Mechanics-based scaling laws for the durability of thermal barrier coatings

The durability of thermal barrier systems is governed by a sequence of crack nucleation, propagation and coalescence events that accumulate prior to final failure by large scale buckling and spalling. This sequence is governed by the σ zz stresses that develop normal to the substrate, around imperfections, as the thermally grown oxide (TGO) thickens. Their effect is manifest in the stress intensity factor, K, caused by the σ zz stresses acting on cracks emanating from them. In turn, these events are governed by scaling laws, ascribed to non-dimensional groups governing σ zz and K. In this article the basic scaling relations are identified and used to gain some understanding of the relative importance of the various mechanisms that arise for application scenarios with minimal thermal cycling. These mechanisms are based on stresses that develop because of TGO growth strains in combination with thermal expansion misfit. The results are used to identify a critical TGO thickness at failure and express it in terms of the governing material variables. The changes in behavior that arise upon extensive thermal cycling, in the presence of TGO ratcheting, are elaborated elsewhere.