You may never have stopped to look, but the edge of a popped balloon is rippled like a row of shark’s teeth. Inspired by this observation, a team of researchers has found that fractures in rubber can develop as either straight lines or waves depending on how hard the material is pulled. The group doesn’t yet have a complete explanation for the effect, described in the 7 January print issue of PRL, but the mystery may offer a fresh perspective on the great unsolved problem in fracture dynamics: predicting where a crack will go after it forms.
Physicists and engineers already have a good grasp on when a material will break, which allowed the field of aeronautics to take off, but beyond that, many details are murky. They still have little clue why fractures take the paths they do. “We don’t really know what sets the direction of motion,” says Michael Marder of the University of Texas (UT) at Austin. Insights into those ultimate laws may emerge as crack researchers pursue less daunting mysteries, like why fractures sometimes oscillate from side to side or branch off into a “Y” shape, adds Marder’s UT coworker Robert Deegan.
So when a colleague pointed out the balloon ripple to Deegan, he asked a graduate student to stretch a series of rubber sheets in two directions simultaneously, and then prick each one with a pin. The pin generated cracks that zipped along at nearly the speed of sound in rubber, as judged by high-speed video footage. By examining the remains of broken sheets, the researchers found that the tear took one of two forms, or phases: one relatively smooth-edged, the other sine-wave like, with a centimeter-sized wavelength and peaks of around a millimeter in height.
Oscillations cropped up along the tear when they stretched the rubber beyond a certain point. As tension increased, the changes in frequency and wavelength of the wavy phase matched the properties of a so-called Hopf bifurcation. This phenomenon appears in many other areas, such as certain chemical reactions that generate pinwheel patterns of alternating colors and fluids trapped between two concentric cylinders. It also pops up when wiggly cracks form in rapidly cooled pieces of heated glass.
The team ruled out several potential explanations for the fracture’s oscillating motion that were intrinsic to the rubber itself, including drum-like vibrations in the sheet and periodic hardening of the material, suggesting that the phenomenon may apply to cracks in any material. Marder says the answer probably has to do with the combination of very large strains in multiple directions, but adds that so far the problem has proven “interestingly baffling,” not to mention fun.
Whatever the cause, such studies are helpful because they suggest what a good theory should be able to explain, says Herbert Levine of the University of California in San Diego. Engineering models often focus on narrow issues like crack speeds in a given material under a certain strain, Levine explains. “Sometimes a lot of the fundamental issues don’t get focused on at all.” This group is one of a couple, he says, who are “providing the experiments for the physics [theorist] community to think about.”