Yuse A, Sano M
Nature. 1993 Mar 25;362(6418):329-331. doi: 10.1038/362329a0.
THE study of fracture is an old topic, but only recently has an understanding begun to emerge of crack formation, propagation and morphology (which is often fractal) . When a brittle material such as glass is broken under tensile stress, the cracks have a complicated morphology. Fineberg et al. 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 changes. 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 bifurcation, 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.
对断裂的研究是一个古老的话题，但直到最近人们才开始对裂纹的形成、扩展和形态（通常是分形的）有所了解。当像玻璃这样的脆性材料在拉应力下破裂时，裂纹具有复杂的形态。芬伯格等人表明，这个过程可能是由动态不稳定性引起的，即裂纹扩展速度增加，直到接近声速：此时，复杂结构出现。但在准静态断裂中，裂纹尖端速度远小于声速时，裂纹形态也会出现显著变化。在这里，我们展示了由突然但精确控制的冷却导致的玻璃板中裂纹扩展的研究。我们观察到随着尖端速度增加，裂纹从直线形转变为规则的波浪形。适当定义的弛豫时间的标度行为表明，这种转变是一种霍普夫分岔，类似于在各种其他非线性系统中看到的情况。在更高的速度下，振荡裂纹首先分裂成两个，然后是四个或更多分支。
