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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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2007, 75 (1), pp.016104. 〈10.1103/PhysRevE.75.016104〉
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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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