Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel.
Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA.
Phys Rev Lett. 2018 Sep 28;121(13):134301. doi: 10.1103/PhysRevLett.121.134301.
The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here, we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.
二维振动裂纹不稳定性在强烈动态条件下的一类脆性材料中得到了实验观察，最近被一种非线性相场断裂理论重现。在这里，我们通过展示它存在于表现出广泛不同的近裂纹尖端弹性非线性的材料中，并通过证明在与耗散相关的和非线性弹性固有长度尺度的基础上，振动波长遵循通用的主曲线，来突出这种不稳定性的普遍性。此外，我们还表明，随着断裂驱动力的增加，会出现高速尖端分裂不稳定性，这与实验观察到的情况一致。分析最终得到了二维脆性断裂的综合稳定性相图，其显著特性和拓扑结构与近尖端非线性的形式无关。
