Shearing a glass and the role of pinning delay in models of interface depinning

Abstract

When a disordered solid is sheared, yielding is followed by the onset of intermittent response that is characterized by slip in local regions usually labeled shear-transformation zones (STZ). Such intermittent response resembles the behavior of earthquakes or contact depinning, where a welldefined landscape of pinning disorder prohibits the deformation of an elastic medium. Nevertheless, a disordered solid is evidently different in that pinning barriers of particles are due to neighbors that are also subject to motion. Microscopic yielding leads to destruction of the local microstructure and local heating. It is natural to assume that locally a liquid emerges for a finite timescale before cooling down to a transformed configuration. For including this characteristic transient in glass depinning models, we propose a general mechanism that involves a "pin-delay" time T pd , during which each region that slipped evolves as a fluid. The new timescale can be as small as a single avalanche timestep. We demonstrate that the inclusion of this mechanism causes a drift of the critical exponents towards higher values for the slip sizes τ , until a transition to permanent shear-banding behavior happens causing almost oscillatory, stick-slip response. Moreover, it leads to a proliferation of large events that are highly inhomogeneous and resemble sharp slip band formation. Our model appears to be qualitatively consistent with recent experiments and simulations of disordered solids under shear.Extreme phenomena in nature appear in a wide range of scales, from the abrupt nano-deformation of materials to earthquake faults that extend several miles. At all scales, avoiding such phenomena requires a deep understanding of the disparate timescales leading to separate as well as collections of events. Material plastic deformation displays characteristic intermittency in a wide range of systems: single crystals [1], bulk metallic glasses (BMG) [2-4], disordered granular solids [5,6], colloids [7], frictional contacts [8,9]. While numerical simulations of materials can be very detailed at short timescales, the detailed study of a collection of abrupt events remains still out of reach. The theoretical intuition for such systems comes from the thorough study of interface depinning: a d-dimensional elastic string travelling on a landscape of quenched disorder in d+1 dimensions under the help of a uniform external force [10]. In complex disordered solids, though, while the assumption of an elastic medium appears reasonable, the one related to quenched disorder should be placed under scrutiny: the pinning disorder for every particle originates in the actual interface that attempts to depin (other nearby particles); a disordered solid pins itself during deformation. A basic consequence is that local glass depinning is not immediately followed by re-pinning; instead, in short-time transients (compared to typical avalanche durations), the system behaves locally as a fluid of finite viscosity η; In the context of depinning models we call this ...

Deformation and flow of amorphous solids: Insights from elastoplastic models

“…Exploiting this opportunity, Karimi et al (2017) analyzed the effect of inertia on the avalanche statistics and compared it with results from atomistic simulations. (Note that the effect of a delay in signal propagation had already been contemplated in an effective way by Lin et al (2014a), while, for the same purpose, Papanikolaou (2016) introduced a pinning delay in his EPM based on the depinning framework.) It was then possible to investigate the influence of the damping strength on the rheology of the elastoplastic system, which was indeed done by Karimi and Barrat (2016).…”

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Learning local, quenched disorder in plasticity and other crackling noise phenomena

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Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

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