How collective asperity detachments nucleate slip at frictional interfaces

Abstract

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius Ac governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding xσ presents a pseudo-gap P (xσ) ∼ (xσ) θ , where θ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius Ac diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally. Significance statementUnderstanding how slip at a frictional interface initiates is important for a range of problems including earthquake prediction and precision engineering. The force needed to start sliding a solid object over a flat surface is classically described by a 'static friction coefficient': a constant established by measurements. It was recently questioned if such constant exists, as it was shown to be poorly reproducible. We provide a model supporting that it is stochastic even for very large system sizes: sliding is nucleated when, by chance, an avalanche of microscopic detachments reaches a critical radius, beyond which slip becomes unstable and propagates along the interface. It leads to testable predictions on key observables characterising the stability of the interface.

Earthquake Nucleation Along Faults With Heterogeneous Weakening Rate

“…This small event destabilizes the interface as a whole, generating a complex dynamics of multiple slip pulses (see velocity map in Figure 3d for which 𝐴𝐴 𝐴𝐴𝑥𝑥 = 0.01𝐿𝐿 hom c = 2𝐿𝐿 min c ). Along natural faults, these small ruptures may be arrested by local barriers of strength 𝐴𝐴 𝐴𝐴p , but they may trigger a cascade of nucleation events centered on other weakest spots until the entire fault fails (de Geus et al, 2019;Noda et al, 2013;Zhang et al, 2003). Note that (a) these brittle asperities influence the effective nucleation length 𝐴𝐴 𝐴𝐴c far LEBIHAIN ET AL.…”

Stochastic Properties of Static Friction

“…How interfacial randomness causes variation in these observations has, however, not been studied so far. Only most recently, Amon et al (2017) and Geus et al (2019) have considered variability in friction. Amon et al (2017) showed that systems with a nonuniform initial stress state with long range coupling are characterized by two regimes: at low loading, small patches of the system undergo sliding in an uncorrelated fashion; at higher loading, instabilities occur at regular intervals over patches of increasing size -just like confined stick-slip events (Kammer et al, 2015;Bayart et al, 2016) -and eventually span the whole system.…”

“…Amon et al (2017) showed that systems with a nonuniform initial stress state with long range coupling are characterized by two regimes: at low loading, small patches of the system undergo sliding in an uncorrelated fashion; at higher loading, instabilities occur at regular intervals over patches of increasing size -just like confined stick-slip events (Kammer et al, 2015;Bayart et al, 2016) -and eventually span the whole system. Geus et al (2019) simulated interface asperities as an elasto-plastic continuum with randomness in its potential energy and show that the stress drop during a stick-slip cycle is a stochastic property which vanishes with increasing number of asperities. These results demonstrate well the stochastic character of macroscopic friction due to random interface properties.…”

The Nanocaterpillar's Random Walk: Diffusion With Ligand-Receptor Contacts

“…For example, solid state sliding friction is created by bonds breaking between atoms. Close neighbor interactions between bonds, originating from mechanical interactions, can result in dramatic avalanches of bond breaking that change the sliding motion [91,92]. Similar correlations between nearby bonds could be at play in some nanocaterpillars.…”