Quantitative assessment of the surface crack density in thermal barrier coatings

In this paper, a modified shear-lag model is developed to calculate the surface crack density in thermal barrier coatings（TBCs）. The mechanical properties of TBCs are also measured to quantitatively assess their surface crack density. Acoustic emission（AE） and digital image correlation methods are applied to monitor the surface cracking in TBCs under tensile loading. The results show that the calculated surface crack density from the modified model is in agreement with that obtained from experiments. The surface cracking process of TBCs can be discriminated by their AE characteristics and strain evolution. Based on the correlation of energy released from cracking and its corresponding AE signals, a linear relationship is built up between the surface crack density and AE parameters, with the slope being dependent on the mechanical properties of TBCs.     

Reliability assessment on interfacial failure of thermal barrier coatings

Thermal barrier coatings (TBCs) usually exhibit an uncertain lifetime owing to their scattering mechanical properties and severe service conditions. To consider these uncertainties, a reliability assessment method is proposed based on failure probability analysis. First, a limit state equa-tion is established to demarcate the boundary between failure and safe regions, and then the failure probability is calculated by the integration of a probability density function in the failure area according to the first-or second-order moment. It is shown that the parameters related to interfacial failure follow a Weibull distribution in two types of TBC. The inter-facial failure of TBCs is significantly affected by the thermal mismatch of material properties and the temperature drop in service.     

Critical cooling rates to avoid transient-driven cracking in thermal barrier coating (TBC) systems

This paper presents critical cooling rates to avoid cracking in thermal barrier coatings (TBCs) driven by thermal transients. A complete thermomechanical model is presented for multilayers; it determines the history of temperature, deformation and stress distributions in the layers, as well as the steady-state energy release rate (ERR) for delamination for all possible crack locations. The model is used to analyze bilayers over a broad range of properties and cooling rates; critical cooling rates are identified that distinguish scenarios in which the transient delamination driving force is higher than that associated with the fully cooled state. Implications for coating the durability are discussed.     

Acoustic emission monitoring of crack propagation in additively manufactured and conventional titanium components

Additive manufacturing (AM) is a novel and innovative production technology that can produce complex and lightweight engineering products. In AM components, as in all engineering materials, fatigue is considered as one of the principle causes of unexpected failure. In order to detect, localise and characterise cracks in various material components and metals, acoustic emission (AE) is used as a non-destructive monitoring technique. One of the main advantages of AE is that it can be also used for dynamic damage characterisation and specifically for crack propagation monitoring. In this research, we use AE to monitor the fatigue crack growth behaviour of Ti6Al4V components under four-point bending. The samples were produced by means of AM as well as conventional material. Notched and unnotched specimens were investigated with respect to the crack severity and crack detection using AE. The main AE signal parameters –such as cumulative events, hits, duration, average frequency and rise time– were evaluated and indicate sensitivity to damage propagation in order to lead to a warning against the final fracture occurrence. This is the first time that AE is applied in AM components under fatigue.     

Fracture mechanical damage modelling of thermal barrier coatings

Summary The problem of how to avoid damage of TBCs has been approached by calculating the energy release rate of two crack configurations under thermal loading. This has been done for the limiting cases of perfect and lacking heat transfer across the crack. Suitable grading of TBCs is a means of suppressing the tendency to delamination and damage by both decreasing the energy release rate G and increasing its critical value G _c . TBCs can be graded such that delamination cracks would be deflected into depth where G _c is sufficiently high to avoid crack propagation. Received 31 March 1999; accepted for publication 10 June 1999     

Acoustic emission monitoring of carbon-fiber-reinforced-polymer bridge stay cables in large-scale testing

This paper presents acoustic emission (AE) monitoring of damage initiation and progression in carbon-fiber-reinforced-polymer (CFRP) stay cables subject to largescale laboratory tests. The research is part of the University of California, San Diego (UCSD), larger project on the design and construction of a new cable-stayed bridge made of advanced composites. No previous use of AE on large-size CFRP stay cables appears in the literature. Three types of cables of potential use in the UCSD composite bridge were tested at lengths ranging from 5500 mm to 5870 mm. The AE events were monitored to detect damage and provide a qualitative correlation with the type of structural failure. The tests allowed a comparative characterization of the failure behavior of the three types of cables under investigation. An additional study was performed to characterize acoustic attenuation and dispersion phenomena that are relevant to AE testing of largescale CFRP cables. It is shown that despite their large size, these cables are excellent acoustic wave guides exhibiting very low attenuation. Finally, this study shows promising results for an effective use of in situ AE for health monitoring of these structural components in service.     

Multiple cracking of elastic coatings under transient thermal load

A periodic array of cracks in an elastic coating bonded to a homogeneous substrate is considered. The medium is subjected to mechanical loads and/or thermal loads. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. In addition to the time-varying stress intensity factors and stresses for various parameters of the problem, the effect of periodic cracking on the relaxation of the transient stress on the coating surface is discussed. Solution techniques for a single elastic layer and an elastic coating bonded to an infinite substrate are given. It is found that, if the crack density attains a saturation value, the transient thermal stress in the medium could be released significantly, suggesting that further cracking is difficult.     

Use of equivalent body forces for acoustic emission from a crack in a plate

A method to determine acoustic emission of surface waves from a crack near the free edge of a plate, is presented, in terms of the function f(t), which defines the time dependence of the crack opening process, the crack opening volume per unit thickness of the plate, and the elastic constants of the plate. The determination of the time-varying displacement is based on the use of equivalent body forces, which are shown to be two double forces. The acoustic emission of the crack, or the equivalent radiation from the double forces, has been obtained by a novel use of the elastodynamic reciprocity theorem. It is of interest that the normal surface-wave displacement at a position x₀ of the free edge comes out as depending on df/dt evaluated at x₀ for t > x₀/c_R, where c_R is the velocity of surface waves on the free edge.     

A multi-scale constitutive model for the sintering of an air-plasma-sprayed thermal barrier coating, and its response under hot isostatic pressing

A micromechanical model is developed for the sintering of an air-plasma-sprayed, thermal barrier coating, and is used to make predictions of microstructure evolution under free sintering and under hot isostatic pressing. It is assumed that the splats of the coating are separated by penny-shaped cracks; the faces of these cracks progressively sinter together at contacting asperities, initially by the mechanism of plastic yield and subsequently by interfacial diffusion. Diffusion is driven by the reduction in interfacial energy at the developing contacts of the cracks and also by the local contact stress at asperities. The contact stress arises from the remote applied stress and from mechanical wedging of the rough crack surfaces. Sintering of the cracks leads to an elevation in both the macroscopic Young's modulus and thermal conductivity of the coating, and thereby leads to a degradation in thermal performance and durability. An assessment is made of the relative roles of surface energy, applied stress and crack face roughness upon the sintering response and upon the evolution of the pertinent mechanical and physical properties. The evolution in microstructure is predicted for free sintering and for hot isostatic pressing in order to provide guidance for experimental validation of the micromechanical model.     

Residual stress evolution regularity in thermal barrier coatings under thermal shock loading

Residual stress evolution regularity in thermal barrier ceramic coatings (TBCs) under different cycles of thermal shock loading of 1100°C was investigated by the microscopic digital image correlation (DIC) and micro-Raman spectroscopy, respectively. The obtained results showed that, as the cycle number of the thermal shock loading increases, the evolution of the residual stress undergoes three distinct stages: a sharp increase, a gradual change, and a reduction. The extension stress near the TBC surface is fast transformed to compressive one through just one thermal cycle. After different thermal shock cycles with peak temperature of 1100°C, phase transformation in TBC does not happen, whereas the generation, development, evolution of the thermally grown oxide (TGO) layer and micro-cracks are the main reasons causing the evolution regularity of the residual stress.     

A methodology to model the complex morphology of rough interfaces

A methodology is proposed to model the complex morphology of rough interfaces using Fourier techniques and image analysis. It allows an optimal representation of a rough interface so as to enable a realistic calculation of the local stress and strain fields in the interface vicinity using finite element techniques. The methodology is illustrated through a sensitivity analysis carried out on a thermal barrier coating system. Typical bi-material interfaces with different levels of morphological complexity are described in 2D and 3D using both periodic (sinusoidal) and Fourier functions. The results are discussed in terms of their relative accuracy.     

热障涂层弹性模量和残余应力测试研究

采用数字图像相关法实验研究了热喷涂制作的热障涂层的弹性模量和残余应力。首先,采用三点弯测试方法对热障涂层试件进行加载,并利用二维数字图像相关方法对热障涂层试件加装过程中的弯曲变形进行了精确的测量,进而获得了热障涂层在受拉和受压两种状态下的弹性模量,结果表明,受拉时热障涂层试件陶瓷层的弹性模量为31GPa,而受压时其弹性模量为34GPa。其次,基于内力平衡,推导了考虑曲率变化的涂层残余应力计算公式;利用三维数字图像相关法测量了喷涂前后基体曲率的变化,进而获得了涂层残余应力的大小,结果表明,热喷涂后的热障涂层残余应力为压应力,大小为-86^-70MPa。     

Buckling delamination in compressed multilayers on curved substrates with accompanying ridge cracks

Residually compressed films and coatings are susceptible to buckle delamination. The buckles often have linear or telephone cord morphology. When the films are brittle, such buckles are susceptible to the formation of ridge cracks that extend along their length, terminating close to the propagating front. The ridge-cracked buckles are invariably straight-sided (not telephone cord) and differ in width. Buckle delaminations of this type occur on flat and curved substrates: having greatest technological relevance in the latter. They occur not only in single layer films but also in multilayers, such as thermal barrier systems. Establishing the mechanics of ridge-cracked buckle delaminations for multilayers on curved substrates serves two purposes. (a) It allows the prediction of buckle delamination and spalling for technologically important systems. (b) It provides a test protocol for measuring properties such as the delamination toughness of the interface and the stresses in the layers. Both objectives are addressed in the article: the latter by devising an inverse algorithm. Implementation of the algorithm is demonstrated for diamond-like carbon films on planar glass substrates and a thermal barrier multilayer on a curved superalloy substrate.     

Fracture Mechanics of Corrosion Cracking in Concrete by Acoustic Emission

Nucleation of microcracks can be detected and analyzed by acoustic emission (AE), by which crack kinematics of locations, types and rientations are quantitatively estimated. The procedure was applied to clarify mechanisms of corrosion cracking. Based on fracture mechanics, numerical analysis was conducted by the boundary element method (BEM). Relations between the stress intensity factors and crack types were investigated by BEM solutions. In experiments, four types of crack patterns were nucleated by employing expansive agent. Following the surface crack, the diagonal crack and/or the horizontal crack propagated. The internal crack extended after the surface crack was terminated. Depending on the crack types, contributions of mode-I and mode-II were varied. According to AE results, four crack patterns observed differently consisted of tensile, mixed-mode and shear cracks. It is demonstrated that mechanisms of corrosion cracking in concrete are dominantly of mode-I failure along with a minor contribution of mixed-mode and mode-II.     

An analytical model of rumpling in thermal barrier coatings

Multilayer thermal barrier coatings (TBCs) deposited on superalloy turbine blades provide protection from combustion temperatures in excess of 1500 °C. One of the dominant failure modes comprises cracking from undulation growth, or rumpling, of the highly compressed oxide layer that grows between the ceramic top coat and the intermetallic bond coat. In this paper, a mechanistic model providing an analytical approximation of undulation growth is presented for realistic cyclic thermal histories. Thickening, lateral growth straining and high temperature yielding of the oxide layer are taken into account. Undulation growth in TBC systems is highly nonlinear and characterized by more than 20 material and geometric parameters, highlighting the importance of a robust yet computationally efficient model. At temperatures above 600 °C, the bond coat creeps. Thermal expansion mismatch occurs between the superalloy substrate and the oxide layer and, in some systems, the bond coat. In addition, some bond coats, such as PtNiAl, exhibit a martensitic phase transformation accompanied by nearly a 1% linear expansion, giving rise to a large effective mismatch. These two mismatches promote undulation growth. Nonlinear interaction between the stress in the bond coat induced by the constraining effect of the thick substrate and normal tractions applied at the surface of the bond coat by the compressed, undulating oxide layer produces an increment of undulation growth during each thermal cycle, before the stress decays by creep. A series of problems for systems without the ceramic top coat are used to elucidate the mechanics of undulation growth and to replicate trends observed in a series of experiments and in prior finite-element simulations. The model is employed to study for the first time the effect on undulation growth of a shift in the temperature range over which the transformation occurs, as well as the relative importance of the transformation compared to thermal expansion mismatch. The role of the top coat and other viable ways of reducing undulation growth are considered.     

Elastic thermal stresses in a hollow circular overlay/substrate system

This paper investigates the thermal elastic fields in the hollow circular overlay fully bonded to a rigid substrate, which is subjected to a temperature change. Following our previous work for a solid circular overlay/substrate system (Yuan and Yin, Mech. Res. Commun. 38, 283–287, 2011), this paper presents a closed form approximate solution to the axisymmetric boundary value problem using the plane assumption, whose accuracy is verified by the finite element models. When the inner radius is reduced to zero, the present solution recovers the previous solution. When the outer radius approaches infinite, the solution provides the elastic fields for a tiny hole in the overlay. The effects of thickness and width of the overlay are investigated and discussed. When a circular crack initiates in a solid circular overlay, the fracture energy release rate is investigated. This solution is useful for thermal stress analysis of hollow circular thin film/substrate systems and for fracture analysis of spiral cracking in the similar structures.     

Rapid evaluation of the fatigue limit in composites using infrared lock-in thermography and acoustic emission

Fatigue limit determination via the conventional Wöhler-curve method is associated with extended experimental times as it requires testing of a large number of specimens. The current paper introduces a methodology for fast, reliable and experimentally economic determination of the fatigue limit in monolithic and composite materials by means of combined usage of two nondestructive inspection methods, namely infrared (IR) lock-in thermography and acoustic emission (AE). IR thermography, as a real-time and non-contact technique, allowed the detection of heat waves generated due to thermo-mechanical coupling as well as of the energy dissipated intrinsically during dynamic loading of the material. AE, on the other hand, was employed to record the transient waves resulting from crack propagation events. Aluminum grade 1050 H16 and cross-ply SiC/BMAS ceramic matrix composites were subjected to fatigue loading at various stress levels and were monitored by an IR camera and AE sensors. The fatigue limit of the monolithic material, obtained by the lock-in infrared thermography technique and supported by acoustic emission was found to be in agreement with measurements obtained by the conventional S–N curve method. The fatigue limit of the ceramic matrix composite was validated with acoustic emission data.     

Numerical analysis of interface fatigue of fiber reinforced composites

A numerical analysis of the interface debonding process is carried out for fiber–matrix composites under cyclic loading. The results show that the interface friction plays an important role in resisting debonding under fatigue. The degradation coefficient of interface friction influences the debonding velocity. An approximate formula of interface friction is found for fatigue debonding.     

A fundamental model of cyclic instabilities in thermal barrier systems

Cyclic morphological instabilities in the thermally grown oxide (TGO) represent a source of failure in some thermal barrier systems. Observations and simulations have indicated that several factors interact to cause these instabilities to propagate: (i) thermal cycling; (ii) thermal expansion misfit; (iii) oxidation strain; (iv) yielding in the TGO and the bond coat; and (v) initial geometric imperfections. This study explores a fundamental understanding of the propagation phenomenon by devising a spherically symmetric model that can be solved analytically. The applicability of this model is addressed through comparison with simulations conducted for representative geometric imperfections and by analogy with the elastic/plastic indentation of a half space. Finite element analysis is used to confirm and extend the model. The analysis identifies the dependencies of the instability on the thermo-mechanical properties of the system. The crucial role of the in-plane growth strain is substantiated, as well as the requirement for bond coat yielding. It is demonstrated that yielding of the TGO is essential and is, in fact, the phenomenon that differentiates between cyclic and isothermal responses.