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Mathematical Problems in Engineering
Volume 2013, Article ID 515792, 8 pages
Research Article

Thermoelastic Characteristics in Thermal Barrier Coatings with a Graded Layer between the Top and Bond Coats

1Department of Mathematics, Changwon National University, 9 Sarim-dong, Changwon 641-773, Republic of Korea
2School of Nano and Advanced Materials Engineering, Changwon National University, 9 Sarim-dong, Changwon 641-773, Republic of Korea

Received 6 December 2012; Accepted 20 February 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Seokchan Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A graded layer was introduced at the interface between the top and bond coats to reduce the risk of failure in a thermal barrier coating (TBC) system, and the thermoelastic behavior was investigated through mathematical approaches. Two types of TBC model with and without the graded layer, subject to a symmetric temperature distribution in the longitudinal direction, were taken into consideration to evaluate thermoelastic behaviors such as temperature distribution, displacement, and thermal stress. Thermoelastic theory was applied to derive two governing partial differential equations, and a finite volume method was developed to obtain approximations because of the complexity. The TBC with the graded layer shows improved durability in thermoelastic characteristics through mathematical approaches, in agreement with the experimental results. The results will be useful in discovering technologies for enhancing the thermomechanical properties of TBCs.