Pattern formation in thin-film failure

Abstract

While thin films bonded to solid substrates are integral to most modern technologies, their failure mechanisms are not well understood. It has long been observed, however, that the mechanical failure of thin films under large stresses produces a rich phenomenology of pattern formation. In this paper, we describe the results of computer simulations of stress relief in thin films under either tensile or compressive stress applied by their substrates. For films which contain quenched disorder, tensile stress relief results in the fragmentation of the film layer into a patchwork of undamaged film surrounded by cracks. When the applied stress is moderate, the dynamics of the cracks are sufficiently simple that a mean-field theory can be constructed to describe the crack-length statistics in the final fragmented state. For films under large compressive stresses, the simulations reproduce a very peculiar delamination pattern which has been experimentally observed for several decades; the buckled regions of film have a sinusoidal shape behind a propagating tip. These strikingly regular sinusoidal blisters propagate over large distances in the film with constant lateral widths and constant wavelengths.