Int J Fract (2008) 151:107–120DOI 10.1007/s10704-008-9246-y

ORIGINAL PAPER

Interfacial fracture characteristic and crack propagationof thermal barrier coatings under tensile conditionsat elevated temperatures

W. G. Mao · C. Y. Dai · L. Yang · Y. C. Zhou

Received: 13 July 2008 / Accepted: 17 July 2008 / Published online: 8 August 2008© Springer Science+Business Media B.V. 2008

Abstract Thermal barrier coatings (TBCs) have been extensively used in aircraft enginesfor improved durability and performance for more than fifteen years. In this paper, thermalbarrier coating system with plasma sprayed zirconia bonded by a MCrAlY layer to SUS304stainless steel substrate was performed under tensile tests at 1000◦C. The crack nuclea-tion, propagation behavior of the ceramic coatings in as received and oxidized conditionswere observed by high-performance camera and discussed in detail. The relationship of thetransverse crack numbers in the ceramic coating and tensile strain was recorded and used todescribe crack propagation mechanism of thermal barrier coatings. It was found that the frac-ture/spallation locations of air plasma sprayed (APS) thermal barrier coating system mainlylocated within the ceramic coating close to the bond coat interface by scanning electronmicroscope (SEM) and energy dispersive X-Ray (EDX). The energy release rate and inter-face fracture toughness of APS TBCs system were evaluated by the aid of Suo–Hutchinsonmodel. The calculations revealed that the energy release rate and fracture toughness ranged,respectively, from 22.15 J m−2 to 37.8 J m−2 and from 0.9 MPa m1/2 to 1.5 MPa m1/2. Theresults agree well with other experimental results.

Keywords Thermal barrier coatings · Tensile test · Interface fracture toughness ·Crack propagation

1 Introduction

Thermal barrier coatings (TBCs) system of high-temperature components is required in powergenerating units for preventing the surface of the components from excessive heating, erosion

W. G. Mao · C. Y. Dai · L. Yang · Y. C. Zhou (B)Faculty of Materials, Optoelectronics and Physics, Xiangtan University, Hunan 411105, Chinae-mail: zhouyc@xtu.edu.cn

W. G. Mao · C. Y. Dai · L. Yang · Y. C. ZhouKey Laboratory of Low Dimensional Materials & Application Technology, Ministry of Education,Xiangtan University, Hunan 411105, China

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108 W. G. Mao et al.

and corrosion during the operation (Padture et al. 2002). A typical TBC system is composedof a top coating (TC) of yttria partially stabilized zirconia (YSZ), underlying bond coat (BC,usually MCrAlY, where M is Ni, Co or a combination of both) that provides the oxidation re-sistance, and the substrate. In high temperature environment, a thin oxide scale, i.e. thermallygrown oxide (TGO, usually Al2O3), forms and grows between the TC and BC interface dueto the oxidation of the BC layer. In general, the adhesion of the whole TC layer is the mostimportant parameter for the durability of TBC system (Evans et al. 2001). Although variousfailure modes have been observed in service due to aggressive environment and materialsproperties mismatch, one of the most common failure modes is cracking at the TC/TGO orTGO/BC interface, leading to buckling delamination and spalling (Evans et al. 2001; Heet al. 2001; Zhou et al. 2002; Qian et al. 2003). The coating spallation, accompanied withdelamination, has a crucial influence on the function and life expectancy of a thermal barrier.Zhou et al. investigated the fracture behavior of the two-layer APS TBCs rectangular speci-mens by uniaxial tension tests at room temperature. The nucleation, propagation of interfacecracks between the TC layer and bond coat were observed. The interface fracture toughnessevaluated by a shear lag model for the uniaxial tensile test was 0.94 and 0.67 MPa m1/2 forthe different average toughness of bond coat (?). Cracking and fracture behavior in a plasma-sprayed thermal barrier coating system were evaluated using a sandwiched specimen underuniaxial tensile stress combined with an in situ microscope observation at room temperature(Qian et al. 2003). Qian et al. have introduced an effective fracture toughness test which usedinterface fracture mechanics theory for determining fracture resistance of multilayered ther-mal barrier coatings. A crack was embedded within the ceramic coatings in the simple tensileadhesion tests. Their results showed that any defects located within the ceramic coating couldsignificantly weaken a TBC (Qian et al. 1997). However, it is well known that the failure ofthermal barrier coating (TBC) systems under thermo-mechanical loading is very complicatedbecause it is influenced by thermal mismatch, interface roughness, creep, sintering and soon. The above experimental results were mainly obtained at room temperature. Few uniaxialtension test studies were performed at high temperature. The damage evolution process ofthe TBCs system needs more detailed observations at high temperatures.

In this paper we mainly studied crack propagation characteristic of APS TBCs systemunder uniaxial tensile test at room and high temperature. The effects of high temperature andceramic coating thickness on crack nucleation, propagation and spallation in the TBC wouldbe discussed in detail. The transverse cracks density versus tensile strain was described byhigh accurate camera.

2 Experimental

2.1 TBCs specimen preparation

In this work, the TBC system consisted of a plasma-sprayed top coat (TC) of ZrO2–8 wt.%Y2O3 (YSZ), a NiCrAlY bond coat and a SUS304 stainless steel substrate. The dimensions ofthe TBC specimen were showed in Fig. 1. The thickness (hs) of the substrate is 1.8 mm. Thesubstrate specimens were ground and polished to 7µm before grit blasting. The preparationtechniques utilized dry blasting by corundum powder with 50 mesh grain size distribution. Thesubsequent step to the abrasive treatment was preheating in order to remove contaminantssuch as moisture and volatiles. After this procedure, all the substrates were coated withNiCrAlY powder (grain size distribution 20–50µm) applied by low pressure plasma spray.The distance between the plasma torch and the substrate was held constant at 70 mm, for both

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Interfacial fracture characteristic 109

Fig. 1 Dimensions of TBCspecimens in the uniaxial tensiletest

Table 1 Dimension and coating thickness of the TBC specimens for tensile test

TBC sample types Number hc (µm) hb (µm) hs (mm)

1. As-received 5 200 100 1.80

2. Oxidized at 1000◦C for 48 h 5 200 100 1.80

3. Oxidized at 1000◦C for 100 h 5 200 100 1.80

4. As-received 5 300 100 1.80

5. Oxidized at 1000◦C for 48 h 5 300 100 1.80

6. Oxidized at 1000◦C for 100 h 5 300 100 1.80

7. As-received 5 400 100 1.80

8. Oxidized at 1000◦C for 48 h 5 400 100 1.80

9. Oxidized at 1000◦C for 100 h 5 400 100 1.80

10. As-received uncoated substrate 3 – – 1.80

11. Heat treated uncoated substrate (48 h) 3 – – 1.80

bond coat and the following ceramic coating. The thickness of the BC (hb) is about 100µm.The subsequent step was thermal treatment at high temperature in vacuum (∼ 1000◦C/2 h) inorder to diffuse the coated layer and the substrate. The BC was also grit blasted prior to TBCdeposition by plasma sprayed process. The YSZ powder with size distribution of 20 ± 5 µmwas sprayed on the desired bond coat surface. To study the influence of the TC thickness (hc),three different values are chosen, i.e. 200µm, 300µm and 400µm. And then the specimensundergone different thermal aging time (48 h and 100 h) at 1000◦C in order to consist withactual TBC service environment. The thermal cycle consisted of a 10-min heat-up from roomtemperature to 1000◦C, a 100-min holding at 1000◦C and a 10-min forced air quench. Thethermal aging time is approximately 48 h and 100 h, respectively. The type and number ofall specimens for identical experimental conditions were listed in Table 1. There were totalforty-five APS TBC specimens tested in the present work.

2.2 Experimental method

Figure 2 shows the thermo-mechanical uniaxial tension experimental setup of TBCs system.It should be noted that the oxyacetylene torch only heated the surface of the ceramic coatingup to 1000◦C, nor heated the other surfaces of the specimen. Since a high temperature gradientexisted from the coating surface to the substrate bottom, the condition was consistent withactual TBC systems in service. Three thermocouples were used to measure, respectively, thetop surface temperature of the ceramic coating (T1), the bottom surface temperature of the

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110 W. G. Mao et al.

Fig. 2 The tensile test setup ofthermal barrier coating system at1000◦C

substrate (T2) and the cross-section temperature of the TBCs specimen (T3). The process ofthermo-mechanical tensile test was described as follows. The TC surface was heated first up toabout 1000◦C and kept this steady temperature state during the tension test. The oxyacetylenetorch, whose axis was orthogonal to the TC surface, was transferred at a constant velocityof 2 cm/s so that the surface of the TC could be heated uniformly. Furthermore, the maximaltemperature of the TBC surface was easily controlled within the range of 1000 ± 10◦C byadjusting the distance between the torch flame and the TBC surface. And then the tensionloading was applied with constant displacement rate (2.0 mm/min) until the spallation ofthe ceramic coating completely occurred. The interface crack nucleation, propagation andcoating spallation were observed by a miniature testing device and high accuracy camera. Thecritical mechanical loading data and temperature gradient were recorded and used directlyfor fracture toughness evaluation.

3 Results

3.1 Thermo-mechanical tensile fracture process

A representative tensile stress–strain curve of TBC specimens was shown and compared withthat of its substrate material (SUS304 stainless steel) at high temperature. The elasto-plasticbehaviour of the uncoated substrate at 1000◦C was investigated first. The as-received andheat treated uncoated substrate showed similar elastic-plastic characteristic in Fig. 3, i.e. theNo. 10 and 11 type specimens in this study. It indicated that the heat treatment had a littleinfluence on the mechanical behaviour of the uncoated substrate under tension. The stress–strain curve of the heated TBCs specimen (the selected No. 2 type TBCs) was also shown inFig. 3. The surface temperature of the TC layer (T1) was 1000◦C. The bottom temperature ofthe substrate was about 670◦C due to the thermal insulation protection function of the ceramiccoating. It consisted of seven stages for the tensile stress–strain curve of the TBC specimen.It should be noted that the nucleation and propagation of transverse cracks correspond tothese critical points, i.e. points P, A, B, C, D and E. The values of these points are propitiousto determine the interface fracture toughness of the specimen. At OP stage, it is seen that thespecimen shows the linear elastic characteristic because the tensile stress does not reach theyield stress of the substrate. The edge crack was not observed on the ceramic coating surface,

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Interfacial fracture characteristic 111

Fig. 3 The tensile stress–straincurve of APS TBC system and itssubstrate material at 1000◦C

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.00

50

100

150

200

250

300

350

400

450

500

T=1000 oC

T=1000 oC

the No. 10 type specimen

the No. 11 type specimen

the No. 2 type specimenT

1=1000 oC T

2=670 oC

Ten

sile

str

ess

(MP

a)

Tensile strain (%)

EDCB

A

P

as shown in Fig. 4a. After the linear OP stage in the stress–strain curve, the slope of the curvedecreases at PA stage with tensile loading. At point A, an edge surface crack (i.e. transversecrack of the top coat layer perpendicular to the interface) in the coating initiated first onboth sides of the TBCs specimen and penetrated vertically through the bond coat, as shownin Fig. 4b. The AB stage is an important stage. With increasing loading, many edge cracksnear the coating boundary occurred and propagated gradually toward to the central regionof the coating surface. These edge cracks evolved into macro-transverse cracks, as shownin Fig. 4c, d. At BC stage, most of them would eventually penetrate into the next layer (i.e.bond coat). Furthermore, more edge cracks occurred near the both sides of the specimen.At CD stage, with an increase in tensile strain, these edge cracks gradually evolved intotransverse cracks and went into the saturation stage, and the crack–crack spacing reached afixed average space. And then the macro crack propagated transversely towards the TC/bondcoat interface and penetrated through the bond coat. It stopped at the bond coat/substrateinterface and deflected into two new interface cracks, which formed and propagated alongthe bond coat/substrate interface. The two cracks would result in the delamination/spallationof the ceramic coating. For the later stages (e.g. DE stage), transverse cracks had approachedthe saturation state, as shown in Fig. 4e, f. The top layer spalled continually from the substrateuntil the substrate ruptured under tensile loading.

However, the other tensile fracture characteristic of the TBC specimens was found andrepresentatively shown in Fig. 5. It was seen that many transverse cracks existed on thecoating surface. Part of the ceramic coating had spalled from the bond coat. For this kind offracture behaviour, EDX analysis revealed that the delamination or spallation place of thecoating located within the ceramic coating, not the TC/bond coat and bond coat/substrateinterfaces. The reason may be that the bond coat (NiCrAlY) displays ductile material cha-racteristic in these samples because the ductile-to-brittle transition temperature (DBTT) ofthe bond coat (NiCrAlY) is about 650◦C (Ray et al. 2005). So bond coat can possess largerstrain compatibility than the ceramic coating at high temperature. There was forty-two TBCspecimens occurred with this fracture characteristic in all TBC specimens.

3.2 SEM observations and EDX analysis

In order to identify the interface fracture location above, the components of the bottomsurface region of the spalt coating were examined by SEM and EDX. Figure 6 representsthe SEM micrograph of the fracture morphology of the selected No. 2 type TBC specimen

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112 W. G. Mao et al.

Fig. 4 The fracture/spallation process of the TBC specimen under the thermo-mechanical tensile loading athigh temperature

Fig. 5 The representative fracture morphology graphs of the TBC specimens under the thermo-mechanicaltensile tests at 1000◦C

(shown in Fig. 4). It was clearly seen that many transverse cracks existed. The bond coat(NiCrAlY) and TGO (mainly Al2O3) overlapped each other. EDX analysis indicated that thematerial components of the selected region in Fig. 7a consisted of the Al2O3 and NiCrAlYmixed material, while the 8 wt% Y2O3–ZrO2 materials was not found, as shown in Fig. 7b.It meant that the fracture place of the tensile failure located within the bond coat close to theBC/Substrate interface, not the TC layer or TC/TGO interface. The experimental results aresimilar to the previous results obtained at room temperature (Qian et al. 2003). However, itwas not expected that the delamination/spallation position occurred at the bond coat/substrate

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Interfacial fracture characteristic 113

Fig. 6 SEM micrographs of the fracture morphology of the spalt TBC fragment after the thermo-mechanicaltensile tests

Fig. 7 EDX analysis of thefracture surface of the selectedTBC specimen, as shown inFig. 6

interface (Padture et al. 2002). It means that the enhancement of this interface may be helpfulfor lengthening the TBCs lifetime in some applications (Qian et al. 1997). In the present work,this kind of fracture characteristic only occurred about three TBC specimens. The proportionoccupies 3/45 in all TBC specimens. This damage and failure phenomena are similar to thatobserved in APS TBC system under tensile test at room temperature (Qian et al. 2003).

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114 W. G. Mao et al.

Fig. 8 SEM micrographs of the fracture morphology of (a) the TBC specimen surface and (b) its spalledfragment after the thermo-mechanical tensile tests

Figure 8a shows that the SEM micrographs of the fracture morphology of the other TBCspecimens showed in Fig. 5. The irregular fracture morphology of the corresponding spaltfragment was displayed in Fig. 8b. It was seen that some original ceramic coating attachedin partial region and most coating had detached from the bond coat. EDX analysis in Fig. 8aindicated that the material components of the spalt part were all ZrO2–8 wt%Y2O3 materials,as shown in Fig. 9. It revealed that the fracture position located within the ceramic coating,not the TBC/TGO or TBC/BC interface, even if some transverse cracks had penetrated intothe underlying bond coat layer. This proportion was 42/45. This typical failure mode wascharacterized by the ceramic coating spallation. Major cracks developed and propagatedparallel to the TC/bond coat interface, but always within the ceramic coating layer for APSTBCs system (Padture et al. 2002; Bose and DeMasi-Marcin 1997). Although the transversecracking observed under the large thermal gradient and shock on thick TBCs is not wellunderstood (Bose and DeMasi-Marcin 1997; Zhu and Miller 1998), the present experimentalresults may provide complementary information on damage evolution of the ceramic coatingat high temperature gradient by thermo-mechanical tensile tests.

3.3 Number of transverse cracks versus tensile strain

Figure 10 shows the number of transverse cracks in the ceramic coating versus tensile strainfor the different type TBC specimens. The evolution of each transverse crack can be dividedinto three phases: initial cracking, multiple transverse crack and crack saturation. The initialtransverse crack occurred correspond to the different tensile strain value for the differenttype TBC samples. For the same geometry size TBC samples, e.g. the No. 1, 2, 3 typeTBC samples, thermal aging time (48 h and 100 h) has a few influence on the relationship oftransverse crack number and tensile strain. The reason may be that the fracture strength ofthe ceramic coating increase due to itself sintering effect after thermal cycles. The criticaltensile strain value is, respectively, 3.25, 3.6 and 4.0 for the No. 1, 2, 3 type TBC samples.On the other hand, it is found that the thickness of the ceramic coating also exhibits someinfluence on the transverse crack evolution. For example, the corresponding tensile strainvalue equals to, respectively, 3.25, 2.4 and 2.7 the No. 1, 4, 7 type TBC samples when thefirst initial edge crack on the ceramic coating surface was observed during the tensile tests.However, compared with the experimental results obtained at room temperature, Qian et alhave found that the corresponding tensile strain value is about 0.13 when the first initialedge crack on the ceramic coating surface was observed (Qian et al. 2003). In our previous

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Interfacial fracture characteristic 115

Fig. 9 EDX analysis of therepresentative fracturemorphology of the selected TBCspecimen, as shown in Fig. 8a

Fig. 10 The number oftransverse cracks versus tensilestrain for the different type APSTBC specimens at 1000◦C underthe tensile tests

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.00

5

10

15

20

25

30

35

40

45

50

Crack saturation

Multiple transverse cracks

Initial edge cracking

Num

ber

of tr

ansv

erse

cra

cks

Tensile strain (%)

T1=1000 oC

T2=600~750 oC

No.1 type No.2 type No.3 type No.4 type No.5 type No.6 type No.7 type No.8 type No.9 type

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116 W. G. Mao et al.

work, although the experimental phenomena are similar at elevated and room temperature,the transverse crack number and critical tensile strain value correspond to the first transversecrack appearance are quite different. The main reason may be that the ceramic material inTBC system represents ductile material characteristic at high temperature condition. Thepartial edge cracks began to propagate along the transverse and longitudinal direction whentensile loading increased. They would link each other to surface macro-cracks. Finally, theincreasing rate of crack number with tensile strain is reduced gradually and approaches to asaturation state eventually.

4 Discussions

4.1 Damage evolution model

According to the above SEM and EDX observations, the thermo-mechanical tensile fai-lure processes of two different fracture characteristics were schematically plotted in Fig. 11.The Fig. 11a–e denoted the first fracture behaviour. The other failure process was descri-bed by Fig. 11a–c, f, and g. Every failure characteristic were divided into five stages, i.e.(a) Pre-loading state; (b) with increasing tensile stress, the first crack initiation and trans-verse propagation in the ceramic coating layer; (c) more and more edge transverse cracksmultiplication; (d) each crack tip did not deflect at the TC/BC interface and directly pas-sed through the BC layer; (e) this transverse crack approached the BC/substrate interfaceand was divided into two parallel interface crack, which propagated along the BC/substrateinterface. All cracking began to saturation in the BC/substrate interface. However, it was alsofound the other failure mode, i.e. (f) when cracks passed through the interface between thecoating and BC layers and deflected into three different trajectories. Both of them propagatedparallel to the TC/BC interface. Anothers continued to penetrate the BC layer perpendicular

The ceramic coating Bond coat (a)

(b)

(c)

The first transverse crack observed

Tensile stress

Crack tip divided into three crack trajectories at the TBC/BC interface, which propagate along the three different directions. (d)

(e)

(f)

(g)

Plastic deformation region below decohesion interface.

Cracks deflections don t occur, passing through the TC/BC interface.

Substrate

Multiple fragmentation of TC

Tensile stress Tensile stress

Tensile stress

Crack tip divided into two paths at the BC/Substrate, which propagate parallel to the interface.

Plastic deformation region below decohesion interface.

The transverse crack tip, which directly passed through the BC, divided again into two crack trajectories at the BC/substrate interface.

Fig. 11 Schematic diagram showing the damage evolution of TBCs system under the thermo-mechanicaltensile tests

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Interfacial fracture characteristic 117

to the TC/BC interface. (g) the transverse crack deflection and growth at the BC/substrateinterface. So the (a)→(b)→(c)→(d)→(e) and (a)→(b)→(c)→(f)→(g) five-stages model,respectively, describe the two different fracture characteristic. The former characteristic wasthat multiple tensile cracks initiated on the surface of the ceramic coating, propagated to-wards the TC/BC interface, and deflected at the BC/substrate interface. The fracture positionlocated within the BC layer close to the BC/substrate interface. The later fracture behaviourwas that the multiple tensile cracks also initiated on the surface of the ceramic coating,propagated towards the TC/BC interface. But transverse cracks deflected at the TC/BC andBC/substrate interfaces. The interface cracks within the TC layer, propagating parallel to theTC/BC interface, finally resulted in the spallation of the ceramic coating. It was expectedthat transverse cracks in the top coat layer should deflect at the interface between the top coatand bond coat because the bond coat is a metal (Qian et al. 2003). This fracture phenomenonin the present work consists well with the previous results (Padture et al. 2002; Wen et al.2006; Sohn et al. 2001; Hu and Evans 1989) for brittle coating.

4.2 Evaluation of energy release rates and fracture toughness

In this section, interface fracture toughness, energy release rate and stress intensity factorwere assessed by Suo–Hutchinson analysis of interface cracking between two elastic layers(13). For simplicity, the material in TBCs specimen are assumed to be isotropic and linearlyelastic. The stress states of the TBCs specimens are approximately taken as symmetrical andequi-biaxial plane stress under tensile stress and thermal stress. When the crack is long com-pared to the thickness of the TC layer but still lying within the central region of the specimen,the specimen can be well approximated by the system in Fig. 12 (Suo and Hutchinson 1990).So the right half section of the specimen was only considered, as shown in Fig. 12. So thestress intensity factor of interface cracking is exactly equivalent to that induced by load andmoment combinations given by Suo and Hutchinson (1990),

P1 = σchc M1 = 0 P3 = σchc − σsub M3 = −σchc

(hs − δ + hc

2

)(1)

where δ represents the distance between the neutral axis and substrate bottom. σsub and σc

denote, respectively, tensile stress in the substrate and stress (including residual stress andthermal stress) in the ceramic coating. σc is evaluated using the following formula (Mao et al.2006),

σc = σ(z, t) + E(T )

1 − v(T )× z − tb

γ(2)

where σ(z, t) denotes the accumulated residual stress in TBC system during thermal cycles(Mao et al. 2006). In Eq. 2, the last item represents the stress induced by bend and momentdue to temperature gradient and strain mismatch. γ and tb are given in Appendix A. Sincethe number of load parameters controlling the crack tip singularity can be reduced to onlytwo, P and M , given by Suo and Hutchinson (1990),

Fig. 12 Schematicrepresentation of the tensilefailure behavior used to modelTBC cracking at the TC/BCinterface

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118 W. G. Mao et al.

⎧⎨⎩

P = P1 − C1 P3 − C2M3

hcM = M1 − C3 M3

(3)

The C’s are dimensionless numbers defined in Appendix B. Substituting Eq. 1 to 3, theequivalent load P and M can be obtained. The energy release rate and stress intensity factorwere written as follows (Suo and Hutchinson 1990),

G = c1

16

[P2

Ahc+ M2

I h3c

+ 2P M√AI h2

c

sin γ

](4)

|K |2 = p2

2

[P2

Ahc+ M2

I h3c

+ 2P M√AI h2

c

sin γ

](5)

The corresponding parameters in Eqs. 4 and 5 are given in Appendix B. The temperaturedependent material properties in TBCs specimens cited from our previous results (Mao et al.2006, ?). It is found that the energy release rates and fracture toughness between the TC/BCinterface at 1000◦C, ranges, respectively, from 22.15 J m−2 to 37.8 J m−2, from 0.9 MPa m1/2

to 1.5 MPa m1/2. These results agree with the experimental results (Arai et al. 2007; Guoet al. 2005; Choi et al. 2005).

5 Conclusions

The present uniaxial tensile tests under the large thermal gradient simulate the evolutionmechanism of transverse crack of the air plasma sprayed TBC system. It is helpful to provideimportant information for quantitative analysis and simulation of damage in the TBC underthe complicated high temperature service. Based on the above experimental results anddiscussions, conclusions can be summarized as follows:

(1) Edge crack first initiated near the boundary of the ceramic coating when tensile stress wascontinuously loaded under the large thermal gradient. The number of edge cracks gra-dually increase with increasing tensile stress. These edge cracks transversely propagatedtowards bond coat. And then crack deflected between the TC/BC or BC/substrate inter-face. Cracks multiplied on the coating surface and saturated in the top coating layer. Thespallation place of the coating mainly located within the ceramic coating, rather than BClayer or BC/substrate interface. Few interface decohesion occurred at the BC/substrateinterface.

(2) The relationship of the number of transverse cracks in the ceramic coating versus tensilestrain indicates that the thickness of the ceramic coating and heat treated time had animportant influence on the evolution of the transverse crack number. Each transversecrack evolution included mainly three phases: initial cracking, multiple transverse crackand crack saturation.

(3) By the aid of the Suo–Hutchinson model, the energy release rates and fracture tough-ness between the TC/BC interface at 1000◦C, ranges, respectively, from 22.15 J m−2 to37.8 J m−2, from 0.9 MPa m1/2 to 1.5 MPa m1/2.

Acknowledgements This work was supported in part by Project supported by Hunan Provincial NaturalScience Foundation of China (No: 08JJ3003) and the science research startup fund of Xiangtan University,China (No: 08QDZ07). The authors also acknowledge the financial support provided by the Cultivation Fund

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Interfacial fracture characteristic 119

of the Key Scientific and Technical innovation Projects, Ministry of Education of China (076044), NationalNatural Science Foundation of China (NSFC) (No: 50772093) and National Natural Science Foundation ofChina for Distinguished Young Scholars (No: 10525211).

Appendix A

In Eq. 2, the expressions of σ(z, t), γ and tb are listed as follows,

σ(z, t) = C +t∫

0

E(T )

1 − v(T )× [(

dεeq/dt) − α(T ) × (dT (z, t)/dt)

− 2 f1(z)F(t)B(T )(t/t0)−s] dt (A1)

1

γ=

−∫ H

0

∫ t0

E(T )1−v(T )

× [(dεeq/dt

) − α(T ) (dT (z, t)/dt)− 2B(T ) f1(z)F(t)(t/t0)−s]dt×(z−tb)dz∫ H

0E(T )

1−ν(T )× (z−tb)2dz

(A2)

tb =∫ H

0E(T )

1−ν(T )× zdz

∫ H0

E(T )

1 − ν(T )dz

(A3)

In above equations, E(T ), v(T ), α(T ), respectively, denote dependent-temperatureYoung’s modulus, Poisson’s ratio and thermal expansion coefficient. γ , tb and dεeq repre-sent the radius of curvature, bend axis and creep strain increment of the ceramic coating,respectively. The other parameters are listed in the reference (Mao et al. 2006).

Appendix B

In Eq. 3, P1 and P3 are loads per unit thickness, and M1 and M3 are moments per unitthickness, as defined in (Suo and Hutchinson 1990). The other parameters are listed asfollows,

C1 = �

A0C2 = �

Io

(1

η− + 1

2

)C3 = �

12Io(B1)

Ao = 1

η+ � Io = 1

3

{�

[3

( − 1

η

)2

− 3

( − 1

η

)+1

]+ 3

η

( − 1

η

)+ 1

η3

}

(B2)

= 1 + 2�η + �η2

2η (1 + �η)� = 1 + α

1 − αη = hc

hs(B3)

123

120 W. G. Mao et al.

α = (κ2 + 1) − (κ1 + 1)

(κ2 + 1) + (κ1 + 1)β = (κ2 − 1) − (κ1 − 1)

(κ2 + 1) + (κ1 + 1)δ = 1 + 2�η + �η2

2η (1 + �η)hc

(B4)

c1 = κ1 + 1

µ1κ =

{3 − 4v for plane strain3−v1+v

for plane stressµ = E

2(1 + v)(B5)

p =√

1 − α

1 − β2 A = 1

1 + �(4η + 6η2 + 3η3

) I = 1

12(1 + �η3

) (B6)

sin γ = 6�η2 (1 + η)√

AI (B7)

where E and v, respectively, denote Young’s modulus, Poisson’s ratio in the system.

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