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Ponson L, Shabir Z, Abdulmajid M, Van der Giessen E, Simone A. Unified scenario for the morphology of crack paths in two-dimensional disordered solids. Phys Rev E 2021; 104:055003. [PMID: 34942738 DOI: 10.1103/physreve.104.055003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Accepted: 08/05/2021] [Indexed: 11/07/2022]
Abstract
A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.
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Affiliation(s)
- L Ponson
- Institut Jean Le Rond d'Alembert, CNRS - Sorbonne Université, 75005 Paris, France
| | - Z Shabir
- Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CN Delft, the Netherlands
| | - M Abdulmajid
- Institut Jean Le Rond d'Alembert, CNRS - Sorbonne Université, 75005 Paris, France
| | - E Van der Giessen
- Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, the Netherlands
| | - A Simone
- Department of Industrial Engineering, University of Padova, 35131 Padua, Italy
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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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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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