Statistics of fracture surfaces

We analyze 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 monoaffine, 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 monoaffine behavior. We discuss for the latter, the relevance of a multiaffine analysis and the influences of the discreteness resulting from material microstructures or experimental sampling.