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.     

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.     

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.     

Simulation of thermal barrier coating spallation induced by the initiation/growth/coalescence of internal crack and interfacial crack based on a real image model

In the furnace cycle test, the growth of oxide film leads to the propagation and coalescence of multiple cracks near the interface, which should be responsible for the spallation of thermal barrier coatings (TBCs). A TBC model with real interface morphology is created, and the near-interface large pore is retained. The purpose of this work is to clarify the mechanism of TBC spallation caused by successive initiation, propagation, and linkage of cracks near the interface during thermal cycle. The dynamic growth of thermally grown oxide (TGO) is carried out by applying a stress-free strain. The crack nucleation and arbitrary path propagation in YSZ and TGO are simulated by the extended finite element method (XFEM). The debonding along the YSZ/TGO/BC interface is evaluated using a surface-based cohesive behavior. The large-scale pore in YSZ near the interface can initiate a new crack. The ceramic crack can propagate to the YSZ/TGO interface, which will accelerate the interfacial damage and debonding. For the TGO/BC interface, the normal compressive stress and small shear stress at the valley hinder the further crack propagation. The growth of YSZ crack and the formation of through-TGO crack are the main causes of TBC delamination. The accelerated BC oxidation increases the lateral growth strain of TGO, which will promote crack propagation and coalescence. The optimization design proposed in this work can provide another option for developing TBC with high durability.     

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.     

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.     

Dynamic crack growth mechanism and lifetime assessment in plasma sprayed thermal barrier system upon temperature cycling

Failure of plasma-sprayed thermal barrier coatings (TBCs) is very complicated upon temperature cycling, therefore, to ascertain the crack propagation behavior is beneficial to understand the failure mechanism and life prediction of TBCs. In this paper, a finite element model is developed by coupling the dynamic growth of thermally grown oxide and dynamic crack propagation to explore the failure of TBCs induced by the instability of the interface between top coat (TC) and bond coat (BC). The thermal cyclic lifetime is deduced by obtaining the thermal cycles corresponding to the occurrence of complete delamination. The influence of the non-uniformity of the interface on thermal cyclic lifetime is quantitatively evaluated. Sensitivity studies including the effects of constituent properties and crack distance to the interface on the thermal cyclic lifetime are further examined. The results show that the incipient cracks usually nucleate above the valley due to the large tensile stress, and the shear stress near the peak plays a very crucial role. The crack growth involves three stages with different fracture dominated-mode. The crack propagation behavior obtained by simulation is in line with that observed by experiments. The TBCs system with a uniform interface exhibits a longer thermal cyclic lifetime compared to the non-uniform interface. Coating optimization methods proposed in this work may provide an alternative option for developing a TBCs system with longer service lifetime.     

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.     

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.     

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.     

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.     

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.     

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.     

Stresses and Microstructural Development of Thermal Barrier Coatings Using AIP/D-gun Two-Step Processing

After depositing a Ni–32Co–20Cr–8Al–0.5Y–1Si–0.03B (wt%) bond coat on a Ni-base superalloy using arc ion plating (AIP), a ceramic top coat with hollow spherical powder of ZrO₂–8 wt%Y₂O₃ (HSP–YSZ) was deposited using detonation gun (D-gun) spraying. Thermal exposure behaviors of thermal barrier coatings (TBCs) were investigated at 1100°C. The thermal growth oxides (TGO) layer thickened and became more undulated during thermal exposure. Yttrium aluminum garnet (YAG) was observed within TGO, which produced thickness imperfections and thus aided to build up out-of-plane stresses. As a result, radial cracks initiated at the defects around TGO imperfections and separation developed through crack nucleation, propagation, and coalescence at the weaker TGO/bond coat interface. With further thermal exposure, coalescence of interfacial separations created a connected crack. The TBC detached and final failure occurred at the TGO/bond coat interface, leading to spallation of TBC when cooling to ambient. The stress distributions in the TGO layer with different thermal exposure times were also measured using luminescence spectroscopy. The stresses were independent of time after a transient period from θ-Al₂O₃ to α-Al₂O₃ scale. It is suggested that the lifetime of AIP/D-gun TBCs with an HSP–YSZ coat is controlled by the initiation and linking of a sub-critical interfacial crack.     

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.     

Comprehensive understanding of horizontal and vertical crack effects on failure mechanism of lamellar structured thermal barrier coatings

The local spalling induced by the propagation and coalescence of cracks in the ceramic layer is the fundamental reason for the thermal barrier coatings (TBCs) failure. To clarify the effects of horizontal and vertical cracks on the coating failure, an integrated model combining dynamic TGO growth and ceramic sintering is developed. The effects of cracks on the normal and shear stress characteristics are analyzed. The driving force and propagation ability of cracks under different configurations are evaluated. The interaction between horizontal and vertical cracks is explored by analyzing the variation of the crack driving force. The results show that TGO growth causes the ratcheting increase of σ₂₂ tensile stress above the valley, and the σ₁₂ shear stress is on both sides of the peak. Ceramic sintering mainly contributes to the ratcheting increase of σ₁₁ tensile stress. There is minimum strain energy when the horizontal crack extends to the peak. The vertical cracks on the surface of the ceramic layer are easier to propagate through the coating than that of other locations. When the horizontal and vertical cracks simultaneously appear near the valley, they can promote the propagation of each other. The present results can offer theoretical support for the design of an advanced TBC system in the future.     

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.     

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.     

Vertical crack distribution effect on the TBC delamination induced by crack growth from the ceramic surface and near the interface

The propagation of vertical crack on the surface of thermal barrier coatings (TBCs) may affect the interface cracking and local spallation. This research aims to establish a TBC model incorporating multiple cracks to comprehensively understand the effects of vertical crack distribution on the coating failure. The continuous TGO growth and ceramic sintering are together introduced in this model. The influence of the vertical crack spacing and non-uniform distribution on the stress state, crack driving force, and dynamic propagation is examined. Moreover, the influence of coating thickness on the crack growth driving is also explored. The results show that large spacing will lead to early crack propagation. The uniform distribution of vertical cracks can delay the spallation. When the spacing is less than 4 times ceramic coat thickness, the cracking driving force will come in a steady-state stage with the increase of vertical crack length. Prefabrication of vertical cracks with spacing less than 0.72 mm on the coating surface can greatly decrease the strain energy. The results in this study will contribute to the construction of an advanced TBC system with long lifetime.