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Gaussian Statistics of Fracture Surfaces

Stéphane Santucci·Joachim Mathiesen·Knut Jørgen Måløy·Alex Hansen·Jean Schmittbuhl·Loic Vanel·Arnaud Delaplace·Jan Øistein Haavig Bakke·Purusattam Ray
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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 a new analysis based on the structure functions. For length scales $δ$ larger than a characteristic scale $δ^*$, we find that the distribution of the height increments $Δh = h(x+ δ) -h(x)$ is Gaussian. Self-affinity enters through the scaling of the standard deviation $σ$, which is proportional to $δ^ζ$ with a unique roughness exponent. Below the scale $δ^*$ we observe an effective multi-affine behavior of the height fluctuations and a deviation from a Gaussian distribution which is related to the discreteness of the measurement or of the material.

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Stéphane Santucci, Joachim Mathiesen, Knut Jørgen Måløy, Alex Hansen, Jean Schmittbuhl, Loic Vanel, Arnaud Delaplace, Jan Øistein Haavig Bakke, Purusattam Ray. 2006-07-14. Gaussian Statistics of Fracture Surfaces. https://doi.org/10.1103/physreve.75.016104

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