Theory of unconventional singularities of frictional shear cracks

TL;DR

This paper reveals that frictional shear cracks exhibit unconventional singularities influenced by friction laws and loading conditions, challenging the traditional square root singularity assumption and impacting their energy and dynamic behavior.

Contribution

It introduces a theory for unconventional singularities in frictional shear cracks, showing their dependence on friction laws, speed, and loading mode, with explicit calculations for viscous friction.

Findings

Singularity order $\xi$ varies from the classical -1/2.

$\xi$ depends on friction law, speed, and loading mode.

Explicit $\xi$ calculations for viscous friction in shear cracks.

Abstract

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