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Slip avalanches in metallic glasses and granular matter reveal universal dynamics

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 Added by Dmitry Denisov
 Publication date 2016
  fields Physics
and research's language is English




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Universality in materials deformation is of intense interest: universal scaling relations if exist would bridge the gap from microscopic deformation to macroscopic response in a single material-independent fashion. While recent agreement of the force statistics of deformed nanopillars, bulk metallic glasses, and granular materials with mean-field predictions supports the idea of universal scaling relations, here for the first time we demonstrate that the universality extends beyond the statistics, and applies to the slip dynamics as well. By rigorous comparison of two very different systems, bulk metallic glasses and granular materials in terms of both the statistics and dynamics of force fluctuations, we clearly establish a material-independent universal regime of deformation. We experimentally verify the predicted universal scaling function for the time evolution of individual avalanches, and show that both the slip statistics and dynamics are universal, i.e. independent of the scale and details of the material structure and interactions. These results are important for transferring experimental results across scales and material structures in a single theory of deformation.



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Inelastic deformation of metallic glasses occurs via slip events with avalanche dynamics similar to those of earthquakes. For the first time in these materials, measurements have been obtained with sufficiently high temporal resolution to extract both the exponents and the scaling functions that describe the nature, statistics and dynamics of the slips according to a simple mean-field model. These slips originate from localized deformation in shear bands. The mean-field model describes the slip process as an avalanche of rearrangements of atoms in shear transformation zones (STZs). Small slips show the predicted power-law scaling and correspond to limited propagation of a shear front, while large slips are associated with uniform shear on unconstrained shear bands. The agreement between the model and data across multiple independent measures of slip statistics and dynamics provides compelling evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.
The enhancement of surface diffusion (DS) over the bulk (DV) in metallic glasses (MGs) is well documented and likely to strongly influence the properties of glasses grown by vapor deposition. Here, we use classical molecular dynamics simulations to identify different factors influencing the enhancement of surface diffusion in MGs. MGs have a simple atomic structure and belong to the category of moderately fragile glasses that undergo pronounced slowdown of bulk dynamics with cooling close to the glass transition temperature (Tg). We observe that DS exhibits a much more moderate slowdown compared to DV when approaching Tg, and DS/DV at Tg varies by two orders of magnitude among the MGs investigated. We demonstrate that both the surface energy and the fraction of missing bonds for surface atoms show good correlation to DS/DV, implying that the loss of nearest neighbors at the surface directly translates into higher mobility, unlike the behavior of network- and hydrogen-bonded organic glasses. Fragility, a measure of the slowdown of bulk dynamics close to Tg, also correlates to DS/DV, with more fragile systems having larger surface enhancement of mobility. The deviations observed in the fragility and DS over DV relationship are shown to be correlated to the extent of segregation or depletion of the mobile element at the surface. Finally, we explore the relationship between the diffusion pre-exponential factor (D0) and activation energy (Q) and compare to a ln(D0)-Q correlation previously established for bulk glasses, demonstrating similar correlations from MD as in the experiments and that the surface and bulk have very similar ln(D0)-Q correlations.
Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.
We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. % with transform boundaries. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent on particle shape and in good agreement with the Gutenberg-Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omoris law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy.
The bulk and surface dynamics of Cu50Zr50 metallic glass were studied using classical molecular dynamics (MD) simulations. As the alloy undergoes cooling, it passes through liquid, supercooled, and glassy states. While bulk dynamics showed a marked slowing down prior to glass formation, with increasing activation energy, the slowdown in surface dynamics was relatively subtle. The surface exhibited a lower glass transition temperature than the bulk, and the dynamics preceding the transition were accurately described by a temperature-independent activation energy. Surface dynamics were much faster than bulk at a given temperature in the supercooled state, but surface and bulk dynamics were found to be very similar when compared at their respective glass transition temperatures. The manifestation of dynamical heterogeneity, as characterized by the non-Gaussian parameter and breakdown of the Stokes-Einstein equation, was also similar between bulk and surface for temperatures scaled by their respective glass transition temperatures. Individual atom motion was dominated by a cage and jump mechanism in the glassy state for both the bulk and surface. We utilize this cage and jump mechanisms to separate the activation energy for diffusion into two parts: (i) cage-breaking barrier (Q1), associated with the rearrangement of neighboring atoms to free up space and (ii) the subsequent jump barrier (Q2). It was observed that Q1 dominates Q2 for both bulk and surface diffusion, and the difference in activation energies for bulk and surface diffusion mainly arose from the differences in cage-breaking barrier Q1.
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