Linear elastic fracture mechanics predicts the propagation distance of frictional slip

TL;DR

This paper models the propagation of frictional slip as a fracture process using linear elastic fracture mechanics, accurately predicting precursor lengths and revealing key factors influencing slip propagation.

Contribution

It introduces a fracture mechanics-based model for frictional slip propagation, aligning well with experiments and simulations, and identifies dominant parameters affecting precursor lengths.

Findings

Precursor lengths depend mainly on the kinetic friction coefficient.

The model agrees quantitatively with laboratory experiments and simulations.

Sources of non-linearity in precursor growth are identified.

Abstract

When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model's prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize frictional slip as a fracture phenomenon. We show that predicted precursor lengths depend, within given uncertainty ranges, mainly on the kinetic friction coefficient, and only weakly on other interface and material parameters. By simplifying the fracture mechanics model we also reveal sources for the observed non-linearity in the growth of precursor lengths as a function of the applied force. The discrete nature of precursors as well as the shear tractions caused by frustrated Poisson's expansion are found to be the dominant factors. Finally, we apply our model to a different, symmetric set-up and provide a prediction of the propagation distance of frictional slip for future experiments.