Crack spacing in strained films

Consider a thin film resting on a relatively thick substrate. When the substrate is subjected to an axial strain transverse cracks, normal to the direction, of the applied strain may appear in the film. It is observed that, for a given strain, the spacing between such cracks is uniform, with a clearly identifiable characteristic length scale that can be used to provide bounds on the spacing. Further, as the strain is increased, there is a densification of the cracks up to a saturation limit. Beyond the saturation limit additional strain produces no further cracks and the characteristic crack length scale for the given system remains fixed. This paper presents analytical models that can be used to predict the characteristic length scale both at the saturation limit and during the densification process. The models are shown to be applicable across a wide range of length scales; with abilities to determine the crack space length scale in both asphalt pavements (~100m) subjected to a thermal loading and strained ceramic films (~100$\mu$m)