Oscillating fracture paths in thin brittle sheets: When geometry rules crack propagation

We report a new kind of quasi-static oscillatory crack propagation when a cutting tool, of moderately large width, is driven through a thin brittle polymer film (Roman [1], Ghatak [2]). In our experiments, a cutting tool is perpendicularly driven through a brittle thin sheet, clamped at its boundaries, and progressively cuts the material as it advances. For large enough tools, the crack tip follows a highly periodic path, leaving behind a striking oscillatory pattern. The amplitude and wavelength of the oscillatory crack paths scale linearly with the width of the cutting tip, over a wide range of length scales, but are independent of both the width of the sheet and the cutting speed. We propose a geometrical model (Audoly [3]) that accurately reproduces the behaviour observed experimentally, far away from threshold. The central idea of our formulation is a coupling between the Griffith criterion for crack propagation and out-plane-deformations of the film. We show that, for our case, the propagation of cracks in brittle sheets follows a simple geometrical construction.