Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Abstract

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.

Learning local, quenched disorder in plasticity and other crackling noise phenomena

“…2 The evidence for quenched disorder in initial defect microstructures has been accumulated through observations of abrupt plastic events or material-crackling noise in a large variety of materials, such as FCC and BCC crystals, [3][4][5][6] amorphous solids 7 and also earthquake geological faults. 8,9 This crackling noise 10 has been commonly explained by random field models 11,12 or interface depinning ones, [13][14][15][16][17][18] where the major component is homogeneous solid elasticity, but also a spatially inhomogeneous and random distribution of local, quenched disorder (typically entering local flow stress information) 4,17,[19][20][21] and the allowed microstates are characterized by its stress and strain and minimize the elastic energy functional. The evidence of crackling noise has led to an extensive study of the local, statistical properties of abrupt events and their properties, such as their sizes, durations, average shapes, and their critical exponents.…”

“…For each sample j, a vector may be constructed that contains all moments up to a maximum resolution scale p max and max order n max , with total length M = n max p max . The parameters n max and p max are controlled by the resolution of the timeseries and can be estimated through: p max ' log 2 ðTÞ=2 and n max ∈ , 3,8 given that identified moments remain non-zero for the given resolution. Then, the effective data matrix D eff is built through these vectors and has dimensions N × M. D eff is used towards unsupervised machine learning through principal component analysis (PCA) and k-means clustering.…”

Experimental evidence for both progressive and simultaneous shear during quasistatic compression of a bulk metallic glass

“…Regions of excess free volume nucleate shear transformation zones when the metallic glass is subjected to stress, and the collective propagation of shear transformation zones leads to shear banding/avalanche behavior. Recently, a mean field model for plastic deformation based on the premise of elastically coupled slipping weak spots 3,4 has been applied to high temporal-resolution data for the stress drops during constant displacement-rate compression of Zr 45 Hf 12 Nb 5 Cu 15.4 Ni 12.6 Al 10 bulk metallic glass. 5 Because the model predictions for both the scaling statistics of the stress drops for avalanche events and the dynamics of individual avalanche events agree with high temporalresolution stress measurements of serrations, that work provides experimental evidence for shear transformation zones as the mechanism of deformation in metallic glasses.…”

“…Avalanche behavior is observed across decades of length scale in small volumes of crystalline materials, metallic glasses, granular media, and earthquakes, to name a few systems of interest. [1][2][3][4][5][6][7][8][9][10][11][12] Metallic glasses, by virtue of their amorphous structure, have spatial variations in the amount of free volume. Regions of excess free volume nucleate shear transformation zones when the metallic glass is subjected to stress, and the collective propagation of shear transformation zones leads to shear banding/avalanche behavior.…”

Avalanche criticalities and elastic and calorimetric anomalies of the transition from cubic Cu-Al-Ni to a mixture of18Rand2Hstructures

“…AE measurements render clearly different exponents, namely ε = 2 (β ↔ 18R) and ε = 1.5 (β ↔ 2H ). The exponent for the majority transformation β ↔ 18R is far removed from the expected mean field value [4] while the lower value may coincide with mean-field theory if the boundary conditions are carefully chosen [41]. The phase mixture shows an intermediate exponent ∼1.7 in AE.…”