176 Journal of the American Ceramic Society-Bai et al Vol. 90. No. I ments that are apparently in agreement with the design map in these results are presented in Figs. 9 and 10 ly, the concern that stresses in the EBC can degrade the intrinsic fracture strength of the substrate is addressed quanti- tatively. The general result is given by Eqs.(27)and(28), while the approximate result, which should suffice for most applica tions, is given by Eq (29). The most notable feature of Eq. (29) is that the columnar structure of the bond coat reduces the frac ture-stress penalty to less than 5% VIL. Conclusions 20um A general architecture for an environmental barrier coating is presented. It consists of a topcoat material which resists corro- sion, a columnar bond coat that is strain tolerant and the chem- ical bond coat that helps the adhesion of the columnar structure and the topcoat to the substrate. The function of the compliant bond coat is to accommodate the mismatch between the thermal expansion coefficients of the topcoat and the substrate. The stresses and displacements in the topcoat and columnar aminates while a thin topc structure are analyzed. The fracture criterion in the columns is ap in Fig. 6. related to the maximum bending stress produced in them. The safe "design of the coating is based upon the maximum stress design criterion, does indeed survive the exposure. These obser oat, as this would prevent delamination of the coating. The vations are in approximate agreement with the design guidelines nalysis then leads to the design map shown in Fig. 6. Expe ments reported in Figs. 9 and 10 are agreement with the pre- developed in this article. r\ cannot be expected to provide hermetic isolation between the environment and the substrate. The topcoat will necessarily de- High-temperature EBCs are multifunctional; they not only pro- velop periodic cracks if the thermal stress in it is greater than its tect the substrate from environmental attack but also must be fracture strength; however, the spacing between such cracks in designed to withstand thermal shock. In general, silicon con- the top coat can be controlled by the design of the columnar taining ceramics are unstable in streaming water-vapor env structure(the half spacing between the cracks in the topcoat will onment at high temperatures due to volatilization of the silica al to the decay distance shown ald scale which otherwise is protective in static oxidation conditions. The main purpose of the topcoat is to subdue the velocity of the environment at the substrate interface convert to hydroxides in humid conditions, such as zirconia or Finally, formal analysis shows that the tractions exerted by hafnia, are a natural choice for the topcoat in EBCs. However, the above architecture of the coating on the substrate surface these oxides also have a much larger coefficient of thermal ex pansion relative to silicon-based ceramics. The accommodation strength of the substanc at influence on the intrinsic fracture will have an insignificant of this thermal expansion strains by employing a compliant interlayer is the main topic of this article The compliant interlayer is assumed to be constructed from a columnar structure of beams "which can flex to accommodate References the columnar structure and the dense topcoat deposited on to it, Patent No. 4,321,331 an, ""Columnar Grain Ceramic Thermal Barrier Coatings" U.S. lies in the condition that the maximum value of the stress in the -T.E. Strangman and J. L. Schiele, "Tailoring Zirconia Coatings for Per olumns, due to fiexure, must be less than the stress in the top- farine Gas Turbine Environment. " J. Engin. Gas Turbines Power. coat. In this case, if both the columns and the topcoat are made l12.531-5(1990) of the Oxidation Rate of Silicon Nitride with Vapor Pres- from the same material. then the columns would not fracture sure,J. Am. Ceram. Soc., 82[3]625-36(1999) thereby precluding delamination of the topcoat N. S. Jacobson."Corrosion of silicon-Based Ceramics in Combustion envir- The analysis in the article focuses on the analysis of the stresses in the topcoat and the fiexure displacements in the columns. The 133-134. 1-7(2000) approach is conceptually similar to the shear lag models for the B. Sudhir and R. Raj, Effect of Steam Velocity on the Hydrothermal Oxida- interplay between the in-plane stress in thin films and the shear tion/Volatilization of Silicon Nitride, "J. Am. Ceram. Soc., 89[91 1380-7(2006). tractions at the interface when the film is mechanically loaded by Evaluation of Environmental Barier coatings for Silicon Nitride" United tech- shear tractions in the interfacial layer are borne by the flexure of TN, November 18, 20 in array of discreetly distributed columns. The analysis is formulated in terms of a non-dimensional arer.37126570(1989) K. More, unpublished work, parameter, c, given by Eq(14). The displacements in the col- Ige National Laboratory, Knoxville. TN Design and Evaluation of a High Term- umns are given by the set of difference equations in Eqs. (8)and perature Environmental Coating for Si-Based Ceramics, "J Am. Ceram. Soc. (9). These equations lead to the full solution to the probler Figure 4 gives the stress distribution in the topcoat, and the dis- IF. P. Beer, E. R. Jr. Johnston, and J. T. De Wolf (eds). Mechanics of Ma HilL. New York 2006 placements in the columns, as a function of the distance from a free edge of a crack in the topcoat. The effective decay distan of the displacements is plotted as a function of c in Fig. 5. The on /nnovative Processing and Synthesis of Ceramics, Glasses, and Composites at the criterion for safe design leads to the map in Fig. 6. The map shows two"safe"regimes, one at low aspect ratio of the columns IH. Tada, P. C. Paris, and G. R. Irwin (eds), The Stress Analys nd the other for the high aspect ratio of the columns. Experi Cracks Handhook. 3rd edition. ASME Press. New York. 2000.design criterion, does indeed survive the exposure. These obser￾vations are in approximate agreement with the design guidelines developed in this article. VI. Summary High-temperature EBCs are multifunctional; they not only pro￾tect the substrate from environmental attack but also must be designed to withstand thermal shock. In general, silicon con￾taining ceramics are unstable in streaming water-vapor envir￾onment at high temperatures due to volatilization of the silica scale which otherwise is protective in static oxidation conditions. It is therefore likely that oxides, especially those that do not convert to hydroxides in humid conditions, such as zirconia or hafnia, are a natural choice for the topcoat in EBCs. However, these oxides also have a much larger coefficient of thermal ex￾pansion relative to silicon-based ceramics. The accommodation of this thermal expansion strains by employing a compliant interlayer is the main topic of this article. The compliant interlayer is assumed to be constructed from a columnar structure of ‘‘beams’’ which can flex to accommodate the thermal strain, without fracture. Indeed the safe design of the columnar structure and the dense topcoat deposited on to it, lies in the condition that the maximum value of the stress in the columns, due to flexure, must be less than the stress in the top￾coat. In this case, if both the columns and the topcoat are made from the same material, then the columns would not fracture, thereby precluding delamination of the topcoat. The analysis in the article focuses on the analysis of the stresses in the topcoat and the flexure displacements in the columns. The approach is conceptually similar to the shear lag models for the interplay between the in-plane stress in thin films and the shear tractions at the interface when the film is mechanically loaded by thermal strain. The difference in the present problem is that the shear tractions in the interfacial layer are borne by the flexure of an array of discreetly distributed columns. The analysis is formulated in terms of a non-dimensional parameter, c, given by Eq. (14). The displacements in the col￾umns are given by the set of difference equations in Eqs. (8) and (9). These equations lead to the full solution to the problem. Figure 4 gives the stress distribution in the topcoat, and the dis￾placements in the columns, as a function of the distance from a free edge of a crack in the topcoat. The effective decay distance of the displacements is plotted as a function of c in Fig. 5. The criterion for safe design leads to the map in Fig. 6. The map shows two ‘‘safe’’ regimes, one at low aspect ratio of the columns and the other for the high aspect ratio of the columns. Experi￾ments that are apparently in agreement with the design map in Fig. 6 are described; these results are presented in Figs. 9 and 10. Finally, the concern that stresses in the EBC can degrade the intrinsic fracture strength of the substrate is addressed quanti￾tatively. The general result is given by Eqs. (27) and (28), while the approximate result, which should suffice for most applica￾tions, is given by Eq. (29). The most notable feature of Eq. (29) is that the columnar structure of the bond coat reduces the frac￾ture-stress penalty to less than 5%. VII. Conclusions A general architecture for an environmental barrier coating is presented. It consists of a topcoat material which resists corro￾sion, a columnar bond coat that is strain tolerant, and the chem￾ical bond coat that helps the adhesion of the columnar structure and the topcoat to the substrate. The function of the compliant bond coat is to accommodate the mismatch between the thermal expansion coefficients of the topcoat and the substrate. The stresses and displacements in the topcoat and columnar structure are analyzed. The fracture criterion in the columns is related to the maximum bending stress produced in them. The ‘‘safe’’ design of the coating is based upon the maximum stress in the columns being less than the maximum stress in the top￾coat, as this would prevent delamination of the coating. The analysis then leads to the design map shown in Fig. 6. Experi￾ments reported in Figs. 9 and 10 are agreement with the pre￾diction from this map. It should be noted that the topcoat cannot be expected to provide hermetic isolation between the environment and the substrate. The topcoat will necessarily de￾velop periodic cracks if the thermal stress in it is greater than its fracture strength; however, the spacing between such cracks in the top coat can be controlled by the design of the columnar structure (the half spacing between the cracks in the topcoat will be equal to the decay distance shown along the y-axis in Fig. 5). The main purpose of the topcoat is to subdue the velocity of the environment at the substrate interface. Finally, formal analysis shows that the tractions exerted by the above architecture of the coating on the substrate surface will have an insignificant influence on the intrinsic fracture strength of the substrate. References 1 T. E. Strangman, ‘‘Columnar Grain Ceramic Thermal Barrier Coatings’’; U.S. Patent No. 4,321,331, 1982. 2 T. E. Strangman and J. L. Schienle, ‘‘Tailoring Zirconia Coatings for Per￾formance in Marine Gas Turbine Environment,’’ J. Engin. Gas Turbines Power, 112, 531–5 (1990). 3 J. Opila, ‘‘Variation of the Oxidation Rate of Silicon Nitride with Vapor Pres￾sure,’’ J. Am. Ceram. Soc., 82 [3] 625–36 (1999). 4 N. S. Jacobson, ‘‘Corrosion of Silicon-Based Ceramics in Combustion Envir￾onment,’’ J. Am. Ceram. Soc., 76 [1] 3–28 (1993). 5 K. N. Lee, ‘‘Current status of EBCs for Si Based Ceramics,’’ Surf. Coat. Tech., 133–134, 1–7 (2000). 6 B. Sudhir and R. Raj, ‘‘Effect of Steam Velocity on the Hydrothermal Oxida￾tion/Volatilization of Silicon Nitride,’’ J. Am. Ceram. Soc., 89 [9] 1380–7 (2006). 7 T. Bhatia, H. Eaton, J. Holowczak, E. Sun, and V. Vedula, ‘‘Development and Evaluation of Environmental Barrier Coatings for Silicon Nitride’’; United Tech￾nologies Research Center, East Hartford, CT, DOE-EBC Workshop, Nashville, TN, November 18, 2003. 8 D. C. Agrawal and R. Raj, ‘‘Measurement of the Ultimate Shear Strength of a Metal Ceramic Interface,’’ Acta Met. Mater., 37 [4] 1265–70 (1989). 9 K. More, unpublished work, Oak Ridge National Laboratory, Knoxville, TN. 10S. R. Shah and R. Raj, ‘‘Multilayer Design and Evaluation of a High Tem￾perature Environmental Coating for Si-Based Ceramics,’’ J. Am. Ceram. Soc., (2006), in press. 11F. P. Beer, E. R. , Jr. Johnston, and J. T. DeWolf (eds), Mechanics of Ma￾terials, 4th edition, McGraw Hill, New York 2006. 12K. Sharma, P. S. Shankar, and J. P. Singh, ‘‘Mechanical Behavior of Si3N4 Substrates with Environmental Barrier Coatings’’; Proceedings of the Symposium on Innovative Processing and Synthesis of Ceramics, Glasses, and Composites at the 105th American Ceramic Society Annual Meeting and Exposition, Nashville, TN, April 27–30, 2003. 13H. Tada, P. C. Paris, and G. R. Irwin (eds), The Stress Analysis of Cracks Handbook, 3rd edition, ASME Press, New York, 2000. & Fig. 10. A thick topcoat delaminates while a thin topcoat does not, in agreement with the design-map in Fig. 6. 176 Journal of the American Ceramic Society—Bai et al. Vol. 90, No. 1