Undulation instability of a compressed elastic film on a nonlinear creeping substrate

Undulation instabilities in a tri-layer system subject to variations of temperature are studied for the purpose of revealing a mechanism leading to the failure of thermal barrier systems. A pre-compressed oxide film with a small initial non-planarity is attached to a metal bond coat layer that is, in turn, attached to a thick superalloy substrate. The oxide film and the superalloy substrate are elastic, while the bond coat undergoes power-law creep at high temperature. The bond coat and the oxide film are subject to equi-biaxial stress changes whenever the temperature changes due to thermal mismatch with the superalloy substrate. The mismatch can be very large for some bond coat materials, such as PtNiAl, as a result of a reversible phase transformation that occurs while the temperature is changing. In the bond coat layer, the stress decays due to creep during periods at high temperature. However, during the initial stages of the decay period, the bond coat is highly susceptible to transverse deformation due to the nonlinear character of power-law creep, enabling the compressed film to undergo significant undulation growth over hundreds of thermal cycles. These periods of susceptibility appear to be a primary mechanism for undulation growth in a film that is initially nearly planar, and they explain the observation that undulation growth under cyclic temperature histories far exceeds that under isothermal conditions for the same total time exposure at high temperature. Although the behavior of the bond coat is highly nonlinear, an approximation has been developed which permits accurate description of undulation development under quite general conditions. Possibilities for reducing the susceptibility to undulation growth are discussed, as are further avenues for research.