Analytical modeling of oxide thickness effects on residual stresses in thermal barrier coatings

The residual thermal stress normal to the interface in the ceramic top coat and close to the thermally grown oxide (TGO) is of interest, since it could result in cracking and spallation of the plasma-sprayed thermal barrier coating (TBC). The effects of the TGO thickness on this residual stress were qualitatively interpreted in the present study by using an analytical model of three concentric circles. An effective coefficient of thermal expansion (CTE) was defined to illustrate the qualitative trends of the TGO thickness effects. To model a convex interface asperity, phases 1,2, and 3 in Figure 1 correspond to bond coat, TGO, and top coat, respectively. The residual radial stress at r=b (i.e., at the top coat/TGO interface), sigma sub b , is of interest. The stress state of sigma sub b can be obtained by comparing alpha sub 3 with the effective CTE in the region of r < b which is a function of dimensions, elastic constants, and CTEs of phases 1 and 2 (Figure 2). To model a concave interface asperity, phases 1, 2, and 3 in Figure 1 correspond to top coat, TGO, and bond coat, respectively. The residual radial stress at r=a (i.e., at the top coat/TGO interface), sigma sub a , is of interest. The stress state of sigma sub a can be obtained by comparing alpha sub 1 with the effective CTE in the region of a < r < c which is a function of dimensions, elastic constants, and CTEs of phases 2 and 3 (Figure 3).