Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations

Strain-dependent evolution of avalanche dynamics in bulk metallic glass

Avalanche phenomena characterized by power-law scaling are observed in amorphous solids and many other nonequilibrium systems during their deformation. Avalanches in these systems often exhibit scale invariance, a feature reminiscent of critical phenomena and universality classes, although their fundamental nature remains unclear. In this paper, we use in situ acoustic emission techniques to experimentally investigate the characteristics and evolution of avalanches during the deformation process of bulk metallic glass (BMG), a representative amorphous solid. We observed abundant avalanche events from the microplastic deformation region to the failure of the sample. We find that avalanches are power-law distributed with an exponent decreasing from 1.61 to 1.49 with increasing deformation throughout the tensile experiment. By quantitatively analyzing the strong strain dependence of various avalanche characteristics, we highlight the importance of additional coefficients that complete the widely studied finite size scaling description of avalanche dynamics and revealed a strain-mediated avalanche scaling mechanism. Through surface morphology analysis and spectral analysis of avalanche signals in BMG samples, we conclude that the underlying process of these avalanches are not macroscopic, such as cracks and large shear band propagation, but is instead related to nanoscale microstructural adjustments. Our results encourage further exploration into the microscopic origins of avalanches and suggest that theoretical frameworks beyond finite-size scaling merit more in-depth investigations.

Avalanche properties at the yielding transition: from externally deformed glasses to active systems

We investigated the yielding phenomenon in the quasistatic limit using numerical simulations of soft particles. Two different deformation scenarios, simple shear (passive) and self-random force (active), and two interaction potentials were used. Our approach reveals that the exponents describing the avalanche distribution are universal within the margin of error, showing consistency between the passive and active systems. This indicates that any differences observed in the flow curves may have resulted from a dynamic effect on the avalanche propagation mechanism. The evolution time required to reach a steady state differs significantly between active and passive scenarios under similar conditions. However, we demonstrated that plastic avalanches under athermal quasistatic simulation dynamics display a similar scaling relationship between avalanche size and relaxation time, which cannot explain the different flow curves.

Scale Separation of Shear-Induced Criticality in Glasses

In a sheared steady state, glasses reach a nonequilibrium criticality called yielding criticality. We report that the qualitative nature of this nonequilibrium critical phenomenon depends on the details of the system and that responses and fluctuations are governed by different critical correlation lengths in specific situations. This scale separation of critical lengths arises when the screening of elastic propagation of mechanical signals is not negligible. We also discuss the determinant of the impact of screening effects from the viewpoint of the microscopic dissipation mechanism.

Synthesis and mechanical properties of highly structure-controlled Zr-based metallic glasses by thermal rejuvenation technique

A novel thermal rejuvenation treatment facility for Zr-based bulk metallic glass (BMG) was developed, consisting of a rapid heating and indirect liquid nitrogen quenching process. The re-introduction of free volume into thermally rejuvenated BMG results in more disordered state. The rejuvenation improves ductility, implying that the re-introduced free volume aids in the recovery of the shear transformation zone (STZ) site and volume. Actually, it is confirmed that relaxation significantly reduces STZ volume; however, it is recovered by thermal rejuvenation. Molecular dynamics simulations also indicate that rejuvenation enhances homogeneous deformation. The current findings indicate that the thermal rejuvenation method is extremely effective for recovering or improving the ductility of metallic glass that has been lost due to relaxation.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

Unified view of avalanche criticality in sheared glasses

Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent τ. Although the so-called mean-field depinning (MFD) theory predicts a universal value of this exponent, τ_{MFD}=1.5, such a simplification is now known to connote qualitative disagreement with realistic systems. Numerically and experimentally, different values of τ have been reported depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results have been reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent τ in the steady state follows the prediction of MFD theory, τ_{MFD}=1.5. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the nonuniversal behavior of the avalanche size distribution and is likely to be the cause of the varying values of τ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. The degree of criticality is encoded in the fractal dimension of the avalanches, which starts from zero in the off-critical unperturbed state and saturates in the steady state. Moreover, the critical exponent τ is consistent with the prediction of the MFD τ_{MFD} universally, regardless of the amount of applied shear, once the system becomes critical.

The role of friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

Variety of scaling behaviors in nanocrystalline plasticity

We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, submicron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.

Structural relaxation affecting shear-transformation avalanches in metallic glasses

Avalanche behaviors, characterized by power-law statistics and structural relaxation that induces shear localization in amorphous plasticity, play an essential role in deciding the mechanical properties of amorphous metallic solids (i.e., metallic glasses). However, their interdependence is still not fully understood. To investigate the influence of structural relaxation on elementary avalanche behavior, we perform molecular-dynamics simulations for the shear deformation test of metallic glasses using two typical metallic-glass models comprising a less-relaxed (as-quenched) glass and a well-relaxed (well-aged) glass exhibiting a relatively homogeneous deformation and a shear-band-like heterogeneous deformation, respectively. The data on elementary avalanches obtained from both glass models follow the same power-law statistics with different maximum event sizes, and the well-relaxed glass shows shear localization. Evaluating the spatial correlation functions of the nonaffine squared displacements of atoms during each elementary avalanche event, we observe that the shapes of the elementary avalanche regions in the well-relaxed glasses tend to be anisotropic, whereas those in the less-relaxed glasses are relatively isotropic. Furthermore, we demonstrate that a temporal clustering in the direction of the avalanche propagation emerges, and a considerable correlation between the anisotropy and avalanche size exists in the well-relaxed glass model.