Kooij Stefan, van Dalen Gerard, Molinari Jean-François, Bonn Daniel
Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, The Netherlands.
Unilever Research and Development Vlaardingen, Olivier van Noortlaan, Vlaardingen, The Netherlands.
Nat Commun. 2021 May 4;12(1):2521. doi: 10.1038/s41467-021-22595-1.
Anyone who has ever broken a dish or a glass knows that the resulting fragments range from roughly the size of the object all the way down to indiscernibly small pieces: typical fragment size distributions of broken brittle materials follow a power law, and therefore lack a characteristic length scale. The origin of this power-law behavior is still unclear, especially why it is such an universal feature. Here we study the explosive fragmentation of glass Prince Rupert's drops, and uncover a fundamentally different breakup mechanism. The Prince Rupert's drops explode due to their large internal stresses resulting in an exponential fragment size distribution with a well-defined fragment size. We demonstrate that generically two distinct breakup processes exist, random and hierarchical, that allows us to fully explain why fragment size distributions are power-law in most cases but exponential in others. We show experimentally that one can even break the same material in different ways to obtain either random or hierarchical breakup, giving exponential and power-law distributed fragment sizes respectively. That a random breakup process leads to well-defined fragment sizes is surprising and is potentially useful to control fragmentation of brittle solids.
任何打碎过盘子或玻璃杯的人都知道，破碎后的碎片大小不一，从大致与物体大小相当到小得难以分辨：脆性材料破碎后的典型碎片尺寸分布遵循幂律，因此没有特征长度尺度。这种幂律行为的起源尚不清楚，尤其是为什么它是如此普遍的特征。在这里，我们研究了玻璃鲁珀特之泪的爆炸破碎，并发现了一种根本不同的破碎机制。鲁珀特之泪由于其巨大的内部应力而爆炸，导致碎片尺寸呈指数分布且具有明确的碎片尺寸。我们证明，一般存在两种不同的破碎过程，随机破碎和分层破碎，这使我们能够充分解释为什么在大多数情况下碎片尺寸分布是幂律的，而在其他情况下是指数的。我们通过实验表明，甚至可以以不同方式破碎同一种材料，分别获得随机或分层破碎，从而得到指数分布和幂律分布的碎片尺寸。随机破碎过程会导致明确的碎片尺寸，这一点令人惊讶，并且可能有助于控制脆性固体的破碎。
