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Diksha, Eswar G, Biswas S. Prediction of depinning transitions in interface models using Gini and Kolkata indices. Phys Rev E 2024; 109:044113. [PMID: 38755897 DOI: 10.1103/physreve.109.044113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 03/12/2024] [Indexed: 05/18/2024]
Abstract
The intermittent dynamics of driven interfaces through disordered media and its subsequent depinning for large enough driving force is a common feature for a myriad of diverse systems, starting from mode-I fracture, vortex lines in superconductors, and magnetic domain walls to invading fluid in a porous medium, to name a few. In this work, we outline a framework that can give a precursory signal of the imminent depinning transition by monitoring the variations in sizes or the inequality of the intermittent responses of a system that are seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, i.e., the Gini index and the Kolkata index, for the case of the unequal responses of precritical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale-free size distribution of the responses, we calculate the expressions for these indices, evaluate their crossing points, and give a recipe for forecasting depinning transitions. We apply this method to the Edwards-Wilkinson, Kardar-Parisi-Zhang, and fiber bundle model interface with variable interaction strengths and quenched disorder. The results are applicable for any interface dynamics undergoing a depinning transition. The results also explain previously observed near-universal values of Gini and Kolkata indices in self-organized critical systems.
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Affiliation(s)
- Diksha
- Department of Physics, SRM University - AP, Andhra Pradesh 522240, India
| | - Gunnemeda Eswar
- Department of Physics, SRM University - AP, Andhra Pradesh 522240, India
| | - Soumyajyoti Biswas
- Department of Physics, SRM University - AP, Andhra Pradesh 522240, India
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2
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Mazarei M, Åström J, Westerholm J, Karttunen M. Effect of substrate heterogeneity and topology on epithelial tissue growth dynamics. Phys Rev E 2023; 108:054405. [PMID: 38115499 DOI: 10.1103/physreve.108.054405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 09/20/2023] [Indexed: 12/21/2023]
Abstract
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure of the extracellular matrix and nutrient concentration. We used the CellSim3D model, a kinetic cell division simulator, to investigate the growth kinetics and interface roughness dynamics of epithelial tissue growth on heterogeneous substrates with varying topologies. The results show that the presence of quenched disorder has a clear effect on the colony morphology and the roughness scaling of the interface in the moving interface regime. In a medium with quenched disorder, the tissue interface has a smaller interface roughness exponent, α, and a larger growth exponent, β. The scaling exponents also depend on the topology of the substrate and cannot be categorized by well-known universality classes.
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Affiliation(s)
- Mahmood Mazarei
- Department of Physics and Astronomy, Western University, 1151 Richmond Street, London, Ontario, Canada N6A 3K7
| | - Jan Åström
- CSC Scientific Computing Ltd, Kägelstranden 14, 02150 Esbo, Finland
| | - Jan Westerholm
- Faculty of Science and Engineering, Åbo Akademi University, Vattenborgsvägen 3, FI-20500 Åbo, Finland
| | - Mikko Karttunen
- Department of Physics and Astronomy, Western University, 1151 Richmond Street, London, Ontario, Canada N6A 3K7
- Department of Chemistry, Western University, 1151 Richmond Street, London, Ontario, Canada N6A 5B7
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3
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Valizadeh N, Hamzehpour H, Samadpour M, Najafi MN. Edwards-Wilkinson depinning transition in fractional Brownian motion background. Sci Rep 2023; 13:12300. [PMID: 37516759 PMCID: PMC10387108 DOI: 10.1038/s41598-023-39191-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 07/21/2023] [Indexed: 07/31/2023] Open
Abstract
There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards-Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time [Formula: see text] that separates the dynamics into two distinct regimes: for [Formula: see text], we observe the typical behavior of pinned surfaces, while for [Formula: see text], the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ([Formula: see text]) and correlated ([Formula: see text]) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent [Formula: see text] to increase monotonically with H.
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Affiliation(s)
- N Valizadeh
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - H Hamzehpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran.
| | - M Samadpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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Roy A, Haque RAI, Mitra AJ, Tarafdar S, Dutta T. Combinatorial topology and geometry of fracture networks. Phys Rev E 2022; 105:034801. [PMID: 35428072 DOI: 10.1103/physreve.105.034801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Accepted: 02/21/2022] [Indexed: 06/14/2023]
Abstract
A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.
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Affiliation(s)
- A Roy
- Physics Department, Charuchandra College, Kolkata 700029, India
- Physics Department, St. Xavier's College, Kolkata 700016, India
- Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700032, India
| | - R A I Haque
- Physics Department, St. Xavier's College, Kolkata 700016, India
- Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700032, India
| | - A J Mitra
- Mathematical Sciences, Montana Tech, Butte, Montana 59701, USA
| | - S Tarafdar
- Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700032, India
| | - T Dutta
- Physics Department, St. Xavier's College, Kolkata 700016, India
- Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700032, India
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5
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Alés A, López JM. Roughening of the anharmonic elastic interface in correlated random media. Phys Rev E 2021; 104:044108. [PMID: 34781530 DOI: 10.1103/physreve.104.044108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 09/21/2021] [Indexed: 11/07/2022]
Abstract
We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and Kolton [Phys. Rev. E 99, 032105 (2019)2470-004510.1103/PhysRevE.99.032105], to investigate the effect of higher-order corrections to linear elasticity in the fate of interfaces. We find analytical expressions for the critical exponents as a function of the anharmonicity index n, the noise correlator range θ∈[0,1/2], and dimension d. In d=1 we find that the interface becomes faceted and exhibits anomalous scaling for θ>1/4 for any degree of anharmonicity n>1. Analytical expressions for the anomalous exponents α_{loc} and κ are obtained and compared with a numerical integration of the model. Our theoretical results show that anomalous roughening cannot exist for this model in dimensions d>1.
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Affiliation(s)
- Alejandro Alés
- Instituto de Física de Materiales Tandil, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000 Tandil, Argentina.,Consejo Nacional de Investigaciones Científicas y Técnicas, Godoy Cruz 2290, Buenos Aires, Argentina
| | - Juan M López
- Instituto de Física de Cantabria, CSIC-Universidad de Cantabria, 39005 Santander, Spain
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6
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Dubois A, Bonamy D. Dynamic crack growth along heterogeneous planar interfaces: Interaction with unidimensional strips. Phys Rev E 2021; 103:013004. [PMID: 33601604 DOI: 10.1103/physreve.103.013004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 12/21/2020] [Indexed: 11/07/2022]
Abstract
We examine theoretically and numerically fast propagation of a tensile crack along unidimensional strips with periodically evolving toughness. In such dynamic fracture regimes, crack front waves form and transport front disturbances along the crack edge at speed less than the Rayleigh wave speed and depending on the crack speed. In this configuration, standing front waves dictate the spatiotemporal evolution of the local crack front speed, which takes a specific scaling form. Analytical examination of both the short-time and long-time limits of the problem reveals the parameter dependency with strip wavelength, toughness contrast and overall fracture speed. Implications and generalization to unidimensional strips of arbitrary shape are lastly discussed.
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Affiliation(s)
- Alizée Dubois
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191, Gif-sur-Yvette, France.,ENS Lyon, CNRS, Laboratoire de Physique, UMR 5672, F-69364 Lyon, France
| | - Daniel Bonamy
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191, Gif-sur-Yvette, France
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7
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Effect of Characteristic Time on Scaling of Breakthrough Time Distribution for Two-Phase Displacement in Percolation Porous Media. Transp Porous Media 2019. [DOI: 10.1007/s11242-019-01343-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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8
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Kundu M, Mukherjee S, Biswas S. Record-breaking statistics near second-order phase transitions. Phys Rev E 2018; 98:022103. [PMID: 30253517 DOI: 10.1103/physreve.98.022103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2018] [Indexed: 06/08/2023]
Abstract
When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models near their critical points. Specifically, we choose the transversely driven Edwards-Wilkinson model for interface depinning in (1+1) dimensions and the Ising model in two dimensions, as paradigmatic and simple examples of nonequilibrium and equilibrium critical behaviors, respectively. The total number of record-breaking events in the time series of the order parameters of the models show maxima when the system is near criticality. The number of record-breaking events and associated quantities, such as the distribution of the waiting time between successive record events, show power-law scaling near the critical point. The exponent values are specific to the universality classes of the respective models. Such behaviors near criticality can be used as a precursor to imminent criticality, i.e., abrupt and catastrophic changes in the system. Due to the extreme nature of the records, its measurements are relatively free of detection errors and thus provide a clear signal regarding the state of the system in which they are measured.
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Affiliation(s)
- Mily Kundu
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
| | - Sudip Mukherjee
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
- Barasat Government College, Barasat, Kolkata 700124, India
| | - Soumyajyoti Biswas
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
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9
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Ponson L, Pindra N. Crack propagation through disordered materials as a depinning transition: A critical test of the theory. Phys Rev E 2017; 95:053004. [PMID: 28618481 DOI: 10.1103/physreve.95.053004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Indexed: 11/07/2022]
Abstract
The dynamics of a planar crack propagating within a brittle disordered material is investigated numerically. The fracture front evolution is described as the depinning of an elastic line in a random field of toughness. The relevance of this approach is critically tested through the comparison of the roughness front properties, the statistics of avalanches, and the local crack velocity distribution with experimental results. Our simulations capture the main features of the fracture front evolution as measured experimentally. However, some experimental observations such as the velocity distribution are not consistent with the behavior of an elastic line close to the depinning transition. This discrepancy suggests the presence of another failure mechanism not included in our model of brittle failure.
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Affiliation(s)
- Laurent Ponson
- Institut Jean le Rond d'Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005 Paris, France
| | - Nadjime Pindra
- Institut Jean le Rond d'Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005 Paris, France.,Département de mathématiques, Université de Lomé, 1515 Lomé, Togo
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10
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Vernède S, Ponson L, Bouchaud JP. Turbulent fracture surfaces: a footprint of damage percolation? PHYSICAL REVIEW LETTERS 2015; 114:215501. [PMID: 26066444 DOI: 10.1103/physrevlett.114.215501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2014] [Indexed: 06/04/2023]
Abstract
We show that a length scale ξ can be extracted from the spatial correlations of the "steep cliffs" that appear on a fracture surface. Above ξ, the slope amplitudes are uncorrelated and the fracture surface is monoaffine. Below ξ, long-range spatial correlations lead to a multifractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales larger than ξ, the surface is the trace left by an elastic line propagating in a random medium, while for scales smaller than ξ, the highly correlated patterns on the surface result from the merging of interacting damage cavities.
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Affiliation(s)
| | - Laurent Ponson
- Institut Jean le Rond d'Alembert (UMR 7190), CNRS-Université Pierre et Marie Curie, 75005 Paris, France
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11
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Cambonie T, Bares J, Hattali ML, Bonamy D, Lazarus V, Auradou H. Effect of the porosity on the fracture surface roughness of sintered materials: from anisotropic to isotropic self-affine scaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012406. [PMID: 25679627 DOI: 10.1103/physreve.91.012406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Indexed: 06/04/2023]
Abstract
To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of postmortem fracture surfaces in homemade materials of adjustable microstructure length scale and porosity, obtained by sintering monodisperse polystyrene beads. Beyond the characteristic size of disorder, the roughness profiles are found to exhibit self-affine scaling features evolving with porosity. Starting from a null value and increasing the porosity, we quantitatively modify the self-affine scaling properties from anisotropic (at low porosity) to isotropic (for porosity >10%).
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Affiliation(s)
- T Cambonie
- Université Paris-Sud, CNRS, UMR 7608, Laboratoire FAST, Bat. 502, Campus Université, F-91405 Orsay, France
| | - J Bares
- CEA, IRAMIS, SPEC, SPHYNX Laboratory, F-91191 Gif sur Yvette, France
| | - M L Hattali
- Université Paris-Sud, CNRS, UMR 7608, Laboratoire FAST, Bat. 502, Campus Université, F-91405 Orsay, France
| | - D Bonamy
- CEA, IRAMIS, SPEC, SPHYNX Laboratory, F-91191 Gif sur Yvette, France
| | - V Lazarus
- Université Paris-Sud, CNRS, UMR 7608, Laboratoire FAST, Bat. 502, Campus Université, F-91405 Orsay, France
| | - H Auradou
- Université Paris-Sud, CNRS, UMR 7608, Laboratoire FAST, Bat. 502, Campus Université, F-91405 Orsay, France
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12
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Přemyslovská E, Koňas P. Relation between geometry of fracture surfaces and impact work of wood composite materials. ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS 2014. [DOI: 10.11118/actaun200654020091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
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13
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Mohamed Abdelhaye YO, Chaouche M, Van Damme H. Fracture surfaces of granular pastes. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:128. [PMID: 24241751 DOI: 10.1140/epje/i2013-13128-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Accepted: 10/14/2013] [Indexed: 06/02/2023]
Abstract
Granular pastes are dense dispersions of non-colloidal grains in a simple or a complex fluid. Typical examples are the coating, gluing or sealing mortars used in building applications. We study the cohesive rupture of thick mortar layers in a simple pulling test where the paste is initially confined between two flat surfaces. After hardening, the morphology of the fracture surfaces was investigated, using either the box counting method to analyze fracture profiles perpendicular to the mean fracture plane, or the slit-island method to analyze the islands obtained by cutting the fracture surfaces at different heights, parallel to the mean fracture plane. The fracture surfaces were shown to exhibit scaling properties over several decades. However, contrary to what has been observed in the brittle or ductile fracture of solid materials, the islands were shown to be mass fractals. This was related to the extensive plastic flow involved in the fracture process.
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Affiliation(s)
- Y O Mohamed Abdelhaye
- College of Sciences and Arts, Al Jouf University, P.O. Box 756, Al-Qurayat, Saudi Arabia,
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14
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Barai P, Nukala PKVV, Alava MJ, Zapperi S. Role of the sample thickness in planar crack propagation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042411. [PMID: 24229193 DOI: 10.1103/physreve.88.042411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2013] [Indexed: 06/02/2023]
Abstract
We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.
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Affiliation(s)
- Pallab Barai
- Department of Mechanical Engineering, Texas A & M University, College Station, Texas 77843, USA
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15
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Gjerden KS, Stormo A, Hansen A. Universality classes in constrained crack growth. PHYSICAL REVIEW LETTERS 2013; 111:135502. [PMID: 24116791 DOI: 10.1103/physrevlett.111.135502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2013] [Revised: 07/29/2013] [Indexed: 06/02/2023]
Abstract
Based on an extension of the fiber bundle model we investigate numerically the motion of a crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39±0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion, giving a roughness exponent consistent with 2/3, the gradient percolation value. The length of the crack front is fractal in this regime. Its fractal dimension is 1.77±0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.
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Affiliation(s)
- Knut S Gjerden
- Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
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16
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Padilla L, Mártin HO, Iguain JL. Anisotropic anomalous diffusion modulated by log-periodic oscillations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011106. [PMID: 23005367 DOI: 10.1103/physreve.86.011106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2012] [Indexed: 06/01/2023]
Abstract
We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites where the diffusion of a single random walk presents an anomalous anisotropic behavior modulated by log-periodic oscillations. The anisotropy is revealed by two different random-walk exponents ν(x) and ν(y) in the x and y directions, respectively. The values of these exponents as well as the periods of the oscillations are obtained analytically and confirmed by Monte Carlo simulations.
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Affiliation(s)
- L Padilla
- Instituto de Investigaciones Físicas de Mar del Plata and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, AR-7600 Mar del Plata, Argentina.
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17
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Tallakstad KT, Toussaint R, Santucci S, Schmittbuhl J, Måløy KJ. Local dynamics of a randomly pinned crack front during creep and forced propagation: an experimental study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:046108. [PMID: 21599241 DOI: 10.1103/physreve.83.046108] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Revised: 01/24/2011] [Indexed: 05/30/2023]
Abstract
We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.
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Affiliation(s)
- Ken Tore Tallakstad
- Department of Physics, University of Oslo, PB 1048 Blindern, NO-0316 Oslo, Norway
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18
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Simeone D, Luneville L. Concentration profile distortion under ion beam mixing: an example of Levy flight. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021115. [PMID: 20365538 DOI: 10.1103/physreve.81.021115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2009] [Indexed: 05/29/2023]
Abstract
In order to model the evolution of concentration profiles induced by ion beam mixing in thick layers, Monte Carlo simulations were performed to study in detail the transition probability controlling the evolution of this profile within the binary collision approximation. We demonstrate that this transition probability can be factorized in two distinct functions. The first one can be understood as a scale factor. The second one controls the dynamics of ion beam mixing which can be analyzed as a Levy flight. The power law form of the tail of this function closely linked to the cross section of a collision event is responsible for long tails of concentration profiles. We demonstrate that the Levy flight nature of ion beam mixing induces an enhancement of the evolution of the initial concentration profile.
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Affiliation(s)
- D Simeone
- CEA, DEN, SRMA, LA2M, Equipe Mixte MFE, F-91191 Gif sur Yvette, France.
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19
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Lechenault F, Pallares G, George M, Rountree C, Bouchaud E, Ciccotti M. Effects of finite probe size on self-affine roughness measurements. PHYSICAL REVIEW LETTERS 2010; 104:025502. [PMID: 20366607 DOI: 10.1103/physrevlett.104.025502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2009] [Indexed: 05/29/2023]
Abstract
The roughness of fracture surfaces exhibits self-affinity for a wide variety of materials and loading conditions. The universality and the range of scales over which this regime extends are still debated. The topography of these surfaces is however often investigated with a finite contact probe. In this case, we show that the correlation function of the roughness can only be measured down to a length scale Deltax{c} which depends on the probe size R, the Hurst exponent zeta of the surface and its topothesy l, and exhibits spurious behavior at smaller scales. First, we derive the dependence of Deltax{c} on these parameters from a simple scaling argument. Then, we verify this dependence numerically. Finally, we establish the relevance of this analysis from AFM measurements on an experimental glass fracture surface and provide a metrological procedure for roughness measurements.
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Affiliation(s)
- F Lechenault
- CEA, IRAMIS, SPCSI, Grp. Complex Systems & Fracture, F-91191 Gif Sur Yvette, France.
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Bonamy D, Ponson L, Prades S, Bouchaud E, Guillot C. Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics. PHYSICAL REVIEW LETTERS 2006; 97:135504. [PMID: 17026045 DOI: 10.1103/physrevlett.97.135504] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2006] [Indexed: 05/12/2023]
Abstract
We investigate the scaling properties of postmortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular, a roughness exponent zeta approximately 0.75 in homogeneous glass and zeta approximately 0.4 in glassy ceramics. The ranges of length scales over which these two scalings are observed are shown to be below and above the size of the process zone, respectively. A model derived from linear elastic fracture mechanics in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect the damage screening occurring for length scales below the size of the process zone.
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Affiliation(s)
- D Bonamy
- Service de Physique et Chimie des Surfaces et Interfaces, DSM/DRECAM/SPCSI, CEA Saclay, F-91191 Gif sur Yvette, France
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21
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Ponson L, Auradou H, Vié P, Hulin JP. Low self-affine exponents of fractured glass ceramics surfaces. PHYSICAL REVIEW LETTERS 2006; 97:125501. [PMID: 17025979 DOI: 10.1103/physrevlett.97.125501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2006] [Indexed: 05/12/2023]
Abstract
The geometry of postmortem rough fracture surfaces of porous glass ceramics made of sintered glass beads is shown experimentally to be self-affine with an exponent zeta=0.40+/-0.04, remarkably lower than the "universal" value zeta=0.8 frequently measured for many materials. This low value of zeta is similar to that found for sandstone samples of similar microstructure and is also practically independent on the porosity phi in the range investigated (3%< or =phi< or =26%) as well as on the bead diameter d and of the crack growth velocity. In contrast, the roughness amplitude normalized by d increases linearly with phi while it is still independent, within experimental error, of d and of the crack propagation velocity. An interpretation of this variation is suggested in terms of a transition from transgranular to intergranular fracture propagation with no influence, however, on the exponent zeta.
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Affiliation(s)
- Laurent Ponson
- Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR 7608, Universités Pierre et Marie Curie-Paris 6 et Paris-Sud, Bâtiment 502, Campus Paris Sud, 91405 Orsay Cedex, France.
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22
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Måløy KJ, Santucci S, Schmittbuhl J, Toussaint R. Local waiting time fluctuations along a randomly pinned crack front. PHYSICAL REVIEW LETTERS 2006; 96:045501. [PMID: 16486839 DOI: 10.1103/physrevlett.96.045501] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2005] [Indexed: 05/06/2023]
Abstract
The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, P(v) alpha v-eta with eta=2.55+/-0.15, for velocities v larger than the average front speed <v>. The burst size distribution is also a power law, P(S) alpha S-gamma with gamma=1.7+/-0.1. Above a characteristic length scale of disorder Ld approximately 15 microm, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H=0.66.
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Affiliation(s)
- Knut Jørgen Måløy
- Fysisk Institutt, Universitetet i Oslo, P.O. Boks 1048 Blindern, N-0316 Oslo 3, Norway
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23
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Ponson L, Bonamy D, Bouchaud E. Two-dimensional scaling properties of experimental fracture surfaces. PHYSICAL REVIEW LETTERS 2006; 96:035506. [PMID: 16486727 DOI: 10.1103/physrevlett.96.035506] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/06/2023]
Abstract
The self-affine properties of postmortem fracture surfaces in silica glass and aluminum alloy were investigated through the 2D height-height correlation function. They are observed to exhibit anisotropy. The roughness, dynamic, and growth exponents are determined and shown to be the same for the two materials, irrespective of the crack velocity. These exponents are conjectured to be universal.
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Affiliation(s)
- L Ponson
- Fracture Group, Service de Physique et Chimie des Surfaces et Interfaces, DSM/DRECAM/SPCSI, CEA Saclay, F-91191 Gif sur Yvette, France
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24
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Della Bona A. Characterizing ceramics and the interfacial adhesion to resin: I - The relationship of microstructure, composition, properties and fractography. J Appl Oral Sci 2005; 13:1-9. [DOI: 10.1590/s1678-77572005000100002] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
The appeal of ceramics as structural dental materials is based on their light weight, high hardness values, chemical inertness, and anticipated unique tribological characteristics. A major goal of current ceramic research and development is to produce tough, strong ceramics that can provide reliable performance in dental applications. Quantifying microstructural parameters is important to develop structure/property relationships. Quantitative microstructural analysis provides an association among the constitution, physical properties, and structural characteristics of materials. Structural reliability of dental ceramics is a major factor in the clinical success of ceramic restorations. Complex stress distributions are present in most practical conditions and strength data alone cannot be directly extrapolated to predict structural performance.
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25
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Hinojosa M, González V, Sánchez J, Ortiz U. Scaling properties of the fracture surfaces of a crystalline polymer. POLYMER 2004. [DOI: 10.1016/j.polymer.2004.04.069] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Hansen A, Schmittbuhl J. Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone. PHYSICAL REVIEW LETTERS 2003; 90:045504. [PMID: 12570432 DOI: 10.1103/physrevlett.90.045504] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2002] [Indexed: 05/24/2023]
Abstract
We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.
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Affiliation(s)
- Alex Hansen
- International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília, Distrito Federal, Brazil
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27
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Lapique F, Meakin P, Feder J, Jøssang T. Self-affine fractal scaling in fracture surfaces generated in ethylene and propylene polymers and copolymers. J Appl Polym Sci 2002. [DOI: 10.1002/app.11081] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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28
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Szabó G, Alava M, Kertész J. Shortest paths and load scaling in scale-free trees. ACTA ACUST UNITED AC 2002; 66:026101. [PMID: 12241231 DOI: 10.1103/physreve.66.026101] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2002] [Revised: 05/08/2002] [Indexed: 11/07/2022]
Abstract
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.
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Affiliation(s)
- Gábor Szabó
- Helsinki University of Technology, Laboratory of Physics, P.O. Box 1100, FIN-02015 HUT, Finland
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29
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Balankin AS, Susarrey O, Bravo A. Self-affine nature of the stress-strain behavior of thin fiber networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066131. [PMID: 11736260 DOI: 10.1103/physreve.64.066131] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2001] [Indexed: 05/23/2023]
Abstract
The stress-strain behavior of toilet paper is studied. We find that the damaged parts of stress-strain curves possess a self-affine scaling invariance. Moreover, we find that the stress-strain behavior and the rupture line roughness are characterized by the same scaling (Hurst) exponent H, which is not universal: rather it changes from sample to sample. The variations on H are mainly due to fluctuations in the paper structure, which are larger than statistical errors within a sample. Furthermore, the same exponent governs the changes in the stress-strain curve as the strain rate increases. The fractal damage model is employed to explain experimental observations.
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Affiliation(s)
- A S Balankin
- SEPI-ESIME, Edificio 5, 3er Piso, Instituto Politécnico Nacional, Mexico, Distrito Federal 07738, Mexico.
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30
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Måløy KJ, Schmittbuhl J. Dynamical event during slow crack propagation. PHYSICAL REVIEW LETTERS 2001; 87:105502. [PMID: 11531484 DOI: 10.1103/physrevlett.87.105502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2001] [Indexed: 05/23/2023]
Abstract
We address the role of material heterogeneities on the propagation of a slow rupture at laboratory scale. With a high speed camera, we follow an in-plane crack front during its propagation through a transparent heterogeneous Plexiglas block. We obtain two major results. First, the slip along the interface is strongly correlated over scales much larger than the asperity sizes. Second, the dynamics is scale dependent. Locally, mechanical instabilities are triggered during asperity depinning and propagate along the front. The intermittent behavior at the asperity scale is in contrast with the large scale smooth creeping evolution of the average crack position. The dynamics is described on the basis of a Family-Vicsek scaling.
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Affiliation(s)
- K J Måløy
- Fysisk Institutt, Universitetet i Oslo, P.O. Boks 1048 Blindern, N-0316 Oslo 3, Norway
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31
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Sharon E, Cohen G, Fineberg J. Propagating solitary waves along a rapidly moving crack front. Nature 2001; 410:68-71. [PMID: 11242041 DOI: 10.1038/35065051] [Citation(s) in RCA: 80] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A rapidly moving crack in a brittle material is often idealized as a one-dimensional object with a singular tip, moving through a two-dimensional material. However, in real three-dimensional materials, tensile cracks form a planar surface whose edge is a rapidly moving one-dimensional singular front. The dynamics of these fronts under repetitive interaction with material inhomogeneities (asperities) and the morphology of the fracture surface that they create are not yet understood. Here we show that perturbations to a crack front in a brittle material result in long-lived and highly localized waves, which we call 'front waves' These waves exhibit a unique characteristic shape and propagate along the crack front at approximately the Rayleigh wave speed (the speed of sound along a free surface). Following interaction, counter-propagating front waves retain both their shape and amplitude. They create characteristic traces along the fracture surface, providing cracks with both inertia and a new mode of dissipation. Front waves are intrinsically three-dimensional, and cannot exist in conventional two-dimensional theories of fracture. Because front waves can transport and distribute asperity-induced energy fluctuations throughout the crack front, they may help to explain how cracks remain a single coherent entity, despite repeated interactions with randomly dispersed asperities.
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Affiliation(s)
- E Sharon
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram, Israel
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32
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Lahiri R, Barma M, Ramaswamy S. Strong phase separation in a model of sedimenting lattices. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:1648-1658. [PMID: 11046448 DOI: 10.1103/physreve.61.1648] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/1999] [Indexed: 05/23/2023]
Abstract
We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.
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Affiliation(s)
- R Lahiri
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
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33
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Delaplace A, Schmittbuhl J, Måløy KJ. High resolution description of a crack front in a heterogeneous Plexiglas block. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1337-43. [PMID: 11969893 DOI: 10.1103/physreve.60.1337] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/1999] [Indexed: 11/07/2022]
Abstract
We study experimentally the propagation of an in-plane fracture into a transparent and heterogeneous Plexiglas block. A stable crack propagation in mode I is monitored by an imposed displacement. The experimental setup allows a high resolution observation of the crack front in situ. Self-affine properties of the crack front are described over more than three decades using several techniques: variable bandwidth, return probability, Fourier spectrum, and wavelet analysis. The different methods lead to a roughness exponent of 0.63+/-0.03, consistent with a previous work.
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Affiliation(s)
- A Delaplace
- Fysisk Institutt, Universitetet i Oslo, P.O. Boks 1048 Blindern, 0316 Oslo 3, Norway
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34
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Daguier P, Henaux S, Bouchaud E, Creuzet F. Quantitative analysis of a fracture surface by atomic force microscopy. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:5637-5642. [PMID: 9964920 DOI: 10.1103/physreve.53.5637] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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36
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Plouraboué F, Winkler KW, Petitjean L, Hulin JP, Roux S. Experimental study of fracture surface roughness on rocks with crack velocity. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:277-283. [PMID: 9964257 DOI: 10.1103/physreve.53.277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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37
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Nakano A, Kalia RK, Vashishta P. Dynamics and morphology of brittle cracks: A molecular-dynamics study of silicon nitride. PHYSICAL REVIEW LETTERS 1995; 75:3138-3141. [PMID: 10059504 DOI: 10.1103/physrevlett.75.3138] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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38
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Schmittbuhl J, Roux S, Vilotte JP. Interfacial crack pinning: Effect of nonlocal interactions. PHYSICAL REVIEW LETTERS 1995; 74:1787-1790. [PMID: 10057757 DOI: 10.1103/physrevlett.74.1787] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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39
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Bouchaud E, Bouchaud J. Fracture surfaces: Apparent roughness, relevant length scales, and fracture toughness. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:17752-17755. [PMID: 9976208 DOI: 10.1103/physrevb.50.17752] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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40
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Nakano A, Kalia RK, Vashishta P. Growth of pore interfaces and roughness of fracture surfaces in porous silica: Million particle molecular-dynamics simulations. PHYSICAL REVIEW LETTERS 1994; 73:2336-2339. [PMID: 10057034 DOI: 10.1103/physrevlett.73.2336] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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