on the penetration depth, particle ricochet velocity and interface stress state were studied, and the key parameters such as particle size, initial velocity and erosion position were also considered. The cosine curve with constant wavelength and varying amplitude was used to represent different interface roughness of TBCs. The results show that the interface morphology has little effect on the penetration depth of top coat (TC) and the particle ricochet velocity. The influence of particle erosion position related to the interface morphology is obvious. Basically, the greater the interface roughness is, the more violent the interfacial stress fluctuation is. During the erosion process, the stress in the middle of the interface is significantly higher than that at other positions. These results facilitate understanding of the particle erosion failure mechanism of APS TBCs. The influence of interface morphology should be considered in erosion research.     

Isothermal oxidation and TGO growth behaviors of YAG/YSZ double-ceramic-layer thermal barrier coatings

In this study, yttrium aluminum garnet/yttria-stabilized zirconia (YAG/YSZ) double-ceramic-layer thermal barrier coatings (DCL TBC) and yttria-stabilized zirconia (YSZ) single-ceramic-layer thermal barrier coatings (SCL TBC) were deposited by atmosphere plasma spray (APS) on the Inconel 738 alloy substrate, and isothermal oxidation tests were performed to investigate the formation and growth behavior of thermally grown oxide (TGO). Results showed that the Al₂O₃ TGO thickness of both TBC groups increased by increasing the isothermal oxidation time，and then slowly decreased with the appearance and growth of the adverse multilayer structure comprising CoCr₂O₄, (Ni,Co)Al₂O₄, NiCr₂O₄, and NiO mixed oxides. However, since the significant inhibition effect of the YAG coating to oxygen ionic diffusion, the mixed oxides appearance time and TGO growth behaviors were delayed in the DCL TBC. As a result, the TGO thickness of the DCL TBC was always smaller than that of the SCL TBC in the entire oxidation process. And the Al₂O₃ layer thickness proportion in the total TGO of the DCL TBC was greater than or equal to that of the SCL TBC after oxidation for the same period. The results of weight gain showed that compared with the SCL TBC, the parabolic oxidation rate of the DCL TBC was decreased approximately 35%. Consequently, the DCL TBC has better high-temperature oxidation resistance than the SCL TBC.     

Stress-dependent sintering behavior of porous thermal barrier coatings

Thermal barrier coatings (TBCs) are subjected to high temperature and complex stress fields during service in gas turbines. In this process, densification and hardening take place as the result of sintering, which is sensitive to boundary condition/external load. The stress-dependent sintering behaviors of porous TBCs were investigated in this work using a customized four-point bending method. Furthermore, stress-dependent sintering model was developed and implemented in finite element analysis to elucidate sintering mechanisms. It was found that stress gradient induced nonlinear differential sintering behavior, due to the accelerating and retarding effects of compressive and tensile stresses, respectively. In addition, microstructure-mechanical property relation was determined following the exponential law and high-throughput method was proposed for the characterization of stress dependence. The in-depth understanding of stress-dependent sintering behavior could provide guidance to the design and failure analysis of TBCs applied on complex shaped components in the hot section of gas turbines.     

Microstructure and thermal shock resistance of AlBOw- and BNw-whisker-modified thermal barrier coatings

To improve the crack propagation resistance of YSZ thermal barrier coatings during the thermal cycle, three kinds of thermal barrier coatings were prepared by atmospheric plasma spraying: YSZ, AlBOw-modified YSZ and BNW-modified YSZ. SEM, EDS and XRD were used to analyse the morphology, composition and phase composition of the sprayed powder and coating section. The phase structures of the YSZ, YSZ+AlBOw and YSZ+BNw coatings were t' phase. The cross-section of the coating presents a layered structure with pores inside. The porosity values of the YSZ, YSZ+AlBOw and YSZ+BNw coatings are 10.33%, 14.17% and 12.52%, respectively. The thermal shock resistance of three groups of coatings after 5 min at 1000 °C was analysed. The failure behaviour of the coatings after several thermal cycles was studied. The results show that the thermal shock resistance of the coatings with AlBOw is slightly lower than that of the YSZ coatings. The thermal shock resistance of the BNw coatings is 62.2% higher than that of the YSZ coatings. The whisker inhibits the crack propagation and prolongs the life of the coatings via crack deflection, whisker pull-out and whisker bridging.