Film fragmentation on curved substrates

When subjected to mechanical, chemical, thermal or other loads, film–substrate systems may exhibit diverse fracture modes, depending on their mechanical properties, geometric shapes, and loading conditions. Among others, fragmentation often occurs in thin films in both nature and industry, such as thermal barrier coatings. In this paper, we investigate the fragmentation of thin films bonded on curved substrates, which involves coupled film cracking and interfacial debonding. Through dimensional analysis and peridynamic simulations, the conditions of three typical fragmentation modes are given in terms of the mechanical and geometric parameters of the film and the interface. A scaling law is established to describe the debonding width, revealing an inverse correlation between interfacial curvature radius and debonding width. Peridynamic simulations demonstrate that the interfacial curvature radius has a distinct influence on the fragment sizes. Moreover, as the interfacial toughness increases, the fracture mode may shift from a coupled cracking–debonding pattern to a purely film cracking mode. A phase diagram is provided to clarify the underlying regulatory mechanisms of fragmentation in curved film–substrate systems. This work also offers insights for the design of film–substrate systems and layered structures.