Thermal barrier coating (TBC) systems are highly advanced material systems and usually applied to insulate components from large and prolonged heat loads by utilizing thermally insulating materials. In this study, the characteristics of the interface of thermal barrier coating systems have been simulated by the finite-element method (FEM). The emphasis was put on the stress distribution at the interface which is beneath the indenter. The effect of the interface roughness, the thermally grown oxide (TGO) layer’s thickness, and the modulus ratio ( ) of the thin film with the substrate has been considered. Finite-element results showed that the influences of the interface roughness and the TGO layer’s thickness on stress distribution were important. At the same time, the residual stress distribution has been investigated in detail. 1. Introduction Thermal barrier coating (TBC) systems are widely used in modern gas turbines and jet engines. They protect materials and allow hot gas temperatures to increase the efficiency of the engine [1–4]. Their local failure in hot spots with severe impacts on the structural integrity of the engine has been prevented during operation. Therefore, the failure of TBC systems should be sufficiently understood. Experimental observations showed that the failure of TBC system is very complex and mostly affected by a superposition of different mechanisms. For instance, the initiation of cracks very close to the interface between the TBC and the bond coat (BC) seemed to be explained well by the residual stress calculations made by Chang et al. [5] and others [6–9], but their propagation was not similar with the result observed through experiment. Meanwhile, numerous models based upon different conceptions have been proposed, which might qualitatively explain how cracks propagated [6, 10–12]. All models considered oxidation at the rough interface between TBC and BC and the phenomena resulting from the redistribution of residual stresses induced by volume increasing or morphological instability of the thermally grown oxide (TGO) layer [12–17] as the driving force of crack propagation. However, all models lacked quantitative verification. It is very interesting to apply the indentation technology to thin film/substrate (especially TBC) systems. Now many models to determine the adhesion strength have been presented [18–20]. It is important to analyze the stress characteristics of thin film/substrate systems. For example, the stress distribution of the layers has been studied by Njiwa and von Stebut [21] and Diao [22] with the boundary
References
[1]
A. A. Volinsky, N. R. Moody, and W. W. Gerberich, “Interfacial toughness measurements for thin films on substrates,” Acta Materialia, vol. 50, no. 3, pp. 441–466, 2002.
[2]
A. Vasinonta and J. L. Beuth, “Measurement of interfacial toughness in thermal barrier coating systems by indentation,” Engineering Fracture Mechanics, vol. 68, no. 7, pp. 843–860, 2001.
[3]
D. R. Mumm and A. G. Evans, “On the role of imperfections in the failure of a thermal barrier coating made by electron beam deposition,” Acta Materialia, vol. 48, no. 8, pp. 1815–1827, 2000.
[4]
S. Q. Guo, D. R. Mumm, A. M. Karlsson, and Y. Kagawa, “Measurement of interfacial shear mechanical properties in thermal barrier coating systems by a barb pullout method,” Scripta Materialia, vol. 53, no. 9, pp. 1043–1048, 2005.
[5]
G. C. Chang, W. Phucharoen, and R. A. Miller, “Behavior of thermal barrier coatings for advanced gas turbine blades,” Surface and Coatings Technology, vol. 30, no. 1, pp. 13–28, 1987.
[6]
A. G. Evans, M. Y. He, and J. W. Hutchinson, “Mechanics-based scaling laws for the durability of thermal barrier coatings,” Progress in Materials Science, vol. 46, no. 3-4, pp. 249–271, 2001.
[7]
A. M. Freborg, B. L. Ferguson, W. J. Brindley, and G. J. Petrus, “Modeling oxidation induced stresses in thermal barrier coatings,” Materials Science and Engineering A, vol. 245, no. 2, pp. 182–190, 1998.
[8]
J. R？sler, M. B？ker, and M. Volgmann, “Stress state and failure mechanisms of thermal barrier coatings: role of creep in thermally grown oxide,” Acta Materialia, vol. 49, no. 18, pp. 3659–3670, 2001.
[9]
S. R. Choi, J. W. Hutchinson, and A. G. Evans, “Delamination of multilayer thermal barrier coatings,” Mechanics of Materials, vol. 31, no. 7, pp. 431–447, 1999.
[10]
A. G. Evans, D. R. Mumm, J. W. Hutchinson, G. H. Meier, and F. S. Pettit, “Mechanisms controlling the durability of thermal barrier coatings,” Progress in Materials Science, vol. 46, no. 5, pp. 505–553, 2001.
[11]
R. A. Miller and C. E. Lowell, “Failure mechanisms of thermal barrier coatings exposed to elevated temperatures,” Thin Solid Films, vol. 95, no. 3, pp. 265–273, 1982.
[12]
A. G. Evans, G. B. Crumley, and R. E. Demaray, “On the mechanical behavior of brittle coatings and layers,” Oxidation of Metals, vol. 20, no. 5-6, pp. 193–216, 1983.
[13]
W. J. Quadakkers, A. K. Tyagi, D. Clemens, R. Anton, and L. Singheiser, “The significance of bond coat oxidation for the life of TBC coatings,” in Elevated Temperature Coatings: Science and Technology III, J. M. Hampikian and N. B. Dahotre, Eds., pp. 119–130, The Minerals, Metals & Materials Society, Warrendale, Pa, USA, 1999.
[14]
H. E. Evans, “Stress effects in high temperature oxidation of metals,” International Materials Reviews, vol. 40, no. 1, pp. 1–40, 1995.
[15]
D. M. Lipkin, D. R. Clarke, M. Hollatz, M. Bobeth, and W. Pompe, “Stress development in alumina scales formed upon oxidation of (111) NiAl single crystals,” Corrosion Science, vol. 39, no. 2, pp. 231–242, 1997.
[16]
E. Schumann, C. Sarioglu, J. R. Blachere, F. S. Pettit, and G. H. Meier, “High-temperature stress measurements during the oxidation of NiAl,” Oxidation of Metals, vol. 53, no. 3, pp. 259–272, 2000.
[17]
V. K. Tolpygo and D. R. Clarke, “Competition between stress generation and relaxation during oxidation of an Fe-Cr-Al-Y alloy,” Oxidation of Metals, vol. 49, no. 1-2, pp. 187–212, 1998.
[18]
L. Heqing, C. Xun, M. Feng, et al., “Determination of the interfacial bonding strength of thin films and coatings using indentation method,” Materials For Mechanical Engineering, vol. 26, no. 4, pp. 11–13, 2002.
[19]
W. Yeih, J. J. Chang, and C. L. Tsai, “Enhancement of the bond strength of epoxy coated steel by the addition of fly ash,” Cement and Concrete Composites, vol. 26, no. 4, pp. 315–321, 2004.
[20]
J.-J. Kim, J.-H. Jeong, K.-R. Lee, and D. Kwon, “A new indentation cracking method for evaluating interfacial adhesion energy of hard films,” Thin Solid Films, vol. 441, no. 1-2, pp. 172–179, 2003.
[21]
R. K. Njiwa and J. von Stebut, “Boundary element numerical modelling as a surface engineering tool: application to very thin coatings,” Surface and Coatings Technology, vol. 116–119, pp. 573–579, 1999.
[22]
D. F. Diao, “Finite element analysis on local yield map and critical maximum contact pressure for yielding in hard coating with an interlayer under sliding contact,” Tribology International, vol. 32, no. 1, pp. 25–32, 1999.
[23]
G. M. Hamilton and L. E. Goodman, “The stress field created by a sliding circular contact,” Journal of Applied Mechanics, vol. 88, pp. 371–376, 1966.
[24]
G. M. Hamilton, “Explicit equations for the stresses beneath a sliding spherical contact,” Proceedings of the Institution of Mechanical Engineers C, vol. 197, pp. 53–59, 1983.
[25]
J. G. Swadenera, E. P. Georgea, and G. M. Pharra, “The correlation of the indentation size effect measured with indenters of various shapes,” Journal of the Mechanics and Physics of Solids, vol. 50, no. 4, pp. 681–694, 2002.
[26]
K. L. Johnson, Contact Mechanics, Cambridge University Press, 1985.
[27]
D. A. Anghel, A. R. Sterian, and P. E. Sterian, “Modeling quantum well lasers,” Mathematical Problems in Engineering, vol. 2012, Article ID 736529, 11 pages, 2012.
[28]
A. R. Sterian, “Computer modeling of the coherent optical amplifier and laser system,” in Computational Science and Its Applications (ICCSA '07), vol. 4705 of Lecture Notes in Computer Science, pp. 436–449, 2007.
[29]
B. Mitrica, “Design study of an underground detector for measurements of the differential muon flux,” Advances in High Energy Physics, vol. 2013, Article ID 641584, 9 pages, 2013.
[30]
B. Mitrica, “20 years of cosmic muons research performed in ifin-hh, exotic nuclei and nuclear/particle astrophsics (IV): from nuclei to stars book seris,” in Proceedings of the Carpathian Summer School of Physics (CSSP '07), vol. 1498 of AIP Conference Proceedings, p. 291, 2007.
[31]
B. Mitrica, “Asymmetry of charge ratio for low energetic muons,” in Proceedings of the Carpathian Summer School of Physics (CSSP '07), vol. 972 of AIP Conference Proceedings, pp. 500–504, August 2007.
[32]
Wan, Simulation of the indentation test and fatigue behavior of the grain boundary [M.S. thesis], 2001.
