Scaling theory for the statistics of slip at frictional interfaces

Abstract

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress ${\sigma }^{\ast }$, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a powerlaw corresponding to `avalanches', and a `narrow' distribution of system-spanning `fracture' events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

References in corpus (7)

• The dependence of the dry friction threshold on rupture dynamics
• Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study
• Depinning exponents of the driven long-range elastic string
• Earthquake Nucleation along Faults with Heterogeneous Weakening Rate
• Stochastic Properties of Static Friction
• Nucleation of frictional sliding by coalescence of microslip
• Velocity-driven frictional sliding: Coarsening and steady-state pulse trains

Cited by in corpus (3)

• Nucleation of frictional slip: A yielding or a fracture process?
• Stick-slip in a stack: how slip dissonance reveals aging
• Armouring of a frictional interface by mechanical noise