Gaussian Statistics of Fracture Surfaces

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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 δζ 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.