Delamination Cracking in Thermal Barrier Coating System

Transcription

1 Y. C. Zou Fracture Researc Institute, Tooku University, Sendai , Japan and Institute of Fundamental Mecanics and Materials Engineering, Xiangtan University, Xiangtan, Hunan 405, P. R. Cina T. Hasida Fracture Researc Institute, Tooku University, Sendai , Japan Delamination Cracking in Termal Barrier Coating System Delamination cracking in termal barrier coating (TBC) system is studied wit te newly developed teoretical model. A semi-infinite long interface crack is pre-existing. Te termal stress and temperature gradient in TBC system are designated by a membrane stress P and a bending moment M. In tis case, te effects of plastic deformation, creep of ceramic coating, as well as termal growt oxidation and temperature gradient in TBC system are considered in te model due to te fact tat tese effects are considered in te calculation of termal stress. Te energy release rate, mode I and mode II stress intensity factors, as well as mode mixed measure, are derived. Te empatic discussion about PSZ/Ni-alloy reveals tat te TBC system may not fail in te form of coating delamination during te period of eat old. However, te failure may be in te form of coating delamination during cooling or in te eating period during te second cycle or later cycles. Te conclusion is consistent wit te experimental observations. Te delamination of ceramic coating is induced by te compressive load in te coating. DOI: 0.5/ Introduction Termal barrier ceramic coating TBC is used to protect an alloy operating at ig temperature, for example, at 500 C and so tat ig termal efficiency for an advanced gas turbine could be acieved. A TBC provides performance, efficiency, and durability benefits by reducing turbine cooling air requirements and lowering metal temperatures. Previous work as demonstrated tat tere are some important effects on TBC life. Te effects are termal fatigue 2 4, termal growt oxidation TGO between te bond coat and termal barrier ceramic coating 5 7, and te surface rougness of te bond coat 7,8, as well as oxygen and sulfur penetration along te grain boundary 9. As we know, a TBC system is used to provide termal insulation to critical aircooled components by overlaying a strain-tolerant ceramic top coating. In tis case, tere must be a temperature gradient in te tickness direction of te TBC system. Te temperature gradient as an important effect on te TBC system failure mecanism, suc as te initiation and propagation of a surface crack or interface crack as observed in te experiment 0,. However, te failure mecanism of te TBC system is te combined results of oxidation, residual stress, and termal mecanical fatigue as well as te creep of te TBC system 2. Teir nonlinear coupled effects govern te service life. Generally te composition of TGO is similar to a brittle ceramic suc as alumina (Al 2 O 3 ). Te cycles of ig-temperature loading and unloading not only make TGO tick but also create microvoids and microcracks initiate in te TGO. Subsequently, te degradation of te TGO will induce te spallation or delamination of te termal barrier ceramic coatings. Te previous experimental and teoretical studies sowed tat te macrocrack would ave been formed in te termally grown oxide layer due to te aforementioned effects 6 7. As long as te microcrack forms, it may propagate along interface or kink out of te plane of te crack at an angle. Terefore, mixed-mode cracking is an important damage mecanism in te TBC system. However, te analysis of a mixed-mode crack is very complicated for teoretical as well as experimental analyses. Fortunately, te basic ideas founded by previous researcers suc as Si et al. 3, Rice et al. To wom correspondence sould be addressed. Contributed by te IGTI Tecnical Committee of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in te ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received by te IGTI Tecnical Committee July 2000; final revision received by te ASME Headquarters September 200. Associate Editor: J. Conner. 4, Dundurs 5, and Erdogan 6, and te results of te delamination of tin films and coatings from a substrate studied by Evans and Hutcinson 7, and Hutcinson and Suo 8 can be used to investigate te failure mecanism of te TBC system operating at ig temperature. Te purpose of te investigation is to study te failure mecanism of a TBC system by exploring te energy release rate, termal stress intensity factors, and te relative amount of mode II to mode I at te crack tip for te termal mixed crack. In te model, te TBC system wit an interface crack is assumed as a composite beam. Wit te composite teory 9, te energy release rate is expressed by a termal strain and mecanical loads suc as membrane stress P and bending moment M. Te membrane stress P and bending moment M are calculated wit integrating te termal stress along te tickness direction of te TBC system wit a temperature gradient. On te oter and, in te calculation of termal stress, te combined effects of plastic deformation, creep of ceramic coating as well as termal growt oxidation and temperature gradient in TBC system were considered 2. Subsequently, in te model, te delamination in te TBC system is te combined effects of plastic deformation and creep of ceramic coating, as well as termal growt oxidation and temperature gradient. Stress Wit Interface Crack To consider te contribution of termal stress and temperature gradient on te mixed-mode crack propagation, a teoretical mode is proposed. Te system consists of a ceramic coating of material No. wit tickness of deposited on a substrate of material No. 2 wit tickness of H. Eac material is taken to be isotropic and linearly elastic. An interface crack is pre-existing. Te problem is asymptotic in tat two material layers are infinitely long and te crack is semi-infinite. Te structure is loaded as sown in Fig. a, were te membrane stresses P are loads per unit tickness and te bending moments M are moments per unit tickness. Te temperature gradient along te y-direction and te temperaturedependent pysical parameters are also considered in te analysis. Constitutive Equations. Te termal stresses are considered to be two-dimensional. Te general Hook s constitutive relation in a two-dimensional state can be written as 20 xx 2 xx 4 3 xx yy E xx E zz () 922 Õ Vol. 24, OCTOBER 2002 Copyrigt 2002 by ASMransactions of te ASME Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

2 yy 2 yy 4 3 xx yy E yy E zz. (2) In te above, equation E is used to denote te eigenstrain wic may be a plastic strain and termal expansion strain, as defined by Mura 2. Te eigenstrain E zz is te normal strain perpendicular to te plane tat is of interest. In te present study, only te eigenstrain of termal expansion strain is considered. Terefore, E xx E yy E zz, were T(y)T 0, T(y) and T 0 are, respectively, te operating temperature of te TBC system and room temperature and is termal expansion coefficient. Moreover, and denote te Poisson s ratio and sear moduli, respectively, 34, for plane strain, and (3)/(), 0 for plane stress. Stress Fields. Te stresses far beind or aead of te crack tip can be obtained by using te composite beam teory 9. In te model, te material properties are all temperature-dependent. In tis case, te position of neutral axis can be first determined and tey are expressed by, 2, and 3 as sown in Fig.. Te stresses can be obtained for te upper beam far beind te crack tip denoted by i wen te beam is loaded by te membrane stress P and bending moment M as sown in Fig. a. Te stress comes from tree parts, te first one is due to te strain of te neutral axis, te second one is due to te curvature, and tird one is due to te termal strain. Wit te same manipulating metod, te stresses can be obtained for te lower beam far beind te crack tip denoted by i2 and te composite beam far aead of te crack tip denoted by i3. Terefore, te stresses can be written as i xx P i,m i 8 j j i xx0 P i K i M i y 2 i j E xx j E j zz. (3) In te expression, j and 2 present te coating and substrate, (i) respectively. In te above expression, xx0, K (i), and i are defined as i xx0 P i e i e P i ic 3 K i M i s i s M i ic 3 2 i 0 ii/i! i 2 i (4) were e i i i e 3 i i 8 i 0 ii/i! s i 4J i 0 ii/i! 2 i 2 i i s 3 i i J i 0 3 ii/i! (5) (i) were xx0 and K (i) are te strain of te neutral axis and te curvature for beam i, respectively. Te nondimensional material parameters suc as j k, j k, and J i are defined in Appendix A. Te following dimensionless quantities, suc as te geometrical parameter 0, bimaterial parameters are used, 0 H, C 2, (6) C were C is defined as C(T )/(T ), T is te average temperature over te coating or substrate. Inspecting te expressions 4, 5 and A2), one can see tat te strain of te neutral axis (i) comes from two parts. One is expressed by e and it is te i contribution of termal strain, i.e., temperature gradient along te tickness direction. Anoter is te contribution of mecanical loads suc as P i. Tis case is te same for te curvature of te beam. On te oter and, one can see tat te contribution of termal strain to te strain of te neutral axis and curvature comes from te expression k j. Te contribution of mecanical loads to te strain of neutral axis and curvature comes from te expression k j. In line wit te treatment of Zuo and Hutcinson 22, te failure of te TBC system can be induced by equivalent loads P and M as sown in Fig. b by using te superimposition metod. Te equivalent loads P, M, and M* are given by PP 8 3 xx0 P 3 C 4K 3 M 3 2 C C MM 4 3 xx0 P 3 2 C 2 8K 3 M 3 3 C C 2 (8) (7) M*M 2 P 2. (9) Once te solution to te problem in Fig. b is obtained, te solution to te problem in Fig. a can be readily constructed by reinterpreting P and M. Inspecting expressions 7 9, one can see again tat te equivalent loads P and M come from two parts. One is te contribution of termal strain and te oter is te contribution of mecanical loads suc as P i and M i. Te insertion of termal strain in constitutive Eqs. 2 results in te different form for te energy release rate wit te case of nontermal strain in constitutive equations as discussed in te following. Energy Release Rate Te energy release rate can be computed exactly witin te context of plane stress or plane strain by taking te difference between te energy stored in te structure per unit lengt far aead and far beind te crack tip, u j G lim Wn ij n i (0) 0 x d, were W is stress work, ij and u i are te Cartesian components of te stress and displacement, n i is te unit vector normal to, and d is te arc lengt as depicted in Fig. b. As we know, te value of te J-integration is independent on te integral pat. In tis case, te pat of te J-integration is cosen as depicted in Fig. b and te J-integral is GW xx xx dy. () Te strain energy density W is defined as te mecanical work of strain, W 2 ij ij kk 2 xx xx 2 yy yy (2) Terefore, te energy release rate is obtained as Journal of Engineering for Gas Turbines and Power OCTOBER 2002, Vol. 24 Õ 923 Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

3 Fig. Conventions and geometry for te analysis of delamination cracking in te TBC system; a te delamination cracking in te TBC system is induced by te membrane stresses P i iä,2,3 and bending moments M i iä,2,3, b te failure of te TBC system can be induced by equivalent loads P and M G P2 C 2 E s 2 M 2 C S 3 2 PMC 2 P 2 E 2 M 2 S 2 (3) were te related nondimensional parameters are defined as E k ij e k i e k j S k ij s k i s k j k 2 s k (4) In order to analyze te stress intensity factors as in te next section, te energy release rate is rewritten in anoter useful form as G C PC 5 MC MC PMC PC (5) were te coefficients suc as i,(i,...,5)canbeknown by comparing te above two expressions of te energy release rate in 3 and 5. Inspecting te equivalent loads P and M in expressions 7 and 8, we find tat te equivalent loads are consisted of two parts. Te first part is te general mecanical loads suc as P, M, P 2, M 2, P 3, and M 3. Te second part is termal load or te named eigenload. In expression 5, te first term, second term, and tird term are te second-order function of nondimensional quantities PC / and MC / 2. Te dependence of te energy release rate on te second-order function form of nondimensional loads is te same as tat case of nonconsidering termal strain in a constitutive relation 22. But te fourt term and fift term are te linear function of nondimensional quantities PC / and MC / 2. Te dependence of te energy release rate on te linear function form of nondimensional loads is due to te termal strain in te constitutive relation. Te form of te energy release rate is different from te results obtained by Zuo and Hutcinson 22 in wic te termal strain is not considered. Stresses Intensity Factors Te above energy release rate can reflect te composite effect of loads on crack propagation. However, crack propagation sould be in mixed mode form for interface crack problems. In order to know te effect of te loading mode on crack propagation, for example, to understand wic mode, weter mode I or mode II dominates te crack propagation, we must know te stress intensity factors. Te TBC system is not an isotropic material and te system can be considered as a transverse isotropic body. For generally anisotropic materials, Hooke s law can be written as 6 i j B ij j eign i, j,...,6 (6) were i eign is assumed to be an eigenstrain as defined by 2. Te standard correspondence is adopted 23,24 and B ij is a sixby-six symmetric matrix, referred to as te compliance matrix, wit 2 independent elements. Te TBC system described in Fig. may be assumed as transverse isotropic materials and te compliance matrix as only five independent elements 23,24. Itis assumed tat te symmetry plane is normal to te y-axis as described in Fig.. Te components B ij are determined by five parameters wic are parameter 0, sear modulus, 2 or Young s modulus E, E 2 and Poisson ratio, 2 of material and material 2. Te compliance matrix B ij is obtained by connecting te relation of engineering constants, E L, A, T, A, and T for te transverse isotropic materials and engineering constants, 2 or E, E 2,, and 2 for te bimaterial system as discussed in references 23,24. Te details of compliance matrix B ij are given in Appendix B. In tis case, te stressstrain relation for te deformation in te x, y plane can be reduced to i j,2,6 b ij j eign i, i,2,6 (7) were b ij B ij for plane stress and b ij B ij B i3 B j3 /B 33 for plane strain. 924 Õ Vol. 24, OCTOBER 2002 Transactions of te ASME Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

4 Te complex interface stress intensity factor kk ik 2 as real and imaginary parts k and k 2, respectively, wic play similar roles to te conventional mode I and mode II intensity factors. For te anisotropic body in wic zero eigenstrain exists, te energy release rate is obtained by Si, Paris, and Irwin 3 and Suo 25 and G only depends on two rater tan tree nondimensional elastic parameters b, 2b 2b 66. (8) b 22 2b b 22 Te energy release rate is related to te stress intensity factors of mode I, K I and Mode II, K II by Gb /4 /2 K 2 I K 2 II (9) were te constant is defined by 2. (20) However, for te problem studied in te present case, te eigenstrain sould contribute to te energy release rate as discussed above. Te energy release rate is not only dependent on te second-order function of nondimensional quantities PC / and MC / 2, but also dependent on te linear function of nondimensional quantities PC / and MC / 2. In tis case, te energy release rate is assumed in te form Gb /4 kka (2) were k is a complex interface stress intensity factor and A is a complex constant. By comparing Eq. 9 and Eq. 2, te complex stress intensity factor k can be written as kk ik 2 /2 K I ik II. (22) Equating te two energy release rate expressions 5 and 2, one can obtain te following relation: were k 2 /4 b C PC 2 2 cos 0 2 MC 2 Let te complex stress intensity factor k be 2 MC 2 2 (23) cos (24) k /4 b C a PC b 2 MC 2 (25) were a and b are nondimensional complex numbers. On te similar lines of discussion given by Suo and Hutcinson 22, te complex numbers a and b do not depend on loads P and M, but only depend on geometric parameter 0 and Dundurs parameters and, 2 2, 2 2, (26) were / 2. Te complex numbers a and b can be expressed as acos i sin, bcos 0 i sin 0. (27) In te above expressions, only one parameter is not known. Te angle was determined by Suo and Hutcinson 22 and Hutcinson et al. 26 wit integral equation metods in wic te semi-infinite interface crack was represented by a distribution of dislocations lying along te negative x-axis. Te numerical solution of te integral equation ad been carried and te numerical results were given in tabular form 22,26. Te angle depends on 0 and only, i.e., ( 0,) and te excellent approximation wit a numerical fit is Terefore, we ave cos k b C /4 PC cos 2 MC 2 0 (28) sin k 2 b C /4 PC sin 2 MC 2 0. (29) Te relative amount of mode II to mode I at te crack tip is measured by te angle as tan K II K I tan /2 PC PC sin 2 MC 2 cos 2 MC 2 Calculated Results and Discussions sin 0 cos 0. (30) Calculated Model. In tis section te results of te calculated energy release rate and termal stress intensity factors TSIFs for te TBC system operating at ig temperature conditions are given in detail to te possible extent. Te main idea for te calculated model is te following: Te termal stress is first calculated and te details suc as te teoretical model and te constitutive equation, as well as material parameters, are given in 2. 2 Te membrane stress P i and bending moment M i are second calculated by integrating te termal stress along te tickness direction of te TBC system wit a temperature gradient and te formulas are given in expression Te equivalent loads suc as membrane stress P and bending moment M are tird calculated according to Eqs. 7 and 8. 4 Te energy release rate, stress intensity factors, and mixed mode are finally calculated according to 5, 28, 29, and 30, respectively. Te TBC system for termal stress calculation is illustrated scematically in Fig. 2. Te ceramic coating system is assumed to be partially stabilized ZrO 2 by 8wt%Y 2 O 3 (PSZ) over a NiCrAlY bond coat sprayed on SUS340 stainless steel or Ni-superalloy substrate. In te laser eating/cooling fatigue experiment, one found tat te interface delamination cracks in TBC system always occurred just above te interface between bond coat NiCrAlY layer and PSZ layer 4. Te interface delamination for termal barrier ceramic coating exposed to laser eating is sown in Fig. 3. In te test, te coating was exposed to six termal fatigue cycles and te exposed time for every cycle was 70 s and te igest temperature on coating and substrate was 200 C and 600 C, respectively. On te oter and, te elastic parameters for NiCrAlY bond coat and stainless steel SUS304 substrate are very close. Terefore, te combination of bond coat and SUS304 stainless steel is tougt as a substrate in te following discussions. Te material of substrate SUS340 stainless steel as termal and elastic properties similar to Ni-based superalloys. Terefore, te real caracterization of TBC system is reflected by te assumption tat te substrate of Ni-alloy is considered to be plastic and creep in te calculation of termal stress fields 2. In order to study te effect of te constitutive model of substrate on TBC system failure induced by Journal of Engineering for Gas Turbines and Power OCTOBER 2002, Vol. 24 Õ 925 Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

5 delemination, te substrate of steel is assumed to be elastic. Te ceramic coating PSZ is considered to be elastic and creep. TGO is considered in te calculation of te termal stress field and it is assumed to be elastic. Te bond coat is considered to be elasticperfectly plastic. Generally, TBC system is not a plane plate. Tere must be a curvature in some place, for example, te leading edge of a gas turbine blades is winding. It is assumed tat te TBC system is a cylindrical sell wit four layers wic are te substrate, bond coat, termal grown oxidation as well as te ceramic coating as scemed in Fig. 2. Te tickness of te substrate, bond coat, and ceramic coating is, respectively, 0.20 cm, 0.0 cm, and cm. Te inner radius of te cylindrical sell is 0.2 cm. In order to investigate te effect of TGO on te failure mecanism of te TBC system, te initial tickness of TGO is assumed to be 45 m and te evolution of TGO tickness is given by Zou and Hasida 2. Te system is considered to be in plane-strain condition. Te mecanical parameters are all temperature-dependent as given by Zou and Hasida 2. Loads in te TBC System wit Interface Crack. Te loads P, M, P 3, and M 3 are defined as M 0 P yr 4,tdy 0 M 3 H yr 4,t y 2 dy 0 P 3 H 0 yr 4,tdy yr 4,t y 2 3 dy (32) were (r,t) are circumferential stresses wic ave te same effect as xx studied in te above and te analytical and numerical results of (r,t) are obtained by Zou and Hasida. r 4 is te inner radius of te ceramic coating as described in Fig. 2 and or 3 is defined in expression 4. Te temperature fields are also te same as tat in 2 and te temperatures on ceramic and substrate surfaces wit one cycle of eating, eat old, and cooling are given in Fig. 4. Figure 5 sows te istories of membrane stresses P, P 3, and P. Note tat te negative value of P designates te ceramic coating to be in te tensile state according to Fig. a. It is seen tat membrane stresses P 3 are less tan loads P bot in Ni-alloy and steel substrates. During te period ofeating and olding te eat, te ceramic coating is in te tensile state and te substrate is in te compressive state. However, ceramic coating is in te compressive state and te substrate is in te tensile state for te TBC system during te cooling period. Generally, te residual loads of P become larger. By analyzing te constitutive equation discussed by Zou and Hasida 2, it is concluded tat te iger creep rate of PSZ coating results in te iger residual loads of P in te PSZ ceramic coating. Figure 6 sows te istories of bending moments M, M 3, and M. During te period of eating and olding te eat, te values of M and M 3 are bot negative. Te related values are positive on te end of cooling. Te same reasons of ceramic creep result in te ig positive residual loads M for PSZ coating on te end of cooling. Te values of equivalent loads M in bot studied TBC systems are negative during te period of eating and olding te eat and tose are positive on every end of cooling. Te Effect of Temperature Gradient on TBC System Failure. Temperature gradient as an important effect on te failure mecanism of te TBC system as described in 4,0. It is reasonable to assume te different linear temperature distribution along te tickness direction by inspecting te temperature fields in te TBC system 2. Te temperature at te outer surface of te Fig. 2 Sceme of te analytical model for termal stresses fields in te TBC system operating at ig temperature ceramic coating is 000 C, and te temperature at te inner surface of substrate is 700 C. Te temperature in te interface between material No. and material No. 2 Fig. reflects te level of te temperature gradient. In order to ave te concept of stress intensity factors, te energy release rate as derived in 5 is expressed by K i as K i /4 G. (33) b Te dimension of K i is MPa.m /2 and terefore, K i is te mixed stress intensity factor MSIF. Figure 7 sows te TSIFs K i, k, and k 2 as a function of temperature on te interface of bi-materials, were te original loads are P 7.0 MPa.cm, M MPa.cm 2, P MPa.cm, and M 3.0 MPa.cm 2. Te original loads are typical loads for te PSZ/Ni-alloy TBC system operating at te eat old period. In te figure, te experimental value of interface fracture tougness is also plotted, were te TBC system was partially stabilized ZrO 2 by 8wt%Y 2 O 3 over a NiCrAlY bond coat sprayed on a SUS 304 stainless steel substrate 27. As sown in Fig. 7 for te PSZ/Ni-alloy system, te mediate interface temperature results in negative energy release rate, i.e., zero MSIF. For a PSZ/steel system wit an elastic substrate, te ig interface temperature results in zero MSIF. Te negative mode I SIF sown in Fig. 7 means tat te TBC system will not fail in te form of a mode I crack. It is seen tat te temperature gradient does ave an important effect on TSIFs. By inspecting Dundurs parameters and, one finds tat and bot decrease wit Fig. 3 SEM micrograps sowing interface delamination cracking for termal barrier ceramic coating subjected to six termal fatigue cycles, were te exposed time for every cycle was 70 s and te igest temperature on te coating and substrate was 200 C and 600 C, respectively 926 Õ Vol. 24, OCTOBER 2002 Transactions of te ASME Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

6 Fig. 4 Boundary conditions of temperature for te TBC system at te typical operating state increasing interface temperature as sown in Fig. 8. Tere sould be a correlation between K i and Dundurs parameters and, wic is not known at present and it may be obtained by nondimensional analysis. Failure Evolution. Figure 9 sows te istories of TSIFs for PSZ/Ni-alloy and PSZ/steel TBC systems. Te temperature istories on outer and inner surfaces are sown in Fig. 4. Note tat in te model Ni-alloy is in te plastic state and steel is in te elastic state. Te difference of te constitutive model results in te different caracterizations of TSIF in Ni-alloy and steel substrates. Let us focus on te caracterizations of TSIFs for te PSZ/Nialloy system. Te MSIF during te period of eat old is lower tan tat during te period of cooling for PSZ/Ni-alloy system. Te MSIF in te eat old becomes lower and lower for te system operating wit tree cycles of eating/cooling. Generally, te MSIF during te period of te eat old is lower tan te interface fracture tougness K ic. Tis means tat interface crack may not propagate for te system during te eat old period. However, te MSIF becomes iger and iger for te system during te cooling period. Te MSIF may be iger tan te interface fracture tougness K ic. Terefore, te interface crack may propagate during cooling or during te eating period for te second or later cycles. It is concluded tat te TBC system may not fail in te form of interface delamination during te period of eat old, but it may fail in te form of interface delamination during cooling or during te eating period for te second cycle or after te second cycle. Te conclusion is consistent wit te experimental observations as sown in 4,0. In4,0, one as te fact tat te interface delamination may take place during eating or cooling period and even on te end of cooling in wic te temperature gradient along te tickness direction was zero. Te failure evolution of PSZ/Ni-alloy in te form of interface delamination may be explained by inspecting te caracterization of equivalent loads P and M as sown in Figs. 5 and 6. Te coating is in te tensile state during eating for te first cycle or during eat old. Tese type of loads cannot lead to coating delamination. However, due to plastic and creep beavior of te ceramic and substrate, te coating is in te compressive state wen te system is cooling. Te compression of ceramic coating is similar to te condition of te blister test 27. Altoug te new eating cycle may relax te compressive loads, te compressive load is so ig tat not all te compressive load is relaxed. Te residual compressive load in te coating is sufficient to cause delamination. Terefore, te interface delamination is caused by Fig. 5 Histories of membrane stresses; a original membrane stresses P and P 3, b equivalent membrane stresses P Journal of Engineering for Gas Turbines and Power OCTOBER 2002, Vol. 24 Õ 927 Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

7 Fig. 6 Histories of bending moments; a original bending moments M and M 3, b equivalent bending moments M compressive loading in te coating. TSIFs for mode I and mode II sown in Fig. 9 reveal tat te interface delamination crack in te period of eating or cooling is a mixed mode. Neiter te mode I nor mode II crack singly dominates te crack propagation. Conclusions Delamination cracking in te termal barrier coating system is studied in te present paper. A teoretical model concerning interface delamination cracking in te TBC system at operating state is proposed. In te model, a semi-infinite long interface crack is pre-existing. Te termal stress and temperature gradient in te TBC system are designated by a membrane stress P and a bending moment M. In tis case, te coupled effect of plastic deformation, creep of ceramic coating, as well as termal growt oxidation and temperature gradient in te TBC system was considered in te model. Te energy release rate, mode I and mode II stress intensity factors, as well as mode mixed measure are derived. Temperature gradient as an important effect on te failure mecanism of te TBC system. Tere sould be correlation of K i wit Dundurs parameters and. Te numerical results of TSIFs reveal some same results as obtained in te experimental test. For example, te TBC system may not fail in te form of coating delamination during te period of eat old, but it may fail in te form of coating delamination during cooling or in te eating period for te second cycle or later cycles according to te model. In te experiment 4,0, one as te fact tat te interface 928 Õ Vol. 24, OCTOBER 2002 Transactions of te ASME Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

8 Fig. 7 TSIFs K i, K I, and K II as a function of temperature on te interface of bimaterials, were te original loads P ÄÀ7.0 MPa.cm, M ÄÀ7.0Ã0 À3 MPa.cm 2, P 3 Ä4.0 MPa.cm, and M 3 ÄÀ.0 MPa.cm 2 delamination may take place during te eating or cooling period and even on te end of cooling in wic te temperature gradient along te tickness direction was zero. Due to plastic and creep beavior of te ceramic and substrate, te coating is in te compressive state wen te system is cooling. Te interface delamination is caused by compressive loading in te coating. Te interface delamination crack during te period of eating or cooling is a mixed mode. Neiter mode I nor mode II crack singly dominates te crack propagation. Fig. 9 Histories of TSIFs in TBC coating system; a Ni-alloy substrate, b steel substrate Acknowledgment Te collaborative researc grant for foreign researcers in Japan is provided to first autor YCZ by JSPS Japan Society for te Promotion of Science. Tis support is gratefully acknowledged. A part of tis work was supported by te Grant-in-Aid for COE Center of Excellence Researc No. CE2003, te Japan Ministry of Education, Science, Sports and Culture under Grant-in- Aid for Joint Researc wit te private sector. Te autors express teir appreciation for te grant. Te autors sow teir sincere gratitude to te referees for teir careful proofreading and many valuable suggestions. Fig. 8 Dundurs parameters and as a function of temperature on te interface of bimaterials Appendix A j In tis Appendix, te following material parameters suc as k j and k are defined: C k j y k 2 C 2 2 H k j2 2 y k j H ky k dy, k,2,3 j,2 (A) Journal of Engineering for Gas Turbines and Power OCTOBER 2002, Vol. 24 Õ 929 Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms

9 k j H C k E xx E zz j y k 2 C 2 2 H k E 2 xx 2 E 2 zz j2 2 yky k dy k,2 j,2 3 k 2 ik k 0 k k, (A2) 3 k 2 k 0 k k, k,2 (A3) In te above expressions, te related functions are defined as ij i j 0 i j y 0 Hy0 0y 2 y Hy0 (A4) 0 0y Appendix B i 2 8 J i 3 3 i 2 2 i i,2,3. (A5) In tis Appendix, te compliance matrix in Eq. 29 for te TBC system is given. were Bl A A E L T T A E L A E L A T 0 E 0 E 2 0, E L 0E E 2 E E 2 0 A A A m T A 2 A 2 E 2 0 E 2 2 A. (B) E L (B2) References Yuri, I., Hisamatsu, T., Watanabe, K., and Etori, Y., 997, Structural Design and Hig Pressure Test of a Ceramic Combustor for 500 C Class Industrial Gas Turbine, ASME J. Eng. Gas Turbines Power, 9, pp Kokini, K., and Takeuci, Y. R., 996, Surface Termal Cracking of Termal Barrier Coatings Owing to Stress Relaxation: Zirconia vs. Mullite, Surf. Coat. Tecnol., 82, pp Zu, D. M., and Miller, R. A., 998, Investigation of Termal Hig Cycle and Low Cycle Fatigue Mecanisms of Tick Termal Barrier Coatings, Mater. Sci. Eng., A, 245A, pp Jian, C. Y., 996, Study on Evaluation Metod of Ceramic Coating System for Gas Turbine Rotator Blades, Doctor s tesis, Tooku University. 5 Tolpygo, V. K., Dryden, J. R., and Clarke, D. R., 998, Determination of te Growt Stress and Strain in -Al 2 O 3 Scales During te Oxidation of Fe-22Cr- 4.8Al-0.3Y Alloy, Acta Mater., 463, pp Ogawa, K., Minkov, D., Soji, T., Sato, M., and Hasimoto, H., 999, NDE of Degradation of Termal Barrier Coating by Means of Impedance Spectroscopy, NDT & E Int., 32, pp Gell, M., et al., 999, Mecanism of Spallation in Platinum Aluminide/ Electron Beam Pysical Vapor Deposited Termal Barrier Coatings, Metall. Trans. A, 30A2, pp He, M. Y., Evans, A. G., a nd Hutcinson, J. W., 998, Effects of Morpology on te Decoesion of Compressed Tin Films, Mater. Sci. Eng., 245, pp Bernstein, H. L., and Allen, J. M., 992, Analysis of Cracked Gas Turbine Blades, ASME J. Eng. Gas Turbines Power, 4, pp Zou, Y. C., and Hasida, T., 2000, Coupled Effects of Temperature Gradient and Oxidation on te Termal Barrier Coating Failure, Life Assessment of Hot Section Gas Turbine Components, R. Townsend, et al., eds., Cambridge University Press, London, UK, pp Zou, Y. C., and Hasida, T., 2002, Termal Fatigue in Termal Barrier Coating, JSME Int. J., A45, pp Zou, Y. C., and Hasida, T., 200, Coupled Effects of Temperature Gradient and Oxidation on te Termal Stress in Termal Barrier Coating, Int. J. Solids Struct., 38, pp Si, G. C., Paris, P. C., and Irwin, G. R., 965, On Cracks in Rectilinearly Anisotropic Bodies, Int. J. Fract. Mec.,, pp Rice, J. R., and Si, G. C., 965, Plane Problems of Cracks in Dissimilar Media, ASME J. Appl. Mec., 32, pp Dundurs, J., 969, Edge-Bonded Dissimilar Ortogonal Elastic Wedges, ASME J. Appl. Mec., 36, pp Erdogan, F., 965, Stress Distribution in Bonded Dissilimar Materials Wit Cracks, ASME J. Appl. Mec., 32, pp Evans, A. G., and Hutcinson, J. W., 984, On te Mecanics of Delamination and Spalling in Compressed Films, Int. J. Solids Struct., 20, pp Hutcinson, J. W., and Suo, Z., 992, Mixed Mode Cracking in Layered Materials, Adv. Appl. Mec., 29, pp Timosenko, S. P., and Gere, J. M., 972, Mecanics of Materials, D.Van Nostrand, New York. 20 Dundurs, J., 990, Boundary Conditions at Interfaces, Micromecanics and Inomogeneous. G. J. Weng, et al., eds., Springer-Verlag, New York, pp Mura, T., 982, Micromecanics of Defects in Solid, Martinus Nijoff Publisers, Te Hague. 22 Suo, Z., and Hutcinson, J. W., 990, Interface Crack Between Two Elastic Layers, Int. J. Fract., 43, pp Witney, J. M., and McCulloug, R. L., 990, Micromecanical Materials Modeling, Vol.2, Tecnomic Lancaster, PA. 24 Leknitskii, S. G., 963, Teory of Elasticity of an Anisotropic Elastic Body, Holden-Day, Oakland, CA. 25 Suo, Z., 990, Delamination Specimens for Ortotropic Materials, ASME J. Appl. Mec., 57, pp Hutcinson, J. W., Mear, M. E., and Rice, J. R., 987, Crack Paralleling an Interface Between Dissimilar Materials, ASME J. Appl. Mec., 54, pp Zou, Y. C., Hasida, T., and Jian, C. Y., 2002, Determination of Interface Fracture Tougness in Termal Barrier Coating System by Blister Tests, ASME J. Eng. Mater. Tec., 24, in press. 930 Õ Vol. 24, OCTOBER 2002 Transactions of te ASME Downloaded From: ttp://gasturbinespower.asmedigitalcollection.asme.org/ on 06/2/205 Terms of Use: ttp://asme.org/terms