Effects of TGO growth on the stress distribution and evolution of three-dimensional cylindrical thermal barrier coatings based on finite element simulations

Based on the ultrasonic C-scan results of 8YSZ coatings after thermal cycles, three-dimensional cylindrical numerical simulations of the physical geometry model of the thermal barrier coating (TBC) sinusoidal surfaces were conducted with finite elements to estimate the stress distribution and evolution law of the top coat (TC)/bond coat (BC) interface, including the centre and edge of the specimen affected by the dynamic growth of the thermally grown oxide (TGO). The results show that when a layer of TGO is grown on the TC/BC interface, compressive stress is uniformly distributed on the TGO interface, and the stress value decreases as a function of the TGO layer thickness. When the thickness of the TGO exceeds a certain value, the compressive stress of all parts of the interface gradually changes to tensile stress; meanwhile, the edges of the model affected by the crest and trough effects of the wave are reflected in the radial and circumferential directions, especially along the axial direction, with alternating concentrated tensile and compressive stresses. TGO growth imposes a minor influence on the magnitude and distributions of the radial and circumferential stresses at the BC interface. The linear elasticity, creep, fatigue, and stress accumulation effects of each layer of TBCs in each thermal cycle were fully considered in this model. The model not only interprets the crest and trough effects of the TC/BC surface interface during the growth of TGO, but also interprets the effects of the core and edge of the cylindrical model, further revealing the reason for which the core and edge of the TBC will most likely form cracks.     

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.     

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.     

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.     

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.     

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.     

Influences of interface morphology and thermally grown oxide thickness on residual stress distribution in thermal barrier coating system

Calculation of residual stress with finite element method is a basic work in failure mechanism investigation in thermal barrier coating (TBC) system because the residual stress is main driving force for crack nucleation and propagation. In this work, a complicated cosine curve with gradually increasing amplitude was used to simulate interface morphologies between layers so as to study the residual stress behavior during the cooling process in air plasma spraying TBC system by finite element method. The substrate, thermally grown oxide (TGO) and top coat (TC) are considered to be elastic and bond coat (BC) elastic-perfectly plastic. The material properties are all temperature dependent. The stress result comparison between models with and without substrate shows the effect of substrate on the residual stress distribution around layers interfaces should not be ignored as the substrate influences the value of normal residual stress as well as the stress distribution along undulating interfaces. Then the model with substrate was used to study the residual stress evolution along interfaces during cooling down from the temperature of 1000 °C to room temperature. The influences of the thickness of TGO and the amplitude and wavelength of interface on the residual stress distributions near interfaces were considered. The results show that these influences are very complicated. Meanwhile, it's found that the hybrid roughness parameter containing information for height and spacing is more suitable to describe the interface complicacy. The results facilitate understanding the failure mechanism relevant to interface morphology and TGO thickness.     

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.     

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.     

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.     

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.     

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.     

Non-destructive evaluation of thermally grown oxides in thermal barrier coatings using impedance spectroscopy

The growth of thermally grown oxide (TGO) layers in thermal barrier coatings (TBCs) due to the oxidation of the bondcoat alloy is a critical factor affecting the durability of TBCs. In the present study, diverse TBC specimens were subjected to long-term oxidation at various temperatures. The TGO growth mechanism was investigated according to cross-sectional images of the oxidized specimens. Impedance spectroscopy (IS) was performed to measure the electrical properties of the integrated TBCs non-destructively. Considering the influence of the TGO composition, the derived TGO electrical capacitance was found to have a good correspondence to the observed TGO thickness over a wide range 0–18.3 μm, regardless of the diverse specimens and oxidation conditions. The error was less than ±2.0 μm. With a certain design of the electrode size, IS is generalized and is recommended as an accurate and practical non-destructive evaluation method for the determination of TGO thickness within a very wide range in TBC systems under real operating conditions.     

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.     

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.     

Research progress on hafnium-based thermal barrier coatings materials

Thermal barrier coatings (TBC) are important materials applied to hot part components of aero-engines in order to improve their service temperature. Increasing inlet temperature is an important factor to achieve elevated thrust-to-weight ratio and high heat engine efficiency. In recent years, traditional TBC materials have gradually reached their operating limits due to the increase in turbine operating temperature. Hafnium-based materials become promising new candidates for TBC because of the similar structure, higher temperature phase stability and lower thermal conductivity compared to traditional zirconium-based materials. In this review, recent progresses in the research and development for hafnium-based TBC materials are summarized. The phase stability, thermal and mechanical properties of rare-earth (RE)-doped HfO₂ and RE hafnate materials are introduced. RE-doped HfO₂ has good thermal properties and phase stability at high temperatures whereas relatively low fracture toughness. The RE hafnates possess the advantages of a higher phase transition temperature, lower thermal conductivity and superior fracture toughness than RE zirconates. However, the thermal expansion coefficients of most RE hafnates are quite different from the alloy matrix. Finally, further research directions for hafnium-based TBC materials are prospected in this study.     

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.     

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.     

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.     

Effect of the thermally grown oxide and interfacial roughness on stress distribution in environmental barrier coatings

To clarify the role of interface morphology and thermally grown oxide (TGO) in the failure of environmental barrier coatings (EBCs). In this study, the effect of chemical expansion on free energy was considered based on the continuous thermodynamic framework. The effects of roughness and TGO growth on the stress distribution of EBCs were investigated. The results showed that the stress coupling effect led to the inhomogeneous growth of TGO by affecting the gas diffusion and gas inflow rate. The TGO thickness at the peak increased with increasing roughness, and the TGO thickness at the valley and the middle position decreased with increasing roughness. The y-direction at the TGO/EBC valley and the TGO/BC peak under tensile stress increased with the TGO thickness and roughness and may be the first to fail in delamination. The calculation results of the model can provide a theoretical basis for the coating design and manufacturing process.