Disentangling Scaling Properties in Anisotropic Fracture

TL;DR

This paper analyzes the complex scaling behaviors of anisotropic fracture surfaces by decomposing structure functions into symmetry-based sectors, revealing dominant isotropic scaling and proposing an experiment to observe these effects.

Contribution

It introduces a symmetry-based decomposition of fracture surface structure functions, simplifying the analysis of anisotropic scaling properties and highlighting the dominant isotropic sector.

Findings

Dominant isotropic scaling exponent at small scales

Anisotropic structure functions can be reconstructed from the first few sectors

Proposes an experiment to measure the isotropic scaling exponent

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.