Transition between crack patterns in quenched glass plates.

THE study of fracture is an old topic1, but only recently has an understanding begun to emerge of crack formation, propagation and morphology (which is often fractal) 2-8. When a brittle material such as glass is broken under tensile stress9, the cracks have a complicated morphology10. Fineberg et al.11 showed that this process may be caused by a dynamic instability, whereby the speed of crack propagation increases until it approaches the speed of sound: at this point, complex structures appear. But crack morphology in quasistatic fracture, where the speed of the crack tip is much smaller than the speed of sound, can also exhibit marked changes12. Here we present studies of crack propagation in glass plates caused by sudden but carefully controlled cooling. We observe a transition from straight to regular, wavy cracks as the tip speed increases. The scaling behaviour of an appropriately defined relaxation time suggests that this transition is a Hopf bifurcation13, like those seen in a variety of other nonlinear systems. At still higher speeds, the oscillatory cracks split into first two and then four or more branches.