1
|
Oyama N, Mizuno H, Ikeda A. Unified view of avalanche criticality in sheared glasses. Phys Rev E 2021; 104:015002. [PMID: 34412287 DOI: 10.1103/physreve.104.015002] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
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.
Collapse
Affiliation(s)
- Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
| |
Collapse
|
2
|
Saitoh K. The role of friction in statistics and scaling laws of avalanches. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:85. [PMID: 34165652 DOI: 10.1140/epje/s10189-021-00089-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
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.
Collapse
Affiliation(s)
- Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan.
| |
Collapse
|
3
|
McFaul LW, Sparks G, Sickle J, Uhl JT, Wright WJ, Maaß R, Dahmen KA. Applied-force oscillations in avalanche dynamics. Phys Rev E 2020; 101:053003. [PMID: 32575338 DOI: 10.1103/physreve.101.053003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2018] [Accepted: 03/12/2020] [Indexed: 11/07/2022]
Abstract
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.
Collapse
Affiliation(s)
- Louis W McFaul
- Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Gregory Sparks
- Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA
| | - Jordan Sickle
- Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Jonathan T Uhl
- Department of Mechanical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Wendelin J Wright
- Department of Mechanical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA.,Department of Chemical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Robert Maaß
- Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA
| | - Karin A Dahmen
- Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| |
Collapse
|
4
|
Baró J, Dahmen KA, Davidsen J, Planes A, Castillo PO, Nataf GF, Salje EKH, Vives E. Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials. PHYSICAL REVIEW LETTERS 2018; 120:245501. [PMID: 29956947 DOI: 10.1103/physrevlett.120.245501] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2018] [Indexed: 06/08/2023]
Abstract
The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.
Collapse
Affiliation(s)
- Jordi Baró
- Department of Physics, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW Calgary, Alberta T2N 1N4, Canada
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1. 08028 Barcelona, Catalonia, Spain
| | - Karin A Dahmen
- Department of Physics, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA
| | - Jörn Davidsen
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW Calgary, Alberta T2N 1N4, Canada
| | - Antoni Planes
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1. 08028 Barcelona, Catalonia, Spain
| | - Pedro O Castillo
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1. 08028 Barcelona, Catalonia, Spain
- CONACYT, Instituto Tecnológico de Oaxaca, Av. Ing. Víctor Bravo Ahuja 125, Oaxaca de Juárez 68030, México
| | - Guillaume F Nataf
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1. 08028 Barcelona, Catalonia, Spain
- Department of Materials Science, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Ekhard K H Salje
- Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, United Kingdom
| | - Eduard Vives
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1. 08028 Barcelona, Catalonia, Spain
| |
Collapse
|