Mathematical Analysis of Thermoelastic Characteristics in Plasma-Sprayed Thermal Barrier Coatings

The thermoelastic characteristics of plasma-sprayed thermal barrier coatings (TBCs) have been analyzed using mathematical modeling. Two types of TBC model, cylinder and circular disk which are commercial plasma-sprayed TBCs, subjecting to symmetric temperature distribution to the radial and longitudinal directions, respectively, were taken into consideration. Based on the thermoelastic theories, a second order ordinary differential equation was derived for the cylinder model and a pair of partial differential equations were set up for the circular disk model. The analytic solution was obtained from the ordinary differential equation, while a finite volume method was developed for numerical solutions to the pair of partial differential equations due to the complexity of governing equations. The thermoelastic characteristics of TBC models, such as temperature distributions, displacements, and stresses, were displayed according to the obtained solutions. The rate of heat conduction in the section of the top coat is relatively slow in comparison with the substrate, and no profound difference appears in the temperature distribution between two TBC models. The highest longitudinal tensile stress is expressed at the bond coat of both models, and the substrate is under the compressive stresses to the circumferential direction. While the cylinder expands to the positive longitudinal direction only, the expansion in the circular disk occurs to both the positive and negative longitudinal directions. Relatively large displacement and stresses exhibit in the cylinder as compared with the circular disk. In the circular disk, the stresses to the radial direction undulate at each section, and the displacement profile displays that the width of the circular disk is slightly narrowed. The results demonstrate that the mechanical and thermal properties of the top and bond coats are the crucial factors to be considered in controlling the thermoelastic characteristics of plasma-sprayed TBCs.