Fracture Surfaces as Multiscaling Graphs

Bouchbinder, Eran; Procaccia, Itamar; Santucci, Stéphane; Vanel, Loïc

doi:10.1103/physrevlett.96.055509

Cited by 52 publications

(57 citation statements)

References 22 publications

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“…In this range of δz values, it would be possible to rescale all the moments (h(z + δz) − h(z)) p 1/p by using several exponents ζ p (not shown here): The relevance of such a multiscaling description at length scales for which the geometry of a single grain has a predominant effect is however questionable. These results bring new insight to a recently debated question concerning crack lines resulting from the rupture of paper sheets that were found to exhibit multiscaling [23], at least at small scales, i.e. at length scales comparable with the length of the fibers of the paper.…”

Section: B Statistical Distribution Of the Fluctuations Of Heightmentioning

confidence: 96%

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

et al. 2007

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In an effort to investigate the link between failure mechanisms and the geometry of fractures of compacted grains materials, a detailed statistical analysis of the surfaces of fractured Fontainebleau sandstones has been achieved. The roughness of samples of different widths W is shown to be self affine with an exponent ζ = 0.46 ± 0.05 over a range of length scales ranging from the grain size d up to an upper cut-off length ξ ≃ 0.15W . This low ζ value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions π δz (δh) of the variations of height over different distances δz > d can be collapsed onto a single Gaussian distribution with a suitable normalisation and do not display multifractal features. The roughness amplitude, as characterized by the height−height correlation over fixed distances δz, does not depend on the sample width, implying that no anomalous scaling of the type reported for other materials is present. It is suggested, in agreement with recent theoretical work, to explain these results by the occurence of brittle fracture (instead of damage failure in materials displaying a higher value of ζ ≃ 0.8).

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Section: B Statistical Distribution Of the Fluctuations Of Heightmentioning

confidence: 96%

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

et al. 2007

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“…II we show that the statistical properties of rupture lines cannot be fully characterized by the scaling invariance of Eq. (16). In that case, the more complex structure of the probability distribution function leads to multiscaling in contrast with monoscaling implied by Eq.…”

Section: Figmentioning

confidence: 75%

“…In a recent work [16] we have shown that the phenomenology is much richer and fracture lines are multiscaling. An example that provides us with information of sufficient accuracy to establish the multiscaling characteristics is rupture lines in paper.…”

Section: Multiscaling In 1+1 Dimensional Fracturementioning

confidence: 99%

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Statistical Physics of Fracture Surfaces Morphology

2006

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Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.It is a privilege to dedicate this paper to Pierre Hohenberg and Jim Langer who contributed, respectively, decisive ideas to scaling concepts in statistical physics and to the study of fracture. It is our hope that the marriage of these two issues in the present paper may give them some degree of pleasure.

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“…To quantify the fluctuations in the crack morphology as a function of the sample thickness, we follow the multiscaling analysis commonly employed to study fracture fronts [27,[38][39][40] and compute the q moments of the correlation function,…”

Section: Crack Front Roughness and Avalanchesmentioning

confidence: 99%

Role of the sample thickness in planar crack propagation

et al. 2013

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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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Fracture Surfaces as Multiscaling Graphs

Cited by 52 publications

References 22 publications

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Statistical Physics of Fracture Surfaces Morphology

Role of the sample thickness in planar crack propagation

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