An Athermal Brittle to Ductile Transition in Amorphous Solids

Brittle materials exhibit sharp dynamical fractures when meeting Griffith's criterion, whereas ductile materials blunt a sharp crack by plastic responses. Upon continuous pulling ductile materials exhibit a necking instability which is dominated by a plastic flow. Usually one discusses the brittle to ductile transition as a function of increasing temperature. We introduce an athermal brittle to ductile transition as a function of the cut-off length of the inter-particle potential. On the basis of extensive numerical simulations of the response to pulling the material boundaries at a constant speed we offer an explanation of the onset of ductility via the increase in the density of plastic modes as a function of the potential cutoff length. Finally we can resolve an old riddle: in experiments brittle materials can be strained under grip boundary conditions, and exhibit a dynamic crack when cut with a sufficiently long initial slot. Mysteriously, in molecular dynamics simulations it appeared that cracks refused to propagate dynamically under grip boundary conditions, and continuous pulling was necessary to achieve fracture. We argue that this mystery is removed when one understands the distinction between brittle and ductile athermal amorphous materials.Comment: 5 pages 7 figure

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change due to thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses --- an intrinsic signature of glassy frustration ---, anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal $\omega^4$ density of states of quasi-localized low-frequency vibrational modes. When the spatial thermal energy field --- a `softness field' --- is considered, this power-law tail manifests itself by highly localized spots which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal-modes-based approach. These results offer a general, system/model-independent, physical-observable-based approach to identify structural properties of quiescent glasses and to relate them to glassy dynamics.Comment: 8 pages, 4 figures + Supporting Information, shorter title, minor textual change

Statistical Physics of Elasto-Plastic Steady States in Amorphous Solids: Finite Temperatures and Strain Rates

The effect of finite temperature $T$ and finite strain rate $\dot\gamma$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, $T<T_{\rm cross}(N)$, and the strain is quasi-static. In this regime the elasto-plastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime $T_{\rm cross}(N)<T<T_{\rm max}(\dot\gamma)$ the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the cross-over is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second cross-over temperature $T_{\rm max}(\dot\gamma)$ where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.Comment: 12 pages, 13 figure

Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System

In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $\xi$ that increases rapidly with lowering the temperature and which determines the $\alpha$-relaxation time $\tau_\alpha$ as $\tau_\alpha \sim \exp(\mu\xi/T)$ with $\mu$ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.Comment: 4 pages, 6 figure

Shear Transformation Zones: State Determined or Protocol Dependent?

The concept of a Shear Transformation Zone (STZ) refers to a region in an amorphous solid that undergoes a plastic event when the material is put under an external mechanical load. An important question that had accompanied the development of the theory of plasticity in amorphous solids for many years now is whether an STZ is a {\em region} existing in the material (which can be predicted by analyzing the unloaded material), or is it an {\em event} that depends on the loading protocol (i.e., the event cannot be predicted without following the protocol itself). In this Letter we present strong evidence that the latter is the case. Infinitesimal changes of protocol result in macroscopically big jumps in the positions of plastic events, meaning that these can never be predicted from considering the unloaded material.Comment: 4 pages, 5 figure