Anomalous roughening of wood fractured surfaces

Morel, Stéphane; Schmittbuhl, Jean; López, Juan M.; Valentin, G.

doi:10.1103/physreve.58.6999

Cited by 92 publications

(112 citation statements)

References 30 publications

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“…For mortar, the geometry can be considered as self-affine only up to length scales of the order of 15 % of the specimen width W [18]. A systematic study of wood samples with various values of W leads to ξ = 0.1 W [17]. Figure 6 displays the variations of the correlation function ∆h(δz) as a function of δz for samples of different widths W .…”

Section: Dependence Of the Statistical Properties On The Sample Widthmentioning

confidence: 99%

“…In the transient propagation region of fractures initiated from a straight notch, the amplitude of the roughness is observed to depend at all length scales on the distance to the initiation [16,17,18]. This variation may be described by a so called anomalous scaling law involving a new exponent ζ global > ζ referred as the global roughness exponent.…”

Section: Introductionmentioning

confidence: 99%

“…While most studies dedicated to the roughness of cracks dealt with surfaces with ζ ≃ 0.8 [5,6,7,8,9,10,16,17,18,19], the present work investigates these problems through an extensive analysis of the statistical properties of the roughness of fractured Fontainebleau sandstone for which ζ ≃ 0.4 − 0.5.…”

Section: Introductionmentioning

confidence: 99%

“…This variation may be described by a so called anomalous scaling law involving a new exponent ζ global > ζ referred as the global roughness exponent. A consequence of anomalous scaling is expected in regions far from the initiation and where the roughness is fully developed [17,20]: The roughness amplitude in a window of size δz normal to the crack propagation would then scale with the width W of the fracture surface as:…”

Section: Introductionmentioning

confidence: 99%

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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: Dependence Of the Statistical Properties On The Sample Widthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

et al. 2007

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“…Recent experiments 43,44 have shown that fracture surfaces could be affected by anomalous scaling. This in turn has been interpreted 45 as the mark of the anisotropy of the roughness exponent measured at large lenght scales.…”

Section: Discussionmentioning

confidence: 99%

Relation between driving energy, crack shape, and speed in brittle dynamic fracture

Parisi

Ball

2005

Phys. Rev. B

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We report results on the interrelation between driving force, roughness exponent, branching and crack speed in a finite element model. We show that for low applied loadings the crack speed reaches the values measured in the experiments, and the crack surface roughness is compatible with logarithmic scaling. At higher loadings, the crack speed increases, and the crack roughness exponent approaches the value measured at short length scales in experiments. In the case of high anisotropy, the crack speed is fully compatible with the values measured in experiments on anisotropic materials, and we are able to interpret explicitly the results in terms of the efficiency function introduced by us in our previous work [A. Parisi and R. C. Ball, Phys. Rev. B 66(16) 165432 (2002)]. The mechanism which leads to the decrease of crack speed and the appearence of the logarithmic scaling is attempted branching, whilst power law roughness develops when branches succeed in growing to macroscopic size.

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Heterogeneous Materials

2003

Interdisciplinary Applied Mathematics

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Mechanics and Materials R.V. KohnSystems and Control S.S. Sastry, P.S. Krishnaprasad Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics.The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, and well as point towards new and innovative areas of applications; and, secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself.The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.

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Anomalous roughening of wood fractured surfaces

Cited by 92 publications

References 30 publications

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Relation between driving energy, crack shape, and speed in brittle dynamic fracture

Heterogeneous Materials

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