Forced tearing of ductile and brittle thin sheets

Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertina-like folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petal-like tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations and simple theories. In particular, we describe the transition from brittle oscillatory tearing via a single crack to ductile concertina tearing with two tears by deriving laws that describe the crack paths and wavelength of the concertina folds and provide a simple phase diagram for the morphologies in terms of the material properties of the sheet and the relative size of the tool.