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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.

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