Why the Crackling Deformations of Single Crystals, Metallic Glasses, Rock, Granular Materials, and the Earth’s Crust Are So Surprisingly Similar

Recent experiments show that the deformation properties of a wide range of solid materials are surprisingly similar. When slowly pushed, they deform via intermittent slips, similar to earthquakes. The statistics of these slips agree across vastly different structures and scales. A simple analytical model explains why this is the case. The model also predicts which statistical quantities are independent of the microscopic details (i.e., they are universal ), and which ones are not. The model provides physical intuition for the deformation mechanism and new ways to organize experimental data. It also shows how to transfer results from one scale to another. The model predictions agree with experiments. The results are expected to be relevant for failure prediction, hazard prevention, and the design of next-generation materials

Force Oscillations Distort Avalanche Shapes

Contradictory scaling behavior in experiments testing the principle of universality may be due to external oscillations. Thus, the effect of damped oscillatory external forces on slip avalanches in slowly deformed solids is simulated using a mean-field model. Akin to a resonance effect, oscillatory driving forces change the dynamics of avalanches with durations close to the oscillation period. This problem can be avoided by tuning mechanical resonance frequencies away from the range of the inverse avalanche durations. The results provide critical guidance for experimental tests for universality and a quantitative understanding of avalanche dynamics under a wide range of driving conditions

Avalanche Statistics from Data with Low Time Resolution

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distribution of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents

Applied-force oscillations in avalanche dynamics

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or “slip avalanches.” In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force control. The studies show very good agreement between simulations and experiments. We find that an oscillatory external driving force changes the average avalanche shapes only for avalanches with durations close to the period of oscillation of the external force. This effect on the avalanche shapes can be addressed in experiments by choosing suitable specimen dimensions so that the mechanical resonance does not interact with the avalanche dynamics. These results are important for the interpretation of avalanche experiments with built-in oscillators, and for the prediction and analysis of avalanche dynamics in systems with resonant vibrations

Bulk Metallic Glasses Deform via Slip Avalanches

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.Comment: Article: 11 pages, 4 figures, plus Supplementary Material: 16 pages, 8 figure

Universal Slip Dynamics in Metallic Glasses and Granular Matter – Linking Frictional Weakening with Inertial Effects

Slowly strained solids deform via intermittent slips that exhibit a material-independent critical size distribution. Here, by comparing two disparate systems - granular materials and bulk metallic glasses - we show evidence that not only the statistics of slips but also their dynamics are remarkably similar, i.e. independent of the microscopic details of the material. By resolving and comparing the full time evolution of avalanches in bulk metallic glasses and granular materials, we uncover a regime of universal deformation dynamics. We experimentally verify the predicted universal scaling functions for the dynamics of individual avalanches in both systems, and show that both the slip statistics and dynamics are independent of the scale and details of the material structure and interactions, thus settling a long-standing debate as to whether or not the claim of universality includes only the slip statistics or also the slip dynamics. The results imply that the frictional weakening in granular materials and the interplay of damping, weakening and inertial effects in bulk metallic glasses have strikingly similar effects on the slip dynamics. These results are important for transferring experimental results across scales and material structures in a single theory of deformation dynamics

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes

Nanomechanics Of Slip Avalanches In Amorphous Plasticity

Discrete stress relaxations (slip avalanches) in a model metallic glass under uniaxial compression are studied using a metadynamics algorithm for molecular simulation at experimental strain rates. The onset of yielding is observed at the first major stress drop, accompanied, upon analysis, by the formation of a single localized shear band region spanning the entire system. During the elastic response prior to yielding, low concentrations of shear transformation deformation events appear intermittently and spatially uncorrelated. During serrated flow following yielding, small stress drops occur interspersed between large drops. The simulation results point to a threshold value of stress dissipation as a characteristic feature separating major and minor avalanches consistent with mean-field modeling analysis and mechanical testing experiments. We further interpret this behavior to be a consequence of a nonlinear interplay of two prevailing mechanisms of amorphous plasticity, thermally activated atomic diffusion and stress-induced shear transformations, originally proposed by Spaepen and Argon, respectively. Probing the atomistic processes at widely separate strain rates gives insight to different modes of shear band formation: percolation of shear transformations versus crack-like propagation. Additionally a focus on crossover avalanche size has implications for nanomechanical modeling of spatially and temporally heterogeneous dynamics

Slip statistics for a bulk metallic glass composite reflect its ductility

Serrations in the stress-time curve for a bulk metallic glass composite with microscale crystalline precipitates were measured with exceptionally high temporal resolution and low noise. Similar measurements were made for a more brittle metallic glass that did not contain crystallites but that was also tested in uniaxial compression. Despite significant differences in the structure and stress-strain behavior, the statistics of the serrations for both materials follow a simple mean-field model that describes plastic deformation as arising from avalanches of slipping weak spots. The presence of the crystalline precipitates reduces the number of large slips relative to the number of small slips as recorded in the stress-time data, consistent with the model predictions. The results agree with mean-field predictions for a smaller weakening parameter for the composite than for the monolithic metallic glass; the weakening parameter accounts for the underlying microstructural differences between the two