Residual stress relaxation processes in thermal barrier coatings under tension at high temperature

A model of failure is considered that can be applied to n-phase brittle materials (in particular to thermal barrier coatings (TBCs)). The authors attempt to solve a physical problem of the description of failure of a microscopically inhomogeneous solid as stochastic process of the cracking of individual structural elements. The above mentioned model is applied to describe the mechanical behavior of single-phase ceramic-based coatings with given statistical distribution of grains sizes. The failure process is found to have several stages. If the stage of the catastrophic microcracking is reached, the microcracking process in a TBC reaches saturation when the average distance between cracks approximately equals the lamella thickness of 4–5 μm. Large multigrain cracks with sizes within the range 1–32 μm are observed in the TBC after thermal cycling. These microcracks can be explained by the model proposed. They are the result of unstable microcracking during the fourth stage of the stochastic failure process. In such a way, the model proposed provides a means to describe some features of thermal stress relaxation in a TBC during thermal cycling.