Quantitative analysis of crack patterns in coatings

Crack networks in thin films often emerge through a sequential process governed by the temporal ordering of fracture events. However, experimental observations frequently reveal disconnected patterns, characterized by incomplete junctions and fragmented pathways, which deviate from this idealized scenario. In this work, we investigate the physical origins of the transition between disconnected and connected crack networks, linking it to the mechanical response of the film. The degree of connectivity is quantified through morphological descriptors that capture the extent of crack intersection and network organization. Combining this quantitative analysis with controlled experiments on coatings, we demonstrate that film thickness critically influences the fracture dynamics: thin films favor simultaneous cracking and yield disconnected networks, whereas thicker films undergo sequential fracture, forming highly connected structures. The results are interpreted within a unified energetic framework, in which a dimensionless parameter comparing elastic and fracture energies governs the transition between these distinct cracking regimes.