Disentangling Scaling Properties in Anisotropic Fracture

Abstract

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 non vanishing 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.