Thin film cracking modulated by underlayer creep

In devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. In this paper we analyze a channel crack advancing in an elastic film, while an underlayer creeps. The film is subject to a tensile stress. As the underlayer creeps, the stress field in the film relaxes in the crack wake, and intensifies around the crack tip. In a blanket film, the crack can attain a steady velocity, set by two rate processes: subcritical decohesion at the crack tip, and creep in the underlayer. In a thin-film microbridge over a viscous stripe, the crack cannot grow when the bridge is short, and can grow at a steady velocity when the bridge is long. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process, and an extended finite element method to simulate the moving crack with an invariant, relatively coarse mesh. On the basis of the theoretical findings, we propose new experiments to measure fracture toughness and creep laws in small structures. As a byproduct, an analytical formula is found for the growth rate per temperature cycle of a channel crack in a brittle film, induced by ratcheting plastic deformation in a metal underlayer.