RESUMO
We report a new oscillatory propagation of cracks in thin films where three cracks interact mediated by two delamination fronts. Experimental observations indicate that delamination fronts joining the middle crack to the lateral crack tips swap contact periodically with the crack tip of the middle crack. A model based on a variational approach analytically predicts the condition of propagation and geometrical features of three parallel cracks. The stability conditions and oscillating propagation are found numerically and the predictions are in favorable agreement with experiments. We found that the physical mechanism selecting the wavelength structure is a relaxation process in which the middle crack produces a regular oscillatory path.
RESUMO
Cutting a brittle thin sheet with a blunt object leaves an oscillating crack that seemingly violates the principle of local symmetry for fracture. We experimentally find that at a critical value of a well chosen control parameter the straight propagation is unstable and leads to an oscillatory pattern whose amplitude and wavelength grow by increasing the control parameter. We propose a simple model that unifies this instability with a related problem, namely that of a perforated sheet, where through a similar bifurcation a series of radial cracks spontaneously spiral around each other. We argue that both patterns originate from the same instability.
RESUMO
We study multiple tearing of a thin, elastic, brittle sheet indented with a rigid cone. The n cracks initially prepared symmetrically propagate radially for n≥4. However, if n<4 the radial symmetry is broken and fractures spontaneously intertwine along logarithmic spiral paths, respecting order n rotational symmetry. In the limit of very thin sheets, we find that fracture mechanics is reduced to a geometrical model that correctly predicts the maximum number of spirals to be strictly 4, together with their growth rate and the perforation force. Similar spirals are also observed in a different tearing experiment (this time up to n=4, in agreement with the model), in which bending energy of the sheet is dominant.
RESUMO
Thin adhesive films have become increasingly important in applications involving packaging, coating or for advertising. Once a film is adhered to a substrate, flaps can be detached by tearing and peeling, but they narrow and collapse in pointy shapes. Similar geometries are observed when peeling ultrathin films grown or deposited on a solid substrate, or skinning the natural protective cover of a ripe fruit. Here, we show that the detached flaps have perfect triangular shapes with a well-defined vertex angle; this is a signature of the conversion of bending energy into surface energy of fracture and adhesion. In particular, this triangular shape of the tear encodes the mechanical parameters related to these three forms of energy and could form the basis of a quantitative assay for the mechanical characterization of thin adhesive films, nanofilms deposited on substrates or fruit skin.
RESUMO
We identify and study a persistent structure characteristic of the post-buckling regime of a thin cylindrical shell subjected to axial torsion. It consists of a pair of developable cones ( d cones) joined by an S-shaped ridge, having a size of the order of the radius of the cylinder. We study its formation by applying a concentrated load at the center of the shell, which creates an isolated pair of d cones, joined by a straight ridge that progressively tilts when a torsion angle is imposed. We interpret this response as the equilibrium state of a pair of interacting d cones in the presence of an in-plane shear field, created by axial torsion, which tends to drive them away from each other. We find that the amplitude of displacement of the d cones for a given torsion angle is amplified by decreasing the thickness of the sheet, therefore concluding that the equilibrium state is the result of a balance between bending and stretching energies. We propose a model where the driving effect is the coupling between the deformation field around the d cones and the imposed shear field, while the stabilizing effect is the increasing bending energy of the system.