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.     

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.     

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.     

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.     

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.     

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.     

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.     

Stress states in plasma-sprayed thermal barrier coatings upon temperature cycling: Combined effects of creep,plastic deformation,and TGO growth

To ascertain material parameter effects on the stress states is beneficial to comprehend the crack growth behavior and delamination mechanism in thermal barrier coatings (TBCs). In this work, numerical models are established to explore the combined effects of material parameters including creep, plastic deformation, and thermally grown oxide (TGO) growth on the stress states upon temperature cycling. For all layers, thermal-physical properties reliant on temperature are incorporated into the model. The process of bond coat (BC) oxidation, namely TGO growth, is materialized by changing material properties with cycles. Based on the principle of a single variable, the residual stress states are explored using many different material combinations. The results indicate that the tensile stress in the ceramic top coat (TC) decreases with the increase in the TGO lateral strain distribution gradient. Increasing the BC yield strength or decreasing the TGO growth stress can reduce the tensile stress in TC if there is no creep in the model. When BC yield strength is relatively high (≥150 MPa), BC creep will strengthen the TC tensile stress. TGO creep can decrease the tensile stress in TC irrespective of TGO growth stress and BC creep. When TGO creep rate is higher than 10B^tgo, an exceedingly small tensile stress can always be achieved. This work could provide significant theory direction for material selection and composition control towards advanced TBCs with prolonged lifetime.     

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.     

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.     

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.     

Analysis of crack initiation and propagation in Thermal Barrier Coatings using SEM-Based geometrical model with extended finite element method

Thermal Barrier Coatings (TBC) are widely used to protect the metallic components that operate at harsh conditions of elevated temperatures and oxidizing environments. Thermally grown oxide (TGO) causes cracks formation in the top coat (TC) that may lead to spallation failure of TBC. This work investigates effect of pores and TGO thickness on crack initiation and propagation due to thermal mismatch between TBC layers. Image processing is used to convert an SEM image, including pores, into a finite element (FE) model. An FE model using XFEM implemented in ABAQUS was developed to investigate crack initiation and propagation for various TGO thicknesses considering the effect of plastic deformation of BC, TGO and substrate. Results show that presence of pores changes the critical sites for crack initiation from the TC/TGO interface to be around the pores within the TC. Crack initiation temperatures and crack lengths were found to be affected with both TGO thickness and pores.     

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.     

Experimental and numerical life evaluation of TBCs with different BC and diffusion coating under cyclic thermal loading

This paper experimentally and numerically investigates the thermally grown oxide (TGO), lifetime, and stress values in thermal barrier coatings with different bond coat (BC), without top coat (TC), and diffusion coating under cyclic thermal loading. Scanning electron microscope (SEM) analysis shows that the atmospheric plasma spraying (APS) and high-velocity oxygen fuel (HVOF) fabricated sample has the highest and lowest TGO thickness and growth rate, respectively. The new coating with two BCs has a maximum lifetime of 102 cycles. After that, the lifetime of the coatings with HVOF-BC, diffusion coating, and APS-BC reach 84, 56, and 44 cycles, respectively. The diffusion coating does not have much effect on the TGO thickness; however, it delays the Al interdiffusion to the substrate. In the sample without the TC layer, oxygen contact with the BC layer has increased, leading to a rise in the BC oxidation rate. The numerical analysis of the stress values based on SEM images shows that the more intense TGO layer growth in APS coating caused an increase in TC layer stress values. Furthermore, the results show that the new coating with two-layer BC has the lowest stress values. The TC absence causes the loss of compressive stresses caused by TC on TGO and increases the tensile stress values in this layer.     

Effect of oxide growth on the stress development in double-ceramic-layer thermal barrier coatings

A numerical study is conducted to investigate the effect of oxide growth on the stress development within the plasma sprayed double-ceramic-layer thermal barrier coatings. The roles of oxide morphology, growth rate, and oxidation duration are discussed. A two-dimensional periodical unit-cell model is developed, taking into account the different interfacial roughnesses among the coatings layers. Thermal gradient conditions are imposed during the high-temperature period to represent the non-uniform temperature distributions throughout the coatings thickness. It is found that stresses in the regions that close to the interface of the ceramic layers result from the thermal expansion mismatch and the non-uniform temperature field, in which the oxide growth reveals negligible influence on the development of the stresses. The gradually thickening thermally grown oxide (TGO) mainly contributes to the variations of stress and inelastic strain evolutions in its nearby regions. The residual stress fields in the coatings are almost unaffected by the oxide thickness after operating for a sufficiently long time. During long-term operation, the large inelastic deformation is found to be the intrinsic reason responsible for the cracking in the vicinity of TGO.     

Residual Stress Development in Adhesive Joints Subjected to Thermal Cycling

The effect of thermal cycling on the state of residual stress in thermoviscoelastic polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a bimaterial system. Due to the complexity of developing a closed-form solution for a system with time- and temperature-dependent material properties, and time-varying temperature and coupled boundary conditions, numerical techniques were used to acquire approximate solutions.

The results indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Potentially damaging tensile axial and peel stresses develop over time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release rate at the ends of layered or sandwich specimens is shown to increase as axial stress develops. The rate of these changes is dependent upon the thermal cycling profile and the adhesive's thermo-mechancial response. Discussion of the results focuses on the possiblility that the increasing tensile residual stresses induced in an adhesive bond subjected by thermal cycling may lead to damage and debonding, thus reducing bond durability.     

Fatigue life prediction of thermal barrier coatings using a simplified crack growth model

Models that can predict the life of thermal barrier coatings (TBCs) during thermal cycling fatigue (TCF) tests are highly desirable. The present work focuses on developing and validating a simplified model based on the relation between the energy release rate and the TCF cycles to failure. The model accounts for stresses due to thermal mismatch, influence of sintering, and the growth of TGO (alumina and other non-protective oxides). The experimental investigation of TBCs included; 1) TCF tests at maximum temperatures of 1050 °C, 1100 °C, 1150 °C and a minimum temperature of 100 °C with 1 h and 5 h (1100 °C) hold times. 2) Isothermal oxidation tests at 900, 1000 and 1100 °C for times up to 8000 h. The model was calibrated and validated with the experimental results. It has been shown that the model is able to predict the TCF life and effect of hold time with good accuracy.     

An innovative model coupling TGO growth and crack propagation for the failure assessment of lamellar structured thermal barrier coatings

The failure of plasma-sprayed thermal barrier coating (TBC) is often caused by the coating spallation due to crack propagation. In this study, a new model with stacking lamellae is developed based on the cross-section micrograph to explore crack propagation behavior within the ceramic top coat (TC) during isothermal cycling. The dynamic growth process of thermally grown oxide (TGO) is simulated via material properties change step by step. The stress profiles in the lamellar model are first evaluated, and the pore and lamellar interface crack effects on the stress state are further explored. Then, the successive crack growth, linkage, and ultimate coating spallation process is simulated. The results show that the stress intensity in TC enhances with thermal cycling. Large stress concentration always occurs near the pore and lamellar interface crack, which can result in the incipient crack growth. Moreover, the lamellar interface crack also changes the stress distribution within the TC and at the TC/bond coat interface. The multiple crack propagation upon temperature cycling is explored, and the possible coalescence mechanism is proposed. The lamellar crack steadily propagates at the early stage. The crack length sharply increases before the occurrence of coating spallation. The simulated coat spalling path is in line with the experimental result. Therefore, the new lamellar model developed in this work is beneficial to further reveal coating failure mechanism and predict coating lifetime.