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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