Oscillatory fracture paths
in thin elastic sheets
B. Roman, P. M. Reis, B. Audoly
S. DeVilliers, V. Viguié, D. Vallet
PMMH, UMR 7636 CNRS/ESPCI, 10 rue Vauquelin 75231 cedex 5 Paris, France
Manchester Center for Nonlinear Dynamics, Dept. physics and astronomy, University of Manchester, M139PL UK
LMM, UMR 7607 CNRS/UPMC, 4 place Jussieu, case 162, 75252 Paris cedex 05, France
Fracture is an old subject, but many puzzling questions remain unsolved, as the prediction of the direction of the crack path for example. A well controlled fracture experiment in a thermally quenched thin glass strip where oscillatory fracture was observed (Yuse and Sano, 1993) has stimulated many recent studies on this topic.
Here we report novel experimental results on oscillatory fracture in a new experimental context involving the cutting of thin sheets.
Experiment A 'blunt' cutting tip (with cylindrical or rectangular profile) is perpendicularly driven through a strip of thin brittle sheet, held at its boundaries. As the tip advances, it progressively cuts the material leaving behind a well defined and highly reproducible oscillatory path. Moreover, there is a threshold for the tip width, below which the crack paths are straight. See a video of a typical experimental run.
Geometrical model We have developed a simple geometrical model which accurately reproduces the oscillatory paths observed in the experiment, far from threshold that is for tip much wider than plate thickness. The model accounts for the energetics of thin elastic sheets, and its connection with the geometry of surfaces. We defined a propagation criterion from the interplay between geometry and the advance of the crack tip (see preprint).
Model and experiments: comparison A numerical simulation of this model yields oscillating paths that are very similar to the experimental ones. Moreover, some the detailed features of the propagation are captured by our model. For example, the crack propagates through quasi-static phases followed by a sudden kink (change in direction) and a dynamical jump. Excellent agreement is found.
The amplitude and wavelength of the oscillations are observed to scale linearly with the cutting tip size, independently of the thickness and material. Counter-intuitively, the oscillations are independent of both the cutting speed (much smaller than the materials sound speed) and the lateral width of the sheet. Both of these observations are actually predicted by our geometrical model where no time scale is included.
Conclusion We report a very robust oscillating crack path in thin plates that we observed on almost 3 decades of lengthscales of the cutting tip. We built a simple geometrical model that accounts for the scaling laws of the phenomenon, and correctly describes the details of the propagation (wavy patterns, kinks, alternating dynamic and quasi-static regimes).