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 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.

Failure of heterogeneous materials: A dynamic phase transition?

“…This result strongly suggests the universality of the structure function, and, as we will see in Section 6, the relevance of models of elastic lines pulled through randomly distributed obstacles. This universality was however questioned recently by Bouchbinder and coworkers [91], who proposed that the anisotropy evidenced by Ponson et al [52] is entirely due to the breaking of isotropy by the initial conditions (long notch, or precrack). Their analysis, which mixes the parallel and perpendicular scaling regimes and exponents, results quite naturally in measuring nonuniversal apparent exponents.…”

Roughness exponent measurements for the central force model

“…18 Three-dimensional fracture surfaces with anisotropic roughness exponents have also been studied. 19,20 For twodimensional fracture profiles there is an ongoing controversy whether they show self-affine scaling or multiaffine scaling. 21,22 Also the previous universal value of 2D = 0.7 is questioned.…”

Why Does Theoretical Physics Fail to Explain and Predict Earthquake Occurrence?

“…In laboratory experiments, a crack d e v elops instabilities which make its path and propagation velocity highly chaotic and unpredictable (Marder, 1998Sharon and Fineberg, 1999Bouchbinder et al, 2005. These instabilities and a sensitive dependence on the initial conditions are due to crack propagation, especially at a speed close to the elastic wave v elocity.…”