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 $-\frac{1}{2}$ 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.

沿摩擦界面传播的类似裂纹的物体，即摩擦剪切裂纹，在广泛的摩擦现象中起主要作用。如线性弹性断裂力学所预测的那样，通常假定这种摩擦裂纹具有理想剪切裂纹的普遍平方根近边缘奇异性。在这里，我们表明，由于形成摩擦界面的物体是相同的且主要是线性弹性，因此，由于摩擦强度对滑移率的内在依赖性，这不是一般情况。取而代之的是，摩擦剪切裂纹具有以奇异阶为特征的非常规奇异$\xi$ 有别于传统 $-\frac{\mathrm{1个}}{\mathrm{2个}}$一。结果表明$\xi$取决于摩擦定律，传播速度和载荷的对称模式。我们讨论了非常规奇异理论的一般结构，以及它们对能量平衡和摩擦裂纹动力学的影响。最后，我们给出了显式的计算$\xi$ 以及相关的用于线性粘性摩擦的近边缘场（对于平面内（模式II）和反平面（模式III）剪切载荷而言，它可能是非线性摩擦定律的摄动近似值或单独出现） 。