Theory of unconventional singularities of frictional shear cracks
Theory of unconventional singularities of frictional shear cracks
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DOI：
10.1016/j.jmps.2021.104466
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发表时间：
2021-05-18
影响因子：
5.3
通讯作者：
Bouchbinder, Eran
中科院分区：
文献类型：
--
作者：
Brener, Efim A.;Bouchbinder, Eran
沿摩擦界面传播的类裂纹物体，即摩擦剪切裂纹，在广泛的摩擦现象中起着重要作用。这类摩擦裂纹通常被认为具有线性弹性断裂力学所预测的理想剪切裂纹的普适平方根近边奇异性。这里我们表明，这不是一般情况，因为摩擦强度对滑移率的内在依赖，即使形成摩擦界面的物体是相同的，主要是线弹性的。相反，摩擦剪切裂缝具有非常规的奇点，其奇点阶xi与传统的- 1/2不同。结果表明，xi与摩擦规律、传播速度和加载的对称模式有关。我们讨论了非常规奇点理论的一般结构，以及它们对摩擦裂纹的能量平衡和动力学的影响。最后，对于平面内（ii型）和反平面（iii型）剪切载荷，我们给出了xi和相关线性粘摩擦的近边场的明确计算-它可能作为非线性摩擦定律的微扰近似或单独出现。
Crack-like objects that propagate along frictional interfaces, i.e. frictional shear cracks, play a major role in a broad range of frictional phenomena. Such frictional cracks are commonly assumed to feature the universal square root near-edge singularity of ideal shear cracks, as predicted by Linear Elastic Fracture Mechanics. Here we show that this is not the generic case due to the intrinsic dependence of the frictional strength on the slip rate, even if the bodies forming the frictional interface are identical and predominantly linear elastic. Instead, frictional shear cracks feature unconventional singularities characterized by a singularity order xi that differs from the conventional - 1/2 one. It is shown that xi depends on the friction law, on the propagation speed and on the symmetry mode of loading. We discuss the general structure of a theory of unconventional singularities, along with their implications for the energy balance and dynamics of frictional cracks. Finally, we present explicit calculations of xi and the associated near-edge fields for linear viscous-friction - which may emerge as a perturbative approximation of nonlinear friction laws or on its own - for both in-plane (mode-II) and anti-plane (mode-III) shear loadings.