Disentangling scaling properties in anisotropic fracture

Structure functions of rough fracture surfaces in isotropic materials exhibit complicated scaling properties due to the broken isotropy in the fracture plane generated by a preferred propagation direction. Decomposing the structure functions into the even order irreducible representations of the SO(2) symmetry group indexed by (m = 0, 2, 4, . . .) results in a lucid and quickly convergent description. The scaling exponent of the isotropic sector (m = 0) dominates at small length scales. One can reconstruct the anisotropic structure functions using only the isotropic and the first nonvanishing anisotropic sector (m = 2) [or at most the next one (m = 4)]. The scaling exponent of the isotropic sector should be observed in a proposed, yet unperformed, experiment.