Determination of the universality class of crystal plasticity

Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to accurately measure scaling exponents and functions. Here we present comprehensive simulations of two-dimensional dislocation dynamics under shear, using finite-size scaling to extract scaling exponents and the avalanche profile scaling function from time-resolved measurements of slip-avalanches. Our results provide compelling evidence that both the static and dynamic universality classes are consistent with the mean-field interface depinning model.Comment: 6 pages, 4 figures. Figure 4 inset has been corrected as compared to the EPL publication. We thank Michael Zaiser for bringing its incorrect caption to our attention. The correction leaves all results unaffecte

Competitive Equilibrium with Middlemen: An Empirical Study

Public distrust of middlemen frequently occurs in market systems. Boycotts, regulations, and investigations of middlemen are not uncommon [3; 7]. This position of disfavor is somewhat paradoxical since application of economic theory suggests that competition among middlemen can be relied upon to protect consumers and producers. According to received doctrine any differences in purchase and resale prices would reflect the costs involved in market making. Nevertheless public suspicion remains

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

Aftershocks in Slowly Compressed Bulk Metallic Glasses: Experiments and Theory

We observe two distinct interevent time patterns in the slip avalanches of compressed bulk metallic glasses (BMGs). Small slip avalanches cluster together in time, but large slip avalanches recur roughly periodically. We compare the timing patterns of BMG slip avalanches with timing patterns of earthquakes and with the predictions of a mean-field model. The time clustering of small avalanches is similar to the known time clustering of earthquake foreshocks and aftershocks

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

Statistics of Dislocation Slip Avalanches in Nanosized Single Crystals Show Tuned Critical Behavior Predicted by a Simple Mean Field Model

We show that slowly sheared metallic nanocrystals deform via discrete strain bursts (slips), whose size distributions follow power laws with stress-dependent cutoffs. We show for the first time that plasticity reflects tuned criticality, by collapsing the stress-dependent slip-size distributions onto a predicted scaling function. Both power-law exponents and scaling function agree with mean-field theory predictions. Our study of 7 materials and 2 crystal structures, at various deformation rates, stresses, and crystal sizes down to 75 nm, attests to the universal characteristics of plasticity

Experimental evidence that shear bands in metallic glasses nucleate like cracks

Highly time-resolved mechanical measurements, modeling, and simulations show that large shear bands in bulk metallic glasses nucleate in a manner similar to cracks. When small slips reach a nucleation size, the dynamics changes and the shear band rapidly grows to span the entire sample. Smaller nucleation sizes imply lower ductility. Ductility can be increased by increasing the nucleation size relative to the maximum (“cutoff”) shear band size at the upper edge of the power law scaling range of their size distribution. This can be achieved in three ways: (1) by increasing the nucleation size beyond this cutoff size of the shear bands, (2) by keeping all shear bands smaller than the nucleation size, or (3) by choosing a sample size smaller than the nucleation size. The discussed methods can also be used to rapidly order metallic glasses according to ductility

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