Local yield stress statistics in model amorphous solids

We develop and extend a method presented in [S. Patinet, D. Vandembroucq, and M. L. Falk, Phys. Rev. Lett., 117, 045501 (2016)] 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 non-perturbative 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

Local shear rearrangements in glassy systems : from micromechanics to structural relaxation in supercooled liquids

Dans cette thèse, la méthode de la limite d’élasticité locale est appliquée et approfondie pour étudier d’une part les réarrangements atomiques isolés et irréversibles induits par cisaillement et d’autre part la relaxation structurelle dans un liquide formateur de verre, un mélange binaire Lennard-Jones 2D. La méthode permet d’obtenir la réponse mécanique locale d’un état inhérent de manière directe et non-perturbatrive tout en contrôlant les échelles de longueur et les directions de chargement. Dans la première partie, l’accent est mis sur une petite inclusion du verre. Sa réponse micromécanique est sondée dans la limite athermique quasi-statique. L’influence de l’échelle de longueur, sur laquelle la réponse mécanique est sondée, est discutée. La variation des statistiques de seuil en fonction de la taille de la zone de sondage peut être comprise sur la base d’un argument géométrique simple et d’une hypothèse de maillon faible. Ensuite, en déterminant la limite d’élasticité critique locale avec une résolution angulaire élevée sur la direction de chargement, on observe que seul un nombre fini et discret de réarrangements de cisaillement est accessible, chacun d’eux se caractérisant par un plan faible distinct. De plus, la limite d’élasticité critique montre une grande sensibilité à la pression. On constate que pour l’échelle de longueur étudiée, le critère d’élasticité de Mohr-Coulomb décrit par morceaux la contrainte de cisaillement critique avec précision. Dans la deuxième partie, un lien fort entre la structure et la dynamique des liquides surfondus est établi. La nouveauté du présent travail est la caractérisation de la structure par des seuils de glissement locaux. Une forte corrélation est trouvée entre d’une part les barrières de contrainte dans la direction la plus faible calculée dans l’état inhérent et d’autre part les observables associées à la relaxation de la structure à l’état liquide. Comme attendu, un coefficient de corrélation plus élevé est constaté pour les liquides équilibrés à des températures plus basses, signe que le paysage d’énergie potentielle influence davantage la dynamique.In this thesis, the local yield stress method is applied and extended to study single, irreversible atomistic rearrangementsas well as structural relaxation in a model glass-forming liquid, a two dimensional binary Lennard-Jones mixture. Themethod gives access to the local mechanical response of an inherent configuration in a direct and non-perturbativemanner while controlling the length scales and loading directions. In the first part, the focus is on a small inclusion ofthe glass. Its micromechanical response is probed in the athermal quasi-static limit. The influence of the length scale,at which the mechanical response is probed, is discussed. The variation of the threshold statistics with the size of theprobing zone can be understood on the basis of a simple geometric argument and a weakest link assumption. Then, upondetermining the dependence of the local critical yield stress on the shear loading direction with a high angular resolution,it is observed that only a finite and discrete number of shear rearrangements is accessible, each of them having a distinctweak plane. Furthermore, the critical yield stress shows a high sensitivity towards the pressure in the simulation box. It isfound that for the length scale studied, a Mohr-Coulomb yield criterion describes piecewise accurately the critical shearstress. In the second part, a connection between structure and dynamics of model supercooled liquids is established. Thenovelty in the present work is the characterization of the structure through local slip thresholds. A strong correlation isfound between the stress barriers in the softest direction calculated in the as-quenched state and observables associatedto the relaxation of the liquid structure at parent temperature. As expected, a higher correlation coefficient is detected forliquids equilibrated at lower temperatures, as the potential energy landscape increasingly influences the dynamics

Réarrangements locaux dans les verres modèles : de la micromécanique aux processus de relaxation dans un liquide surfondu

In this thesis, the local yield stress method is applied and extended to study single, irreversible atomistic rearrangementsas well as structural relaxation in a model glass-forming liquid, a two dimensional binary Lennard-Jones mixture. Themethod gives access to the local mechanical response of an inherent configuration in a direct and non-perturbativemanner while controlling the length scales and loading directions. In the first part, the focus is on a small inclusion ofthe glass. Its micromechanical response is probed in the athermal quasi-static limit. The influence of the length scale,at which the mechanical response is probed, is discussed. The variation of the threshold statistics with the size of theprobing zone can be understood on the basis of a simple geometric argument and a weakest link assumption. Then, upondetermining the dependence of the local critical yield stress on the shear loading direction with a high angular resolution,it is observed that only a finite and discrete number of shear rearrangements is accessible, each of them having a distinctweak plane. Furthermore, the critical yield stress shows a high sensitivity towards the pressure in the simulation box. It isfound that for the length scale studied, a Mohr-Coulomb yield criterion describes piecewise accurately the critical shearstress. In the second part, a connection between structure and dynamics of model supercooled liquids is established. Thenovelty in the present work is the characterization of the structure through local slip thresholds. A strong correlation isfound between the stress barriers in the softest direction calculated in the as-quenched state and observables associatedto the relaxation of the liquid structure at parent temperature. As expected, a higher correlation coefficient is detected forliquids equilibrated at lower temperatures, as the potential energy landscape increasingly influences the dynamics.Dans cette thèse, la méthode de la limite d’élasticité locale est appliquée et approfondie pour étudier d’une part les réarrangements atomiques isolés et irréversibles induits par cisaillement et d’autre part la relaxation structurelle dans un liquide formateur de verre, un mélange binaire Lennard-Jones 2D. La méthode permet d’obtenir la réponse mécanique locale d’un état inhérent de manière directe et non-perturbatrive tout en contrôlant les échelles de longueur et les directions de chargement. Dans la première partie, l’accent est mis sur une petite inclusion du verre. Sa réponse micromécanique est sondée dans la limite athermique quasi-statique. L’influence de l’échelle de longueur, sur laquelle la réponse mécanique est sondée, est discutée. La variation des statistiques de seuil en fonction de la taille de la zone de sondage peut être comprise sur la base d’un argument géométrique simple et d’une hypothèse de maillon faible. Ensuite, en déterminant la limite d’élasticité critique locale avec une résolution angulaire élevée sur la direction de chargement, on observe que seul un nombre fini et discret de réarrangements de cisaillement est accessible, chacun d’eux se caractérisant par un plan faible distinct. De plus, la limite d’élasticité critique montre une grande sensibilité à la pression. On constate que pour l’échelle de longueur étudiée, le critère d’élasticité de Mohr-Coulomb décrit par morceaux la contrainte de cisaillement critique avec précision. Dans la deuxième partie, un lien fort entre la structure et la dynamique des liquides surfondus est établi. La nouveauté du présent travail est la caractérisation de la structure par des seuils de glissement locaux. Une forte corrélation est trouvée entre d’une part les barrières de contrainte dans la direction la plus faible calculée dans l’état inhérent et d’autre part les observables associées à la relaxation de la structure à l’état liquide. Comme attendu, un coefficient de corrélation plus élevé est constaté pour les liquides équilibrés à des températures plus basses, signe que le paysage d’énergie potentielle influence davantage la dynamique

Rejuvenation and shear banding in model amorphous solids

International audienceWe 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

Origin of the Bauschinger Effect in Amorphous Solids

International audienceWe 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, ∆τc, for arbitrary loading orientations and find that plastic deformation generically induces material polarization, i.e., a forward-backward asymmetry in the ∆τc 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 ∆τ 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-∆τ c region and, consequently, in the Bauschinger effect. This scenario is quite generic, which explains the pervasiveness of the effect