Intrinsic nature of anomalous crack roughening in an anisotropic brittle composite

Crack traces in paper sheets obey different scaling behaviours, according to whether a crack grows along or across the machine direction of the paper. Cracks across the machine direction possess statistical self-affine invariance, governed by the local roughness (Hurst) exponent H < 1, whereas cracks growing along the machine direction display an anomalous roughening, characterized by different roughness exponents in the local and global scales. Although the local roughness exponent H does not depend on the crack orientation in a given paper, both the local (H < 1) and global (α > H) exponents are dependent on the material structure. The cause of anomalous roughening is the intrinsically anomalous power spectrum (structure factor) of cracks growing along the fibres. A diffusion model of brittle crack growth in an anisotropic composite is developed.