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.     

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.     

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.     

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.     

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.     

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.     

Stress states and crack behavior in plasma sprayed TBCs based on a novel lamellar structure model with real interface morphology

To ascertain the crack growth behavior and coalescence mechanism in thermal barrier coatings (TBCs) is beneficial for understanding the failure of TBCs and proposing the probable optimization methods. In this work, a novel lamellar structure model with real interface morphology is developed to explore the crack growth behavior and the failure mechanism of TBCs during thermal cycling. Three typical defects which include pore, inter-splat crack, and intra-splat are incorporated in the model. To simulate the oxidation process of the bond coat (BC) realistically, The oxidation growth process is simulated via changing the BC properties to thermally grown oxide (TGO) properties layer by layer. The effects of the lateral growth strain distribution through TGO thickness on the stress states are executed. Moreover, the influences of BC creep on the crack growth and coating lifetime are further elaborated. The results show that the larger the lateral growth strain gradient, the smaller the residual tensile stress. The irregular interface morphology results in the redistribution of residual stresses. Although the pores and cracks can alleviate the tensile stress near the valley, large stress concentration will occur near them. At the early phase of thermal cycling, the cracks grow steadily. After more cycles, the cracks propagate rapidly and merge with others. The simulated delamination path is in agreement with the experiment results. Not only does BC creep change the crack coalescence mechanism, it also decreases the thermal cyclic lifetime of TBCs. The coating optimization method proposed in this study provides another option for developing advanced TBCs with longer lifetime.     

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.     

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.     

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.     

Effect of substrate curvature on residual stresses and failure modes of an air plasma sprayed thermal barrier coating system

A set of aerofoil shaped air plasma sprayed thermal barrier coated (APS-TBC) specimens were adopted in this paper to investigate the stress distributions in the ceramic top coat (TC) and the thermally grown oxide (TGO), the mechanism of local crack generation and propagation at the TC/BC (bond coat) interface. The failure mode of the TBC system, the distribution of asperities at TC/BC interface, thickness of the TC and BC, and the TC microstructure were found to be influenced by substrate curvature. Residual stress was therefore measured across the thickness of the TC, along the undulating TGO and mapped at locations of asperities where failure tended to occur to interpret the initiation of local failure. The role of the TGO was investigated via its chemical bonding with the TC and the decohesion occurring at the TGO/BC interface. The crack propagation at the interface has been discussed with respect to the macro-failure of the TBC system.     

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.     

Fabrication of ceramic sealing coatings for shell bionic structures and their failure mechanism during thermal cycling

The porous ceramic coating as a "brick" layer sprayed by air plasma spraying(APS) and MK resin as a "mud" layer prepared by a high viscosity spray gun were characterized and tested. Three specifications of the "brick-mud" layered ceramic sealing coating were fabricated through the cyclic and orderly deposition of the "brick" layer and "mud" layer, and the thermal cycling performance and failure mechanism of the three new coatings were studied. The results showed that the agglomerated Y₂O₃ partially stabilized ZrO₂ (YSZ) particles had porous spherical structures and good sprayability, and the content of the YSZ phase in the prepared "brick" layer was 54.2%. The "mud" layer had good phase stability and was amorphous SiO₂ at and below 1100 °C. The fracture toughness of the pure YSZ coating was 2.295 ± 0.135 MPa?m^0.5, and which of the “mud” layer was reduced by 72.3%. The thermal cycling life of the conventional coating was only 67.3 times, which of A1, A2 and A3 coatings with 2, 3 and 6 "mud" layers were increased by 32.4%, 124.8% and 88.3%, respectively. In the thermal cycling process, the "weak" layer in the "brick-mud" layered coating led to the redistribution of internal stress and reduced the stress concentration in the top coating (TC)/TGO interface. Moreover, the initiation of microcracks in the "weak" layer, along with the "crack branching" effect and the "crack deflection" effect during the crack propagation process, could consume partial internal stress. Thus, the crack growth rates in the TC coating/TGO interface of the A1, A2 and A3coatings were lower than that of the conventional coating due to the above stress release mechanisms. In addition, the thermal cycling lives of the three new coatings with 2, 3 and 6 "mud" layers were improved to different degrees because of different stress effects.     

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.     

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.     

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 segmented cracks on TGO growth and life of thick thermal barrier coating under isothermal oxidation conditions

This paper is devoted to a comparative study on the isothermal oxidation of thick thermal barrier coating (TTBC) with and without segmented cracks produced by atmospheric plasma spray (APS) process. Accordingly, the growth of thermally grown oxide (TGO) and its effect on the degradation of the coating were investigated. Thick top coat in both segmented crack and conventional thick TBC reduced the double layered TGO growth rate slightly. The segmented crack thick TBC demonstrated longer isothermal oxidation life in comparison with that of the conventional thick TBC at 1100 °C. The dominant failure mechanism was spallation due to lateral cracking within the TGO and/or within TBC near the TGO layer, called mixed failure. Stress, and consequently strain, induced on the TTBC due to progressive TGO growth, seems to be primarily responsible for the crack initiation and propagation leading to the coating failure. Increment of elastic energy stored within the top coat due to the increasing of TGO thickness, finally causes thick thermal barrier coating failure in high temperature isothermal oxidation.     

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.     

Solution precursor thermal spraying of gadolinium zirconate for thermal barrier coating

Gadolinium zirconate (GZ) is an attractive material for thermal barrier coatings (TBCs). However, a single layer GZ coating has poor thermal cycling life compared to Yttria Stabilized Zirconia (YSZ). In this study, Solution Precursor High Velocity Oxy-Fuel (SP-HVOF) thermal spray was used to produce a double layer GZ/YSZ TBC and compared the thermal cycling performance with the single layer YSZ TBC. The temperature behaviour of the solution precursor GZ was studied, and single splat tests were carried out to obtain an optimised spray parameter. In thermal cycling tests, the single-layer YSZ reached 20 % failure at 85 ± 5 cycles, whereas the double-layer GZ/YSZ was at 70 ± 15 cycles. The single-layer failed at the topcoat/TGO interface, whereas the double-layer failed at GZ/YSZ interface and topcoat/TGO interface. Moreover, Gd diffusion occurred near the GZ/YSZ interface, resulting in porosities in the GZ layer.