1
|
Agoritsas E, Barés J. Loss of memory of an elastic line on its way to limit cycles. Phys Rev E 2024; 109:L042901. [PMID: 38755875 DOI: 10.1103/physreve.109.l042901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 03/10/2024] [Indexed: 05/18/2024]
Abstract
Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.
Collapse
Affiliation(s)
- Elisabeth Agoritsas
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil (LMGC), UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
| |
Collapse
|
2
|
Barés J, Bonamy D. Controlling crackling dynamics by triggering low-intensity avalanches. Phys Rev E 2021; 103:053001. [PMID: 34134297 DOI: 10.1103/physreve.103.053001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 04/23/2021] [Indexed: 11/07/2022]
Abstract
We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.
Collapse
Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
| | - Daniel Bonamy
- Service de Physique de l'État Condensée, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
| |
Collapse
|
3
|
Le Priol C, Le Doussal P, Rosso A. Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions. PHYSICAL REVIEW LETTERS 2021; 126:025702. [PMID: 33512216 DOI: 10.1103/physrevlett.126.025702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 10/14/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this Letter we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.
Collapse
Affiliation(s)
- Clément Le Priol
- Laboratoire de Physique de l'Ecole Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Pierre Le Doussal
- Laboratoire de Physique de l'Ecole Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| |
Collapse
|
4
|
Le Priol C, Chopin J, Le Doussal P, Ponson L, Rosso A. Universal Scaling of the Velocity Field in Crack Front Propagation. PHYSICAL REVIEW LETTERS 2020; 124:065501. [PMID: 32109111 DOI: 10.1103/physrevlett.124.065501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2019] [Revised: 12/11/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are, however, difficult to characterize in experiments at a finite drive. Here, we show that the correlation functions of the velocity field along the front allow us to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient, and can be extended to all systems displaying avalanche dynamics.
Collapse
Affiliation(s)
- Clément Le Priol
- CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Julien Chopin
- Instituto de Física, Universidade Federal da Bahia, Salvador-BA, 40170-115, Brazil
| | - Pierre Le Doussal
- CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France
| | - Laurent Ponson
- Institut Jean le Rond d'Alembert, Sorbonne Université, 75252 Paris Cedex 05, France
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| |
Collapse
|
5
|
Barés J, Bonamy D, Rosso A. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks. Phys Rev E 2019; 100:023001. [PMID: 31574622 DOI: 10.1103/physreve.100.023001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 11/07/2022]
Abstract
Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.
Collapse
Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Daniel Bonamy
- SPEC/SPHYNX, DSM/IRAMIS CEA Saclay, Bat. 772, F-91191 Gif-sur-Yvette, France
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| |
Collapse
|
6
|
Abed Zadeh A, Barés J, Behringer RP. Crackling to periodic dynamics in granular media. Phys Rev E 2019; 99:040901. [PMID: 31108659 DOI: 10.1103/physreve.99.040901] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2018] [Indexed: 06/09/2023]
Abstract
We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.
Collapse
Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Robert P Behringer
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| |
Collapse
|
7
|
Vu CC, Amitrano D, Plé O, Weiss J. Compressive Failure as a Critical Transition: Experimental Evidence and Mapping onto the Universality Class of Depinning. PHYSICAL REVIEW LETTERS 2019; 122:015502. [PMID: 31012687 DOI: 10.1103/physrevlett.122.015502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2018] [Revised: 09/13/2018] [Indexed: 06/09/2023]
Abstract
Acoustic emission (AE) measurements performed during the compressive loading of concrete samples with three different microstructures (aggregate sizes and porosity) and four sample sizes revealed that failure is preceded by an acceleration of the rate of fracturing events, power law distributions of AE energies and durations near failure, and a divergence of the fracturing correlation length and time towards failure. This argues for an interpretation of compressive failure of disordered materials as a critical transition between an intact and a failed state. The associated critical exponents were found to be independent of sample size and microstructural disorder and close to mean-field depinning values. Although compressive failure differs from classical depinning in several respects, including the nature of the elastic redistribution kernel, an analogy between the two processes allows deriving (finite-) sizing effects on strength that match our extensive data set. This critical interpretation of failure may have also important consequences in terms of natural hazards forecasting, such as volcanic eruptions, landslides, or cliff collapses.
Collapse
Affiliation(s)
- Chi-Cong Vu
- University of Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
| | - David Amitrano
- University of Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
| | - Olivier Plé
- University of Savoie Mont-Blanc, CNRS, LOCIE, 73736 Le Bourget du Lac Cedex, France
| | - Jérôme Weiss
- University of Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
| |
Collapse
|
8
|
Barés J, Bonamy D. Crack growth in heterogeneous brittle solids: intermittency, crackling and induced seismicity. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:20170386. [PMID: 30478198 PMCID: PMC6282407 DOI: 10.1098/rsta.2017.0386] [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: 10/12/2018] [Indexed: 06/09/2023]
Abstract
Crack growth is the basic mechanism leading to the failure of brittle materials. Engineering addresses this problem within the framework of continuum mechanics, which links deterministically the crack motion to the applied loading. Such an idealization, however, fails in several situations and in particular cannot capture the highly erratic (earthquake-like) dynamics sometimes observed in slowly fracturing heterogeneous solids. Here, we examine this problem by means of innovative experiments of crack growth in artificial rocks of controlled microstructure. The dynamical events are analysed at both global and local scales, from the time fluctuation of the spatially averaged crack speed and the induced acoustic emission, respectively. Their statistics are characterized and compared with the predictions of a recent approach mapping fracture onset to the depinning of an elastic interface. Finally, the overall time-size organization of the events is characterized to shed light on the mechanisms underlying the scaling laws observed in seismology.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.
Collapse
Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, 163 rue Auguste Broussonnet, 34090 Montpellier, France
| | - Daniel Bonamy
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
| |
Collapse
|
9
|
Barés J, Dubois A, Hattali L, Dalmas D, Bonamy D. Aftershock sequences and seismic-like organization of acoustic events produced by a single propagating crack. Nat Commun 2018; 9:1253. [PMID: 29593272 PMCID: PMC5871842 DOI: 10.1038/s41467-018-03559-4] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 02/22/2018] [Indexed: 11/28/2022] Open
Abstract
Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology, but also rules the acoustic events produced by a propagating crack. This simpler situation has permitted us to relate these laws to the overall scale-free distribution of inter-event time and energy and to uncover their selection by the crack speed. These results provide a comprehensive picture of how acoustic events are organized upon material failure in the most fundamental of fracture states: single propagating cracks. The multiple microcracking events underlying damage in inhomogeneous brittle materials form characteristic aftershocks sequences obeying similar laws to those in seismology. Here, Barés et al. evidence and explain the same organization in the acoustic noise produced by a single propagating crack.
Collapse
Affiliation(s)
- Jonathan Barés
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.,Laboratoire de Mécanique et Génie Civil Université de Montpellier CNRS, 163 rue Auguste Broussonnet, 34090, Montpellier, France
| | - Alizée Dubois
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France
| | - Lamine Hattali
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.,Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France
| | - Davy Dalmas
- Laboratoire de Tribologie et Dynamique des Systemes, CNRS, Ecole Centrale de Lyon, 36, Avenue Guy de Collongue, 69134, Ecully, Cedex, France
| | - Daniel Bonamy
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.
| |
Collapse
|
10
|
Ponson L, Pindra N. Crack propagation through disordered materials as a depinning transition: A critical test of the theory. Phys Rev E 2017; 95:053004. [PMID: 28618481 DOI: 10.1103/physreve.95.053004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Indexed: 11/07/2022]
Abstract
The dynamics of a planar crack propagating within a brittle disordered material is investigated numerically. The fracture front evolution is described as the depinning of an elastic line in a random field of toughness. The relevance of this approach is critically tested through the comparison of the roughness front properties, the statistics of avalanches, and the local crack velocity distribution with experimental results. Our simulations capture the main features of the fracture front evolution as measured experimentally. However, some experimental observations such as the velocity distribution are not consistent with the behavior of an elastic line close to the depinning transition. This discrepancy suggests the presence of another failure mechanism not included in our model of brittle failure.
Collapse
Affiliation(s)
- Laurent Ponson
- Institut Jean le Rond d'Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005 Paris, France
| | - Nadjime Pindra
- Institut Jean le Rond d'Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005 Paris, France.,Département de mathématiques, Université de Lomé, 1515 Lomé, Togo
| |
Collapse
|
11
|
Mbarek S, Baroni P, Noirez L. Highlighting delayed elastic processes at zero stress in a polymer glass. POLYM INT 2015. [DOI: 10.1002/pi.4950] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Souad Mbarek
- MINES ParisTech; Centre de Mise en Forme des Matériaux (CEMEF); 06904 Sophia Antipolis Cédex France
- Laboratoire de Mécanique de Sousse (LMS), LR11ES36; Ecole Nationale d'Ingénieurs de Sousse; Tunisie
| | - Patrick Baroni
- Laboratoire Léon Brillouin (CEA-CNRS); CE-Saclay; 91191 Gif-sur-Yvette Cédex France
| | - Laurence Noirez
- Laboratoire Léon Brillouin (CEA-CNRS); CE-Saclay; 91191 Gif-sur-Yvette Cédex France
| |
Collapse
|
12
|
Barés J, Hattali ML, Dalmas D, Bonamy D. Fluctuations of global energy release and crackling in nominally brittle heterogeneous fracture. PHYSICAL REVIEW LETTERS 2014; 113:264301. [PMID: 25615343 DOI: 10.1103/physrevlett.113.264301] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2014] [Indexed: 06/04/2023]
Abstract
The temporal evolution of mechanical energy and spatially averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burstlike dynamics, with power-law distributed fluctuations spanning a broad range of scales. Yet, the elastic power released at each time step is proportional to the global velocity all along the process, which enables defining a material-constant fracture energy. We characterize the intermittent dynamics by computing the burst statistics. This latter displays the scale-free features signature of crackling dynamics, in qualitative but not quantitative agreement with the depinning interface models derived for fracture problems. The possible sources of discrepancies are pointed out and discussed.
Collapse
Affiliation(s)
- J Barés
- Laboratoire SPHYNX, Service de Physique de l'Etat Condensé, IRAMIS, CEA Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
| | - M L Hattali
- Laboratoire SPHYNX, Service de Physique de l'Etat Condensé, IRAMIS, CEA Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
| | - D Dalmas
- Unité Mixte CNRS/Saint-Gobain, Surface du Verre et Interfaces, 39 Quai Lucien Lefranc, 93303 Aubervilliers cedex, France
| | - D Bonamy
- Laboratoire SPHYNX, Service de Physique de l'Etat Condensé, IRAMIS, CEA Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
| |
Collapse
|