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Yan C, Guan D, Wang Y, Lai PY, Chen HY, Tong P. Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line. PHYSICAL REVIEW LETTERS 2024; 132:084003. [PMID: 38457705 DOI: 10.1103/physrevlett.132.084003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Revised: 11/13/2023] [Accepted: 01/16/2024] [Indexed: 03/10/2024]
Abstract
We report direct atomic force microscopy measurements of pinning-depinning dynamics of a circular moving contact line (CL) over the rough surface of a micron-sized vertical hanging glass fiber, which intersects a liquid-air interface. The measured capillary force acting on the CL exhibits sawtoothlike fluctuations, with a linear accumulation of force of slope k (stick) followed by a sharp release of force δf, which is proportional to the CL slip length. From a thorough analysis of a large volume of the stick-slip events, we find that the local maximal force F_{c} needed for CL depinning follows the extreme value statistics and the measured δf follows the avalanche dynamics with a power law distribution in good agreement with the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. The experiment provides an accurate statistical description of the CL dynamics at mesoscale, which has important implications to a common class of problems involving stick-slip motion in a random defect or roughness landscape.
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Affiliation(s)
- Caishan Yan
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Dongshi Guan
- State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yin Wang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Pik-Yin Lai
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
| | - Hsuan-Yi Chen
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
| | - Penger Tong
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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Mäkinen T, Karppinen P, Ovaska M, Laurson L, Alava MJ. Propagating bands of plastic deformation in a metal alloy as critical avalanches. SCIENCE ADVANCES 2020; 6:6/41/eabc7350. [PMID: 33028532 PMCID: PMC7541064 DOI: 10.1126/sciadv.abc7350] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 08/25/2020] [Indexed: 06/11/2023]
Abstract
The plastic deformation of metal alloys localizes in the Portevin-Le Chatelier effect in bands of different types, including propagating, or type "A" bands, usually characterized by their width and a typical propagation velocity. This plastic instability arises from collective dynamics of dislocations interacting with mobile solute atoms, but the resulting sensitivity to the strain rate lacks fundamental understanding. Here, we show, by using high-resolution imaging in tensile deformation experiments of an aluminum alloy, that the band velocities exhibit large fluctuations. Each band produces a velocity signal reminiscent of crackling noise bursts observed in numerous driven avalanching systems from propagating cracks in fracture to the Barkhausen effect in ferromagnets. The statistical features of these velocity bursts including their average shapes and size distributions obey predictions of a simple mean-field model of critical avalanche dynamics. Our results thus reveal a previously unknown paradigm of criticality in the localization of deformation.
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Affiliation(s)
- Tero Mäkinen
- Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Espoo, Finland.
| | - Pasi Karppinen
- ProtoRhino Ltd, Betonimiehenkuja 5C, FI-02150 Espoo, Finland
| | - Markus Ovaska
- Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Espoo, Finland
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Mikko J Alava
- Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Espoo, Finland
- NOMATEN Centre of Excellence, National Centre of Nuclear Research, A. Soltana 7, 05-400 Otwock-Świerk, Poland
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Pan Y, Wu H, Wang X, Sun Q, Xiao L, Ding X, Sun J, Salje EKH. Rotatable precipitates change the scale-free to scale dependent statistics in compressed Ti nano-pillars. Sci Rep 2019; 9:3778. [PMID: 30846841 PMCID: PMC6405840 DOI: 10.1038/s41598-019-40526-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Accepted: 02/14/2019] [Indexed: 11/09/2022] Open
Abstract
Compressed nano-pillars crackle from moving dislocations, which reduces plastic stability. Crackling noise is characterized by stress drops or strain bursts, which scale over a large region of sizes leading to power law statistics. Here we report that this “classic” behaviour is not valid in Ti-based nanopillars for a counterintuitive reason: we tailor precipitates inside the nano-pillar, which “regulate” the flux of dislocations. It is not because the nano-pillars become too small to sustain large dislocation movements, the effect is hence independent of size. Our precipitates act as “rotors”: local stress initiates the rotation of inclusions, which reduces the stress amplitudes dramatically. The size distribution of stress drops simultaneously changes from power law to exponential. Rotors act like revolving doors limiting the number of passing dislocations. Hence each collapse becomes weak. We present experimental evidence for Ti-based nano-pillars (diameters between 300 nm and 2 μm) with power law distributions of crackling noise P(s) ∼ s−τ with τ ∼ 2 in the defect free or non-rotatable precipitate states. Rotors change the size distribution to P(s) ∼ exp(−s/s0). Rotors are inclusions of ω-phase that aligns under stress along slip planes and limit dislocation glide to small distances with high nucleation rates. This opens new ways to make nano-pillars more stable.
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Affiliation(s)
- Yan Pan
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Haijun Wu
- Department of Materials Science and Engineering, National University of Singapore, Singapore, 117575, Singapore
| | - Xiaofei Wang
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Qiaoyan Sun
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Lin Xiao
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Xiangdong Ding
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China.
| | - Jun Sun
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Ekhard K H Salje
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China. .,Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, United Kingdom.
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Santucci S, Tallakstad KT, Angheluta L, Laurson L, Toussaint R, Måløy KJ. Avalanches and extreme value statistics in interfacial crackling dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:20170394. [PMID: 30478206 PMCID: PMC6282413 DOI: 10.1098/rsta.2017.0394] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/29/2018] [Indexed: 06/09/2023]
Abstract
We study the avalanche and extreme statistics of the global velocity of a crack front, propagating slowly along a weak heterogeneous interface of a transparent polymethyl methacrylate block. The different loading conditions used (imposed constant velocity or creep relaxation) lead to a broad range of average crack front velocities. Our high-resolution and large dataset allows one to characterize in detail the observed intermittent crackling dynamics. We specifically measure the size S, the duration D, as well as the maximum amplitude [Formula: see text] of the global avalanches, defined as bursts in the interfacial crack global velocity time series. Those quantities characterizing the crackling dynamics follow robust power-law distributions, with scaling exponents in agreement with the values predicted and obtained in numerical simulations of the critical depinning of a long-range elastic string, slowly driven in a random medium. Nevertheless, our experimental results also set the limit of such model which cannot reproduce the power-law distribution of the maximum amplitudes of avalanches of a given duration reminiscent of the underlying fat-tail statistics of the local crack front velocities.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.
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Affiliation(s)
- S Santucci
- Laboratoire de Physique, Université de Lyon, ENSL, UCBL, CNRS, Lyon, France
- PoreLab,The Njord Center, Department of Physics, University of Oslo, Blindern, Oslo, Norway
- Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia
| | - K T Tallakstad
- PoreLab,The Njord Center, Department of Physics, University of Oslo, Blindern, Oslo, Norway
| | - L Angheluta
- PoreLab,The Njord Center, Department of Physics, University of Oslo, Blindern, Oslo, Norway
| | - L Laurson
- Department of Applied Physics, Aalto University, PO Box 11100, 00076 Aalto, Espoo, Finland
- Laboratory of Physics, Tampere University of Technology, PO Box 692, 33101 Tampere, Finland
| | - R Toussaint
- PoreLab,The Njord Center, Department of Physics, University of Oslo, Blindern, Oslo, Norway
- Institut de Physique du Globe de Strasbourg, Université de Strasbourg, UMR 7516, CNRS, France
| | - K J Måløy
- PoreLab,The Njord Center, Department of Physics, University of Oslo, Blindern, Oslo, Norway
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Soprunyuk V, Puchberger S, Tröster A, Vives E, Salje EKH, Schranz W. Strain intermittency due to avalanches in ferroelastic and porous materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:224002. [PMID: 28383285 DOI: 10.1088/1361-648x/aa6bd2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The avalanche statistics in porous materials and ferroelastic domain wall systems has been studied for slowly increasing compressive uniaxial stress with stress rates between 0.2 and 17 kPa s-1. Velocity peaks [Formula: see text] are calculated from the measured strain drops and used to determine the corresponding Energy distributions [Formula: see text]. Power law distributions [Formula: see text] have been obtained over 4-6 decades. For most of the porous materials and domain wall systems an exponent [Formula: see text] was obtained in good agreement with mean-field theory of the interface pinning transition. For charcoal, shale and calcareous schist we found significant deviations of the exponents from mean-field values in agreement with recent acoustic emission experiments.
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Affiliation(s)
- V Soprunyuk
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Wien, Austria
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Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes. Sci Rep 2015; 5:16493. [PMID: 26572103 PMCID: PMC4647222 DOI: 10.1038/srep16493] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 10/14/2015] [Indexed: 11/08/2022] Open
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.
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Tarp JM, Angheluta L, Mathiesen J, Goldenfeld N. Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model. PHYSICAL REVIEW LETTERS 2014; 113:265503. [PMID: 25615353 DOI: 10.1103/physrevlett.113.265503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 06/04/2023]
Abstract
Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density 1/f2 at high frequencies f. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternates at irregular times with high populations of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.
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Affiliation(s)
- Jens M Tarp
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Luiza Angheluta
- Department of Physics, Physics of Geological Processes, University of Oslo, Post Office 1048 Blindern, 0316 Oslo Norway
| | - Joachim Mathiesen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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Antonaglia J, Wright WJ, Gu X, Byer RR, Hufnagel TC, LeBlanc M, Uhl JT, Dahmen KA. Bulk metallic glasses deform via slip avalanches. PHYSICAL REVIEW LETTERS 2014; 112:155501. [PMID: 24785049 DOI: 10.1103/physrevlett.112.155501] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2013] [Indexed: 06/03/2023]
Abstract
For the first time in metallic glasses, we extract both the exponents and scaling functions that describe the nature, statistics, and dynamics of slip events during slow deformation, according to a simple mean field model. We model the slips as avalanches of rearrangements of atoms in coupled shear transformation zones (STZs). Using high temporal resolution measurements, we find the predicted, different statistics and dynamics for small and large slips thereby excluding self-organized criticality. The agreement between model and data across numerous independent measures provides evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.
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Affiliation(s)
- James Antonaglia
- Department of Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Wendelin J Wright
- Department of Mechanical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA and Department of Chemical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Xiaojun Gu
- Department of Mechanical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Rachel R Byer
- Department of Physics and Astronomy, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Todd C Hufnagel
- Department of Materials Science and Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - Michael LeBlanc
- 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 Physics and Institute of Condensed Matter Theory, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA and Department of Mechanical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA and Department of Chemical Engineering, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA and Department of Physics and Astronomy, One Dent Drive, Bucknell University, Lewisburg, Pennsylvania 17837, USA and Department of Materials Science and Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, 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
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Spasojević D, Janićević S, Knežević M. Analysis of spanning avalanches in the two-dimensional nonequilibrium zero-temperature random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012118. [PMID: 24580183 DOI: 10.1103/physreve.89.012118] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2013] [Indexed: 06/03/2023]
Abstract
We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.
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Affiliation(s)
- Djordje Spasojević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
| | - Sanja Janićević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
| | - Milan Knežević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
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LeBlanc M, Angheluta L, Dahmen K, Goldenfeld N. Universal fluctuations and extreme statistics of avalanches near the depinning transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022126. [PMID: 23496478 DOI: 10.1103/physreve.87.022126] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2012] [Indexed: 06/01/2023]
Abstract
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities v(m) during avalanches described by the mean-field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.
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Affiliation(s)
- Michael LeBlanc
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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