Long-Term Failure Mechanisms of Thermal Barrier Coatings in Heavy-Duty Gas Turbines

coatings

Review Long-Term Failure Mechanisms of Thermal Barrier Coatings in Heavy-Duty Gas Turbines

Feng Xie 1 , Dingjun Li 2 and Weixu Zhang 1,*

1 State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] 2 State Key Laboratory of Long-Life High Temperature Materials, Dongfang Electric Corporation Dongfang Turbine Co., LTD, Deyang 618000, China; [email protected] * Correspondence: [email protected]

Received: 26 September 2020; Accepted: 19 October 2020; Published: 23 October 2020

Abstract: Thermal barrier coatings serve as thermal insulation and antioxidants on the surfaces of hot components. Different from the frequent thermal cycles of aero-engines, a heavy-duty gas turbine experiences few thermal cycles and continuously operates with high-temperature gas over 8000 h. Correspondingly, their failure mechanisms are different. The long-term failure mechanisms of the thermal barrier coatings in heavy-duty gas turbines are much more important. In this work, two long-term failure mechanisms are reviewed, i.e., oxidation and diffusion. It is illustrated that the growth of a uniform mixed oxide layer and element diffusion in thermal barrier coatings are responsible for the changes in mechanical performance and failures. Moreover, the oxidation of bond coat and the interdiffusion of alloy elements can affect the distribution of elements in thermal barrier coatings and then change the phase component. In addition, according to the results, it is suggested that suppressing the growth rate of uniform mixed oxide and oxygen diffusion can further prolong the service life of thermal barrier coatings.

Keywords: heavy-duty gas turbine; thermal barrier coatings; oxidation; diﬀusion; failure

1. Introduction A heavy-duty gas turbine is an important device for power generation. Thermal barrier coatings (TBCs) serve as a thermal protection structure and protect the hot components in heavy-duty gas turbines [1]. TBCs are made up of a top ceramic coat (TC), intermediate metal bond coat (BC) and the underlying superalloy substrate. A layer of thermally grown oxide (TGO) forms between the TC and BC during the oxidation of TBCs [2,3]. Different from the frequent thermal cycling of aero-engines, a heavy-duty gas turbine continuously operates at high temperature over 8000 h [4,5], as shown in Figure1, and the thermal stress, which mainly originates from the start and stop, is almost released by material creep in the long-term service [6,7]. Moreover, the inlet air of a heavy-duty gas turbine is filtrated and clean. Thus, the attack of calcium-magnesium-aluminum-silicate (CMAS) also almost cannot occur. Accordingly, the spalling of TBCs is mainly induced by oxidation and element diffusion during its long-term service.

Coatings 2020, 10, 1022; doi:10.3390/coatings10111022 www.mdpi.com/journal/coatings Coatings 2020, 10, x FOR PEER REVIEW 2 of 19

CoatingsCoatings 20202020,,10 10,, 1022x FOR PEER REVIEW 22 ofof 1919

Figure 1. Schematic diagram of the typical service conditions of aero-engines and heavy-duty gas Figureturbines. 1. T is the initial temperature. Figure 1. SchematicSchematic0 diagramdiagram of thethe typicaltypical serviceservice conditionsconditions ofof aero-enginesaero-engines andand heavy-dutyheavy-duty gasgas turbines. T0 is the initial temperature. turbines. T0 is the initial temperature. Both oxidation and element diffusion involve long-term atomic exchange processes and exhibit Both oxidation and element diffusion involve long-term atomic exchange processes and exhibit the slow evolution behaviors of material. A typical BC composition is MCrAlY (M = Ni, Co, NiCo) the slowBoth evolution oxidation behaviors and element of material. diffusion A involve typical BClong-term composition atomic is MCrAlYexchange (M processes= Ni, Co, and NiCo) exhibit [8]. [8]. During the long-term oxidation of TBCs, firstly, Al in the BC reacts with the inward O and then Duringthe slow the evolution long-term behaviors oxidation of of material. TBCs, firstly, A typica Al inl theBC BCcomposition reacts with isthe MCrAlY inward (M O and= Ni, then Co, slowlyNiCo) slowly forms a dense α-Al2O3. Then, with the continuous proceeding of oxidation, Al near the forms[8]. During a dense theα -Allong-termO . Then, oxidation with the of continuous TBCs, firstly, proceeding Al in the of BC oxidation, reacts with Al nearthe inward the reaction O and region then reaction region is2 almost3 depleted. While other alloy elements, e.g., Ni and Co, continue to be isslowly almost forms depleted. a dense While α-Al other2O3. Then, alloy elements,with the e.g.,continuous Ni and proceeding Co, continue of tooxidation, be oxidized, Al near and thethe reactionoxidized, region and the is formedalmost depletα-Al2Oed.3 is While consumed other throughalloy elements, the reaction e.g., NiNi +and O +Co, α-Al continue2O3 = NiAl to2 Obe4, formed α-Al2O3 is consumed through the reaction Ni + O + α-Al2O3 = NiAl2O4, accordingly the porous accordingly the porous mixed oxide (MO), which comprises NiO, Cr2O3 and (Ni, Co)(Cr, Al)2O4 [9], mixedoxidized, oxide and (MO), the formed which comprisesα-Al2O3 is NiO,consumed Cr O throughand (Ni, the Co)(Cr, reaction Al) ONi [+9 ],O forms+ α-Al rapidly2O3 = NiAl [10,211O].4, forms rapidly [10,11]. As a result, the mechanical2 3 performance of the2 4 BC changes significantly, Asaccordingly a result, the the mechanical porous mixed performance oxide (MO), of thewhich BC changescomprises significantly, NiO, Cr2O3 which and (Ni, is detrimental Co)(Cr, Al)2 forO4 the[9], which is detrimental for the reliability and durability of TBCs [12–14]. Thus, clarifying the reliabilityforms rapidly anddurability [10,11]. As of TBCsa result, [12 –the14]. mechanical Thus, clarifying performance the long-term of the failure BC changes mechanism significantly, is helpful long-term failure mechanism is helpful for us to evaluate the service performance and predict the forwhich us to is evaluate detrimental the service for the performance reliability and and predict durability the lifetime of TBCs of TBCs [12–14]. in heavy-duty Thus, clarifying gas turbines. the lifetime of TBCs in heavy-duty gas turbines. long-termGenerally, failure oxidation mechanis andm elementis helpful di ffforusion us to are evaluate a continuous the service and related performance process and [2]. Afterpredict TBCs the Generally, oxidation and element diffusion are a continuous and related process [2]. After operatelifetime atofthe TBCs elevated in heavy-duty temperature, gas turbines. under the driving of the difference in chemical potential between TBCsGenerally, operate at oxidation the elevated and temperature, element diffusion under tharee drivinga continuous of the differenceand related in chemicalprocess [2]. potential After the external reservoir, e.g., O2 and coating, the guest atoms, e.g., O, leave the external reservoir and between the external reservoir, e.g., O2 and coating, the guest atoms, e.g., O, leave the external insertTBCs intooperate coating at the at theelevated boundary. temperature, Subsequently, under thethe guestdriving atoms of the continue difference to di inffuse chemical forwards potential in the reservoir and insert into coating at the boundary. Subsequently, the guest atoms continue to diffuse coatingbetween until the theyexternal reach reservoir, the reaction e.g., region, O2 and as coating, shown inthe Figure guest2. atoms, When thee.g., guest O, leave atoms the encounter external forwards in the coating until they reach the reaction region, as shown in Figure 2. When the guest thereservoir outward and alloy insert elements, into coating e.g., at Al the and boundary. Ni, new Subsequently, oxides form and the significantguest atoms stress continue occurs to diffuse due to atoms encounter the outward alloy elements, e.g., Al and Ni, new oxides form and significant stress theforwards surrounding in the coating constraint. until The they induced reach the stress reacti noton only region, causes as theshown failures in Figure of TBCs 2. When but also the a ffguestects occurs due to the surrounding constraint. The induced stress not only causes the failures of TBCs theatoms diff encounterusion and the oxidation outward processes. alloy elements, Thus, oxidation e.g., Al and and Ni, di ffnewusion, oxides as a form whole, and are significant responsible stress for but also affects the diffusion and oxidation processes. Thus, oxidation and diffusion, as a whole, are long-termoccurs due failure to the mechanisms surrounding of cons TBCstraint. in heavy-duty The induced gas stress turbines. not only causes the failures of TBCs butresponsible also affects for thelong-term diffusion failure and mechanismsoxidation processes. of TBCs Thus,in heavy-duty oxidation gas and turbines. diffusion, as a whole, are responsible for long-term failure mechanisms of TBCs in heavy-duty gas turbines.

FigureFigure 2.2. SchematicSchematic diagramdiagram ofof oxidationoxidation andand thethe didiffusiﬀusionon ofof guestguest atomsatoms inin thethe long-timelong-time serviceservice process of thermal barrier coatings (TBCs) in heavy-duty gas turbines. Figureprocess 2. of Schematic thermal barrier diagram coatings of oxidation (TBCs) andin heavy-duty the diffusi gason ofturbines. guest atoms in the long-time service process of thermal barrier coatings (TBCs) in heavy-duty gas turbines.

Coatings 2020, 10, 1022 3 of 19 Coatings 2020, 10, x FOR PEER REVIEW 3 of 19

Up to date, previous studies mainly focus on the fabrication, material, residual stress, cracking, sintering andand thermal thermal properties properties of TBCsof TBCs [15 –[15–24].24]. For instance,For instance, Wang Wang et al. [25et ]al. reviewed [25] reviewed finite element finite methodelement (FEM)method research (FEM) onresearch thermal on insulation, thermal insulation, residual stress residual and thestress related and failurethe related problems failure of TBCs.problems Wang of TBCs. et al. [Wang26] reviewed et al. [26] the reviewed research the on research the stress on and the crack stress problems and crack in problems TBCs during in TBCs the fabrication,during the fabrication, oxidation, sintering oxidation, and sintering CMAS permeation.and CMAS Lvpermeation. et al. [27] alsoLv et reviewed al. [27] also the FEMreviewed research the onFEM stress research analysis, on heatstress transfer analysis, as wellheat astransfer fracture as and well damage as fracture mechanisms and damage in environment mechanisms barrier in coatingsenvironment (EBCs). barrier However, coatings to our (EBCs). best knowledge, However, the to long-termour best failureknowledge, mechanism the long-term of TBCs still failure lacks attention,mechanism let of alone TBCs a related still lacks review. attention, For TBCs let inalone heavy-duty a related gas review. turbines, For the TBCs long-term in heavy-duty oxidation andgas elementturbines, di theffusion long-term are the oxidation dominant and factors element for its diffus failureion and are change the dominant in performance. factors for On its one failure hand, and the BCchange is continuously in performance. oxidized On toone form hand, TGO, the and BC the is undulatingcontinuously TGO oxidized induces to a form tensile TGO, stress, and which the leadsundulating to the occurrenceTGO induces of cracksa tensile and stress, interfacial which delamination leads to the in occurrence TBCs. On the of othercracks hand, and duringinterfacial the fabricationdelamination and in service TBCs. processesOn the other of TBCs, hand, the during diffusion the offabrication atoms, e.g., and O service and Al, processes affects TGO of growthTBCs, the [2] anddiffusion forms of interdi atoms,ff usione.g., O zone and Al, [28 ].affects When TGO element grow dithff [2]usion and is forms promoted, interdiffusion TGO grows zone fast [28]. and When the interdielementff usiondiffusion zone is enlarges. promoted, While TGO creep grows cannot fast releaseand the the interdiffusion induced stress zone timely, enlarges. accordingly, While stresscreep increasescannot release remarkably the induced and then stress accelerates timely, the accord failuresingly, of TBCs. stress Thus, increases it is necessary remarkably to review and then and analyzeaccelerates the the related failures research of TBCs. on long-time Thus, it is oxidation necessary and to elementreview and diffusion. analyze the related research on long-timeTo clarify oxidation the long-term and element failure diffusion. mechanisms of TBCs in heavy-duty gas turbines, in this work, we To clarify the long-term failure mechanisms of TBCs in heavy-duty gas turbines, in this work, review TGO growth and element diffusion, respectively. We analyze the continuous growth process we review TGO growth and element diffusion, respectively. We analyze the continuous growth of TGO and the coupled stress-diffusion process of elements. Finally, a conclusion that highlights process of TGO and the coupled stress-diffusion process of elements. Finally, a conclusion that the roles of MO growth and element diffusion in the failures of TBCs in heavy-duty gas turbines is highlights the roles of MO growth and element diffusion in the failures of TBCs in heavy-duty gas made. Our results can provide some guide for improving the fabrication process and developing the turbines is made. Our results can provide some guide for improving the fabrication process and long-life TBCs. developing the long-life TBCs. 2. Long-Term Oxidation of TBCs 2. Long-Term Oxidation of TBCs During the long-time service of heavy-duty gas turbines, thermal stress is almost released by materialDuring creep the and long-time then TGO service growth of heavy-duty becomes one gas important turbines, causethermal for stress failures is almost of TBCs. released Different by frommaterial the creep short and oxidation then TGO duration growth of aero-engines,becomes one TGOimportant growth cause experiences for failures a continuousof TBCs. Different change from the short oxidation duration of aero-engines, TGO growth experiences a continuous change from α-Al2O3 to MO stage during the long-term oxidation of TBCs in heavy-duty gas turbines. After improvingfrom α-Al2O and3 to optimizingMO stage during the fabrication the long-term process, oxidation the whole of TBCs growth in heavy-duty of uniform gas MO turbines. induces After the large-scaleimproving spallingand optimizing of TBCs, the as shownfabrication in Figure process,3. Thus, the whole the continuous growth of growth uniform of TGOMO needsinduces to the be speciallylarge-scale considered spalling of for TBCs, the long-term as shown failuresin Figure of 3. heavy-duty Thus, the continuous gas turbines. growth of TGO needs to be specially considered for the long-term failures of heavy-duty gas turbines.

Figure 3. The large-scale spalling of TBCs after oxidizing for 500 h at 1100 ◦°C[C [11].11].

2.1. Research Advance on TGO Growth Until now,now, TGO TGO growth growth and and the the related related failures failures of TBCs of TBCs have attractedhave attracted increasing increasing attention attention [29–34]. Experimental[29–34]. Experimental results show results that show TGO exhibitsthat TGO the exhibits undulating the morphologyundulating morphology and cracks mainly and cracks occur aroundmainly theoccur convex around region the [35 convex–39]. Hutchinson region [35–39]. et al. [ 40Hutchinson] and Evans et al.al. [41[40]] investigated and Evans the et bucklingal. [41] ofinvestigated the TGO layer the inducedbuckling by of residual the TGO stress layer and induced established by theresidual critical stress criterion and ofestablished buckling deformation. the critical Mummcriterion et of al. buckling [42] and deformation. He et al. [43 ]Mumm studied et the al. displacement [42] and He instabilityet al. [43] andstudied the inducedthe displacement cracking ofinstability TBCs through and the a induced thermal cyclingcracking experiment of TBCs through and numerical a thermal simulation, cycling experiment respectively. and The numerical results simulation, respectively. The results revealed that the amplitude of the undulating TGO increases

Coatings 2020, 10, 1022 4 of 19 Coatings 2020, 10, x FOR PEER REVIEW 4 of 19 revealedwith the thatnumber the amplitudeof thermal ofcycling, the undulating which is also TGO called increases ratcheting, with the and number cracks of initiate thermal near cycling, TGO whichand gradually is also called propagate. ratcheting, Moreover, and cracksTolpygo initiate and Clarke near TGO [44,45] and found gradually that the propagate. rumpling Moreover, of oxide Tolpygorelated to and the Clarke grain [orientation44,45] found also that affects the rumpling the failur ofes oxide of TBCs. related Su to et the al. grain [46] investigated orientation also the aeffectffects theof TGO failures creep of on TBCs. the Sucrack et al.propagation [46] investigated in TC, theand etheffect results of TGO show creep that on with the crackthe increase propagation of TGO in TC,creep, and the the driving results force show for that crack with propagation the increase gradually of TGO creep, decreases, the driving and even force after for crack the TGO propagation creep is graduallystrong enough, decreases, crack and propagation even after the is TGO suppressed, creep is strong as shown enough, in crack Figure propagation 4. In addition, is suppressed, other asresearchers shown in [47–52] Figure4 investigated. In addition, the other influence researchers of undulating [ 47–52] investigated TGO morphology the influence on residual of undulating stress in TGOTBCs morphologyduring thermal on residualcycling. stressFor instance, in TBCs Chen during et thermalal. [53] adopted cycling. the For finite instance, element Chen method et al. [53 to] adoptedstudy the the effects finite of element different method TGO to asperities study the on eff ectsresidual of di ffstresserent TGOin TBCs, asperities and the on residualobtained stress results in TBCs,show andthat thethe obtained rougher resultsTGO is, show the that more the signific rougherant TGO the is,residual the more tensile significant stress the around residual the tensile peak stressregion around is. The theabove peak research region mainly is. The focuses above research on the undulating mainly focuses TGO on growth the undulating and the induced TGO growth stress andduring the thermal induced cycling. stress during However, thermal heavy-duty cycling. gas However, turbines heavy-duty experience gasfewturbines thermal experiencecycles, and fewthe thermalcontinuous cycles, growth and of the TGO continuous is a key growthfactor in of the TGO failure is a keyof TBCs. factor in the failure of TBCs.

Figure 4.4. TheThe variationvariation of of energy energy release release rate rate with with thermal thermal cycling cycling for diforﬀerent different thermally thermally grown grown oxide (TGO)oxide (TGO) creep [creep46]. [46].

Nowadays, manymany researchers researchers focus focus on continuouson continuous TGO growthTGO growth and the and induced the stressinduced evolution stress inevolution TBCs [54 in– TBCs60]. Evans [54–60]. et al.Evans [61] et utilized al. [61] Eshelby’s utilized Eshelby’s elastic inclusion elastic inclusion method tomethod make to TGO make growth TGO equivalentgrowth equivalent to the self-assembly to the self-assembly process of the proce free expansivess of the TGOfree shell,expansive and then TGO established shell, and a sphere then modelestablished of TGO a sphere growth. model Clarke of TGO [62] investigatedgrowth. Clarke the [62] lateral investigated growth of the TGO lateral at the growth grain of boundary TGO at . g . and obtained a linear relationship between the lateral growth strain rate ε and the thickening rateεhg, the grain boundary and obtained a linear relationship between the laterall growth strain rate l . g . i.e., ε = Doxh, where Dox is the scaleε coeg fficient related to the microstructure of oxide. Sun et al. [63] and lthe thickening rate h , i.e., lox = D h , where Dox is the scale coefficient related to the further set up a multilayer sphere model of the convex TBCs and considered TGO growth along microstructure of oxide. Sun et al. [63] further set up a multilayer sphere model of the convex TBCs with the thickness and in-plane directions, as shown in Figure5a. The results showed that TGO and considered TGO growth along with the thickness and in-plane directions, as shown in Figure growth generates the in-plane tensile stress in the TC, which can induce the occurrence of micro-cracks. 5a. The results showed that TGO growth generates the in-plane tensile stress in the TC, which can Lin et al. [64] and Shen et al. [65] adopted the conception of oxidation front and considered the induce the occurrence of micro-cracks. Lin et al. [64] and Shen et al. [65] adopted the conception of consumption of oxygen in the process of TGO growth, as shown in Figure5b; the obtained results oxidation front and considered the consumption of oxygen in the process of TGO growth, as shown revealed that plasticity, creep and the irregular morphology of TGO affect the induced stress in TBCs. in Figure 5b; the obtained results revealed that plasticity, creep and the irregular morphology of Moreover, TGO growth is more significant at the convex region relative to that at the concave region. TGO affect the induced stress in TBCs. Moreover, TGO growth is more significant at the convex Chai et al. [66] further investigated the stress development induced by “root-like” TGO growth, region relative to that at the concave region. Chai et al. [66] further investigated the stress and the results showed maximum tensile stress changes from the interface to the inside of the BC. development induced by “root-like” TGO growth, and the results showed maximum tensile stress Loeffel et al. [67,68] established a coupled constitutive theory of visco-plasticity, thermal expansion changes from the interface to the inside of the BC. Loeffel et al. [67,68] established a coupled and volumetric deformation induced by chemical reaction, and numerically described the flat and constitutive theory of visco-plasticity, thermal expansion and volumetric deformation induced by undulating TGO growth through the finite element method. However, the above research mainly chemical reaction, and numerically described the flat and undulating TGO growth through the considers the growth of α-Al2O3, which serves as the resistance to oxidation. Moreover, the induced finite element method. However, the above research mainly considers the growth of α-Al2O3, which serves as the resistance to oxidation. Moreover, the induced stress can be almost released by creep

Coatings 2020, 10, 1022 5 of 19

Coatings 2020, 10, x FOR PEER REVIEW 5 of 19 Coatings 2020, 10, x FOR PEER REVIEW 5 of 19 stress can be almost released by creep during the long-term service. Thus, the obtained results are not during the long-term service. Thus, the obtained results are not applicable to the oxidation failures applicableduring the tolong-term the oxidation service. failures Thus of, the TBCs obtained in heavy-duty results are gas not turbines. applicable to the oxidation failures of TBCs in heavy-duty gas turbines. of TBCs in heavy-duty gas turbines.

(a) (b) (a) (b) FigureFigure 5.5.( a()a The) The multilayer multilayer sphere sphere model model of TGO of growthTGO growth [63]; (b [63];) the schematic(b) the schematic diagram ofdiagram oxidation of Figure 5. (a) The multilayer sphere model of TGO growth [63]; (b) the schematic diagram of frontoxidation during front the during TGO growth the TGO [64 growth]. [64]. oxidation front during the TGO growth [64]. Recently,Recently, muchmuch researchresearch showsshows thatthat thethe growthgrowth ofof locallocal MOMO inducesinduces thethe failuresfailures ofof TBCsTBCs afterafter Recently, much research shows that the growth of local MO induces the failures of TBCs after thethe oxidation for for a a period period [69–71]. [69–71]. Busso Busso et etal. al. [72] [72 investigated] investigated the the effect eﬀect of TGO of TGO growth growth around around the the oxidation for a period [69–71]. Busso et al. [72] investigated the effect of TGO growth around the theconvex convex region region on onthe the stress stress evolution evolution in inTBCs, TBCs, and and the the results results showed showed that that the the fast fast growth ofof convex region on the stress evolution in TBCs, and the results showed that the fast growth of non-protectivenon-protective oxideoxide can can enhance enhance the the development development of stress.of stress. Li etLi al.et [al.73 ][73] experimentally experimentally observed observed that non-protective oxide can enhance the development of stress. Li et al. [73] experimentally observed thethat fast the growth fast growth of local of MO local induces MO induces the cracking the crac andking interfacial and interfacial delamination delamination in the TC, in as the shown TC, inas that the fast growth of local MO induces the cracking and interfacial delamination in the TC, as Figureshown6 a.in ZhangFigure et6a. al. Zhang [ 74] and et Xual. et[74] al. and [75] analyticallyXu et al. [75] and analytically numerically and model numerically the growth model of local the shown in Figure 6a. Zhang et al. [74] and Xu et al. [75] analytically and numerically model the MO,growth respectively, of local MO, as shownrespectively, in Figure as 6shownb; the resultsin Figu showedre 6b; the that results the suppression showed that of the local suppression MO growth of growth of local MO, respectively, as shown in Figure 6b; the results showed that the suppression of canlocal prolong MO growth the service can lifeprolong of TBCs. the Moreover, service life Zhang of TBCs. et al. [76Moreover,] healed the Zhang spattering et al. particles[76] healed through the local MO growth can prolong the service life of TBCs. Moreover, Zhang et al. [76] healed the subsequentspattering particles heat treatment through and subsequent then eliminated heat treatm the growthent and of localthen MO;eliminated the experiment the growth results of local showed MO; spattering particles through subsequent heat treatment and then eliminated the growth of local MO; that,the experiment after healing, results the lifetime showed of that, TBCs after is furtherhealing, extended. the lifetime of TBCs is further extended. the experiment results showed that, after healing, the lifetime of TBCs is further extended.

(a) (b) (a) (b) Figure 6. The local growth of mixed oxide (MO); (a) the local MO induces the failures of top ceramic Figure 6.6. The local growth of mixed oxide (MO); (a) the locallocal MOMO inducesinduces thethe failuresfailures ofof toptop ceramicceramic coat (TC) [73]; (b) the numerical model and results of the local MO growth [75]; Among, the thermal coatcoat (TC) [[73];73]; (b) the numerical model and results of the local MO growth [75]; [75]; Among, thethe thermalthermal expansion mismatch of MO and TC induces the interfacial tensile stress and debonding at stage A, expansion mismatchmismatch ofof MO MO and and TC TC induces induces the the interfacial interfacial tensile tensile stress stress and and debonding debonding at stage at stage A, the A, the growth of MO jacks TC up and induces the interfacial tensile stress at stage B, and the growth of growththe growth of MO of MO jacks jacks TCup TC and up inducesand induces the interfacial the interfacial tensile tensile stress stress at stage at stage B, and B,the and growth the growth of local of local MO induces the interfacial delamination at stage C. MOlocal induces MO induces the interfacial the interfacial delamination delamination at stage at stage C. C. However, after local MO growth is suppressed, with the continuous proceeding of oxidation, However, afterafter locallocal MOMO growthgrowth isis suppressed,suppressed, with the continuous proceeding of oxidation, cracking and interfacial delamination still occur in TBCs. Tang et al. [77] experimentally observed cracking and interfacialinterfacial delaminationdelamination still occur in TBCs.TBCs. Tang et al.al. [[77]77] experimentallyexperimentally observedobserved that after the composition of TGO changes from α-Al2O3 to MO, the delamination occurs at the thatthat afterafter thethe compositioncomposition ofof TGOTGO changeschanges fromfrom αα-Al-Al22O3 to MO, the delaminationdelamination occurs at thethe α-Al2O3/MO interface. Bai et al. [78] observed through the oxidation experiment of the CoNiCrAlY α-Al-Al22O3/MO/MO interface. Bai etet al.al. [78[78]] observed observed through through the the oxidation oxidation experiment experiment of theof the CoNiCrAlY CoNiCrAlY BC BC at 1100 °C that the whole growth of uniform MO still induces cracks in TBCs, as shown in BC at 1100 °C that the whole growth of uniform MO still induces cracks in TBCs, as shown in Figure 7. Xie et al. [11] further modeled the whole growth of uniform MO and investigated the Figure 7. Xie et al. [11] further modeled the whole growth of uniform MO and investigated the induced stress evolution, the obtained results revealed that the fast growth and large volumetric induced stress evolution, the obtained results revealed that the fast growth and large volumetric

Coatings 2020, 10, 1022 6 of 19

at 1100 ◦C that the whole growth of uniform MO still induces cracks in TBCs, as shown in Figure7. XieCoatings et al. 2020 [11, 10], further x FOR PEER modeled REVIEW the whole growth of uniform MO and investigated the induced stress6 of 19 evolution, the obtained results revealed that the fast growth and large volumetric expansion of MO expansion of MO generate the catastrophic stress and then lead to the failures of TBCs. Lim and generate the catastrophic stress and then lead to the failures of TBCs. Lim and Meguid [79] adopted the Meguid [79] adopted the coupled simulation of finite volume and finite element methods to coupled simulation of finite volume and finite element methods to numerically analyze the diffusion numerically analyze the diffusion of Cr and O. The results showed that even if the supply of Al is of Cr and O. The results showed that even if the supply of Al is enough, the growth of MO still occurs. enough, the growth of MO still occurs. Mahalingam et al. [80] experimentally investigated the Mahalingam et al. [80] experimentally investigated the effects of the composition and the growth rate effects of the composition and the growth rate of TGO on crack propagation in TBCs. The results of TGO on crack propagation in TBCs. The results showed that the appearance of MO can lead to the showed that the appearance of MO can lead to the fast propagation of the crack, which is consistent fast propagation of the crack, which is consistent with Xie et al.’s calculation results [11]. with Xie et al.’s calculation results [11].

Figure 7.7. The oxidationoxidation resultsresults of of CoNiCrAlY CoNiCrAlY bond bond coat coat (BC) (BC) at 1100at 1100◦C for°C (fora) 200(a) h;200 (b h;) 300 (b) h; 300 (c) h; 500 (c h) and500 h (d and) 1000 (d) h 1000 [78]. h [78]. 2.2. Failure Mechanism of TBCs Induced by the Growth of Uniform MO 2.2. Failure Mechanism of TBCs Induced by the Growth of Uniform MO Just as mentioned above, a heavy-duty gas turbine experiences few thermal cycles and is Just as mentioned above, a heavy-duty gas turbine experiences few thermal cycles and is continuously exposed to a high temperature for a long time, thus the whole growth of uniform MO continuously exposed to a high temperature for a long time, thus the whole growth of uniform MO is the dominant oxidation result. During TGO growth, the resultant stress in TBCs depends on the is the dominant oxidation result. During TGO growth, the resultant stress in TBCs depends on the competition between the stress generated by TGO growth and stress relaxation caused by creep. competition between the stress generated by TGO growth and stress relaxation caused by creep. Compared to the α-Al2O3 growth, MO grows much faster and expands more significantly, as shown in Compared to the α-Al2O3 growth, MO grows much faster and expands more significantly, as shown Figure6; correspondingly, the induced stress is more remarkable. As material creep almost has no time in Figure 6; correspondingly, the induced stress is more remarkable. As material creep almost has to release the induced stress, stress in TBCs increases significantly and even changes from compressive no time to release the induced stress, stress in TBCs increases significantly and even changes from stress to tensile stress, as shown in Figure8. In addition, as α-Al2O3 grows slowly, the induced stress is compressive stress to tensile stress, as shown in Figure 8. In addition, as α-Al2O3 grows slowly, the released by material creep significantly, thus, stress in TBCs is small and nearly compressive, which induced stress is released by material creep significantly, thus, stress in TBCs is small and nearly has been investigated by Sun et al. [63], and when TBCs experience few thermal cycles, the failures compressive, which has been investigated by Sun et al. [63], and when TBCs experience few cannot occur. thermal cycles, the failures cannot occur. During the growth of uniform MO, the out-plane tensile stress at the α-Al2O3/MO interface can induce the delamination and then lead to the spalling of TBCs. As the TC is pushed by the expansive MO, the in-plane stress in the TC is also tensile, which can generate the cracks along with intersplat. Meanwhile, the in-plane tensile stress in α-Al2O3 can lead to the occurrence of micro-cracks and then destroy its protective function. More O atoms and alloy elements diffuse along with the newly formed crack channel, and as a result, MO growth is further accelerated and even appears at the α-Al2O3/BC interface, and spheroidization occurs around the crack, as shown in Figure7. When MO grows faster, there is less time for creep to release the induced stress, thus the resultant stress in TBCs increases sharply, i.e., catastrophic stress develops.

Coatings 2020, 10, x FOR PEER REVIEW 7 of 19

Coatings 2020, 10, 1022 7 of 19 Coatings 2020, 10, x FOR PEER REVIEW 7 of 19

(a) (b)

Figure 8. The stress evolution at the typical locations during the α-Al2O3 and MO growth stages; (a) radial stress; (b) hoop stress [11].

During the growth of uniform MO, the out-plane tensile stress at the α-Al2O3/MO interface can induce the delamination and then lead to the spalling of TBCs. As the TC is pushed by the expansive MO, the in-plane stress in the TC is also tensile, which can generate the cracks along with intersplat. Meanwhile, the in-plane tensile stress in α-Al2O3 can lead to the occurrence of micro-cracks and then destroy its protective fu nction. More O atoms and alloy elements diffuse (a) (b) along with the newly formed crack channel, and as a result, MO growth is further accelerated and even Figureappears 8. TheatThe the stress stress α-Al evolution evolution2O3/BC interface,at at the the typical typical and locations locationsspheroidization during during the the occurs α-Alα-Al2O 23aroundO and3 and MO MOthe growth crack, growth stages; as stages; shown (a) in Figure(radiala) 7. radial When stress; stress; MO(b) (hoopb grows) hoop stress stressfaster, [11]. [11 there]. is less time for creep to release the induced stress, thus the resultant stress in TBCs increases sharply, i.e., catastrophic stress develops. Diﬀerent from the dense microstructure of α-Al2O3, MO exhibits a porous microstructure2 3 and is DifferentDuring the from growth the denseof uniform microstructure MO, the out-plane of α-Al2O tensile3, MO stressexhibits at thea porous α-Al O microstructure/MO interface andcan brittle, accordingly, cracks and interfacial delamination are prone to occur there. Thus, the growth of isinduce brittle, the accordingly, delamination cracks and andthen interfaciallead to the delamination spalling of areTBCs. prone As theto occurTC is there. pushed Thus, by the uniform MO and the induced catastrophic stress are responsible for failures of TBCs in heavy-duty gas growthexpansive of MO,uniform the in-planeMO and stressthe induced in the TC catastrophic is also tensile, stress which are responsiblecan generate for the failures cracks ofalong TBCs with in turbines, e.g., the cracks in α-Al2O3 and TC layers, and the delamination2 3 at the α-Al2O3/MO interface, heavy-dutyintersplat. Meanwhile,gas turbines, the e.g., in -planethe cracks tensile in αstress-Al2O 3 inand α -AlTC Olayers, can andlead the to delaminationthe occurrence at theof as shown in Figure9. According to the results, researchers can control the growth of uniform MO and αmicro-cracks-Al2O3/MO interface,and then asdestroy shown its in protectiveFigure 9. Accordingfunction. More to the O results, atoms researchersand alloy elements can control diffuse the suppress the diﬀusion of oxygen through improving material composition and fabrication processes to growthalong with of theuniform newly MOformed and crack suppress channel, the and diffus as aion result, of oxygenMO growth through is further improving accelerated material and further prolong the service lifetime of TBCs. compositioneven appears and at the fabrication α-Al2O3/BC processes interface, to furt andher spheroidization prolong the service occurs lifetime around of the TBCs. crack, as shown in Figure 7. When MO grows faster, there is less time for creep to release the induced stress, thus the resultant stress in TBCs increases sharply, i.e., catastrophic stress develops. Different from the dense microstructure of α-Al2O3, MO exhibits a porous microstructure and is brittle, accordingly, cracks and interfacial delamination are prone to occur there. Thus, the growth of uniform MO and the induced catastrophic stress are responsible for failures of TBCs in heavy-duty gas turbines, e.g., the cracks in α-Al2O3 and TC layers, and the delamination at the α-Al2O3/MO interface, as shown in Figure 9. According to the results, researchers can control the growth of uniform MO and suppress the diffusion of oxygen through improving material composition and fabrication processes to further prolong the service lifetime of TBCs.

Figure 9. SchematicSchematic diagram of the failures induced by the growth of uniform MO in TBCs [[11].11]. 3. Element Diﬀusion in TBCs

Besides oxidation, element diffusion is also a key factor in the fabrication and long-term failures of TBCs. For instance, the diffusion of Al determines the performance of the as-sprayed NiAl bond coat in the alloying process of cold-sprayed Ni/Al coating [81]. During the oxidation, the diffusion of O atom controls the growth of TGO [82], as shown in Figure 10a. Even the interdiffusion of alloy elements in the BC leads to the formation of Kirkendall voids at the interface [83], as shown in Figure 10b. These element diffusions directly affect the service performance of TBCs and need to be paid special attention. Herein,Figure as the 9. TC Schematic does not diagram involve of the the elementfailures induced diffusion, by the it is growth neglected of uniform in the MO following. in TBCs [11].

Coatings 2020, 10, x FOR PEER REVIEW 8 of 19

3. Element Diffusion in TBCs Besides oxidation, element diffusion is also a key factor in the fabrication and long-term failures of TBCs. For instance, the diffusion of Al determines the performance of the as-sprayed NiAl bond coat in the alloying process of cold-sprayed Ni/Al coating [81]. During the oxidation, the diffusion of O atom controls the growth of TGO [82], as shown in Figure 10a. Even the interdiffusion of alloy elements in the BC leads to the formation of Kirkendall voids at the interface [83], as shown in Figure 10b. These element diffusions directly affect the service performance of TBCsCoatings and2020 need, 10, 1022 to be paid special attention. Herein, as the TC does not involve the element8 of 19 diffusion, it is neglected in the following.

(a) (b)

FigureFigure 10. 10. ((aa)) TheThe didiffusionﬀusion paths paths of Oof and O Aland atoms Al at duringoms during the TGO the growth TGO [ 82growth]; (b) the [82]; interdi (b)ﬀ usionthe interdiffusionof alloy element of alloy between element BC andbetween substrate BC and [83 ].substrate [83].

3.1.3.1. Research Research Progress Progress on on Diffusion Diffusion Nowadays,Nowadays, element element didiffusionffusion has has attracted attracted increasing increasing attention attention [84]. First, [84] Fick. First, [85] investigatedFick [85] investigatedthe diffusion the from diffusion a high from concentration a high concentratio to a low one,n to and a low obtained one, and a linear obtained relationship a linear betweenrelationship flux J and concentration gradient C, which is also∇ called as “Fick’s law”, expressed as between flux J and concentration∇ gradient C , which is also called as “Fick’s law”, expressed as J=−= D ∇ C (1) J −DC∇ (1) where D is diffusivity. Darken [86,87] further considered that the gradient of chemical potential is the where D is diffusivity. Darken [86,87] further considered that the gradient of chemical potential is driving force for diffusion, and the flux is approximatively related to the gradient of chemical potential the driving force for diffusion, and the flux is approximatively related to the gradient of chemical µ, expressed∇μ as potential∇ , expressed as J = MC µ (2) − ∇ =− ∇μ where M is the mobility of the atom, and satisfiesJMC the relationship D = MRT. Equation (2) can describe(2) many diffusion phenomena, including the “uphill diffusion” which cannot be explained by Fick’s law. whereWhen M the chemicalis the mobility potential of the of atoms atom,is and only satisfies determined the relationship by their concentration, D = MRT . Equation (2) iscan the describesame as many Fick’s diffusion law, that phenomena, is, the concentration including gradient the “uphill drives diffusion” the diffusion which of cannot atoms. be explained by Fick’s However,law. When element the chemical diffusion potential induces significantof atoms is stress only in determined TBCs and in by turn their affects concentration, the diffusion Equationprocess. (2) F.Q. is Yangthe same [88], as Wang Fick’s et al.law, [89 that], and is, Zhangthe concentration et al. [90], respectively, gradient drives investigated the diffusion the e ffofect atoms.of stress on diffusion in a plate, hollow cylinder as well as sphere model through considering the contributionHowever, ofelement hydrostatic diffusion stress inducesσm to thesignificant chemical stress potential in TBCsµ, and and the in resultsturn affects revealed the diffusion that stress process.promotes F.Q. di ffYangusion [88], of atoms; Wang hereet al. the [89], expression and Zhan ofg chemicalet al. [90], potential respectively can be, investigated written as the effect of stress on diffusion in a plate, hollow cylinder as well as sphere model through considering the contribution of hydrostatic stress σ µto =theµ chemical+ RT ln X potentialΩσm μ , and the results revealed that(3) m 0 − stress promotes diffusion of atoms; here the expression of chemical potential can be written as where µ0 is the reference, R is gas constant, T is the absolute temperature. X is the fraction concentration, Ω is the partial molar volume and herein assumed to be constant. Moreover, Suo and Shen [91] considered the contribution of chemical reaction to element diffusion, expressed as

∂C . + J + r = 0 (4) ∂t ∇ · . where r is chemical reaction rate. Wang et al. [92] further investigated the transfer processes of O and Al atoms during the concave TGO growth. Coatings 2020, 10, x FOR PEER REVIEW 9 of 19

μμ=+ −Ωσ 0 RTln X m (3)

μ where 0 is the reference, R is gas constant, T is the absolute temperature. X is the fraction concentration, Ω is the partial molar volume and herein assumed to be constant. Moreover, Suo and Shen [91] considered the contribution of chemical reaction to element diffusion, expressed as

∂C +∇⋅Jr +& =0 (4) ∂t

Coatingswhere 2020r& is, 10 chemical, 1022 reaction rate. Wang et al. [92] further investigated the transfer processes9 of of 19O and Al atoms during the concave TGO growth. Meanwhile, Haftbaradaran et al. [93] considered the effect of stress on the energy barrier of Meanwhile, Haftbaradaran et al. [93] considered the effect of stress on the energy barrier of atomic atomic jump during the diffusion and obtained a diffusivity with stress effect, expressed as jump during the diffusion and obtained a diffusivity with stress effect, expressed as ασΩ = αΩσb DDD= D0 expexp (5)(5) 0 RT where D0 is the pre-factor of diffusivity, α is positive dimensionless factor, and σσb is stress. where D0 is the pre-factor of diffusivity, is positive dimensionless factor, and b is stress. Dong et al. [94] adopted the diffusivity with stress effect to investigate the influence of stress on Dong et al. [94] adopted the diffusivity with stress effect to investigate the influence of stress on the the growth of metal oxide, the results showed that the induced stress slows down the thickening growth of metal oxide, the results showed that the induced stress slows down the thickening of of oxide film through retarding the diffusion of oxygen. Fang et al. [95] further observed through oxide film through retarding the diffusion of oxygen. Fang et al. [95] further observed through a a three-point bending experiment of MoCu alloy at 550 C that the thickness of oxide film at the three-point bending experiment of MoCu alloy at 550 °C◦ that the thickness of oxide film at the compressive region is significantly thinner than that at the tensile region, as shown in Figure 11. On compressive region is significantly thinner than that at the tensile region, as shown in Figure 11. On the basis of the above research, we can see that stress significantly affects element diffusion through the basis of the above research, we can see that stress significantly affects element diffusion through changing both the chemical potential and diffusivity. Whether stress accelerates diffusion or not changing both the chemical potential and diffusivity. Whether stress accelerates diffusion or not depends on the actual service condition of TBCs. depends on the actual service condition of TBCs.

Figure 11.11. TheThe three-pointthree-point bending bending experiment experiment results results during during the the oxidation oxidation ofMoCu of MoCu alloy alloy at 55 at◦C[ 5595 °C]; ([95];a) oxide (a) oxide ﬁlm atfilm the at compressive the compressive region; region; (b) oxide (b) oxide ﬁlm at film the at tensile the tensile region. region.

As a heavy-duty gas turbine operates at a high temperature for a long time,time, stress relaxationrelaxation caused by creep isis significant.significant. Moreover, Moreover, both cr creepeep and didiffusionffusion are the samesame time-scaletime-scale atomicatomic processes [96[96,97].,97]. Thus, Thus, creep creep is theis importantthe important stress stress relaxation relaxation mechanism mechanism along with along element with dielementffusion. Xiediffusion. et al.’s Xie [81] et study al.’s [81] revealed study that revealed the concentration that the concentration of Al is low of without Al is low stress without relaxation stress duringrelaxation the alloyingduring the of alloying Ni/Al coating. of Ni/Al Sethuraman coating. Sethuraman et al.’s [98, 99et ]al.’s experimental [98,99] experimental results further results verify further that verify stress relaxationthat stress existsrelaxation in the exists process in ofthe di processffusion andof diff theusion relaxation and the behavior relaxation of stress behavior is more of stress in accordance is more within accordance creep. Brassart with creep. and Suo Brassart [100]considered and Suo [100] the flowconsidered deformation the flow of solidsdeformation induced of by solids the insertioninduced ofby guestthe insertion atoms as of reaction guest atoms flow, andas reaction proposed flow the, and corresponding proposed the rate-dependent corresponding and rate-dependent -independent constitutiveand -independent relationships. constitutive Meanwhile, relationships. many researchers Meanwhile, [101 –103many] consider researchers plasticity [101–103] in the processconsider of elementplasticity di inff usion.the process Zhao of et element al. [104,105 diffusion.] and Di Zhao Leo etet al.al. [[104,105]106] introduced and Di plasticityLeo et al. to[106] accommodate introduced the large volumetric expansion induced by diffusion, and the results showed that plasticity releases the induced stress significantly. Other researchers [107–110] adopted elastic softening, i.e., elastic modulus changes with the concentration, to be responsible for stress relaxation during the diffusion. However, Chang et al.’s [111] work revealed that compared to the diffusivity, elastic softening is not the dominant factor in stress relaxation. In addition, Lu et al. [112] and Xu et al. [113] considered the stress relaxation induced by creep in a low-melting-point Sn electrode during Li diffusion, the results showed that creep can improve the durability of electrode. While for the element diffusion of TBCs in heavy-duty gas turbines, there still lacks the related research to clarify the role of creep. Furthermore, interface property and residual stress also affect the element diffusion in TBCs. In the fabrication and service processes of TBCs, the surface of the BC is inevitably affected by the external Coatings 2020, 10, x FOR PEER REVIEW 10 of 19 plasticity to accommodate the large volumetric expansion induced by diffusion, and the results showed that plasticity releases the induced stress significantly. Other researchers [107–110] adopted elastic softening, i.e., elastic modulus changes with the concentration, to be responsible for stress relaxation during the diffusion. However, Chang et al.’s [111] work revealed that compared to the diffusivity, elastic softening is not the dominant factor in stress relaxation. In addition, Lu et al. [112] and Xu et al. [113] considered the stress relaxation induced by creep in a low-melting-point Sn electrode during Li diffusion, the results showed that creep can improve the durability of electrode. While for the element diffusion of TBCs in heavy-duty gas turbines, there still lacks the related research to clarify the role of creep. CoatingsFurthermore,2020, 10, 1022 interface property and residual stress also affect the element diffusion in 10TBCs. of 19 In the fabrication and service processes of TBCs, the surface of the BC is inevitably affected by the external reservoir, e.g., pre-oxidation, and then changes the interface property, as shown in Figure reservoir, e.g., pre-oxidation, and then changes the interface property, as shown in Figure 12. Similarly, 12. Similarly, during the charging and discharging of Li-ion batteries, solid electrolyte interphase during the charging and discharging of Li-ion batteries, solid electrolyte interphase (SEI) forms at the (SEI) forms at the surface of the electrode and then induces the capacity loss of the Li-ion battery surface of the electrode and then induces the capacity loss of the Li-ion battery [114]. In addition, sand [114]. In addition, sand blast, powder particle impact and quenching also generate residual stress in blast, powder particle impact and quenching also generate residual stress in TBCs. The change of TBCs. The change of interface property and the generated residual stress can significantly affect the interface property and the generated residual stress can significantly affect the insertion of atoms at the insertion of atoms at the boundary and the subsequent diffusion in TBCs. Zhang et al. [115] boundary and the subsequent diffusion in TBCs. Zhang et al. [115] investigated the effect of the initial investigated the effect of the initial TGO thickness on its fracture contraction, the results showed TGO thickness on its fracture contraction, the results showed that the thinner the initial TGO is, the that the thinner the initial TGO is, the easier the fracture contraction is. Xie et al. [81] modeled the easier the fracture contraction is. Xie et al. [81] modeled the alloying process of cold-sprayed Ni/Al alloying process of cold-sprayed Ni/Al coatings, and found that residual stress and interface coatings, and found that residual stress and interface property can significantly affect the diffusion property can significantly affect the diffusion of Al in the coating. However, the present research of Al in the coating. However, the present research [116–119] mainly focuses on the improvement of [116–119] mainly focuses on the improvement of interface property through adjusting the material interface property through adjusting the material composition and fabrication process. The effect of composition and fabrication process. The effect of interface property on element diffusion in TBCs interface property on element diffusion in TBCs still lacks the related research. still lacks the related research.

Figure 12.12. TheThe micromorphology micromorphology of of pre-oxidized BC [[120].120]. ( (aa)) The The surface surface morphology morphology of of the as-sprayed BC; ( b) the micro cross-section of the as-sprayedas-sprayed BC.BC. 3.2. Failure Mechanism of TBCs Related to Element Diffusion 3.2. Failure Mechanism of TBCs Related to Element Diffusion As a long-time evolution process, element diffusion is also closely related to the failures of TBCs in As a long-time evolution process, element diffusion is also closely related to the failures of heavy-duty gas turbines [121–124]. Besides controlling TGO growth, element diffusion between the BC TBCs in heavy-duty gas turbines [121–124]. Besides controlling TGO growth, element diffusion and substrate forms an interdiffusion region and changes the phase component [125]. The accumulation between the BC and substrate forms an interdiffusion region and changes the phase component of vacancy near the interface leads to the appearance of Kirkendall voids [126] and then changes the [125]. The accumulation of vacancy near the interface leads to the appearance of Kirkendall voids interfacial strength, as shown in Figure 10b. Elsass et al. [83] investigated the effect of MCrAlY bond [126] and then changes the interfacial strength, as shown in Figure 10b. Elsass et al. [83] investigated coat fabrication processes on the formation of Kirkendall voids, the results showed that compared to the effect of MCrAlY bond coat fabrication processes on the formation of Kirkendall voids, the bond coats sprayed by high-velocity oxygen fuel (HVOF), bond coat fabricated by low pressure plasma results showed that compared to bond coats sprayed by high-velocity oxygen fuel (HVOF), bond spraying (LPPS) has the less Kirkendall voids during the oxidation, and the location of voids changes coat fabricated by low pressure plasma spraying (LPPS) has the less Kirkendall voids during the from bond coat to superalloy substrate. Texier et al. [127] carried out the micro-tensile experiment of oxidation, and the location of voids changes from bond coat to superalloy substrate. Texier et al. the specimen taken from the interdiffusion region. The obtained results revealed that the existence of [127] carried out the micro-tensile experiment of the specimen taken from the interdiffusion region. void decreases the mechanical property of the interdiffusion region. Qi et al. [128] investigated the cyclic oxidation behavior of β-NiAlHfCrSi coatings at 1150 ◦C, and found that the formation of voids under the oxide layer is the cause for its severe spalling. To evaluate the failures of TBCs induced by element diffusion, it is necessary to make clear the intrinsic mechanism of diffusion. Herein, we take the alloying process of Ni/Al coatings as a typical case to clarify the diffusion process of atoms. When diffusion starts, the Al atom firstly inserts into the Ni splat at the boundary. The insertion of Al induces significant compressive stress and increases the chemical potential. Accordingly, the difference in chemical potential between the external Al reservoir and Ni splat, which serves as the driving force for the insertion, is decreased. Thus, the supply of the Al atom gradually Coatings 2020, 10, x FOR PEER REVIEW 11 of 19

The obtained results revealed that the existence of void decreases the mechanical property of the interdiffusion region. Qi et al. [128] investigated the cyclic oxidation behavior of β-NiAlHfCrSi coatings at 1150 °C, and found that the formation of voids under the oxide layer is the cause for its severe spalling. To evaluate the failures of TBCs induced by element diffusion, it is necessary to make clear the intrinsic mechanism of diffusion. Herein, we take the alloying process of Ni/Al coatings as a typical case to clarify the diffusion process of atoms. When diffusion starts, the Al atom firstly inserts into the Ni splat at the boundary. The insertion of Al induces significant compressive stress and increases the chemical potential. Accordingly, the difference in chemical potential between the external Al reservoir and Ni splat, which serves as the driving force for the insertion, is decreased. Thus, the supply of the Al atom Coatings 2020, 10, 1022 11 of 19 gradually decreases until it vanishes, and then diffusion reaches equilibrium. During the insertion of Al, the flux at the boundary can be written as decreases until it vanishes, and then diffusion reaches equilibrium. During the insertion of Al, the flux =−()μμ − ′ at the boundary can be written as Jk (6) J = k(µ µ0) (6) − − where k is interfacial diffusivity and characterizes the interface property, and μ′ is the chemical where k is interfacial diffusivity and characterizes the interface property, and µ0 is the chemical potential potential of the external reservoir. When residual stress induced by cold spray is tensile, the of the external reservoir. When residual stress induced by cold spray is tensile, the chemical potential chemical potential of Al is decreased, and then the flux at the boundary increases and the of Al is decreased, and then the flux at the boundary increases and the concentration of Al enlarges. concentration of Al enlarges. Otherwise, the concentration of Al in Ni splat is decreased by residual Otherwise, the concentration of Al in Ni splat is decreased by residual compressive stress. Moreover, compressive stress. Moreover, as shown in Figure 13, compared to the case without stress effect, the as shown in Figure 13, compared to the case without stress effect, the flux in the case with stress effect flux in the case with stress effect decreases more significantly. Thus, stress promotes the alloying decreases more significantly. Thus, stress promotes the alloying but decreases the concentration of Al, but decreases the concentration of Al, and the obtained quantitative relationship between the and the obtained quantitative relationship between the thickness of Ni splat and the alloying time thickness of Ni splat and the alloying time significantly deviates from the common parabolic law. significantly deviates from the common parabolic law. While the previous research [90] shows that While the previous research [90] shows that stress accelerates the diffusion, the reason is that the stress accelerates the diffusion, the reason is that the flux at the boundary is kept as a constant. For flux at the boundary is kept as a constant. For element diffusion in TBCs, the common constant element diffusion in TBCs, the common constant concentration or flux condition at the boundary is not concentration or flux condition at the boundary is not applicable, and the flux at the boundary is applicable, and the flux at the boundary is affected by the induced stress and interface property. affected by the induced stress and interface property.

Figure 13. The fluxes at the boundary with and without stress effect, among which, ε0 is the residual Figure 13. The fluxes at the boundary with and without stress effect, among which, ε is the strain [81]. 0 residual strain [81]. After the Al atom inserts into Ni splat, the large chemical potential gradient drives the Al atom to diffAfteruse forwardsthe Al atom in Niinserts splat, into as shownNi splat, in the Figure large 14 chemicala. The insertion potential of gradient Al distorts drives the surrounding the Al atom atomicto diffuse network, forwards and in then Ni splat, induces as significantshown in Figure stress. Meanwhile,14a. The insertion the exchange of Al distorts of atoms the can surrounding release the inducedatomic network, stress and and creep then occurs. induces Thus, significant the resultant stress. stressMeanwhile, depends the on exchange the competition of atoms between can release the stressthe induced generation stress by and atomic creep insertion occurs. andThus, stress the resultant relaxation stress by creep. depends The occurrenceon the competition of stress between not only atheffects stress the generation chemical potential by atomic but insertion also changes and stress the energyrelaxation barrier by creep. of atomic The occurrence jump, thus, of both stress stress not andonly itsaffects gradient the achemicalffect the dipotentialffusion process.but also Withchange thes proceedingthe energy barrier of diffusion, of atomic the chemical jump, thus, potential both gradientstress and in its Ni gradient splat gradually affect the reduces diffusion until process. it vanishes, With and the then proceedi the alloyingng of diffusion, process completes the chemical and Al distributes uniformly, as shown in Figure 14b. During the fabrication and operation of TBCs in heavy-duty gas turbines, element diffusion, creep as well as the induced stress affect the mechanical performance and service lifetime of TBCs. The change of phase component and the occurrence of Kirkendall voids and oxidation, which is closely related to element diffusion, determine the long-term failure patterns and mechanisms of TBCs. According to the results, researchers are encouraged to specially focus and control element diffusion in TBCs through adjusting material composition, imposing external force and developing new interface designs, etc. Coatings 2020, 10, x FOR PEER REVIEW 12 of 19

Coatingspotential2020 gradient, 10, 1022 in Ni splat gradually reduces until it vanishes, and then the alloying process12 of 19 completes and Al distributes uniformly, as shown in Figure 14b.

(a)

(b)

Figure 14. The diffusion diﬀusion of Al in Ni splat during the alloying of NiNi/Al/Al coating [[81];81]; ((a)) the distribution of thethe variationvariation of of chemical chemical potential; potential; (b )(b the) the distribution distribution of concentration of concentrat ofion Al. of Note Al. Note that in that this in work, this stresswork, relaxationstress relaxation and the and change the change of the energyof the en barrierergy barrier of atomic of atomic jump are jump not are considered. not considered.

4. SummaryDuring the fabrication and operation of TBCs in heavy-duty gas turbines, element diffusion, creepAiming as well toas clarify the induced the long-term stress affect failures the ofme TBCschanical in heavy-dutyperformance gas and turbines, service inlifetime this work, of TBCs. the researchThe change on TGOof phase growth component and element and ditheffusion occurrence are reviewed, of Kirkendall which isvoids mainly and related oxidation, to time which effects. is Theclosely failures related of TBCs to element induced diffusion, by the growth determine of uniform the MOlong-term and the failure implied patterns mechanism and aremechanisms summarized. of TheTBCs. atomic According process to ofthe element results, di researchersffusion in TBCsare encouraged and the induced to specially change focus in performance and control areelement also analyzed.diffusion in According TBCs through to the adjusting results, the material following comp conclusionsosition, imposing are drawn: external force and developing new interface designs, etc. a. Oxidation and element diffusion are responsible for the long-term failure mechanisms of TBCs. 4. SummaryDifferent from the failures induced by the frequent thermal cycles in aero-engines, for heavy-duty gas turbines, the initial thermal stress can be almost released by material creep, and the long-time Aimingoxidation to andclarify element the long-term diffusion failures determine of TBCs the changein heavy-duty in performance gas turbines, and in service this work, lifetime the researchof TBCs. on TGO growth and element diffusion are reviewed, which is mainly related to time b.effects.The The catastrophic failures of stressTBCs induced by the growth of uniform MO isand a keythe causeimplied for mechanism the long-term are summarized. The atomic process of element diffusion in TBCs and the induced change in failure of TBCs. Compared to the slow growth of α-Al2O3, the fast growth and large expansion of performance are also analyzed. According to the results, the following conclusions are drawn: MO induce the out-plane tensile stress at the α-Al2O3/MO interface and the in-plane tensile stress in α-Al2O3 and TC layers. Accordingly, interfacial delamination and micro-cracks can appear in

Coatings 2020, 10, 1022 13 of 19

TBCs. Especially, once crack occurs in α-Al2O3 layer, its protective function is destroyed, MO growth is further accelerated and then the lifetime of TBCs is reduced significantly. c. The formations of an interdiffusion region and Kirkendall voids induced by element diffusion also play the key roles in the long-term failures of TBCs, besides controlling TGO growth. The process of element diffusion in TBCs is affected by stress, creep and interface property, etc. Moreover, the interdiffusion of alloy elements, surface oxidation of the BC and residual stress affect the distribution of element in TBCs, and then change the phase component, which leads to change in mechanical performance.

Our results provide an insight into the failures of TBCs in heavy-duty gas turbines and clarify the long-term failure mechanisms. We also suggest that controlling the growth rate of uniform MO, oxygen diﬀusion and interface property of the BC can further prolong the service life of TBCs. On the basis of results, researchers can develop long-life TBCs through adjusting material composition, improving the fabrication process and optimizing the structure design.

Author Contributions: Conceptualization, F.X. and W.Z.; investigation, F.X.; writing—original draft preparation, F.X.; writing—review and editing, F.X., D.L. and W.Z.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Natural Science Foundation of China (NSFC), grant No. 11972025, 11772246, 11472203, 11172227, in part by Program for New Century Excellent Talents in University, grant No. NCET-13-0466. Acknowledgments: We thank Wang, T.J. for his helpful suggestion. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Clarke, D.R.; Oechsner, M.; Padture, N.P. Thermal-barrier coatings for more eﬃcient gas-turbine engines. MRS Bull. 2012, 37, 891–902. [CrossRef] 2. Padture, N.P.; Gell, M.; Jordan, E.H. Materials science-Thermal barrier coatings for gas-turbine engine applications. Science 2002, 296, 280–284. [CrossRef] 3. Zhang, W.W.; Li, G.R.; Zhang, Q.; Yang, G.J. Comprehensive damage evaluation of localized spallation of thermal barrier coatings. J. Adv. Ceram. 2017, 6, 230–239. [CrossRef] 4. Zhou, J.H. The process management and fault treament of 9F gas turbine during A-class maintenance. Intern. Combust. Engine Parts 2017, 60–62. (In Chinese) 5. Zeng, Z. The experience in formulating the repair cycle of gas turbine. Gas Turbine Technol. 2012, 25, 68–72. (In Chinese) 6. Rosler, J.; Baker, M.; Aufzug, K. A parametric study of the stress state of thermal barrier coatings-Part I: Creep relaxation. Acta Mater. 2004, 52, 4809–4817. [CrossRef] 7. Rosler, J.; Baker, M.; Volgmann, M. Stress state and failure mechanisms of thermal barrier coatings: Role of creep in thermally grown oxide. Acta Mater. 2001, 49, 3659–3670. [CrossRef] 8. Lee, C.H.; Kim, H.K.; Choi, H.S.; Ahn, H.S. Phase transformation and bond coat oxidation behavior of plasma-sprayed zirconia thermal barrier coating. Surf. Coat. Technol. 2000, 124, 1–12. [CrossRef] 9. Ali, M.S.; Song, S.H.; Xiao, P. Degradation of thermal barrier coatings due to thermal cycling up to 1150 degrees C. J. Mater. Sci. 2002, 37, 2097–2102. [CrossRef] 10. Ma, K.K.; Schoenung, J.M. Isothermal oxidation behavior of cryomilled NiCrAlY bond coat: Homogeneity and growth rate of TGO. Surf. Coat. Technol. 2011, 205, 5178–5185. [CrossRef] 11. Xie, F.; Sun, Y.L.; Li, D.J.; Bai, Y.; Zhang, W.X. Modelling of catastrophic stress development due to mixed oxide growth in thermal barrier coatings. Ceram. Int. 2019, 45, 11353–11361. [CrossRef] 12. Gupta, M.; Eriksson, R.; Sand, U.; Nylen, P. A diﬀusion-based oxide layer growth model using real interface roughness in thermal barrier coatings for lifetime assessment. Surf. Coat. Technol. 2015, 271, 181–191. [CrossRef] Coatings 2020, 10, 1022 14 of 19

13. Soulignac, R.; Maurel, V.; Remy, L.; Koster, A. Cohesive zone modelling of thermal barrier coatings interfacial properties based on three-dimensional observations and mechanical testing. Surf. Coat. Technol. 2013, 237, 95–104. [CrossRef] 14. Fan, X.L.; Zhang, W.X.; Wang, T.J.; Sun, Q. The effect of thermally grown oxide on multiple surface cracking in air plasma sprayed thermal barrier coating system. Surf. Coat. Technol. 2012, 208, 7–13. [CrossRef] 15. Zhang, J.; Guo, X.Y.; Jung, Y.G.; Li, L.; Knapp, J. Lanthanum zirconate based thermal barrier coatings: A review. Surf. Coat. Technol. 2017, 323, 18–29. [CrossRef] 16. Thakare, J.G.; Pandey, C.; Mahapatra, M.M.; Mulik, R.S. Thermal barrier coatings-A state of the art review. Met. Mater. Int. 2020, 1–22. [CrossRef] 17. Liu, M.J.; Zhang, G.; Lu, Y.H.; Han, J.Q.; Li, G.R.; Li, C.X.; Li, C.J.; Yang, G.J. Plasma spray-physical vapor deposition toward advanced thermal barrier coatings: A review. Rare Met. 2020, 39, 479–497. [CrossRef] 18. Mehta, A.; Vasudev, H.; Singh, S. Recent developments in the designing of deposition of thermal barrier coatings—A review. Mater. Today Proc. 2020, 26, 1336–1342. [CrossRef] 19. Yang, X.; Zhang, J.; Lu, Z.; Park, H.Y.; Jung, Y.G.; Park, H.; Koo, D.D.; Sinatra, R.; Zhang, J. Removal and repair techniques for thermal barrier coatings: A review. Trans. IMF 2020, 98, 121–128. [CrossRef] 20. Zhou, Y.; Liu, Q.; Yang, L.; Wu, D.; Mao, W. Failure mechanisms and life prediction of thermal barrier coatings. Acta Mech. Solida Sin. 2010, 31, 504–531. 21. Miller, R.A. Current status of thermal barrier coatings—An overview. Surf. Coat. Technol. 1987, 30, 1–11. [CrossRef] 22. Vassen, R.; Jarligo, M.O.; Steinke, T.; Mack, D.E.; Stover, D. Overview on advanced thermal barrier coatings. Surf. Coat. Technol. 2010, 205, 938–942. [CrossRef] 23. Mehboob, G.; Liu, M.-J.; Xu, T.; Hussain, S.; Mehboob, G.; Tahir, A. A review on failure mechanism of thermal barrier coatings and strategies to extend their lifetime. Ceram. Int. 2020, 46, 8497–8521. [CrossRef] 24. Hu, Z.-C.; Liu, B.; Wang, L.; Cui, Y.-H.; Wang, Y.-W.; Ma, Y.-D.; Sun, W.-W.; Yang, Y. Research progress of failure mechanism of thermal barrier coatings at high temperature via finite element method. Coatings 2020, 10, 732. [CrossRef] 25. Wang, L.; Li, D.C.; Yang, J.S.; Shao, F.; Zhong, X.H.; Zhao, H.Y.; Yang, K.; Tao, S.Y.; Wang, Y. Modeling of thermal properties and failure of thermal barrier coatings with the use of finite element methods: A review. J. Eur. Ceram. Soc. 2016, 36, 1313–1331. [CrossRef] 26. Wang, T.; Fan, X.; Sun, Y.; Su, L.; Song, Y.; Lv, B. The stresses and cracks in thermal barrier coating system: A review. Chin. J. Solid Mech. 2016, 37, 477–517. 27. Lv, B.W.; Jin, X.C.; Cao, J.; Xu, B.S.; Wang, Y.G.; Fang, D.N. Advances in numerical modeling of environmental barrier coating systems for gas turbines. J. Eur. Ceram. Soc. 2020, 40, 3363–3379. [CrossRef] 28. Elsass, M.; Frommherz, M.; Oechsner, M. The Influence of the coating deposition process on the interdiffusion behavior between nickel-based superalloys and MCrAlY bond coats. J. Therm. Spray Technol. 2018, 27, 379–390. [CrossRef] 29. Wei, Z.Y.; Cai, H.N. Comprehensive effects of TGO growth on the stress characteristic and delamination mechanism in lamellar structured thermal barrier coatings. Ceram. Int. 2020, 46, 2220–2237. [CrossRef] 30. Chai, Y.J.; Lin, C.; Li, Y.M. Effects of creep-plastic behavior on stress development in TBCs during cooling. Ceram. Int. 2017, 43, 11627–11634. [CrossRef] 31. Yang, S.; Peng, H.; Zhang, T. A damage model to evaluate the mechanical properties in the medium-long life stage for coating system subjected to elevated thermal loads with 3D-DIC technique. J. Alloy. Compd. 2020, 832, 154955. [CrossRef] 32. Liu, Y.Z.; Hu, X.B. Segregation and microstructural evolution at interfaces of atmospheric plasma sprayed thermal barrier coatings during thermal cycling. J. Alloy. Compd. 2020, 819, 13. [CrossRef] 33. Yu, Q.M.; Zhou, H.L.; Wang, L.B. Influences of interface morphology and thermally grown oxide thickness on residual stress distribution in thermal barrier coating system. Ceram. Int. 2016, 42, 8338–8350. [CrossRef] 34. Balint, D.S.; Hutchinson, J.W. An analytical model of rumpling in thermal barrier coatings. J. Mech. Phys. Solids 2005, 53, 949–973. [CrossRef] 35. Karlsson, A.M.; Hutchinson, J.W.; Evans, A.G. A fundamental model of cyclic instabilities in thermal barrier systems. J. Mech. Phys. Solids 2002, 50, 1565–1589. [CrossRef] Coatings 2020, 10, 1022 15 of 19

36. Naumenko, D.; Shemet, V.; Singheiser, L.; Quadakkers, W.J. Failure mechanisms of thermal barrier coatings on MCrAlY-type bondcoats associated with the formation of the thermally grown oxide. J. Mater. Sci. 2009, 44, 1687–1703. [CrossRef] 37. Rabiei, A.; Evans, A.G. Failure mechanisms associated with the thermally grown oxide in plasma-sprayed thermal barrier coatings. Acta Mater. 2000, 48, 3963–3976. [CrossRef] 38. Chen, W.R.; Wu, X.; Marple, B.R.; Nagy, D.R.; Patnaik, P.C. TGO growth behaviour in TBCs with APS and HVOF bond coats. Surf. Coat. Technol. 2008, 202, 2677–2683. [CrossRef] 39. Tang, J.J.; Bai, Y.; Liu, K.; Zhang, P.; Li, B.Q.; Yang, J.F. Microstructural evolution of SAPS/HVOF CoNiCrAlY alloy coating during thermal cycling test. Oxid. Met. 2016, 86, 75–87. [CrossRef] 40. Hutchinson, J.W.; He, M.Y.; Evans, A.G. The influence of imperfections on the nucleation and propagation of buckling driven delaminations. J. Mech. Phys. Solids 2000, 48, 709–734. [CrossRef] 41. Evans, A.G.; Mumm, D.R.; Hutchinson, J.W.; Meier, G.H.; Pettit, F.S. Mechanisms controlling the durability of thermal barrier coatings. Prog. Mater. Sci. 2001, 46, 505–553. [CrossRef] 42. Mumm, D.R.; Evans, A.G.; Spitsberg, I.T. Characterization of a cyclic displacement instability for a thermally grown oxide in a thermal barrier system. Acta Mater. 2001, 49, 2329–2340. [CrossRef] 43. He, M.Y.; Hutchinson, J.W.; Evans, A.G. Simulation of stresses and delamination in a plasma-sprayed thermal barrier system upon thermal cycling. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2003, 345, 172–178. [CrossRef] 44. Tolpygo, V.K.; Clarke, D.R. Surface rumpling of a (Ni, Pt)Al bond coat induced by cyclic oxidation. Acta Mater. 2000, 48, 3283–3293. [CrossRef] 45. Tolpygo, V.K.; Clarke, D.R. Wrinkling of alpha-alumina films grown by thermal oxidation-I. Quantitative studies on single crystals of Fe-Cr-Al alloy. Acta Mater. 1998, 46, 5153–5166. [CrossRef] 46. Su, L.; Zhang, W.; Sun, Y.; Wang, T.J. Effect of TGO creep on top-coat cracking induced by cyclic displacement instability in a thermal barrier coating system. Surf. Coat. Technol. 2014, 254, 410–417. [CrossRef] 47. Song, J.N.; Li, S.L.; Yang, X.G.; Qi, H.Y.; Shi, D.Q. Numerical investigation on the cracking behaviors of thermal barrier coating system under different thermal cycle loading waveforms. Surf. Coat. Technol. 2018, 349, 166–176. [CrossRef] 48. Jiang, J.S.; Zou, Z.H.; Wang, W.Z.; Zhao, X.F.; Liu, Y.Z.; Cao, Z.M. Effect of internal oxidation on the interfacial morphology and residual stress in air plasma sprayed thermal barrier coatings. Surf. Coat. Technol. 2018, 334, 215–226. [CrossRef] 49. Zhu, W.; Zhang, Z.B.; Yang, L.; Zhou, Y.C.; Wei, Y.G. Spallation of thermal barrier coatings with real thermally grown oxide morphology under thermal stress. Mater. Des. 2018, 146, 180–193. [CrossRef] 50. Wei, Z.Y.; Cai, H.N.; Li, C.J. Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model. Ceram. Int. 2018, 44, 22556–22566. [CrossRef] 51. Han, Y.J.; Ye, F.X.; Lu, G.X.; Liu, C.; Hao, L.J. Residual stress evolution of thermally grown oxide in thermal barrier coatings deposited onto nickel-base superalloy and iron-base alloy with thermal exposure ageing. J. Alloy. Compd. 2014, 584, 19–27. [CrossRef] 52. Cen, L.; Qin, W.Y.; Yu, Q.M. Finite element analysis of interface undulation and interface delamination in the MCrAlY coating system under thermal cycling: Considering oxide thickness and top-coat effects. J. Therm. Spray Technol. 2020, 29, 597–610. [CrossRef] 53. Chen, Z.; Huang, H.M.; Zhao, K.; Jia, W.B.; Fang, L. Influence of inhomogeneous thermally grown oxide thickness on residual stress distribution in thermal barrier coating system. Ceram. Int. 2018, 44, 16937–16946. [CrossRef] 54. Chai, Y.J.; Lin, C.; Wang, X.; Li, Y.M. Study on Stress Development in the phase transition layer of thermal barrier coatings. Materials 2016, 9, 14. [CrossRef] 55. Chen, H.; Zhang, C.; Xuan, J.; Liu, B.; Yang, G.; Gao, Y.; Luo, H. Effect of TGO evolution and element diffusion on the life span of YSZ/Pt–Al and YSZ/NiCrAlY coatings at high temperature. Ceram. Int. 2020, 46, 813–823. [CrossRef] 56. Lin, C.; Li, Y.M. A coupled mechanical-chemical model for reflecting the influence of stress on oxidation reactions in thermal barrier coating. J. Appl. Phys. 2018, 123, 10. [CrossRef] 57. Liu, Y.Z.; Zheng, S.J.; Zhu, Y.L.; Wei, H.; Ma, X.L. Microstructural evolution at interfaces of thermal barrier coatings during isothermal oxidation. J. Eur. Ceram. Soc. 2016, 36, 1765–1774. [CrossRef] Coatings 2020, 10, 1022 16 of 19

58. Shen, Q.; Yang, L.; Zhou, Y.C.; Wei, Y.G.; Wang, N.G. Models for predicting TGO growth to rough interface in TBCs. Surf. Coat. Technol. 2017, 325, 219–228. [CrossRef] 59. Sun, Y.L.; Zhang, W.X.; Li, J.G.; Wang, T.J. Local stress around cap-like portions of anisotropically and nonuniformly grown oxide layer in thermal barrier coating system. J. Mater. Sci. 2013, 48, 5962–5982. [CrossRef] 60. Zhao, X.; Hashimoto, T.; Xiao, P. Effect of the top coat on the phase transformation of thermally grown oxide in thermal barrier coatings. Scr. Mater. 2006, 55, 1051–1054. [CrossRef] 61. Evans, A.G.; He, M.Y.; Hutchinson, J.W. Mechanics-based scaling laws for the durability of thermal barrier coatings. Prog. Mater. Sci. 2001, 46, 249–271. [CrossRef] 62. Clarke, D.R. The lateral growth strain accompanying the formation of a thermally grown oxide. Acta Mater. 2003, 51, 1393–1407. [CrossRef] 63. Sun, Y.; Li, J.; Zhang, W.; Wang, T.J. Local stress evolution in thermal barrier coating system during isothermal growth of irregular oxide layer. Surf. Coat. Technol. 2013, 216, 237–250. [CrossRef] 64. Lin, C.; Li, Y.M. Interface stress evolution considering the combined creep–plastic behavior in thermal barrier coatings. Mater. Des. 2016, 89, 245–254. [CrossRef] 65. Shen, Q.; Yang, L.; Zhou, Y.C.; Wei, Y.G.; Zhu, W. Effects of growth stress in finite-deformation thermally grown oxide on failure mechanism of thermal barrier coatings. Mech. Mater. 2017, 114, 228–242. [CrossRef] 66. Chai, Y.; Yang, X.; Li, Y.; Ogawa, K. Stress development in thermal barrier coatings with morphology-controlled thermally grown oxide. Ceram. Int. 2019, 45, 20435–20445. [CrossRef] 67. Loeffel, K.; Anand, L. A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction. Int. J. Plast. 2011, 27, 1409–1431. [CrossRef] 68. Loeffel, K.; Anand, L.; Gasem, Z.M. On modeling the oxidation of high-temperature alloys. Acta Mater. 2013, 61, 399–424. [CrossRef] 69. Lv, B.W.; Xie, H.; Xu, R.; Fan, X.L.; Zhang, W.X.; Wang, T.J. Effects of sintering and mixed oxide growth on the interface cracking of air-plasma-sprayed thermal barrier coating system at high temperature. Appl. Surf. Sci. 2016, 360, 461–469. [CrossRef] 70. Dong, H.; Yang, G.; Luo, X.; Li, C. Effects of mixed oxides on thermal cyclic lifetime of plasma-sprayed thermal barrier coatings. China Surf. Eng. 2015, 28, 21–28. 71. Yang, G.J.; Xiang, X.D.; Xing, L.K.; Li, D.J.; Li, C.J.; Li, C.X. Isothermal oxidation behavior of NiCoCrAlTaY coating deposited by high velocity air-fuel spraying. J. Therm. Spray Technol. 2012, 21, 391–399. [CrossRef] 72. Busso, E.P.; Evans, H.E.; Qian, Z.Q.; Taylor, M.P. Effects of breakaway oxidation on local stresses in thermal barrier coatings. Acta Mater. 2010, 58, 1242–1251. [CrossRef] 73. Li, Y.; Li, C.J.; Zhang, Q.; Yang, G.J.; Li, C.X. Influence of TGO Composition on the thermal shock lifetime of thermal barrier coatings with cold-sprayed MCrAlY bond coat. J. Therm. Spray Technol. 2010, 19, 168–177. [CrossRef] 74. Zhang, W.X.; Sun, Y.L.; Wang, T.J. Effect of spinel growth on the delamination of thermal barrier coatings. Key Eng. Mater. 2011, 462–463, 389–394. [CrossRef] 75. Xu, R.; Fan, X.L.; Zhang, W.X.; Wang, T.J. Interfacial fracture mechanism associated with mixed oxides growth in thermal barrier coating system. Surf. Coat. Technol. 2014, 253, 139–147. [CrossRef] 76. Zhang, B.Y.; Shi, J.; Yang, G.J.; Li, C.X.; Li, C.J. Healing of the interface between splashed particles and underlying bulk coating and its influence on isothermal oxidation behavior of LPPS MCrAlY bond coat. J. Therm. Spray Technol. 2015, 24, 611–621. [CrossRef] 77. Tang, J.J.; Bai, Y.; Zhang, J.C.; Liu, K.; Liu, X.Y.; Zhang, P.; Wang, Y.; Zhang, L.; Liang, G.Y.; Gao, Y.; et al. Microstructural design and oxidation resistance of CoNiCrAlY alloy coatings in thermal barrier coating system. J. Alloy. Compd. 2016, 688, 729–741. [CrossRef] 78. Bai, Y.; Ding, C.H.; Li, H.Q.; Han, Z.H.; Ding, B.J.; Wang, T.J.; Yu, L. Isothermal oxidation behavior of supersonic atmospheric plasma-sprayed thermal barrier coating system. J. Therm. Spray Technol. 2013, 22, 1201–1209. [CrossRef] 79. Lim, L.Y.; Meguid, S.A. Modeling and characterisation of depletion of aluminium in bond coat and growth of mixed oxides in thermal barrier coatings. Int. J. Mech. Mater. Des. 2019, 1–17. [CrossRef] Coatings 2020, 10, 1022 17 of 19

80. Mahalingam, S.; Yunus, S.M.; Manap, A.; Afandi, N.M.; Zainuddin, R.A.; Kadir, N.F. Crack propagation and effect of mixed oxides on TGO growth in thick La-Gd-YSZ thermal barrier coating. Coatings 2019, 9, 719. [CrossRef] 81. Xie, F.; Zhang, W.X.; Li, H.M.; Fan, X.L. Modelling of alloying process of cold sprayed Ni/Al coating. Mech. Mater. 2019, 135, 129–143. [CrossRef] 82. Evans, A.G.; Clarke, D.R.; Levi, C.G. The influence of oxides on the performance of advanced gas turbines. J. Eur. Ceram. Soc. 2008, 28, 1405–1419. [CrossRef] 83. Elsass, M.; Frommherz, M.; Scholz, A.; Oechsner, M. Interdiffusion in MCrAlY coated nickel-base superalloys. Surf. Coat. Technol. 2016, 307, 565–573. [CrossRef] 84. Zhao, G.; Xu, B.; Ren, K.; Shao, G.; Wang, Y. Oxygen diffusion through environmental barrier coating materials. Ceram. Int. 2020, 46, 19545–19549. [CrossRef] 85. Fick, A.V. On liquid diffusion. Lond. Edinb. Dublin Philos. Mag. J. Sci. 1855, 10, 30–39. [CrossRef] 86. Darken, L.S. Diffusion of carbon in austenite with a discontinuity in composition. Trans. Am. Inst. Min. Metall. Eng. 1949, 180, 430–438. 87. Darken, L.S. Diffusion, mobility and their interrelation through free energy in binary metallic systems. Trans. Am. Inst. Min. Metall. Eng. 1948, 175, 184–201. 88. Yang, F.Q. Interaction between diffusion and chemical stresses. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2005, 409, 153–159. [CrossRef] 89. Wang, W.L.; Lee, S.; Chen, J.R. Effect of chemical stress on diffusion in a hollow cylinder. J. Appl. Phys. 2002, 91, 9584–9590. [CrossRef] 90. Zhang, X.C.; Shyy, W.; Sastry, A.M. Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc. 2007, 154, A910–A916. [CrossRef] 91. Suo, Y.H.; Shen, S.P. Coupling diffusion-reaction-mechanics model for oxidation. Acta Mech. 2015, 226, 3375–3386. [CrossRef] 92. Wang, X.K.; Fan, X.L.; Sun, Y.L.; Xu, R.; Jiang, P. Modelling and analysis of the oxide growth coupling behaviour of thermal barrier coatings. J. Mater. Sci. 2019, 54, 10270–10283. [CrossRef] 93. Haftbaradaran, H.; Song, J.; Curtin, W.A.; Gao, H.J. Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration. J. Power Sources 2011, 196, 361–370. [CrossRef] 94. Dong, X.L.; Fang, X.F.; Feng, X.; Hwang, K.C. Diffusion and stress coupling effect during oxidation at high temperature. J. Am. Ceram. Soc. 2013, 96, 44–46. [CrossRef] 95. Fang, X.F.; Li, Y.; Yue, M.K.; Feng, X. Chemo-mechanical coupling effect on high temperature oxidation: A review. Sci. China-Technol. Sci. 2019, 62, 1297–1321. [CrossRef] 96. Suo, Z. A continuum theory that couples creep and self-diffusion. J. Appl. Mech.-Trans. ASME 2004, 71, 646–651. [CrossRef] 97. Gao, Y.F.; Cho, M.; Zhou, M. Stress relaxation through interdiffusion in amorphous lithium alloy electrodes. J. Mech. Phys. Solids 2013, 61, 579–596. [CrossRef] 98. Sethuraman, V.A.; Chon, M.J.; Shimshak, M.; Van Winkle, N.; Guduru, P.R. In situ measurement of biaxial modulus of Si anode for Li-ion batteries. Electrochem. Commun. 2010, 12, 1614–1617. [CrossRef] 99. Sethuraman, V.A.; Chon, M.J.; Shimshak, M.; Srinivasan, V.; Guduru, P.R. In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. J. Power Sources 2010, 195, 5062–5066. [CrossRef] 100. Brassart, L.; Suo, Z.G. Reactive flow in solids. J. Mech. Phys. Solids 2013, 61, 61–77. [CrossRef] 101. Huang, S.; Fan, F.; Li, J.; Zhang, S.; Zhu, T. Stress generation during lithiation of high-capacity electrode particles in lithium ion batteries. Acta Mater. 2013, 61, 4354–4364. [CrossRef] 102. Bower, A.F.; Guduru, P.R.; Sethuraman, V.A. A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell. J. Mech. Phys. Solids 2011, 59, 804–828. [CrossRef] 103. Zhao, K.J.; Pharr, M.; Cai, S.Q.; Vlassak, J.J.; Suo, Z.G. Large Plastic Deformation in high-capacity lithium-ion batteries caused by charge and discharge. J. Am. Ceram. Soc. 2011, 94, S226–S235. [CrossRef] 104. Zhao, K.J.; Pharr, M.; Wan, Q.; Wang, W.L.; Kaxiras, E.; Vlassak, J.J.; Suo, Z.G. Concurrent reaction and plasticity during initial lithiation of crystalline silicon in lithium-ion batteries. J. Electrochem. Soc. 2012, 159, A238–A243. [CrossRef] Coatings 2020, 10, 1022 18 of 19

105. Zhao, K.J.; Tritsaris, G.A.; Pharr, M.; Wang, W.L.; Okeke, O.; Suo, Z.G.; Vlassak, J.J.; Kaxiras, E. Reactive flow in silicon electrodes assisted by the insertion of lithium. Nano Lett. 2012, 12, 4397–4403. [CrossRef][PubMed] 106. Di Leo, C.V.; Rejovitzky, E.; Anand, L. Diffusion-deformation theory for amorphous silicon anodes: The role of plastic deformation on electrochemical performance. Int. J. Solids Struct. 2015, 67–68, 283–296. [CrossRef] 107. Moon, J.; Cho, K.; Cho, M. Ab-initio study of silicon and tin as a negative electrode materials for lithium-ion batteries. Int. J. Precis. Eng. Manuf. 2012, 13, 1191–1197. [CrossRef] 108. Yang, F.Q. Diffusion-induced stress in inhomogeneous materials: Concentration-dependent elastic modulus. Sci. China-Phys. Mech. Astron. 2012, 55, 955–962. [CrossRef] 109. Yang, F.Q. Entropy change-induced elastic softening of lithiated materials. Theor. Appl. Mech. Lett. 2015, 5, 255–257. [CrossRef] 110. Hong, C.S.; Qaiser, N.; Nam, H.G.; Han, S.M. Effect of Li concentration-dependent material properties on diffusion induced stresses of a Sn anode. Phys. Chem. Chem. Phys. 2019, 21, 9581–9589. [CrossRef] 111. Chang, S.; Moon, J.; Cho, M. Stress-diffusion coupled multiscale analysis of Si anode for Li-ion battery. J. Mech. Sci. Technol. 2015, 29, 4807–4816. [CrossRef] 112. Lu, Y.J.; Che, Q.; Song, X.; Wang, F.H.; Zhao, X. Stress self-relaxation arising from diffusion-induced creep in bilayer lithium-ion battery electrode. Scr. Mater. 2018, 150, 164–167. [CrossRef] 113. Xu, C.Q.; Deng, Q.F.; Weng, Z.D.; Chen, B.B.; Zhou, J.Q. Lithium-assisted creep deformation behavior of Sn nanoparticle electrode with fracture-resistant ability. J. Mater. Res. 2019, 34, 3887–3898. [CrossRef] 114. Pinson, M.B.; Bazant, M.Z. Theory of SEI formation in rechargeable batteries: Capacity fade, accelerated aging and lifetime prediction. J. Electrochem. Soc. 2013, 160, A243–A250. [CrossRef] 115. Zhang, B.Y.; Meng, G.H.; Yang, G.J.; Li, C.X.; Li, C.J. Dependence of scale thickness on the breaking behavior of the initial oxide on plasma spray bond coat surface during vacuum pre-treatment. Appl. Surf. Sci. 2017, 397, 125–132. [CrossRef] 116. Li, N.W.; Yin, Y.X.; Yang, C.P.; Guo, Y.G. An artificial solid electrolyte interphase layer for stable lithium metal anodes. Adv. Mater. 2016, 28, 1853–1858. [CrossRef] 117. Liu, Y.Y.; Lin, D.C.; Yuen, P.Y.; Liu, K.; Xie, J.; Dauskardt, R.H.; Cui, Y. An artificial solid electrolyte interphase with high Li-ion conductivity, mechanical strength, and flexibility for stable lithium metal anodes. Adv. Mater. 2017, 29, 8. [CrossRef] 118. De la Hoz, J.M.M.; Soto, F.A.; Balbuena, P.B. Effect of the electrolyte composition on SEI reactions at Si anodes of Li-ion batteries. J. Phys. Chem. C 2015, 119, 7060–7068. [CrossRef] 119. Hu, Z.L.; Zhang, S.; Dong, S.M.; Li, W.J.; Li, H.; Cui, G.L.; Chen, L.Q. Poly(ethyl alpha-cyanoacrylate)-based artificial solid electrolyte interphase layer for enhanced interface stability of Li metal anodes. Chem. Mat. 2017, 29, 4682–4689. [CrossRef] 120. Khorramirad, M.M.; Rahimipour, M.R.; Hadavi, S.M.M.; Shirvani, K. Preoxidation of bond coat in

IN-738LC/NiCrAlY/LaMgAl11O19 thermal barrier coating system. Ceram. Int. 2018, 44, 22080–22091. [CrossRef] 121. Song, P.; Yu, X.; Huang, T.H.; He, X.; Ji, Q.; Zang, J.J.; Chen, R.; Lu, J.G.; Lu, J.S. Evolution of in-situ pores and high-temperature thermal-barrier performance of Al-Si coating on NiCoCrAl alloy. Surf. Coat. Technol. 2018, 344, 489–498. [CrossRef] 122. Wang, J.L.; Chen, M.H.; Yang, L.L.; Zhu, S.L.; Wang, F.H. Comparative study of oxidation and interdiffusion behavior of AIP NiCrAlY and sputtered nanocrystalline coatings on a nickel-based single-crystal superalloy. Corros. Sci. 2015, 98, 530–540. [CrossRef] 123. Wang, R.L.; Gong, X.Y.; Peng, H.; Ma, Y.; Guo, H.B. Interdiffusion behavior between NiAlHf coating and Ni-based single crystal superalloy with different crystal orientations. Appl. Surf. Sci. 2015, 326, 124–130. [CrossRef] 124. Wen, J.X.; Cao, R.; Gao, Y.F. Mysterious failure in load-free superalloys under repeated thermal shocks. Acta Mater. 2020, 194, 276–282. [CrossRef] 125. Yang, L.L.; Chen, M.H.; Wang, J.L.; Qiao, Y.X.; Guo, P.Y.; Zhu, S.L.; Wang, F.H. Microstructure and composition evolution of a single-crystal superalloy caused by elements interdiffusion with an overlay NiCrAlY coating on oxidation. J. Mater. Sci. Technol. 2020, 45, 49–58. [CrossRef] 126. Smigelskas, A.D.; Kirkendall, E.O. Zinc diffusion in alpha-brass. Trans. Am. Inst. Min. Metall. Eng. 1947, 171, 130–142. Coatings 2020, 10, 1022 19 of 19

127. Texier, D.; Monceau, D.; Hervier, Z.; Andrieu, E. Effect of interdiffusion on mechanical and thermal expansion properties at high temperature of a MCrAlY coated Ni-based superalloy. Surf. Coat. Technol. 2016, 307, 81–90. [CrossRef] 128. Qi, W.Y.; Peng, H.; He, J.; Li, S.S.; Gong, S.K.; Guo, H.B. Cyclic oxidation and interdiffusion behavior of Pt modified NiAlHfCrSi coatings on single crystal superalloy containing Mo. Surf. Coat. Technol. 2014, 259, 426–433. [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional aﬃliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).