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.     

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.     

The sintering behavior of plasma-sprayed YSZ coating over the delamination crack in low temperature environment

The sintering behavior of plasma-sprayed yttria-stabilized zirconia (YSZ) coating over the delamination crack and its influence on YSZ cracking were investigated via gradient thermal cycling test and finite element model (FEM). The gradient thermal cycling test was performed at a peak surface temperature of 1150 °C with a duration of 240 s for each cycle. A three-dimensional model including delamination cracks with different lengths was employed to elaborate the temperature evolution characteristics in YSZ coating over the delamination cracks. The temperature over the delamination crack increases linearly with the crack propagation, which continuously promotes the sintering of YSZ coating in the region. As a result, the YSZ coating over the delamination crack sinters dramatically despite of the low temperature exposure. Meanwhile, the temperature distribution difference in YSZ coating induces an nonuniform sintering along both free surface and thickness of YSZ coating. Correspondingly, the maximum vertical crack driving force locates at the YSZ free surface over the delamination crack center, which makes the vertical cracks generate in this region and propagate to the interface of YSZ /bond coat with YSZ further sintering. The vertical crack promotes the delamination crack propagation via accelerating the oxidation velocity of the bond coat. The influence of temperature rise on delamination crack propagation can be divided into two stages: the little contribution stage and the promotion stage. For the actual engine exposure to low temperature, the study of phase transformation of YSZ over the delamination crack is indeed needed because of an extended remarkable temperature rise period.     

A constitutive model for the sintering of suspension plasma-sprayed thermal barrier coating with vertical cracks

The degradation of mechanical properties due to sintering is one of the major issues during high temperature service of thermal barrier coating system for advanced gas turbines. In this study, a constitutive model was developed by the variational principle, based on the experimentally observed microstructure features of suspension plasma-sprayed thermal barrier coatings. The constitutive model was further implemented in finite element analysis software, in order to investigate the effect of vertical cracks. The evolution of microstructure during sintering, coating shrinkage and mechanical degradation were predicted. The numerical predictions of Young's modulus were generally in agreement with experimental results. Furthermore, the effect of vertical cracks on the strain tolerance and sintering resistance were discussed. It was confirmed that the introduction of vertical cracks contributed to the improvement of both properties.     

Crack Growth and Damage in Constrained Sintering Films

The constrained sintering of films on substrates leads to a reduction in densification rate and may lead to processing flaws. This paper reports on a study of damage and cracking in sintering films, with particular emphasis on the growth of preexisting cracks. Experiments have been conducted with glass and polycrystalline Al₂O₃ films on various substrates. The effect of important variables (viz., film thickness, crack length, and friction with the substrate) on crack growth is reported. The experiments with glass films show that cracking occurs above a critical film thickness which is in good quantitative agreement with a recent analysis for this problem. In the case of Al₂O₃ films, we observe a diffuse damage zone ahead of cracks. Crack growth occurs by the coalescence of microcracks with each other and with the main crack. Some possible reasons for this difference between the glass and Al₂O₃ films are presented. As a model for diffuse damage, the stability of a sintering film under spatial variations in constitutive parameters is analyzed. It is shown that the film is unstable to small perturbations only in the early stages of densification, and that for viscous sintering the films are usually kinetically stable.     

Crack formation in ceramic films used in solid oxide fuel cells

The manufacture of solid oxide fuel cells (SOFCs) involves fabrication of a multilayer ceramic structure, for which constrained sintering is a key processing step in many cases. Defects are often observed in the sintered structure, but their formation during sintering is not well understood. In this work, various ceramic films were fabricated by screen printing and a variety of defects observed. Some films showed “mud-cracking” defects, whereas others presented distributed large pores. “Mud cracking” defects were found to originate from a network of fine cracks present in the green film and formed during drying and binder burn-out. Control of these early stages is essential for producing crack-free films. In order to investigate how defects evolve during sintering, artificial cracks were introduced in the green films using indentation. It was observed that crack opening always increased during constrained sintering. In contrast, similar initial cracks could be closed and healed during co-sintering.     

Evolution of Defects During Sintering: Discrete Element Simulations

We use discrete element method (DEM) simulations to study the evolution of defects during sintering. In DEM, the particulate nature of the sintering powder is taken explicitly into account because each particle is modeled as a discrete entity interacting with its neighbors. This allows to treat naturally the gain or the loss of contacts between particles, and to explicitly take particle rearrangement into account. These effects are particularly important when looking for the nucleation, growth or healing of local heterogeneities such as defects. We first study the evolution of a crack (generated, e.g., during ejection or drying processes) when no geometrical constraint is imposed. We then investigate how constrained sintering between two parallel planes may lead to crack initiation and growth. We show that the extent of interparticle rearrangement plays a major role in the evolution of the crack under such conditions. The main conclusion of these simulations is that some geometrical constraint is necessary for a defect to grow into a crack and that the presence of an initial defect is not a necessary condition to initiate cracks.     

Cracking and shape deformation of cylindrical cavities during constrained sintering

During constrained sintering of thin films, in which a cylindrical cavity with axis perpendicular to the substrate has been introduced before sintering, cracks emerge that initiate at the cavity surface. By combining experiments with continuum mechanical and particle based simulations, the fundamental causes and effects of this kind of crack formation are identified. A stress analysis performed by finite element (FEM) simulations matches with the cracking behavior observed in experiments. A comparison of discrete element (DEM) results with experiments shows the applicability of this simulation method to describe the effect of cross-sectional stripe dimensions and cavity diameters on the cracking behavior. Moreover, DEM simulations reveal that hair-line cracks in narrow stripe samples formed during pre-sintering manufacturing steps might be a dominant cause for the observed crack damage in such systems.     

Crack initiation,propagation, and arrest in sintering powder aggregates

Cracking during sintering is a common problem in powder processing and is usually caused by constraint that prevents the sintering material from shrinking in one or more directions. Different factors influence sintering-induced cracking, including temperature schedule, packing density, and specimen geometry. Here we use the discrete element method to directly observe the stress distribution and sinter-cracking behavior in edge notched panels sintered under a uniaxial restraint. This geometry allows an easy comparison with traditional fracture mechanics parameters, facilitating analysis of sinter-cracking behavior. We find that cracking caused by self-stress during sintering resembles the growth of creep cracks in fully dense materials. By deriving the constrained densification rate from the appropriate constitutive equations, we discover that linear shrinkage transverse to the loading axis is accelerated by a contribution from the effective Poisson's ratio of a sintering solid. Simulation of different notch geometries and initial relative densities reveals conditions that favor densification and minimize crack growth, alluding to design methods for avoiding cracking in actual sintering processes. We combine the far-field stress and crack length to compute the net section stress, finding that it characterizes the stress profile between the notches and correlates with the sinter-crack growth rate, demonstrating its potential to quantitatively describe sinter-cracking.     

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.     

Bimaterial Composites via Colloidal Rolling Techniques: II, Sintering Behavior and Thermal Stresses

Shrinkage behavior and crack formation during firing have been investigated for Al₂O₃/Ce-TZP composites that have been fabricated by colloidal rolling and folding. These composites show improved sinterability and sinter isotropically after repeated rolling. Interface instability in rolling creates corrugated interfaces with large layer waviness; therefore, rolling can substantially alleviate the in-plane sintering constraints, which leads to improved sinterability. A loss of sintering anisotropy also is observed and is directly correlated to the microstructure instability, which is coincident with the laminate-cellular transition. Sintering cracks during heating and thermal cracks during cooling both are limited to the thick Ce-TZP layers in the composites. The critical layer thickness and the normalized crack spacing of the thermal cracks follow the predicted behavior of elasticity theory. Thus, crack-free, high-density Al₂O₃/Ce-TZP composites with either a laminate or cellular microstructure can be obtained, with a layer thickness of 4-60 µm, via pressureless sintering.     

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.     

Crack development behavior in thermally sprayed anti-oxidation coating under repeated thermal-oxygen coupling environment

The crack development behavior in thermally sprayed anti-oxidation coating was investigated after long-term and short-term oxidation with repeated thermal cycles from 1500 °C to room temperature. According to the distribution characteristics, the formed cracks can be divided into three types: type-A cracks with multi-directional features, type-B cracks originated from the inner interface bulges and type-C cracks initiating at surface oxide layer. Based on the analytical math models (blunt crack model and interface roughness model), the maximum stress at different positions was evaluated from the perspective of inner interface roughness, uneven oxide film, original microcracks and gathering micropores. The original vertical type-A cracks are most dangerous due to the highest crack tip stress. However, the micropore distribution or appropriate interface may promote transformation of vertical type-A cracks to less dangerous horizontal type-A cracks. This study on crack development behavior provides a fundamental insight and further avenues to optimize the composition and structure of thermally sprayed ceramic coating.     

Modeling and simulation of thermal fatigue crack in EB-PVD TBCs under non-uniform temperature

Demand for enhanced jet engine efficiencies has led to a significant increase in the combustion temperature. Thus protecting components against the combustion products is necessary and is possible by using thermal barrier coatings (TBCs). In this research, thermal fatigue and creep interaction are studied via analytical and numerical finite element methods. Thermal stress and crack propagation analyses in the ceramic top coat are carried out based on plane stress condition and under inhomogeneous temperature distribution across the layers. The crack is assumed as a penny-shaped crack in both vertical and inclined growth directions. The study proposed that the creep-plasticity results in thermal stress alleviation and the tensile stress transforms into a compressive stress of − 200 MPa in forwarding cycles that will induce crack closure. In addition, the results confirmed that vertical cracks grow much faster than oblique ones due to single mode crack propagation and about 0.14 MPa√m greater values in stress intensity factor. The modeling and simulation results match together, and the obtained crack behavior is in compliance with other researcher's output.     

Experimental and computational study on sintering of ceramic coating layers with complex porous structures

This study investigated the sintering behavior of an yttria-stabilized zirconia coating for thermal barrier coatings (TBCs) with a complicated porous structure via both experiment and simulation using the finite element method for samples with only a coating (free coating) and samples with coating on a substrate (constrained coating). Sintering and grain growth proceeded from the bottom of the coating, and the coating bent convex upward in the free coating. In the constrained coating, sintering and grain growth proceeded in a manner similar to the free coating; however, the degrees of sintering and grain growth were small. Furthermore, sintering and grain growth were delayed because of substrate constraints. As a simulation result, the free coating was bent in a manner similar to the experiment. The experimental results could be reproduced in terms of time dependency and temperature dependency. The decrease in the porosity of the constrained coating was delayed compared with that in the free coating because of substrate constraints. This simulation result was able to reproduce the experimental results. Thus, the sintering behavior for the complex porous structures of TBCs can be predicted by experimental research and simulation, which could aid in the development of a prediction technology for the delamination of coatings (TBC lifetime).     

Determinations of Residual Thermal Stresses in a SiC-Al2O3 Composite Using Neutron Diffraction

Residual thermal stresses and strains, developed during cooling of a SiC whisker-Al₂O₃ composite, were determined by an experimental neutron diffraction technique and the results were compared with analytically determined values. High compressive residual thermal stresses were generated in the whiskers during cooldown after sintering. Analytical estimates of the residual stresses were obtained by using two self-consistent models: (1) a plane strain composite cylinder model and (2) Eshelby's ellipsoidal inclusion theory. The two models gave almost identical estimates of the stresses and strains in the whiskers. The interpretation of the measured strains in the whiskers by neutron diffraction had some uncertainty because of the lack of a clearly defined crystal structure of SiC.     

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.     

Fatigue crack growth in fiber reinforced plastics

Crack extension during fatigue loading is one of the primary causes of failure in engineering materials. While the fatigue crack resistance of homogeneous and even adhesive systems has received detailed study and characterization, relatively few and scattered results are available for fiber composites. One difficulty with obtaining such data for composites is their tendency to develop complex patterns of intra- and interlaminar damage which expand in a stable manner during fatigue. Such damage usually does not severely reduce the load carrying capacity of a structure but the complexity of the damage geometry has so far frustrated efforts to apply any unifying theories of growth. Measurement of the rate of macroscopic crack growth, through thickness crack extension, has been possible for certain composites and crack direction where the stable damage is constrained. These include cracks in 0°/90° laminates, woven fabric laminates, chopped strand mat laminates, sheet molding (SMC) materials, and short fiber reinforced thermoplastics. Macroscopic interlaminar cracks in continuous fiber systems have also received some recent attention. Fatigue crack growth in glass fiber composites for which most data are available, involves significant contributions from both static and cyclic load effects. A simple model for predicting fatigue crack growth rates from traditional S-N curve and fracture toughness data has proven useful for certain well behaved systems. Limited study has also been made of the effects of moisture and salt water on the fatigue crack growth rate.     

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.     

Thermal shock resistance of air plasma sprayed thermal barrier coatings

The spallation resistance of an air plasma sprayed (APS) thermal barrier coating (TBC) to cool-down/reheat is evaluated for a pre-existing delamination crack. The delamination emanates from a vertical crack through the coating and resides at the interface between coating and underlying thermally grown oxide layer (TGO). The coating progressively sinters during engine operation, and this leads to a depth-dependent increase in modulus. Following high temperature exposure, the coating is subjected to a cooling/reheating cycle representative of engine shut-down and start-up. The interfacial stress intensity factors are calculated for the delamination crack over this thermal cycle and are compared with the mode-dependent fracture toughness of the interface between sintered APS and TGO. The study reveals the role played by microstructural evolution during sintering in dictating the spallation life of the thermal barrier coating, and also describes a test method for the measurement of delamination toughness of a thin coating.