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Effects of three-dimensional coating interfaces on thermo-mechanicalEffects of three-dimensional coating interfaces on thermo-mechanicalstresses within plasma spray thermal barrier coatingsstresses within plasma spray thermal barrier coatings

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Kyaw, Si, Arthur Jones, Mark A.E. Jepson, Tom H. Hyde, and Rachel C. Thomson. 2017. “Effects of Three-dimensional Coating Interfaces on Thermo-mechanical Stresses Within Plasma Spray Thermal BarrierCoatings”. figshare. https://hdl.handle.net/2134/24677.

Materials and Design 125 (2017) 189–204

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Materials and Design

j ourna l homepage: www.e lsev ie r .com/ locate /matdes

Effects of three-dimensional coating interfaces on thermo-mechanicalstresses within plasma spray thermal barrier coatings

Si Kyaw a, Arthur Jones a,⁎, Mark A.E. Jepson b, Tom Hyde a, Rachel C. Thomson b

a Faculty of Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, UKb Department of Materials, Loughborough University, Loughborough LE11 3TU, UK

H I G H L I G H T S G R A P H I C A L A B S T R A C T

• We show that 3D models predict stress-es in TBCs around twice those from 2Dmodels.

• We show probable spallation sitescaused by out-of-plane tensile stress.

• We predict buckling and decohesion ofthe oxide layer due to in-plane com-pressive stress.

⁎ Corresponding author.E-mail address: arthur.jones@nottingham.ac.uk (A. Jon

http://dx.doi.org/10.1016/j.matdes.2017.03.0670264-1275/© 2017 The Authors. Published by Elsevier Ltd

a b s t r a c t

a r t i c l e i n f o

Article history:Received 9 December 2016Received in revised form 21 March 2017Accepted 22 March 2017Available online 23 March 2017

It has been acknowledged that stresses within a thermal barrier coating (TBC) and its durability are significantlyaffected by the coating interfaces. This paper presents a finite element approach for stress analysis of the plasmasprayed TBC system, using three-dimensional (3D) coating interfaces. 3D co-ordinates of the coating surfaceswere measured through 3D reconstruction of scanning electron microscope (SEM) images. These co-ordinateswere post processed to reconstruct finite element models for use in stress analyses. A surface profile unit cell ap-proach with appropriate boundary conditions was applied to reduce the problem size and hence computationtime. It has been shown that for an identical aspect ratio of the coating interface, interfacial out-of-plane stressesfor 3D models are around twice the values predicted using 2D models. Based on predicted stress developmentwithin the systems, possible crack development and failure mechanisms of the TBC systems can be predicted.

© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/).

Keywords:Thermal barrier coatingsFinite element analysisSurface profileStress analysisFailure mechanisms

1. Introduction

Thermal barrier coating (TBC) systems are applied onto various su-peralloy and metal components e.g. gas turbine blades of an aircraft,diesel engine combustion chambers etc. One of the key functions of aTBC is to create a reduction in the substrate temperature by slowing

es).

. This is an open access article under

the rate of thermal conduction of heat from a combustion reaction tothe (cooled) substrate. This allows an increase in the combustion tem-perature which can lead to an increased efficiency. A TBC system typi-cally consists of two applied layers: a metallic bond coat (BC), and aceramic top-coat (TC). The TC is the outermost layer of the system andprovides temperature reduction due to its low thermal conductivity,while the BC provides a structural link with the substrate. Coatings areapplied using different methods and here only an air plasma sprayed(APS) system is considered. The method is more commonly used for

the CC BY license (http://creativecommons.org/licenses/by/4.0/).

190 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

components of land-based gas turbine engines. For this system, the sur-face roughness of the BC provides a mechanical bond to the TC and alsoinfluences its lifetime [1]. The BC is a mixture of β (NiAl), γ′ (Ni3Al) andγ (Ni) phases in various proportions. At high temperature, the composi-tion of the BC evolves either due to formation of a thermally grownoxide (TGO) at the TC/BC interface from oxygen diffusion [2] or due tointerdiffusion at the substrate/BC interface [3,4]. This variation in theBC compositions with service time can affect its mechanical propertiessignificantly [5,6].

Although the rough surface of the BC provides a mechanical bond tothe TC, it can also cause out-of-plane stresseswithin the system as it un-dergoes thermal cycling. Early efforts to relate BC surface roughness andthermo-mechanical stresses within APS TBC systems have been carriedout numerically in Refs. [7–9] where predictions were made usingidealised 2D interfaces, based on micrographs of cross-sections of coat-ing layers. Possible reasons for these simple approaches are: inadequatecomputational power to run FE simulations of actual coating interfaceand, the difficulty involved with the characterisation of interface pro-files from standalone coatings. Idealised interfaces not only fail to givean accurate representation of the actual geometry, but are, therefore,also likely to result in simulated TBC stresseswhich are insufficiently ac-curate for predictions of failure of the TBCs. Therefore, it is desirable toconstruct an FE unit cell to represent the actual surface geometry andhence to predict stress distributions within the TBC system accurately.A recent review [10] explores more generally the use of FE models forpredicting TBC thermal behaviour and failure including the use of 3Dmodels.

Nowadays, complex microstructural features can be measured byvarious advanced methods [11,12]. Furthermore, computational tools(such as object oriented finite element or OOF2 [13]) transform micro-graph images into FE meshes to be used for further FE analyses. The ap-plication of this method for stress analysis of the TBCs can be found inRef. [14]. The work not only captures the roughness profile but also po-rous area within the coatings, which provides useful information to cal-culate the coating's thermal conductivity. Rezvani Rad et al. [15] andNayebpashaee et al. [16] used a similar technique to identify the effectof realistic 2D roughness profiles on out-of-plane stresses under ther-mo-mechanical and thermal fatigue load conditions respectively. Mea-surements of 3D coating profiles were also used by Gupta et al. [17,18]to construct 3D FEmodels and the resultant residual stresseswere com-pared against results from 2D FE models. For similar aspect ratio of theinterface, out-of-plane stresses predicted from 3D models are aroundhalf an order of magnitude higher than those predicted from 2Dmodelsunder similar loading conditions. The results highlight the importanceof 3D interface shape to the estimation of residual stresses within TBCsystems. Work by Saucedo-Mora, et al. [19] considered the microstruc-tural roughness and heterogeneity of the coating for damage develop-ment within coatings using multi-scale FE model. The work not onlydemonstrated the effects of surface roughness on stress profiles, butalso the influence of microstructural features on Young's modulus anddamage within coatings.

Despite current abilities to incorporate complex coating interfacesinto FE analyses, there are still many shortcomings among the modelspresented in the previous paragraph. The models in Refs. [15,18] ignoreoxidation of the BC completely, yet this is very important due to thenon-planar nature of the interface shape.When a BC oxidises, direction-al oxide growth strains and subsequent stresses build upwithin the sys-tem in amanner dependent on interface geometry. Nayebpashaee, et al.[16] considered oxidation by applying an empirical swelling strain to aninitial oxide later without taking account of continuous consumption ofthe BC due to oxidation. Gupta et al. [17] calculated the oxide layerthickness based on the diffusion at the BC interfaces. However, the sim-ulation only used a linear elastic material model to investigate the mis-match stress due to change in temperature. The model also ignored thestress build up and redistribution due to creep of coatings during thesteady state. To address the aforementioned shortcomings, this paper

reports an FE model that has been produced which describes the effectof stresseswithin a coating systemof 3Dmicroscopic features, extractedfrom3D analysis of real coating interfaces. Appropriate boundary condi-tions presented by Li et al. [20] were applied to reduce the size of thesurface profile unit cell and hence its computation time. Changes inma-terial properties of the coating due to oxidation and sintering have alsobeen incorporated to fully describe the changes taking place during ser-vice. A simple case study has been carried out using simplified 2D and3D TGO interface idealisations with identical aspect ratios (ratio of am-plitude towavelength). Subsequently, two FE unit cells based on 3Dmi-croscopic features of the BC were built to carry out analysis of stressdistribution and relate them to the failure of the TBC.

This work fits into the present Journal's priority area [21] of the anal-ysis, structure, morphology and role of interfaces in the context ofmulti-physics phenomena, specifically by describing the influences ofmanufacturing-related interface geometry on the development ofstresses and cracks due to thermo-mechanical and oxidation effects.This paper documents the development of a theoretical model of inter-face stress with the use of experimental data of interface geometrywhich can be used in the design of future turbine blade coatings.

2. Roughness modelling

2.1. Capturing and post processing of TGO surface profiles

Cross-sections of TBC systems are traditionally imaged using a scan-ning electron microscope (SEM). Nevertheless, as these interfaces areoften view in cross-section, their interface roughness and surface profiledatameasured using thismethodmight not always represent the actualaspect ratio. The concept can be appreciated through the examination ofFig. 1where three different sectioning paths of an idealised surfacewithidentical aspect ratio throughout its surface could form radically differ-ent cross-section profiles. To avoid this, 3D images of the coating inter-face were captured for the current work.

The specimen used for the capture of the TGO surface profile wascomposed of a Ni22Co17Cr12Al0.6Y (wt%) BC with an APS TBC whichwas isothermally heated to a temperature of 940 °C for 500 h. In orderto view the TGO/BC interface, the BC was dissolved in hydrochloricacid (36%) for 36 h at ambient temperature to reveal the surface of theoxide interface as used by Sohn et al. [22]. To produce a 3D representa-tion of the TGO/BC interface, secondary electron images were collectedusing a Cambridge 360 Stereoscan SEM at a number of tilt angles andanalysed using Alicona Mex 3D. The x-y-z coordinates of the measuredsurface profile were then saved in ASCII format and post-processedusing ‘Fogale Nanotech Profilometry Software’ (FNPS) [23]. In order toapproximate a TGO layer of constant thickness within the FE model, itwas assumed that both TGO interfaces (i.e. TBC/TGO and TGO/BC) fol-low identical geometries.

The measured TGO surface coordinates in ASCII format wereimported into FNPS, and the roughness profile (shortwavelength undu-lations) and waviness (longer wavelength than the roughness profile)of the interface were separated using a standardised Gaussian filteringmethod (ISO 11562) [24]. The weight function of the filter (S(x)) isgiven by Eq. (1) [25]. The mean line of the raw data was obtained byconvolving it with the weighting function. The roughness and wavinessprofiles were separated by subtracting the mean line from the raw pro-file. The transfer function was obtained by performing a Fourier trans-form of the continuous function S(x) as shown in Eq. (2) [26].

S xð Þ ¼ 1αλc

exp −πx

αλc

� �2 !

ð1Þ

Sf λð Þ ¼Z ∞

−∞S xð Þ exp iλxð Þ dx ¼ exp −π

αλc

λ

� �2 !

ð2Þ

Fig. 1. Possible coating roughness profiles that could be extracted from different 2D cross-sectional micrographs of the coating surface with perfectly periodic asperities.

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whereα ¼ffiffiffiffiffiffiffiln2π

q, x is the distance from the origin of theweight function,

λc is the cut-off for longer wavelength roughness and λ is the actualwavelength of different waves from the raw surface profile.

As observed from Eqs. (1) and (2), the filtering process is mainlycontrolled by the choice of cut-off wavelength (λc). There are severaluncertainties in choosing the cut-off wavelength as it has not only tobe short enough to separate waviness profiles, but also long enough togive a meaningful roughness profile. A longer cut-off wavelength cre-ates a smoother roughness profile and vice versa. Since there is no def-inite standard for the cut-off wavelength, the choice of the wavelengthis entirely dependent on the sizes of the asperities, on which analysesare to be performed. In the present work, a cut-off wavelength of25 μm was used to separate the microscopic roughness features fromlarge protruberances of isolated BC “splats”. The height contour plotsof the roughness and waviness profiles of the TGO/BC interface withinthe sample area of 200 μm × 140 μm are depicted in Fig. 2.

Fig. 2. (i) Waviness and (ii) roughness profiles of the TGO/NiCoCrAlY BC interface with cut offshow out-of-plane profile in μm (height exaggerated).

2.2. Types of interface geometries

Three types of interface geometries were chosen for the various casestudies. They are listed in Table 1.

Firstly, the interface geometrywith amplitude (A) of 6 μmandwave-length (L) of 48 μm (denoted as A6-L48), as used in previous studies[5,6], was used for the axisymmetric and 3D unit cell models as shownin Fig. 3(i) & (ii). The thermo-mechanical stresses were simulated forthese models at 20 °C after aging for 900 h at 1000 °C.

It is assumed that the features of a realistic rough interface, such asthat shown in Fig. 2, can be broken down into three undulation compo-nents at different scales, known respectively as form, waviness androughness. In order to investigate the relative effects of these, each ofthese was modelled separately since the overall problem involving allthree scales would have been too large to model realistically within asingle FE unit cell that includes all of these geometric features. Accord-ingly, separate unit cells were constructed to represent the roughness

wavelength (λc) = 25 μm (profiles were generated using FNPS). Vertical axes and scales

Table 1Geometries used in the current work and specimen from which they are extracted.

Interfacegeometries

Detailed description Specimen

(i) A profile cell measured from SEM micrographs of 2D cross-sections A range of TBC systems [5](ii) A surface profile cell, extracted from 3D coating roughness measurements as shown in Fig. 2 (ii) NiCoCrAlY specimen that had been heat treated

at 940 °C for 500 h (as described in Section 2)(iii) A surface profile cell, which represents the protruberance of a BC splat, whose wavelength is larger than the

roughness sampling length (extracted from Fig. 2 (i))NiCoCrAlY specimen that had been heat treatedat 940 °C for 500 h (as described in Section 2)

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andwaviness, with the form being included in the overall axisymmetricor cylindrical geometry of the unit cell. Additionally, it is assumed thatthe tangential slopes are zero along the symmetry and the periodicityplanes of the unit cells due to limitations imposed by the boundary con-ditions for a 3D unit cell (Section 3). This assumption allows themodel-ling of only a quarter of each microscopic feature.

An asperity extracted from the roughness profile of Fig. 2(ii) is sim-ilar to the idealised 3D interface shown in Fig. 3(ii). However, the aspectratios of the interface for two in-plane directions were different as theactual peaks and troughs of the coating's interface were elliptical asshown in Fig. 4(ii). A and L of the asperity are 3.3 μm and 22.5 μm re-spectively. It was assumed that the coating was covered with periodicfeatures of the represented asperity as shown in Fig. 4(iii). The substratecurvature for this specimenwas 6.2mm in this case andwas incorporat-ed with the unit cell as in Ref. [6].

As shown in Fig. 5, pits with depths significantly larger than those ofthe roughness asperities can be observed at the surface of the TGO. Thisfeature will hereafter be referred to as an ‘oxide loop’. A profile of anoxide loop formed after 500 h of heat treatment at 940 °Cwas extractedfrom the 3D data of the TGO/BC surface. The length and width of the el-liptical oxide loop were 32 μm and 24 μm respectively, and the depthwas 15 μm. Because of the extreme aspect ratio of the oxide loop fea-tures, the form of the substrate was assumed to have no significant ef-fect upon the local stress field compared to that of the oxide loop.Therefore, the substrate was modelled as having zero curvature in ei-ther direction.

3. Boundary conditions formicroscopic featureswith cylindrical andlongitudinal periodicities

In order to make the finite element simulation computationally effi-cient, the interface features identified in Section 2.2 are idealised into aninfinitely-repeating form and appropriate boundary conditions are ap-plied. In the past, it has been assumed [5,6,27,28] that the BC/TGO inter-face has a 2D shape with periodicity either in the circumferential

Fig. 3. (i) Axisymmetric unit cell (L = 48 μm, A = 6 μm) (ii) Comparable 3D unit cell

direction (with wavelength 2rα) or in the longitudinal direction (withwavelength 2b) as shown in Fig. 6(i & ii). Here, an idealised 3D modelwith periodicity in both circumferential and longitudinal directionscan be modelled using a unit cell contained within the domain shownin Eq. (3) [20] and having the repeating pattern shown in Fig. 7.

−b≤x≤b0≤r≤R−α≤θ≤α

ð3Þ

where x, r, and θ are longitudinal, radial and circumferential coordinatesof the cylindrical coordinate system (CSYS), respectively.

In principle, this unit cell involves symmetries about planes x=±band θ=±α. However, purely translational symmetry, such as that pre-sented by Li andWongsto [29] for composite structures with geometri-cally periodic patterns, does not properly consider the rotational aspectsof the circumferential periodicity as they involve consideration of a cy-lindrical coordinate system (CSYS). Moreover, the commercial FE sys-tems do not typically incorporate the ability to apply the appropriatesymmetries in a cylindrical coordinate system, and do not allow thesource code to be extended to incorporate such features. Accordingly,the displacements need to be transformed from a cylindrical CSYS intoa rectangular one using the transformations shown in Eq. (4), basedon simple trigonometry:

ux ¼ uur ¼ v cos θþw sin θuθ ¼ −v sin θþw cos θ

ð4Þ

where ux, ur and uθ are displacements in a cylindrical coordinates sys-tem (x-r-θ) and u, v andw are displacement components in a global Car-tesian coordinate system (x-y-z) as shown in Fig. 8.

Based on this transformation, Li et al. [20] extended the approach of[29] to obtain a set of boundary conditions periodic in both x and θ, ofwhich a special case are conditions where there is symmetry aboutplanes x = ±b and θ = ±α which are applied within a Cartesian

of TBC (Geometry set i). Insets show relationships of main views to 3D geometry.

Fig. 4. i) Surface contour plot of roughness profile and ii) 3D view of extracted asperity using FNPS (NiCoCrAlY system after 500 h of heat treatment at 940 °C) iii) Representative coatingroughness modelled using a repeating unit cell (Geometry set ii) Vertical axis in ii), colour contours and scales show out-of-plane profile in μm (height exaggerated in ii)).

193S. Kyaw et al. / Materials and Design 125 (2017) 189–204

CSYS. These boundary conditions for a 3D unit cell as shown in Fig. 7(iii), for calculation of thermo-mechanical stresses, can be representedin Eq. (5) [20].

At x ¼ 0; u ¼ 0:At x ¼ b; u ¼ b;where ε0x is strain in the X‐direction:At θ ¼ 0; w ¼ 0:At θ ¼ α; −v sin θþw cos θ ¼ 0:

ð5Þ

The first two boundary conditions of Eq. (5) are applied to the unitcell with length, b. The boundary conditions ensure that the unit cellrepresents the infinitely long cylinder by constraining the plane atx = b to remain parallel while allowing displacement to occur in thelongitudinal direction.

Similarly, the last two boundary conditions of Eq. (5) are applied forsymmetry and periodicity conditions in the r-θ plane. In the case forwhich the substrate is flat, simple transverse periodicity was appliedin an analogous manner to the longitudinal periodic constraints in Eq.(5). By using Eq. (5), it is possible to model only a quarter of the 3Dunit cell, as highlighted in Fig. 7, in order to reduce computation timewithout affecting the accuracy of the numerical calculations.

4. FE model

Each aspect of the FE model for 3D coating interfaces is described inthe following sections. The current FE model is based on the previouswork by authors for 2D coating interfaces [6,20] where details of rele-vant aspect of the model can be found. A case study for validation ofthe stresses at the coating interfaces simulated by the model againstRaman and photo-stimulated luminescence piezo-spectroscopic mea-surements was carried out in Ref. [30]. The study showed that residual

stresses predicted from the FE model is of a similar order to the stressesmeasured. The predictions of crack initiation and spallation sites fromthe model are also in agreement with experiments.

4.1. Implementation of boundary and loading conditions

Equation constraints are applied at nodes on planes of symmetryand periodic planes of the unit cell to satisfy the boundary conditionsfrom Eq. (5). In order to implement the periodic boundary conditions,a fictitious or non-structural node is defined to which the x-displace-ments of all the nodes on the boundary x = b are tied via linear con-straint equations, with the x-displacement being made equal to thevalue of εx.

A simulated constant temperature load of 1000 °C was appliedacross the system for a simulated time of 900 h before cooling back toroom temperature. The duration of initial heating to 1000 °C fromroom temperature and cooling down to room temperature was30 min. For the system with the preceding heat treatment duration of500 h at 940 °C, the thickness of the initial TGO was set as 4 μm; other-wise, the thickness was assumed to be 1 μm. However, residual stressesfrom earlier heat treatments were not taken into account and all sys-tems were assumed to be stress-free at the start of the analysis.

4.2. Material properties and oxidation kinetics

For this study, the TC is assumed to be purely elastic whereas creepbehaviours of other layers are considered by using a power law. Apower law creep strain rate ( _εcrij ) is shown in Eq. (6). Power law con-stants for the TGO are A0 = 6800 MPa−n s−1, n = 2.3, Q =4.24 × 105 J/mol. Q and R in Eq. (6) are the activation energy of the

Fig. 5. (i)Waviness profile at the surface of the TGO fromNiCoCrAlY-APS TBC system, which has been heat treated at 940 °C for 500 h; oxide loop feature shown in dotted line is shown indetail in (ii) and (iii) Vertical axis in iii), colour contours and scales show out-of-plane profile in μm (profile height not to scale in iii)).

194 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

reaction and the universal gas constant respectively. For the TC, evolu-tion in its elastic modulus due to sintering is considered. Material prop-erties of the BC (elastic, creep and CTE) are calculated based on itsconstituents that constantly vary due to oxidation or diffusion at theBC/substrate interface. The procedure is explained in Section 4.3. Moredetails can be found in an earlier publication [6].

_εcrij ¼ A0 exp −Q�RT

� �σn ð6Þ

It was assumed that the oxidation of the BC produces isotropic strainaccording to the Pilling-Bedworth Ratio (PBR) of aluminium (Al). As inthemodel in Ref. [27], the PBR of Al is taken to be 1.28. The oxide formedis assumed to bemade up of pure alumina and it is assumed to grow to-wards the BC since the oxygen diffusion ratewithin Al2O3 is higher than

that of Al at the same temperature [31]. The growth strain rate ð _εtrij Þ dueto oxidation is related to the PBR for Al containing phases in the BC (βand γ′) and the oxide formation rate ð _f oxÞ via Eq. (7) [5].

ε: trij ¼ 1�

3 ln PBRβ=γ0�

f:

oxδij ð7Þ

As mentioned by Taylor et al. [32], local Al-depletion zones and ex-ternal growth of non-Al oxides (spinels) are expected around theoxide features with high aspect ratios such as the oxide loop. Due totheir significantly higher PBR than Al, fast growing oxides of Ni, Co

and Cr create a rapid increase in out-of-plane tensile stress within theTBC system during steady state heating. The failure caused by thistype of metal oxidation, due to Al depletion within the BC, is referredto as ‘chemical failure’. However, studying chemical failure is outsidethe scope of this article so therefore spinel formation due to external ox-idation will not be considered here.

4.3. Modelling evolution of material properties of coatings

The high temperatures experienced by TBC systems during industri-al service can cause the properties of thematerials to change with time.Sintering of the ceramic TC at these temperatures can reduce the poros-ity of the TBC. The constitutive model which considers changes in TBCmodulus due to sintering, based on the Arrhenius model, has beencoupled to a FE model of the TBC system by Kyaw et al. [6]. The propor-tions of phases within the BC change continuously during the steadystate period of heating due to oxidation or interdiffusion at the sub-strate/BC interface. These changes can be calculated by using finite dif-ference (FD) calculations in combination with thermodynamiccalculations such as CALPHAD [33] as presented in [34,35]. The atomicflux of Al at the BC/TGO interface is calculated by using an empiricallyderived oxidation law [36]. Currently, a 1D FD/thermodynamics modeldeveloped by Karunaratne et al. [3], is coupled to the FE model of theTBC. Using the proportions of intermetallic phases predicted by themodel, Eshelby's theoremandmaterial properties of the pure BC phases,

Fig. 6. Sinusoidal TGO interfaces i) periodicity in the circumferential directionwithwavelength of 2rα and ii) periodicity in the longitudinal directionwithwavelength of 2b (Cells boundedby double-dashed line are used for FE unit cells).

195S. Kyaw et al. / Materials and Design 125 (2017) 189–204

a constitutive material model was developed in [5] for the aggregateproperties (elastic and creep properties and coefficient of thermal ex-pansion (CTE)) of the BC. This model for the BC will also be adoptedhere.

To transfer the 1D phase proportion data into the 3D FE models, theBC was modelled as a multi-layered structure as shown in Fig. 9. Thethickness of each layer was predefined at the pre-processing stage andthematerial points, atwhich the BCpropertieswere calculated,were as-sumed to lie along themiddle profile of each BC layer as shown in Fig. 9.Sporadically, layers of the BC were also transformed into the TGO layerbased on theoxidation law in Ref. [36]. This transformation also imposesan appropriate growth strain based on the PBRof Al, tomodel oxidation.For the regions further away from the TGO interface, distances of mate-rial points from the TGO interface were estimated from the interface BCshown in Fig. 9. At those regions, errors in estimating distances due tothe undulated nature of the interface are tolerable as the change in BC

Fig. 7. Representative 3D coating surface (A unit cell is highlighted).

composition is subtle. This type of multi-layered modelling approachwould also be suitable for incorporating 1D phase data into complex3D coating tomography such as the one measured by the synchrotron-radiation method [12].

4.4. Finite element mesh

It is necessary to select appropriate element types and mesh densi-ties for the FE models with interface geometries described in Section2.2, in order to obtain accurate results with minimum computation

Fig. 8. Relationship between displacement components ux, ur and uθ in cylindrical x-r-θcoordinate system, and displacement components u, v and w in Cartesian (x-y-z)coordinate system.

Fig. 9. The multilayered nature of the BC to implement 1D FE model for the composition of the BC.

196 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

time. For the axisymmetric models, 4-node linear axisymmetric ele-ments (CAX4)were used for consistencywith otherwork in the presentproject that makes use of ABAQUS features (XFEM and cohesive model-ling) not availablewith higher-order elements. Reduced integration (i.e.use of fewer Gaussian integration points than are required for exact in-tegration of the stiffnessmatrix)was used both for computational econ-omy and to avoid any danger of shear locking [37].

To overcome the inaccuracies in using linear elements with a re-duced integration scheme, a relatively high mesh density is necessaryaround the regions with abrupt changes in displacements and hencein the resultant stress and strain. For TBC systems, stress concentrationsoccur around the TGO interface due to CTEmismatch [38,39] and hence,

Fig. 10. i) Topography of the repeated sinusoidal oxide interface with highlighted uni

higher mesh densities were applied at those regions. A mesh diagramfor the axisymmetric model (geometry set (i), Section 2.2) is illustratedin Ref. [6] while mesh diagrams for geometry set (ii) and (iii) are illus-trated in Fig. 10 and Fig. 11, respectively.

5. Results and discussions

5.1. Stresses predicted by the TBC models with axisymmetric and 3Dinterfaces with identical aspect ratio of geometry set i

A comparison of out-of-plane TBC stresses for both the axisymmetricand 3D models using geometry set (i), at a simulated temperature of

t cell for ii) FE mesh for the unit cell iii) Detail of mesh in the vicinity of the TGO.

Fig. 11. i) Topography of the repeated oxide loop interface with highlighted unit cell ii) FE mesh for the unit cell iii) Detail of mesh in the vicinity of the TGO.

197S. Kyaw et al. / Materials and Design 125 (2017) 189–204

20 °C and a simulated 900 h of aging at 1000 °C, is presented in Fig. 12. Itwas found that when the 3D model was employed, the maximum ten-sile out-of-plane stresses at the TGO/TBC interface increased by a factorof nearly two. Similar findings were also presented by Gupta, et al. [18]and Glynn et al. [40]. These findings illustrate the importance ofemploying 3D models while carrying out stress analyses for TBC sys-tems to avoid the underestimation of stresses caused through the useof a 2D profile.

Higher stress concentrations at the TGO/TBC interfaces for the 3Dmodel can be explained by a simple Lamé approach as described byGong and Clarke [41]. In such an approach, local interfacial stresses atthe peak and valley regions of 2D and 3D models can be idealised asstresses at the coating interface for cylindrical and spherical substratesrespectively. Analytically, it can be proved that, for an identical radius,radial stress at the coating interface for a spherical substrate is around1.5 times higher compared to the cylindrical substrate,which is a similarmagnitude to the stress differences indicated here.

Fig. 12.Out of plane tensile stress within the TBCwith i) axisymmetric TGO interface and ii) 3Dviews to the 3D geometry.

5.2. Stresses predicted by the TBC models with 3D sinusoidal interface(geometry set ii)

Two different simulations were carried out, both with the same in-terface geometry as that shown in Fig. 4. System 1 was a simulated as-sprayed systemwith an assumed initial TGO thickness of 1 μm. By con-trast, for the simulated thermally aged sample, System 2, the initial TGOwas assumed to be 4 μm thick with a fully sintered TBC after an appliedheat treatment of 500 h at 960 °C. Moreover, the FD/thermodynamicsmodel for evolution of the BC material properties (Section 4.3) wasalso modified to ensure the initial properties of the BC were equivalentto those of an aged system. A slower oxide formation rate was also usedin the simulation since diffusion of O and Al will be much slower due tothe thickness of the initial TGO layer.

Firstly, the stresses within the coatings from System 1 and theidealised model from Section 5.1 were compared to investigate the sig-nificance of the coating aspect ratio. The trend of out-of-plane stresses

TGO interface at 20 °C after heating at 1000 °C for 900 h. Insets show relationships of main

198 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

within the TBC and the BC (shown in Fig. 13 and Fig. 14 respectively) atthe end of cooling for both systems was similar despite the unsymmet-rical coating interface of System 1. Generally, out-of-plane stresses arehigher than those predicted using the idealised 3D model (Fig. 13 andFig. 14). This is due to thehigher aspect ratio of the interface (0.15) com-pared to the ratio of the idealised 3D model (0.125). The trend of in-creased residual stresses within the system with increasing aspectratio of the coating interface is similar to the one given from various2D parametric studies [8,28,42] of the effect of aspect ratio on TBCstresses.

Secondly, stresses occurring within System 1 and System 2 werecompared against each other. At the end of the heating period, both sys-tems produced a similar out-of-plane stress pattern as shown in Fig. 15.The highermagnitude of stresses for System 2 is due to the lower straintolerance of the aged TBC [43]. During steady state heating, lateral oxidegrowth imposes compressive in-plane stresses within the TGO. Concur-rently, there will be additional creep strain of the TGO to relax the built-up stresses. Compressive in-plane stress within the growing oxide layerwill impose tensile and compressive out-of-plane stresses at the valleysand peaks at the TGO interfaces. These oxidation stresses are opposed tothe initial thermal mismatch stresses and hence would be expected tolead eventually to stress reversal. In the case of System 1, the stress re-versal occurs rapidly after heat-up as the newly-grown oxide is almostadjacent to the TBC layer. However, in the case of the heat-treatedNiCoCrAlY specimen, both depletion of the Al containing phases and athicker TGO make the oxide formation rate within the system muchslower than System1. Accordingly, the rate of change of the TBC stressesdue to oxide growth is much slower, and stress reversal occurs muchlater as demonstrated in Fig. 15. Moreover, oxide growth stresses pro-duced at the TBC/TGO interface during the steady state heating periodfor System 1 are significantly higher than those produced by System 2at the end of the steady state heating period (Fig. 15). As a result, outof plane stresses at the TBC/TGO interface for System 1 after coolingare at least 40% higher than those predicted from System 2.

The above discrepancies in stresses between Systems 1 and 2 showthe importance of using appropriate initial TGO thickness, diffusionand oxidation models whilst carrying out stress analyses on real inter-face geometries extracted from aged coating systems.

Quantitative comparisons of stresses obtained in this study againstother findings in the literature pose challenges due to differences inmodelling methods (e.g. with or without TGO growth strain during

Fig. 13. Through thickness stress (σ11) in the vicinity of the TBC for (i) System 1 and (ii) ideaviewing direction relative to the 3D geometry.

steady state),material properties (e.g. diffusionmodel for estimating in-stantaneous properties of the BC or fixed properties, inclusion or exclu-sion of creep properties of coatings) and TGO thickness. Generally,stresses predicted in this study using homogenous materials with sim-plified TGO interfaces are higher than those predicted from the modelswith actual TGO interfaces by Gupta et al. [18], and Hansson andSkogsberg [44]. From their studies with microscopically scanned 3DTGO interface, maximum through thickness TBC stress after cooling to100 °C from 1100 °C is around 200MPa for both as-sprayed TBC systemwithout TGO and for the systemwith TGO after 200 h of isothermal heattreatment. Themaximum stress occurs at the peak of the TBC for the as-sprayed system while it is found at the valley of the interface of the as-aged system, in a similar manner to the results obtained in the presentstudy shown in Fig. 13(ii). The maximum TBC stress after cooling inthe present study (~375 MPa) is higher than the magnitude of TBCstress by Gupta for both as-sprayed and aged systems as shown in Fig.13. The reason for this discrepancy could be the lack of TGO growthstress and creep within the models presented in Refs. [18,44] andtheir assumption that the system is stress-free before cooling. Studiesin Refs. [6,45] have shown that the combination of TGO growth stresses,and relaxation caused by the TGO creep at the steady state, results intensile out of plane stress at the TBC valley and these stresses further in-crease during cooling due to CTE mismatches between coating layers.Experimentally, hydrostatic growth stresses when the aluminium-richBC transforms to TGO at 1121 °C have been measured to be around 2–2.5 GPa [46]. Therefore, the TBC system cannot be assumed to bestress-free before cooling, and an appropriate oxide growth model hasto be used to model stresses within the system due to TGO growth dur-ing the steady state.

5.3. Stresses predicted by the TBC models with oxide loop geometry (geom-etry set iii)

Because of the convoluted geometry of the oxide loop, high tensilethrough-thickness stresses are predicted to be concentrated at the TBCpeak at the end of heating to 1000 °C, as shown in Fig. 16(i). In reality,these stresses will be relaxed through the formation of parallel cracksor by creep of the coatings during steady state heating. Only the latterprocess was considered in this case. Due to stress relaxation by coatingcreep, tensile out-of-plane stresses at the TGO interfaces at the end ofthe steady state heating period are predicted to be below the rupture

lised 3D interface at 20 °C after heating at 1000 °C for 900 h. Inset shows relationships of

Fig. 14. Through thickness stress (σ11) in the vicinity of the BC for (i) system 1 and (ii) for idealised 3D interface at 20 °C after heating at 1000 °C for 900 h. Inset shows relationships ofviewing direction relative to the 3D geometry.

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strengths of the interfaces. Thermal mismatch upon cooling will pro-duce tensile out-of-plane stress at the BC peak and at the middle ofthe TBC/TGO interface as shown in Fig. 16(ii). In the region where theinterfacial geometry is flat, out-of-plane stresses are negligibly small al-though high compressive in-plane stresses of up to 6.5 GPa are createdwithin the TGO due to cooling as shown in Fig. 17. Therefore, studies ofboth in-plane and out-of-plane stresses are necessary to predict crackgrowth near the coating asperities similar to the oxide loop model.Gupta et al. [18] also carried out stress analysis of the coating systemusing the TGO interface similar to the oxide loop in this study. By con-trast, however, the feature was idealised as a hemisphere instead ofthe approximately conical shape in the current study. Gupta's studyshows that themaximum through thickness TBC stress (~200 MPa) oc-curs at the peak of the TBC after cooling for the system without TGO.When a TGO layer of 10 μm is used, the maximum TBC stress(~200 MPa) occurs at the middle of the TBC/TGO interface in a similarmanner to the current study as shown in Fig. 16. As mentioned

Fig. 15. Out-of-plane stress at the TBC peak and valley for as-sprayed (Sample

previously, TBC stresses at the end of heating (shown in Fig. 16(i))will be redistributed during steady state due to relaxation caused byTGO creep and due to TGO growth. Neither of these processes was con-sidered in the Guptamodel and hence themagnitude of stress is not di-rectly comparable with the present study.

5.4. Prediction of crack development and failure of the TBC system based onstress distributions within the system

In this paper, crack initiation and subsequent propagation are notmodelled but they are rather predicted from out of plane tensile stressstate (assuming that the coating is brittle and mode I crack growth isthe dominant fracture mode). When the axisymmetric interface withgeometry set (i) is considered, propagation of parallel cracks due to re-sidual stresses at three different stages during a thermal cycle can bepredicted as shown in Fig. 18. Parallel cracks around the TBC peak to-wards the TBC valley after the heating period, are restricted due to the

1) and aged (Sample 2) TBC systems with an identical coating asperity.

Fig. 16. Through thickness stresses (i)within the TBC at the end of heating at 1000 °C and (ii)within the TBC systemnear the TGO interfaces at the end of cooling after heating at 1000 °C for900 h.

200 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

high compressive stress at the valley as shown in Fig. 18(i). However foraged systems, reversal of tensile and compressive stresses is onlypredicted to occur after several hours of steady state heating (Fig. 15)and parallel cracks formed at the TBC peak during heat-upwill continueto propagate. Therefore, premature spallation of the TBC is expected forthermally aged systems. During steady state heating, additional parallelcracks are expected to nucleate at the TBC valley due to stress reversal atthe TBC peak and valley as shown in Fig. 18(ii). When cooling is applied,any CTE mismatch is predicted to cause tensile out-of-plane stresses inthe vicinity of the peak of BC and the valley and slope of the TBC asdepicted in Fig. 18(iii). Therefore, parallel cracks are expected to format those regions. Formation of parallel cracks at the BC peak, however,is not possible due to its high tensile strength [47] at low temperature.Delamination or interfacial cracks are also expected to form at the BC/

Fig. 17. In-plane stress (i) S11 and (ii) S33 within TGO and TB

TGO interface because of higher out-of-plane tensile stresses comparedto those at the TGO/TBC interface. If delamination does occur, the strainenergy release from interfacial cracking could drive further propagationof existing TBC and TGO cracks.

The above predictions of possible parallel crack formations at differ-ent stages of a thermal cycle based on radial stresses within the system(Fig. 18) can be schematised as shown in Fig. 19.

Similarly, local crack growth in the vicinity of 3D asperities based onout-of-plane tensile stresses obtained from stress analyses could occurexcept when significant regions of the interface are flat. In this case,very high compressive in-plane stresses are expected and buckling-driven cracks have to be considered. Buckling is favoured especially ifthere are significant de-cohesion zones at the interface [48]. For a flat in-terface shown in Fig. 20, the minimum compressive stress for initiation

C at the end of cooling after heating at 1000 °C for 900 h.

Fig. 18. Through thickness stress state (σ11) within the TBC system with axisymmetric TGO interface at (i) at the end of heating (ii) after heating at 1000 °C for 13 h (iii) at 20 °C afterheating at 1000 °C for 90 h.

201S. Kyaw et al. / Materials and Design 125 (2017) 189–204

of buckling failure, is directly proportional to the thickness of the coatings(h) and inversely proportional to the temperature changes (ΔT) and halfof the length of interfacial de-cohesion (b), according to the analytical

Fig. 19. Stages of predicted crack growths within the TBC system with axisymmetric TGO inteexaggerated).

derivation by Choi et al. [49]. For the oxide loopmodel (Fig. 11), expectedbuckling zones, along with parallel cracks formed from out-of-plane ten-sile stresses at the end of cooling, are illustrated in Fig. 21.

rface relating to stress states shown in Fig. 18 (Note: Aspect ratio of the TGO interface is

Fig. 20. Schematic diagram of interfacial decohesion at the flat TGO/BC interface.

202 S. Kyaw et al. / Materials and Design 125 (2017) 189–204

6. Conclusions

The following conclusions can bemade from the stress analyses pre-sented in this paper.

Fig. 21. Predicted crack growth within the o

• For identical aspect ratios, the maximum compressive and tensile ra-dial stresses at the TBC/TGO interface of the 3D model are aroundtwice the values predicted using the axisymmetric (2D) model. Thefinding is consistent with analytical results [41], which show an

xide loop model at the end of cooling.

203S. Kyaw et al. / Materials and Design 125 (2017) 189–204

increase of more than 1.5 times in tensile radial stress for a sphericalinterface compared to a cylindrical one.

• For all geometries of the coating interface chosen in this paper, tensilestresses are predicted to be concentrated at the TBC peak and theopening of cracks is expected at the end of the heating period. Thestresses near these cracks relax while their propagation towards thevalley region is opposed by high compressive stress.

• After the heating stage, stress reversal at the TBC peak and valley re-gions does not occur rapidly for the aged system with thick initialTGOs compared to the as-sprayed system. Therefore cracks that nu-cleate at the TBC peak during heating continue to propagate duringthe steady state heating stage for aged systems and premature spall-ation is expected.

• At the end of cooling, tensile delamination cracks are expected to occurat the peak of the TGO/BC interface especially for the oxide loop asper-ity due to its high aspect ratio. Once the interface has delaminated,strain energy stored during the steady state period will be released. Ifcoalescence of TBC and TGO cracks also occurs in the vicinity of the in-terfacial crack opening, strain energy release at the interfacemay drivefurther crack propagation leading to spallation.

• Additionally, buckling failure is expected for relatively flat coatinginterface regions due to the high in-plane compressive stresses,which occur at the end of cooling as observed from the oxide loopmodel.This paper presents stress analyses within TBC systems using differentunit cells of coating asperities, by assuming the coating surface is cov-eredwith an infinite tessellation of identical asperities. However, in re-ality, the coating surface has several irregular microscopic features.Nevertheless, the presented framework, for setting up FE models ofTBC systems, with 3Dmicroscopic features, can be applied with futurestudies to explore the influence of different geometries of asperities oncoating failure.

Acknowledgement

We would like to acknowledge the support of The Energy Pro-gramme, which is a Research Councils UK cross council initiative ledby EPSRC and contributed to by ESRC, NERC, BBSRC and STFC, and spe-cifically the Supergen initiative (Grants GR/S86334/01 and EP/F029748) and the following companies; Alstom Power Ltd., DoosanPower, E.ON, National Physical Laboratory, Praxair Surface TechnologiesLtd., QinetiQ, Rolls-Royce plc, RWE npower, Siemens Industrial Turbo-machinery Ltd. and Tata Steel, for their valuable contributions to theproject. This work was supported by the Engineering and Physical Sci-ences Research Council [grant numbers GR/S86334/01, EP/F029748/1].

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