1
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Shekh Alshabab S, Markert B, Bamer F. Criticality in the fracture of silica glass: Insights from molecular mechanics. Phys Rev E 2024; 109:034110. [PMID: 38632794 DOI: 10.1103/physreve.109.034110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 02/02/2024] [Indexed: 04/19/2024]
Abstract
The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.
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Affiliation(s)
| | - Bernd Markert
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
| | - Franz Bamer
- Institute of General Mechanics, RWTH Aachen University, 52062 Aachen, Germany
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2
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Senapati S, Banerjee A, Rajesh R. Role of composition in fracture behavior of two-phase solids. Phys Rev E 2023; 107:055002. [PMID: 37329015 DOI: 10.1103/physreve.107.055002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 04/11/2023] [Indexed: 06/18/2023]
Abstract
In a two-phase solid, we examine the growth of a preexisting macroscopic crack based on simulations of a random spring network model. We find that the enhancement in toughness, as well as strength, is strongly dependent on the ratio of elastic moduli as well as on the relative proportion of the phases. We find that the mechanism that leads to enhancement in toughness is not the same as that for enhancement in strength; however, the overall enhancement is similar in mode I and mixed-mode loading. Based on the crack paths, and the spread of the fracture process zone, we identify the type of fracture to transition from nucleation type, for close to single-phase compositions, whether hard or soft, to avalanche type for more mixed compositions. We also show that the associated avalanche distributions exhibit power-law statistics with different exponents for each phase. The significance of variations in the avalanche exponents with the relative proportion of phases and possible connections to the fracture types are discussed in detail.
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Affiliation(s)
- Subrat Senapati
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - R Rajesh
- Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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3
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Kumar D, Banerjee A, Rajesh R. Interplay between disorder and hardening during tensile fracture of a quasi-brittle solid. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We examine the specific role of the interplay between hardening and disorder characteristics of a representative quasi-brittle material on its failure mechanisms using a random spring network model. The model incorporates quasi-brittleness in its spring constants and disorder in the failure strain threshold and is shown to be effective in simulating the experimentally observed tensile and fracture behaviour of a quasi-brittle epoxy resin-based polymer. It is shown that rapid localization of deformation and associated damage growth occurs for a weakly hardening solid while for a linear elastic material, damage nucleates at multiple independent sites, and there is significant growth of damage, independent of other nucleating sites, prior to maximum load. The failure mechanism is shown to crossover from an avalanche-dominated fracture for a linear elastic material to nucleation-dominated fracture for a weakly hardening material.
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Affiliation(s)
- Deepak Kumar
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - R. Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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4
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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.
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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
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5
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Kádár V, Pál G, Kun F. Record statistics of bursts signals the onset of acceleration towards failure. Sci Rep 2020; 10:2508. [PMID: 32054929 PMCID: PMC7018714 DOI: 10.1038/s41598-020-59333-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 01/22/2020] [Indexed: 11/23/2022] Open
Abstract
Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast methods predict the lifetime of the system based on the time-to-failure power law of observables describing the final acceleration towards failure. We show that the statistics of records of the event series of breaking bursts, accompanying the failure process, provides a powerful tool to detect the onset of acceleration, as an early warning of the impending catastrophe. We focus on the fracture of heterogeneous materials using a fiber bundle model, which exhibits transitions between perfectly brittle, quasi-brittle, and ductile behaviors as the amount of disorder is increased. Analyzing the lifetime of record size bursts, we demonstrate that the acceleration starts at a characteristic record rank, below which record breaking slows down due to the dominance of disorder in fracturing, while above it stress redistribution gives rise to an enhanced triggering of bursts and acceleration of the dynamics. The emergence of this signal depends on the degree of disorder making both highly brittle fracture of low disorder materials, and ductile fracture of strongly disordered ones, unpredictable.
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Affiliation(s)
- Viktória Kádár
- Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, P.O.Box: 400, H-4002, Debrecen, Hungary
| | - Gergő Pál
- Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, P.O.Box: 400, H-4002, Debrecen, Hungary
- Institute of Nuclear Research (Atomki), P.O.Box: 51, H-4001 Debrecen, Hungary
| | - Ferenc Kun
- Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, P.O.Box: 400, H-4002, Debrecen, Hungary.
- Institute of Nuclear Research (Atomki), P.O.Box: 51, H-4001 Debrecen, Hungary.
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6
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Kumar P, Korkolis E, Benzi R, Denisov D, Niemeijer A, Schall P, Toschi F, Trampert J. On interevent time distributions of avalanche dynamics. Sci Rep 2020; 10:626. [PMID: 31953412 PMCID: PMC6969144 DOI: 10.1038/s41598-019-56764-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Accepted: 11/29/2019] [Indexed: 11/09/2022] Open
Abstract
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, these interevent time distributions look similar to those for earthquakes and, if different from an exponential, are indirect evidence of non trivial space-time correlations among avalanches. Our results therefore indicate that interevent time statistics are essential to characterise the dynamics of avalanches.
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Affiliation(s)
- Pinaki Kumar
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands
| | - Evangelos Korkolis
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Roberto Benzi
- Dip. di Fisica and INFN, Università "Tor Vergata", Via della Ricerca Scientifica 1, I-00133, Roma, Italy
| | - Dmitry Denisov
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - André Niemeijer
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy.
| | - Jeannot Trampert
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
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7
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Kádár V, Kun F. System-size-dependent avalanche statistics in the limit of high disorder. Phys Rev E 2019; 100:053001. [PMID: 31869880 DOI: 10.1103/physreve.100.053001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2019] [Indexed: 11/07/2022]
Abstract
We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasistatic fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a power-law distribution over a finite range, so that the amount of materials' disorder can be controlled by varying the power-law exponent and the upper cutoff of fibers' strength. Analytical calculations and computer simulations, performed in the limit of equal load sharing, revealed that depending on the disorder parameters the mechanical response of the bundle is either perfectly brittle where the first fiber breaking triggers a catastrophic avalanche, or it is quasibrittle where macroscopic failure is preceded by a sequence of bursts. In the quasibrittle phase, the statistics of avalanche sizes is found to show a high degree of complexity. In particular, we demonstrate that the functional form of the size distribution of bursts depends on the system size: for large upper cutoffs of fibers' strength, in small systems the sequence of bursts has a high degree of stationarity characterized by a power-law size distribution with a universal exponent. However, for sufficiently large bundles the breaking process accelerates towards the critical point of failure, which gives rise to a crossover between two power laws. The transition between the two regimes occurs at a characteristic system size which depends on the disorder parameters.
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Affiliation(s)
- Viktória Kádár
- Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary and Institute for Nuclear Research, Hungarian Academy of Sciences (Atomki), P.O. Box 51, H-4001 Debrecen, Hungary
| | - Ferenc Kun
- Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary and Institute for Nuclear Research, Hungarian Academy of Sciences (Atomki), P.O. Box 51, H-4001 Debrecen, Hungary
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8
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Baldassarri A, Annunziata MA, Gnoli A, Pontuale G, Petri A. Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow. Sci Rep 2019; 9:16962. [PMID: 31740801 PMCID: PMC6861274 DOI: 10.1038/s41598-019-53178-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Accepted: 10/11/2019] [Indexed: 12/02/2022] Open
Abstract
Many materials are produced, processed and stored as grains, while granularity of matter can be crucial in triggering potentially catastrophic geological events like landslides, avalanches and earthquakes. The response of grain assemblies to shear stress is therefore of utmost relevance to both human and natural environment. At low shear rate a granular system flows intermittently by distinct avalanches. In such state the avalanche velocity in time is expected to follow a symmetrical and universal average behavior, whose dependence on the slip size reduces to a scale factor. Analyzing data from long lasting experiments, we observe a breakdown of this scaling: While in short slips velocity shows indeed a self-similar and symmetric profile, it does not in long slips. The investigation of frictional response in these different regimes evidences that this breakdown can be traced back to the onset of a friction weakening, which is of dynamical origin and can amplify instabilities exactly in this critical state, the most frequent state for natural hazards.
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Affiliation(s)
- A Baldassarri
- CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Università di Roma Sapienza, P.le A. Moro 2, I-00185, Roma, Italy
| | - M A Annunziata
- CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Università di Roma Sapienza, P.le A. Moro 2, I-00185, Roma, Italy
| | - A Gnoli
- CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Università di Roma Sapienza, P.le A. Moro 2, I-00185, Roma, Italy
| | - G Pontuale
- CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Università di Roma Sapienza, P.le A. Moro 2, I-00185, Roma, Italy
- Consiglio per la Ricerca in Agricoltura e l'Analisi dell'Economia Agraria (CREA) - Research Centre for Forestry and Woods, Via Santa Margherita 80, I-52100, Arezzo, Italy
| | - A Petri
- CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Università di Roma Sapienza, P.le A. Moro 2, I-00185, Roma, Italy.
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9
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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.
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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
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10
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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.
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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
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11
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Ray P. Statistical physics perspective of fracture in brittle and quasi-brittle materials. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:rsta.2017.0396. [PMID: 30478208 DOI: 10.1098/rsta.2017.0396] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/24/2018] [Indexed: 06/09/2023]
Abstract
We discuss the physics of fracture in terms of the statistical physics associated with the failure of elastic media under applied stresses in presence of quenched disorder. We show that the development and the propagation of fracture are largely determined by the strength of the disorder and the stress field around them. Disorder acts as nucleation centres for fracture. We discuss Griffith's law for a single crack-like defect as a source for fracture nucleation and subsequently consider two situations: (i) low disorder concentration of the defects, where the failure is determined by the extreme value statistics of the most vulnerable defect (nucleation regime) and (ii) high disorder concentration of the defects, where the scaling theory near percolation transition is applicable. In this regime, the development of fracture takes place through avalanches of a large number of tiny microfractures with universal statistical features. We discuss the transition from brittle to quasi-brittle behaviour of fracture with the strength of disorder in the mean-field fibre bundle model. We also discuss how the nucleation or percolation mode of growth of fracture depends on the stress distribution range around a defect. We discuss the corresponding numerical simulation results on random resistor and spring networks.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.
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Affiliation(s)
- Purusattam Ray
- The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 40094, India
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12
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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'.
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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
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13
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Roy S. Stability in a fiber bundle model: Existence of strong links and the effect of disorder. Phys Rev E 2018; 97:052130. [PMID: 29906993 DOI: 10.1103/physreve.97.052130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2017] [Indexed: 11/07/2022]
Abstract
The present paper deals with a fiber bundle model which consists of a fraction α of infinitely strong fibers. The inclusion of such an unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value α_{c}. The present work has a twofold purpose: (i) a study of failure abruptness, mainly the brittle to quasibrittle transition point with varying α and (ii) variation of α_{c} as we change the strength of disorder introduced in the model. The brittle to quasibrittle transition is confirmed from the failure abruptness. On the other hand, the α_{c} is obtained from the knowledge of failure abruptness as well as the statistics of avalanches. It is observed that the brittle to quasibrittle transition point scales to lower values, suggesting more quasi-brittle-like continuous failure when α is increased. At the same time, the bundle becomes stronger as there are larger numbers of strong links to support the external stress. High α in a highly disordered bundle leads to an ideal situation where the bundle strength, as well as the predictability in failure process is very high. Also, the critical fraction α_{c}, required to make the model deviate from the conventional results, increases with decreasing strength of disorder. The analytical expression for α_{c} shows good agreement with the numerical results. Finally, the findings in the paper are compared with previous results and real-life applications of composite materials.
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Affiliation(s)
- Subhadeep Roy
- Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, 113-0032 Tokyo, Japan
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14
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Mayya A, Banerjee A, Rajesh R. Role of porosity and matrix behavior on compressive fracture of Haversian bone using random spring network model. J Mech Behav Biomed Mater 2018; 83:108-119. [PMID: 29698930 DOI: 10.1016/j.jmbbm.2018.04.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 03/18/2018] [Accepted: 04/13/2018] [Indexed: 10/17/2022]
Abstract
Haversian remodeling is known to result in improved resistance to compressive fracture in healthy cortical bone. Here, we examine the individual roles of the mean porosity, structure of the network of pores and remodeled bone matrix properties in the fracture behavior of Haversian bone. The detailed structure of porosity network is obtained both pre- and post-testing of dry cubical bone samples using micro-Computed Tomography. Based on the periodicity in the features of porosity along tangential direction, we develop a two dimensional porosity-based random spring network model for Haversian bone. The model is shown to capture well the macroscopic response and reproduce the avalanche statistics similar to recently reported experiments on porcine bone. The predictions suggest that at the millimeter scale, the remodeled bone matrix of Haversian bone is less stiff but tougher than that of plexiform/primary bone.
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Affiliation(s)
- Ashwij Mayya
- Department of Applied Mechanics, IIT-Madras, Chennai 600036, India
| | | | - R Rajesh
- The Institute of Mathematical Sciences, Tharamani, Chennai 600113, India; Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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15
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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.
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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.
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Navas-Portella V, Serra I, Corral Á, Vives E. Increasing power-law range in avalanche amplitude and energy distributions. Phys Rev E 2018; 97:022134. [PMID: 29548208 DOI: 10.1103/physreve.97.022134] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2017] [Indexed: 11/07/2022]
Abstract
Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.
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Affiliation(s)
- Víctor Navas-Portella
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain.,Barcelona Graduate School of Mathematics, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain.,Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, E-08007 Barcelona, Spain
| | - Isabel Serra
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain
| | - Álvaro Corral
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain.,Barcelona Graduate School of Mathematics, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain.,Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria.,Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain
| | - Eduard Vives
- Departament de Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí Franquès 1, 08028 Barcelona, Catalonia, Spain.,Universitat de Barcelona Institute of Complex Systems, Facultat de Física, Universitat de Barcelona, Barcelona, Catalonia, Spain
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17
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Kumar J, Ananthakrishna G. Modeling the complexity of acoustic emission during intermittent plastic deformation: Power laws and multifractal spectra. Phys Rev E 2018; 97:012201. [PMID: 29448439 DOI: 10.1103/physreve.97.012201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 11/07/2022]
Abstract
Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum spread for the type C bands and decreasing with types B and A. We further show that the acoustic emission signals associated with Lüders-like band also exhibit a power-law distribution and multifractality.
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Affiliation(s)
- Jagadish Kumar
- Department of Physics, Utkal University, Bhubaneswar 751004, India
| | - G Ananthakrishna
- Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
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18
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Mayya A, Banerjee A, Rajesh R. Role of matrix behavior in compressive fracture of bovine cortical bone. Phys Rev E 2017; 96:053001. [PMID: 29347807 DOI: 10.1103/physreve.96.053001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2017] [Indexed: 06/07/2023]
Abstract
In compressive fracture of dry plexiform bone, we examine the individual roles of overall mean porosity, the connectivity of the porosity network, and the elastic as well as the failure properties of the nonporous matrix, using a random spring network model (RSNM). Porosity network structure is shown to reduce the compressive strength by up to 30%. However, the load-bearing capacity increases with an increase in either of the matrix properties-the elastic modulus or the failure strain threshold. To validate the porosity-based RSNM model with available experimental data, bone-specific failure strain thresholds for the ideal matrix of similar elastic properties were estimated to be within 60% of each other. Further, we observe the avalanche size exponents to be independent of the bone-dependent parameters as well as the structure of the porosity network.
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Affiliation(s)
- Ashwij Mayya
- Department of Applied Mechanics, Indian Institute of Technology-Madras, Chennai 600036, India
| | - Anuradha Banerjee
- Department of Applied Mechanics, Indian Institute of Technology-Madras, Chennai 600036, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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19
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Tsai ST, Wang LM, Huang P, Yang Z, Chang CD, Hong TM. Acoustic Emission from Breaking a Bamboo Chopstick. PHYSICAL REVIEW LETTERS 2016; 116:035501. [PMID: 26849601 DOI: 10.1103/physrevlett.116.035501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Indexed: 06/05/2023]
Abstract
The acoustic emission from breaking a bamboo chopstick or a bundle of spaghetti is found to exhibit similar behavior as the famous seismic laws of Gutenberg and Richter, Omori, and Båth. By the use of a force-sensing detector, we establish a positive correlation between the statistics of sound intensity and the magnitude of a tremor. We also manage to derive these laws analytically without invoking the concept of a phase transition, self-organized criticality, or fractal. Our model is deterministic and relies on the existence of a structured cross section, either fibrous or layered. This success at explaining the power-law behavior supports the proposal that geometry is sometimes more important than mechanics.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Li-Min Wang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Panpan Huang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Zhengning Yang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Chin-De Chang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Tzay-Ming Hong
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
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20
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Vasseur J, Wadsworth FB, Lavallée Y, Bell AF, Main IG, Dingwell DB. Heterogeneity: The key to failure forecasting. Sci Rep 2015; 5:13259. [PMID: 26307196 PMCID: PMC4549791 DOI: 10.1038/srep13259] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2015] [Accepted: 07/23/2015] [Indexed: 11/17/2022] Open
Abstract
Elastic waves are generated when brittle materials are subjected to increasing strain. Their number and energy increase non-linearly, ending in a system-sized catastrophic failure event. Accelerating rates of geophysical signals (e.g., seismicity and deformation) preceding large-scale dynamic failure can serve as proxies for damage accumulation in the Failure Forecast Method (FFM). Here we test the hypothesis that the style and mechanisms of deformation, and the accuracy of the FFM, are both tightly controlled by the degree of microstructural heterogeneity of the material under stress. We generate a suite of synthetic samples with variable heterogeneity, controlled by the gas volume fraction. We experimentally demonstrate that the accuracy of failure prediction increases drastically with the degree of material heterogeneity. These results have significant implications in a broad range of material-based disciplines for which failure forecasting is of central importance. In particular, the FFM has been used with only variable success to forecast failure scenarios both in the field (volcanic eruptions and landslides) and in the laboratory (rock and magma failure). Our results show that this variability may be explained, and the reliability and accuracy of forecast quantified significantly improved, by accounting for material heterogeneity as a first-order control on forecasting power.
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Affiliation(s)
- Jérémie Vasseur
- Earth and Environmental Sciences, Ludwig Maximilian University, Munich, Germany
| | - Fabian B Wadsworth
- Earth and Environmental Sciences, Ludwig Maximilian University, Munich, Germany
| | - Yan Lavallée
- Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, United Kingdom
| | - Andrew F Bell
- School of Geosciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Ian G Main
- School of Geosciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Donald B Dingwell
- Earth and Environmental Sciences, Ludwig Maximilian University, Munich, Germany
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21
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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.
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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
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22
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Nataf GF, Castillo-Villa PO, Sellappan P, Kriven WM, Vives E, Planes A, Salje EKH. Predicting failure: acoustic emission of berlinite under compression. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:275401. [PMID: 24919038 DOI: 10.1088/0953-8984/26/27/275401] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Acoustic emission has been measured and statistical characteristics analyzed during the stress-induced collapse of porous berlinite, AlPO4, containing up to 50 vol% porosity. Stress collapse occurs in a series of individual events (avalanches), and each avalanche leads to a jerk in sample compression with corresponding acoustic emission (AE) signals. The distribution of AE avalanche energies can be approximately described by a power law p(E)dE = E(-ε)dE (ε ~ 1.8) over a large stress interval. We observed several collapse mechanisms whereby less porous minerals show the superposition of independent jerks, which were not related to the major collapse at the failure stress. In highly porous berlinite (40% and 50%) an increase of energy emission occurred near the failure point. In contrast, the less porous samples did not show such an increase in energy emission. Instead, in the near vicinity of the main failure point they showed a reduction in the energy exponent to ~ 1.4, which is consistent with the value reported for compressed porous systems displaying critical behavior. This suggests that a critical avalanche regime with a lack of precursor events occurs. In this case, all preceding large events were 'false alarms' and unrelated to the main failure event. Our results identify a method to use pico-seismicity detection of foreshocks to warn of mine collapse before the main failure (the collapse) occurs, which can be applied to highly porous materials only.
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Affiliation(s)
- Guillaume F Nataf
- Department d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia. INP Grenoble, 38031 Grenoble Cédex 1, France
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23
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Stojanova M, Santucci S, Vanel L, Ramos O. High frequency monitoring reveals aftershocks in subcritical crack growth. PHYSICAL REVIEW LETTERS 2014; 112:115502. [PMID: 24702388 DOI: 10.1103/physrevlett.112.115502] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2013] [Indexed: 06/03/2023]
Abstract
By combining direct imaging and acoustic emission measurements, the subcritical propagation of a crack in a heterogeneous material is analyzed. Both methods show that the fracture proceeds through a succession of discrete events. However, the macroscopic opening of the fracture captured by the images results from the accumulation of more-elementary events detected by the acoustics. When the acoustic energy is cumulated over large time scales corresponding to the image acquisition rate, a similar statistics is recovered. High frequency acoustic monitoring reveals aftershocks responsible for a time scale dependent exponent of the power law energy distributions. On the contrary, direct imaging, which is unable to resolve these aftershocks, delivers a misleading exponent value.
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Affiliation(s)
- M Stojanova
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
| | - S Santucci
- Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon, Université de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France
| | - L Vanel
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
| | - O Ramos
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
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24
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Creep rupture as a non-homogeneous Poissonian process. Sci Rep 2013; 3:2688. [PMID: 24045539 PMCID: PMC3776199 DOI: 10.1038/srep02688] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Accepted: 08/22/2013] [Indexed: 11/08/2022] Open
Abstract
Creep rupture of heterogeneous materials occurring under constant sub-critical external loads is responsible for the collapse of engineering constructions and for natural catastrophes. Acoustic monitoring of crackling bursts provides microscopic insight into the failure process. Based on a fiber bundle model, we show that the accelerating bursting activity when approaching failure can be described by the Omori law. For long range load redistribution the time series of bursts proved to be a non-homogeneous Poissonian process with power law distributed burst sizes and waiting times. We demonstrate that limitations of experiments such as finite detection threshold and time resolution have striking effects on the characteristic exponents, which have to be taken into account when comparing model calculations with experiments. Recording events solely within the Omori time to failure the size distribution of bursts has a crossover to a lower exponent which is promising for forecasting the imminent catastrophic failure.
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25
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Lennartz-Sassinek S, Main IG, Danku Z, Kun F. Time evolution of damage due to environmentally assisted aging in a fiber bundle model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032802. [PMID: 24125307 DOI: 10.1103/physreve.88.032802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2013] [Indexed: 06/02/2023]
Abstract
Damage growth in composite materials is a complex process which is of interest in many fields of science and engineering. We consider this problem in a fiber bundle model where fibers undergo an aging process due to the accumulation of damage driven by the locally acting stress in a chemically active environment. By subjecting the bundle to a constant external load, fibers fail either when the load on them exceeds their individual intrinsic strength or when the accumulated internal damage exceeds a random threshold. We analyze the time evolution of the breaking process under low external loads where aging of fibers dominates. In the mean field limit, we show analytically that the aging system continuously accelerates in a way which can be characterized by an inverse power law of the event rate with a singularity that defines a failure time. The exponent is not universal; it depends on the details of the aging process. For localized load sharing, a more complex damage process emerges which is dominated by distinct spatial regions of the system with different degrees of stress concentration. Analytical calculations revealed that the final acceleration to global failure is preceded by a stationary accumulation of damage. When the disorder is strong, the accelerating phase has the same functional behavior as in the mean field limit. The analytical results are verified by computer simulations.
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Affiliation(s)
- S Lennartz-Sassinek
- School of Engineering and School of Geosciences, University of Edinburgh, Edinburgh, United Kingdom
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26
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Pradhan S, Chandra AK, Chakrabarti BK. Noise-induced rupture process: phase boundary and scaling of waiting time distribution. Phys Rev E 2013; 88:012123. [PMID: 23944430 DOI: 10.1103/physreve.88.012123] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Revised: 04/29/2013] [Indexed: 11/07/2022]
Abstract
A bundle of fibers has been considered here as a model for composite materials, where breaking of the fibers occur due to a combined influence of applied load (stress) and external noise. Through numerical simulation and a mean-field calculation we show that there exists a robust phase boundary between continuous (no waiting time) and intermittent fracturing regimes. In the intermittent regime, throughout the entire rupture process avalanches of different sizes are produced and there is a waiting time between two consecutive avalanches. The statistics of waiting times follows a Γ distribution and the avalanche distribution shows power-law scaling, similar to what has been observed in the case of earthquake events and bursts in fracture experiments. We propose a prediction scheme that can tell when the system is expected to reach the continuous fracturing point from the intermittent phase.
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27
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Lennartz-Sassinek S, Zaiser M, Main IG, Manzato C, Zapperi S. Emergent patterns of localized damage as a precursor to catastrophic failure in a random fuse network. Phys Rev E 2013; 87:042811. [PMID: 23679477 DOI: 10.1103/physreve.87.042811] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2013] [Indexed: 11/07/2022]
Abstract
We study the failure of disordered materials by numerical simulations of the random fuse model. We identify emergent patterns of localized damage prior to catastrophic failure by statistically averaging the density of damage around the eventual failure nucleation point. The resulting pattern depends on fracture density and obeys the same scaling relations as would be expected for the stress field generated by a critical crack nucleating in a finite, disorder-free effective medium of varying size. The growth of this critical crack absorbs preexisting clusters according to a well-defined scaling relation. Unfortunately, in single model runs such precursory signals are not obvious. Our results imply that reliable and accurate prediction of failure in time-independent, microscopically brittle random materials in a real case is inherently problematic, and degrades with system size.
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Affiliation(s)
- S Lennartz-Sassinek
- School of Engineering and School of Geosciences, University of Edinburgh, Edinburgh, EH9 3JL, United Kingdom.
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28
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Shekhawat A, Zapperi S, Sethna JP. From damage percolation to crack nucleation through finite size criticality. PHYSICAL REVIEW LETTERS 2013; 110:185505. [PMID: 23683218 DOI: 10.1103/physrevlett.110.185505] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2012] [Indexed: 06/02/2023]
Abstract
We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has a mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit.
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Affiliation(s)
- Ashivni Shekhawat
- LASSP, Physics Department, Clark Hall, Cornell University, Ithaca, New York 14853-2501, USA
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29
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Ramos O, Cortet PP, Ciliberto S, Vanel L. Experimental study of the effect of disorder on subcritical crack growth dynamics. PHYSICAL REVIEW LETTERS 2013; 110:165506. [PMID: 23679620 DOI: 10.1103/physrevlett.110.165506] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2012] [Revised: 02/15/2013] [Indexed: 06/02/2023]
Abstract
The growth dynamics of a single crack in a heterogeneous material under subcritical loading is an intermittent process, and many features of this dynamics have been shown to agree with simple models of thermally activated rupture. In order to better understand the role of material heterogeneities in this process, we study the subcritical propagation of a crack in a sheet of paper in the presence of a distribution of small defects such as holes. The experimental data obtained for two different distributions of holes are discussed in the light of models that predict the slowing down of crack growth when the disorder in the material is increased; however, in contradiction with these theoretical predictions, the experiments result in longer lasting cracks in a more ordered scenario. We argue that this effect is specific to subcritical crack dynamics and that the weakest zones between holes at close distance to each other are responsible for both the acceleration of the crack dynamics and the slightly different roughness of the crack path.
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Affiliation(s)
- O Ramos
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France.
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30
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Pradhan S, Hemmer PC. Prediction of the collapse point of overloaded materials by monitoring energy emissions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041116. [PMID: 21599124 DOI: 10.1103/physreve.83.041116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Revised: 01/25/2011] [Indexed: 05/30/2023]
Abstract
A bundle of many fibers with stochastically distributed breaking thresholds is considered as a model of composite materials. The fibers are assumed to share the load equally and to obey Hookean elasticity up to the breaking point. The bundle is slightly overloaded which leads to complete failure. We study the properties of emission bursts in which an amount of energy E is released. The analysis shows that the size of the energy bursts has a minimum when the system is halfway from the collapse point.
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31
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Jagla EA. Creep rupture of materials: insights from a fiber bundle model with relaxation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:046119. [PMID: 21599252 DOI: 10.1103/physreve.83.046119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2010] [Indexed: 05/30/2023]
Abstract
I adapted a model recently introduced in the context of seismic phenomena to study creep rupture of materials. It consists of linear elastic fibers that interact in an equal load sharing scheme, complemented with a local viscoelastic relaxation mechanism. The model correctly describes the three stages of the creep process; namely, an initial Andrade regime of creep relaxation, an intermediate regime of rather constant creep rate, and a tertiary regime of accelerated creep toward final failure of the sample. In the tertiary regime, creep rate follows the experimentally observed creep rate over time-to-failure dependence. The time of minimum strain rate is systematically observed to be about 60%-65 % of the time to failure, in accordance with experimental observations. In addition, burst size statistics of breaking events display a -3/2 power law for events close to the time of failure and a steeper decay for the all-time distribution. Statistics of interevent times shows a tendency of the events to cluster temporarily. This behavior should be observable in acoustic emission experiments.
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Affiliation(s)
- E A Jagla
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica, (8400) Bariloche, Argentina
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32
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Timár G, Kun F. Crackling noise in three-point bending of heterogeneous materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:046115. [PMID: 21599248 DOI: 10.1103/physreve.83.046115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2010] [Indexed: 05/30/2023]
Abstract
We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting-time distributions have a power-law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasibrittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.
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Affiliation(s)
- Gábor Timár
- Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary
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33
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Kumar J, Ananthakrishna G. Multiscale modeling approach to acoustic emission during plastic deformation. PHYSICAL REVIEW LETTERS 2011; 106:106001. [PMID: 21469812 DOI: 10.1103/physrevlett.106.106001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2010] [Indexed: 05/30/2023]
Abstract
We address the long-standing problem of the origin of acoustic emission commonly observed during plastic deformation. We propose a framework to deal with the widely separated time scales of collective dislocation dynamics and elastic degrees of freedom to explain the nature of acoustic emission observed during the Portevin-Le Chatelier effect. The Ananthakrishna model is used as it explains most generic features of the phenomenon. Our results show that while acoustic emission bursts correlated with stress drops are well separated for the type C serrations, these bursts merge to form nearly continuous acoustic signals with overriding bursts for the propagating type A bands.
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Affiliation(s)
- Jagadish Kumar
- Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
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Zapperi S, Vespignani A, Stanley H. Modeling Acoustic Emission In Microfracturing Phenomena. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-409-355] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
AbstractIt has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to clarify the nature of this phenomenon. We model the synthetic material by an array of resistors with random failure thresholds. The failure of a resistor produces an decrease in the conductivity and a redistribution of the disorder. By increasing the applied voltage the system organizes itself in a stationary state. The acoustic emission signal is associated with the failure events. We find scaling behavior in the amplitude of these events and in the times between different events. The model allows us to study the geometrical and topological properties of the micro-fracturing process that drives the system to the self-organized stationary state.
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35
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Yoshioka N, Kun F, Ito N. Kertész line of thermally activated breakdown phenomena. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:055102. [PMID: 21230533 DOI: 10.1103/physreve.82.055102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2010] [Indexed: 05/30/2023]
Abstract
Based on a fiber bundle model we substantially extend the phase-transition analogy of thermally activated breakdown of homogeneous materials. We show that the competition of breaking due to stress enhancement and due to thermal fluctuations leads to an astonishing complexity of the phase space of the system: varying the load and the temperature a phase boundary emerges, separating a Griffith-type regime of abrupt failure analogous to first-order phase transitions from disorder dominated fracture where a spanning cluster of cracks emerges. We demonstrate that the phase boundary is the Kertész line of the system along which thermally activated fracture appears as a continuous phase transition analogous to percolation. The Kertész line has technological relevance setting the boundary of safe operation for construction components under high thermal loads.
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Affiliation(s)
- Naoki Yoshioka
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, 606-8502 Kyoto, Japan
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36
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Ai Q, Liu CX, Chen XR, He P, Wang Y. Acoustic emission of fatigue crack in pressure pipe under cyclic pressure. NUCLEAR ENGINEERING AND DESIGN 2010. [DOI: 10.1016/j.nucengdes.2010.05.022] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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37
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Pugno N, Bosia F. Scaling properties of nanotube-based macroscopic cables through multiscale numerical simulations. IEEE NANOTECHNOLOGY MAGAZINE 2009. [DOI: 10.1109/mnano.2009.934863] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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38
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Hidalgo RC, Kun F, Kovács K, Pagonabarraga I. Avalanche dynamics of fiber bundle models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051108. [PMID: 20364948 DOI: 10.1103/physreve.80.051108] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2009] [Indexed: 05/29/2023]
Abstract
We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model (CDFBM). Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models.
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Affiliation(s)
- R C Hidalgo
- AMADE, Departament de Física, Universitat de Girona, 17071 Girona, Spain
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39
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Pradhan S, Hemmer PC. Breaking-rate minimum predicts the collapse point of overloaded materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041148. [PMID: 19518214 DOI: 10.1103/physreve.79.041148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2009] [Indexed: 05/27/2023]
Abstract
As a model of composite materials, we choose a bundle of fibers with stochastically distributed breaking thresholds for the individual fibers. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We study the evolution of the fiber breaking rate at a constant load in excess of the critical load. The analysis shows that the breaking rate reaches a minimum when the system is half-way from its complete collapse.
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40
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Kumar J, De R, Ananthakrishna G. Intermittent peel front dynamics and the crackling noise in an adhesive tape. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066119. [PMID: 19256917 DOI: 10.1103/physreve.78.066119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2008] [Indexed: 05/27/2023]
Abstract
We report a comprehensive investigation of a model for peeling of an adhesive tape along with a nonlinear time series analysis of experimental acoustic emission signals in an effort to understand the origin of intermittent peeling of an adhesive tape and its connection to acoustic emission. The model represents the acoustic energy dissipated in terms of Rayleigh dissipation functional that depends on the local strain rate. We show that the nature of the peel front exhibits rich spatiotemporal patterns ranging from smooth, rugged, and stuck-peeled configurations that depend on three parameters, namely the ratio of inertial time scale of the tape mass to that of the roller, the dissipation coefficient, and the pull velocity. The stuck-peeled configurations are reminiscent of fibrillar peel front patterns observed in experiments. We show that while the intermittent peeling is controlled by the peel force function, the model acoustic energy dissipated depends on the nature of the peel front and its dynamical evolution. Even though the acoustic energy is a fully dynamical quantity, it can be quite noisy for a certain set of parameter values, suggesting the deterministic origin of acoustic emission in experiments. To verify this suggestion, we have carried out a dynamical analysis of experimental acoustic emission time series for a wide range of traction velocities. Our analysis shows an unambiguous presence of chaotic dynamics within a subinterval of pull speeds within the intermittent regime. Time-series analysis of the model acoustic energy signals is also found to be chaotic within a subinterval of pull speeds. Further, the model provides insight into several statistical and dynamical features of the experimental acoustic emission signals including the transition from burst-type acoustic emission to continuous-type with increasing pull velocity and the connection between acoustic emission and stick-slip dynamics. Finally, the model also offers an explanation for the recently observed feature that the duration of the slip phase can be less than that of the stick phase.
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Affiliation(s)
- Jagadish Kumar
- Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
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41
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Pugno N, Bosia F, Gliozzi AS, Delsanto PP, Carpinteri A. Phenomenological approach to mechanical damage growth analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:046103. [PMID: 18999489 DOI: 10.1103/physreve.78.046103] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2008] [Revised: 06/16/2008] [Indexed: 05/27/2023]
Abstract
The problem of characterizing damage evolution in a generic material is addressed with the aim of tracing it back to existing growth models in other fields of research. Based on energetic considerations, a system evolution equation is derived for a generic damage indicator describing a material system subjected to an increasing external stress. The latter is found to fit into the framework of a recently developed phenomenological universality (PUN) approach and, more specifically, the so-called U2 class. Analytical results are confirmed by numerical simulations based on a fiber-bundle model and statistically assigned local strengths at the microscale. The fits with numerical data prove, with an excellent degree of reliability, that the typical evolution of the damage indicator belongs to the aforementioned PUN class. Applications of this result are briefly discussed and suggested.
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Affiliation(s)
- Nicola Pugno
- Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
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42
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Bonamy D, Santucci S, Ponson L. Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition. PHYSICAL REVIEW LETTERS 2008; 101:045501. [PMID: 18764338 DOI: 10.1103/physrevlett.101.045501] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2008] [Indexed: 05/26/2023]
Abstract
We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation of a crack along a weak heterogeneous plane of a transparent Plexiglas block [K. J. Måløy et al., Phys. Rev. Lett. 96, 045501 (2006)10.1103/PhysRevLett.96.045501]. In this description, the quasistatic failure of heterogeneous media appears as a self-organized critical phase transition. As such, it exhibits universal and to some extent predictable scaling laws, analogous to that of other systems such as, for example, magnetization noise in ferromagnets.
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Affiliation(s)
- D Bonamy
- IRAMIS, SPCSI, Group Complex Systems and Fracture, CEA, F-91191 Gif sur Yvette, France.
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43
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Kumar J, Ciccotti M, Ananthakrishna G. Hidden order in crackling noise during peeling of an adhesive tape. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:045202. [PMID: 18517680 DOI: 10.1103/physreve.77.045202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2007] [Indexed: 05/26/2023]
Abstract
We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.
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Affiliation(s)
- Jagadish Kumar
- Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
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44
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Picallo CB, López JM. Energy dissipation statistics in the random fuse model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:046114. [PMID: 18517697 DOI: 10.1103/physreve.77.046114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2007] [Revised: 02/19/2008] [Indexed: 05/26/2023]
Abstract
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the dissipated energy. In the case of an infinitely slow driving rate (quasistatic model), we find that the probability distribution of the released energy shows two different scaling regions separated by a sharp energy crossover. At low energies, the probability of having an event of energy E decays as approximately E(-1/2), which is robust and independent of the energy quantifier used (or lattice type). At high energies, fluctuations dominate the energy distribution, leading to a crossover to a different scaling regime, approximately E(-2.75), whenever the released energy is computed over the whole system. On the contrary, strong finite-size effects are observed if we consider only the energy dissipated at microfractures. In a different numerical experiment, the quasistatic dynamics condition is relaxed, so that the system is driven at finite strain load rates, and we find that the energy distribution decays as P(E) approximately E(-1) for all the energy range.
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Affiliation(s)
- Clara B Picallo
- Instituto de Física de Cantabria (IFCA), CSIC-UC, E-39005 Santander, Spain.
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45
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Kovács K, Nagy S, Hidalgo RC, Kun F, Herrmann HJ, Pagonabarraga I. Critical ruptures in a bundle of slowly relaxing fibers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036102. [PMID: 18517456 DOI: 10.1103/physreve.77.036102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2007] [Revised: 01/17/2008] [Indexed: 05/26/2023]
Abstract
We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime t(f) of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life t(f) and the characteristic time t(m) of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of t(f) from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements.
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Affiliation(s)
- K Kovács
- Department of Theoretical Physics, University of Debrecen, Debrecen, Hungary
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46
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Meinders MBJ, van Vliet T. Scaling of sound emission energy and fracture behavior of cellular solid foods. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036116. [PMID: 18517470 DOI: 10.1103/physreve.77.036116] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2007] [Revised: 12/21/2007] [Indexed: 05/26/2023]
Abstract
A detailed study was performed of the fracture behavior of toasted rusk rolls, a cellular solid food, at different water activities and morphologies. We find that the energies of the emitted sound pulses follow Gutenberg-Richter power laws with characteristic exponents b ~ 1.5 . The scaling exponents varied only within a range of 0.2 when the method of fracture, humidity, or morphology was changed. However, differences in b were observed, indicating nonuniversal behavior, that seems to be related to morphology and water activity. Also, power law scaling behavior was observed for the waiting time distributions with an exponent a ~ 1.9.
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47
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Pradhan S, Hemmer PC. Energy bursts in fiber bundle models of composite materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031138. [PMID: 18517360 DOI: 10.1103/physreve.77.031138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
A bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered as a model of composite materials. The bundle is loaded until complete failure, to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy E is released. The energy distribution follows asymptotically a universal power law E(-5/2) , for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.
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Affiliation(s)
- Srutarshi Pradhan
- Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway and SINTEF Petroleum Research, Trondheim, Norway.
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48
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Papadimitriou C, Kalimeri M, Eftaxias K. Nonextensivity and universality in the earthquake preparation process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036101. [PMID: 18517455 DOI: 10.1103/physreve.77.036101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2007] [Revised: 11/12/2007] [Indexed: 05/26/2023]
Abstract
We suggest that the activation of a single fault by means of preseismic electromagnetic emissions (PEME) is well-described by recently introduced models for earthquake (EQ) dynamics, which have been rooted in a nonextensive framework starting from first principles. The analysis implies that the activation of a single fault is (i) a reduced self-affine image of the regional seismicity covering many geological faults, and (ii) a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we study whether characteristic signatures emerged in PEME indicating the transition to the last phase of the EQ preparation process. We use the q-Tsallis entropy as a measure of organization. Tsallis entropy gives evidence of state changes leading to the point of global instability: it detects the pattern of alterations in the preseismic electromagnetic signals and is able to discriminate between "injury levels" of the focal area. Importantly, a significant organization increase can be confirmed at the tail of the recorded PEME by means of Tsallis entropy, which is also accompanied by the appearance of persistency. We argue that these footprints may indicate the fracture of the backbone of strong entities that hinders the relative motion of the fault planes.
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Affiliation(s)
- C Papadimitriou
- Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, Zografos, Athens, Greece
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49
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Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S. Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale. Science 2007; 318:251-4. [PMID: 17932293 DOI: 10.1126/science.1143719] [Citation(s) in RCA: 447] [Impact Index Per Article: 26.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Ferenc F Csikor
- Department of Materials Physics, Eötvös University, Post Office Box 32, H-1518 Budapest, Hungary
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50
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Raischel F, Kun F, Herrmann HJ. Local load sharing fiber bundles with a lower cutoff of strength disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:035104. [PMID: 17025689 DOI: 10.1103/physreve.74.035104] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2006] [Indexed: 05/12/2023]
Abstract
We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations revealed that at any range of load redistribution there exists a critical cutoff strength where the macroscopic response of the bundle becomes perfectly brittle, i.e., linearly elastic behavior is obtained up to global failure, which occurs catastrophically after the breaking of a small number of fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95, 125501 (2005)], we demonstrate that approaching the critical cutoff, the size distribution of bursts of breaking fibers shows a crossover to a universal power law form with an exponent 3/2 independent of the range of interaction.
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Affiliation(s)
- Frank Raischel
- ICP, University of Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany.
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