Relevance of Shear Transformations in the Relaxation of Supercooled Liquids.

While deeply supercooled liquids exhibit divergent viscosity and increasingly heterogeneous dynamics as the temperature drops, their structure shows only seemingly marginal changes. Understanding the nature of relaxation processes in this dramatic slowdown is key for understanding the glass transition. Here, we show by atomistic simulations that the heterogeneous dynamics of glass-forming liquids strongly correlate with the local residual plastic strengths along soft directions computed in the initial inherent structures. The correlation increases with decreasing temperature and is maximum in the vicinity of the relaxation time. For the lowest temperature investigated, this maximum is comparable with the best values from the literature dealing with the structure-property relationship. However, the nonlinear probe of the local shear resistance in soft directions provides here a real-space picture of relaxation processes. Our detection method of thermal rearrangements allows us to investigate the first passage time statistics and to study the scaling between the activation energy barriers and the residual plastic strengths. These results shed new light on the nature of relaxations of glassy systems by emphasizing the analogy between the thermal relaxations in viscous liquids and the plastic shear transformation in amorphous solids.

Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear.

We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.

Origin of the Bauschinger Effect in Amorphous Solids.

We study the structural origin of the Bauschinger effect by accessing numerically the local plastic thresholds in the steady state flow of a two-dimensional model glass under athermal quasistatic deformation. More specifically, we compute the local residual strength, Δτ^{c}, for arbitrary loading orientations and find that plastic deformation generically induces material polarization, i.e., a forward-backward asymmetry in the Δτ^{c} distribution. In steady plastic flow, local packings are on average closer to forward (rather than backward) instabilities, due to the stress-induced bias of barriers. However, presumably due to mechanical noise, a significant fraction of zones lie close to reverse (backward) yielding, as the distribution of Δτ^{c} for reverse shearing extends quasilinearly down to zero local residual strength. By constructing an elementary model of the early plastic response, we then show that unloading causes reverse plasticity of a growing amplitude, i.e., reverse softening, while it shifts away forward-yielding barriers. This result in an inversion of polarization in the low-Δτ^{c} region and, consequently, in the Bauschinger effect. This scenario is quite generic, which explains the pervasiveness of the effect.

Compression-induced anti-nematic order in glassy and semicrystalline polymers.

We provide new insights into the molecular origin of the asymmetry between uniaxial tensile and compressive deformation of glassy and semicrystalline polymers using molecular dynamics simulations. The difference between the two responses strongly depends on the chain length and is the largest at intermediate chain lengths. Irrespective of chain length, the intra- and interchain organization of polymers under extension and compression are remarkably distinct. The chains align along the tensile axis leading to a global nematic order of the bonds and end-to-end vectors, whereas compression reorganizes polymers to lie in planes perpendicular to the compressive axis resulting in the emergence of an anti-nematic order and destruction of crystallinity. Regardless of the initial glassy or semicrystalline structure, the deformed state of polymers at large strains converge towards the same kind of structure that only depends on the deformation mode.

Diffusion in Mesoscopic Lattice Models of Amorphous Plasticity.

We present results on tagged particle diffusion in a mesoscale lattice model for sheared amorphous material in athermal quasistatic conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion coefficients depend on system size in dramatically different ways. At short time, we find that the diffusion coefficient, D, scales roughly linearly with system length, D∼L^{1.05}. This short time behavior is consistent with particle-based simulations. The long-time diffusion coefficient scales like D∼L^{1.6}, close to previous studies which found D∼L^{1.5}. Furthermore, we show that the near-field details of the interaction kernel do not affect the short time behavior but qualitatively and dramatically affect the long time behavior, potentially causing a saturation of the mean-squared displacement at long times. Our finding of a D∼L^{1.05} short time scaling resolves a long standing puzzle about the disagreement between the diffusion coefficient measured in particle-based models and mesoscale lattice models of amorphous plasticity.

Anisotropic Superattenuation of Capillary Waves on Driven Glass Interfaces.

Metrological atomic force microscopy measurements are performed on the silica glass interfaces of photonic band-gap fibers and hollow capillaries. The freezing of attenuated out-of-equilibrium capillary waves during the drawing process is shown to result in a reduced surface roughness. The roughness attenuation with respect to the expected thermodynamical limit is determined to vary with the drawing stress following a power law. A striking anisotropic character of the height correlation is observed: glass surfaces thus retain a structural record of the direction of the flow to which the liquid was submitted.

(Finite) statistical size effects on compressive strength.

The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.

Nondestructive measurement of the roughness of the inner surface of hollow core-photonic bandgap fibers.

We present optical and atomic force microscopy measurements of the roughness of the core wall surface within a hollow core photonic bandgap fiber (HC-PBGF) over the [3×10-2 µm-1-30 µm-1] spatial frequency range. A recently developed immersion optical profilometry technique with picometer-scale sensitivity was used to measure the roughness of air-glass surfaces inside the fiber at unprecedentedly low spatial frequencies, which are known to have the highest impact on HC-PBGF scattering loss and, thus, determine their loss limit. Optical access to the inner surface of the core was obtained by the selective filling of the cladding holes with index matching liquid using techniques borrowed from micro-fluidics. Both measurement techniques reveal ultralow roughness levels exhibiting a 1/f spectral power density dependency characteristic of frozen surface capillary waves over a broad spatial frequency range. However, a deviation from this behavior at low spatial frequencies was observed for the first time, to the best of our knowledge.

Topological Symmetry Breaking in Viscous Coarsening.

The crucial role of hydrodynamic pinch-off instabilities is evidenced in the coarsening stage of viscous liquids. The phase separation of a barium borosilicate glass melt is studied by in situ synchrotron tomography at high temperature. The high viscosity contrast between the less viscous phase and the more viscous phase induces a topological symmetry breaking: capillary breakups occur preferentially in the less viscous phase. As a result, contrasting morphologies are obtained in the two phases. This symmetry breaking is illustrated on three different glass compositions, corresponding to different volume fractions of the two phases. In particular, a fragmentation phenomenon, reminiscent of the end-pinching mechanism proposed by Stone and co-workers is evidenced in the less viscous phase.

Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids.

In model amorphous solids produced via differing quench protocols, a strong correlation is established between local yield stress measured by direct local probing of shear stress thresholds and the plastic rearrangements observed during remote loading in shear. This purely local measure shows a higher predictive power for identifying sites of plastic activity when compared with more conventional structural properties. Most importantly, the sites of low local yield stress, thus defined, are shown to be persistent, remaining predictive of deformation events even after fifty or more such plastic rearrangements. This direct and nonperturbative approach gives access to relevant transition pathways that control the stability of amorphous solids. Our results reinforce the relevance of modeling plasticity in amorphous solids based on a gradually evolving population of discrete and local zones preexisting in the structure.

Fragmentation and limits to dynamical scaling in viscous coarsening: an interrupted in situ x-ray tomographic study.

X-ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean, and Gaussian curvatures of the domains of minority phase were measured after reconstruction of the 3D images and segmentation. A linear growth law of the characteristic length scale ℓ∼t was observed. A detailed morphological study was performed. While dynamical scaling holds for most of the geometrical observables under study, a progressive departure from scaling invariance of the distributions of local curvatures was evidenced. The latter results from a gradual fragmentation of the structure in the less viscous phase that also leads to a power-law size distribution of isolated domains.

Quantitative prediction of effective toughness at random heterogeneous interfaces.

The propagation of an adhesive crack through an anisotropic heterogeneous interface is considered. Tuning the local toughness distribution function and spatial correlation is numerically shown to induce a transition between weak to strong pinning conditions. While the macroscopic effective toughness is given by the mean local toughness in the case of weak pinning, a systematic toughness enhancement is observed for strong pinning (the critical point of the depinning transition). A self-consistent approximation is shown to account very accurately for this evolution, without any free parameter.

Hollow-core fibers with reduced surface roughness and ultralow loss in the short-wavelength range.

While optical fibers display excellent performances in the infrared, visible and ultraviolet ranges remain poorly addressed by them. Obtaining better fibers for the short-wavelength range has been restricted, in all fiber optics, by scattering processes. In hollow-core fibers, the scattering loss arises from the core roughness and represents the limiting factor for loss reduction regardless of the cladding confinement power. Here, we report on the reduction of the core surface roughness of hollow-core fibers by modifying their fabrication technique. The effect of the modified process has been quantified and the results showed a root-mean-square surface roughness reduction from 0.40 to 0.15 nm. The improvement in the core surface entailed fibers with ultralow loss at short wavelengths. The results reveal this approach as a promising path for the development of hollow-core fibers with loss that can potentially be orders of magnitude lower than the ones achievable with silica-core counterparts.

Rejuvenation and shear banding in model amorphous solids.

We measure the local yield stress, at the scale of small atomic regions, in a deeply quenched two-dimensional glass model undergoing shear banding in response to athermal quasistatic deformation. We find that the occurrence of essentially a single plastic event suffices to bring the local yield stress distribution to a well-defined value for all strain orientations, thus essentially erasing the memory of the initial structure. It follows that in a well-relaxed sample, plastic events cause the abrupt (nucleation-like) emergence of a local softness contrast and thus precipitate the formation of a band, which, in its early stages, is measurably softer than the steady-state flow. Moreover, this postevent yield stress ensemble presents a mean value comparable to that of the inherent states of a supercooled liquid around the mode-coupling temperature T_{MCT}. This, we argue, explains that the transition between brittle and ductile yielding in amorphous materials occurs around a comparable parent temperature. Our data also permit to capture quantitatively the contributions of pressure and density changes and demonstrate unambiguously that they are negligible compared with the changes of softness caused by structural rejuvenation.

Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity.

We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size L of (i) statistics of individual relaxation events in terms of stress relaxation S, and individual event mean-squared displacement M, and the subsequent load increments Δγ, required to initiate the next event; (ii) static properties of the system encoded by x=σ_{y}-σ, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M. We find a strong correlation between S and M for any particular event, with S∼M^{q} with q≈0.65. The exponent q completely determines the scaling exponents for P(M) given those for P(S). For the distribution of local thresholds, we find P(x) is analytic at x=0, and has a value P(x)|_{x=0}=p_{0} which scales with lateral system length as p_{0}∝L^{-0.6}. The size dependence of the average load increment 〈Δγ〉 appears to be asymptotically controlled by the plateau behavior of P(x) rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing P(x) and those governing P(S). Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by 〈Δγ〉 and the scaling properties of P(M) (in particular from 〈M〉) rather than directly from P(S) as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.

Path-independent integrals to identify localized plastic events in two dimensions.

We use a power expansion representation of plane-elasticity complex potentials due to Kolossov and Muskhelishvili to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first-order singularities of quadrupolar and dipolar symmetry which can be associated, respectively, with pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. By construction of holomorphic functions from the displacement field and its derivatives, it is possible to define path-independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite-element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations, which are believed to be the key mechanisms for plasticity of amorphous materials.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium.

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.

Local yield stress statistics in model amorphous solids.

We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.

From depinning transition to plastic yielding of amorphous media: A soft-modes perspective.

A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d+1-dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning.

Finite-size effects in a model for plasticity of amorphous composites.

We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size dependence of the effective flow stress of the amorphous composite. In particular, the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles, respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in (logN/N)(1/2), where N is the linear size of the system, observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.