Statistics of Fracture Surfaces

Stéphane Santucci 1 Knut Jørgen Måløy 1 Arnaud Delaplace 1 Joachim Mathiesen 2 Alex Hansen 2 Jan Øistein Haavig Bakke 2 Jean Schmittbuhl 3 Loïc Vanel 4 Purusattam Ray 5
1 Department of Physics [Oslo]
2 Department of Physics [Trondheim]
3 IPGS - Institut de physique du globe de Strasbourg
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
5 IMSc - Institute of Mathematical Sciences [Chennai]
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.
Keywords : Fracture Roughness Statistical analysis
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Journal articles
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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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