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

Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow

We present the results of numerical simulations of an atomistic system undergoing plastic shear flow in the athermal, quasistatic limit. The system is shown to undergo cascades of local rearrangements, associated with quadrupolar energy fluctuations, which induce system-spanning events organized into lines of slip oriented along the Bravais axes of the simulation cell. A finite size scaling analysis reveals subextensive scaling of the energy drops and participation numbers, linear in the length of the simulation cell, in good agreement with the observed real-space structure of the plastic events.Comment: 4 pages, 6 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

Stress correlations in glasses

We rigorously establish that, in disordered three-dimensional (3D) isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as $1/r^3$ at long-range, with $r$ the distance, as soon as either pressure or shear stress fluctuations are normal. By normal, we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of $1/r^3$ stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses for windows of increasing volume. Our conclusion is reached because, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, the constraints arising via (ii) from the normality of stress fluctuations demand the spatially anisotropic stress correlation terms to decay as $1/r^3$ at long-range. For the sake of generality, we also examine situations when stress fluctuations are not normal