# Statistics of Fracture Surfaces

Abstract : We analyse the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the distribution to an analysis based on the structure functions. For length scales $\delta$ larger than a characteristic scale $\Lambda$ that corresponds to a material heterogeneity size, we find that the distribution of the height increments $\Delta h = h(x+ \delta) -h(x)$ is Gaussian and mono-affine, {\it i.e.} the scaling of the standard deviation $\sigma$ is proportional to $\delta^\zeta$ with a unique roughness exponent. Below the scale $\Lambda$ we observe a deviation from a Gaussian distribution and a mono-affine behavior. We discuss for the latter, the relevance of a multi-affine analysis and the influences of the discreteness resulting from material micro-structures or experimental sampling.
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Cited literature [20 references]

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00156943
Contributor : Loïc Vanel <>
Submitted on : Sunday, June 24, 2007 - 5:45:43 PM
Last modification on : Tuesday, February 23, 2021 - 7:24:05 PM
Long-term archiving on: : Thursday, April 8, 2010 - 9:24:47 PM

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### Citation

Stéphane Santucci, Knut Jørgen Måløy, Arnaud Delaplace, Joachim Mathiesen, Alex Hansen, et al.. Statistics of Fracture Surfaces. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2007, 75 (1), pp.016104. ⟨10.1103/PhysRevE.75.016104⟩. ⟨ensl-00156943⟩

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