Plastic Response of a 2D Amorphous Solid to Quasi-Static Shear : II - Dynamical Noise and Avalanches in a Mean Field Model

We build a minimal, mean-field, model of plasticity of amorphous solids, based upon a phenomenology of dissipative events derived, in a preceding paper [A. Lemaitre, C. Caroli, arXiv:0705.0823] from extensive molecular simulations. It reduces to the dynamics of an ensemble of identical shear transformation zones interacting via the dynamic noise due to the long ranged elastic fields induced by zone flips themselves. We find that these ingredients are sufficient to generate flip avalanches with a power-law scaling with system size, analogous to that observed in molecular simulations. We further show that the scaling properties of avalanches sensitively depend on the detailed shape of the noise spectrum. This points out the importance of developing a realistic coarse-grained description of elasticity in these systems

Rate-Dependent Avalanche Size in Athermally Sheared Amorphous Solids

We perform an extensive numerical study of avalanche behavior in a 2D LJ glass at T=0, sheared at finite strain rates $\dot\gamma$. From the finite size analysis of stress fluctuations and of transverse diffusion we show that flip-flip correlations remain relevant at all realistic strain rates. We predict that the avalanche size scales as $\dot\gamma^{-1/d}$, with $d$ the space dimension

Ultrafast spherulitic crystal growth as a stress-induced phenomenon specific of fragile glass-formers

We propose a model for the abrupt emergence, below temperatures close to the glass transition, of the ultra-fast (GC) steady mode of spherulitic crystal growth in deeply undercooled liquids. We interpret this phenomenon as controlled by the interplay between the generation of stresses by crystallization and their partial release by flow in the surrounding amorphous visco-elastic matrix. Our model is consistent with both the observed ratios ($\sim10^4$) of fast-to-slow velocities and the fact that fast growth emerges close to the glass transition. It leads us to conclude that the existence of a fast growth regime requires both (i) a high fragility of the glassformer; (ii) the fine sub-structure specific of spherulites. It finally predicts that the transition is hysteretic, thus allowing for an independent experimental test

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity $v = V_c$. For $v > V_c$, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a semi-dilute solution of polymer chain ends hanging from the network. Inspite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than $V_c$, hence with the existence of the healing instability.Comment: 9 pages, 16 figure

Plastic response of a 2D amorphous solid to quasi-static shear : I - Transverse particle diffusion and phenomenology of dissipative events

We perform extensive simulations of a 2D LJ glass subjected to quasi-static shear deformation at T=0. We analyze the distribution of non-affine displacements in terms of contributions of plastic, irreversible events, and elastic, reversible motions. From this, we extract information about correlations between plastic events and about the elastic non-affine noise. Moreover, we find that non-affine motion is essentially diffusive, with a clearly size-dependent diffusion constant. These results, supplemented by close inspection of the evolving patterns of the non-affine tangent displacement field, lead us to propose a phenomenology of plasticity in such amorphous media. It can be schematized in terms of elastic loading and irreversible flips of small, randomly located shear transformation zones, elastically coupled via their quadrupolar fields

Robustness of avalanche dynamics in sheared amorphous solids as probed by transverse diffusion

Using numerical simulations, we perform an extensive finite-size analysis of the transverse diffusion coefficient in a sheared 2D amorphous solid, over a broad range of strain rates, at temperatures up to the supercooled liquid regime. We thus obtain direct qualitative evidence for the persistence of correlations between elementary plastic events up to the vicinity of the glass transition temperature $T_g$. A quantitative analysis of the data, combined with a previous study of the $T$- and $\dot\gamma$-dependence of the macroscopic stress \cite{ChattorajCaroliLemaitre2010}, leads us to conclude that the average avalanche size remains essentially unaffected by temperature up to $T\sim0.75 T_g$

Frictional dissipation of polymeric solids vs interfacial glass transition

We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer/substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyse as resulting from an interaction-induced ``interfacial glass transition'' helped by pressure

Self healing slip pulses along a gel/glass interface

We present an experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity : steady sliding at high velocity (> Vc = 100-125 \mu m/s), caracterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a ``healing instability'' occuring when the local sliding velocity reaches the macroscopic transition velocity Vc. At driving velocities close below Vc, the system exhibits complex spatio-temporal behavior.Comment: 4 pages, 6 figure

Streamer Propagation as a Pattern Formation Problem: Planar Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations.Comment: 4 pages, revtex, 3 ps file

Solid Friction from stick-slip to pinning and aging

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between wacroscopic hard rough solids, whose main dynamical features are well described by the Rice-Ruina rate and state dependent constitutive law. We show that it results from two combined effects : (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure (ii) geometric aging, i.e. slow growth of the real arrea of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsoprtion-induced metastability.Comment: 28 page