Influence of bond coat thickness on the cyclic rumpling of thermally grown oxides

Recent experimental measurements have revealed that the amplitudes of undulations in the thermally grown oxide (TGO) formed on a bond coat subject to cyclic thermal histories depend on the bond coat thickness, hbc, and exhibit a maximum when hbc ≈ 100 μm. The existing rumpling model does not predict the maximum. To account for this effect, the model has been extended to include finite substrate thickness. The embellished code predicts the maximum and demonstrates close correspondence between calculated and measured undulation amplitudes (provided that all of the strain misfits between the bond coat and substrate are included: thermal expansion, martensite transformation and swelling). The presence of the maximum is attributed to two opposing effects. When thin, the bond coat is unable to deform to the extent needed to accommodate the undulations in the TGO. Conversely, when it has finite thickness relative to the substrate, the strains induced in the substrate reduce the constraint imposed on the bond coat, again reducing its ability to accommodate the undulations.