Fracture Roughness and Correlation Length in the Central Force Model

TL;DR

This study measures the roughness and correlation length exponents in a 2D central force model, supporting the idea that fracture roughness is governed by stress-weighted percolation, with no evidence of anomalous scaling.

Contribution

It provides the first detailed measurement of roughness and correlation length exponents in the 2D central force model, confirming theoretical predictions.

Findings

Roughness exponent zeta = 0.75 ± 0.03

Correlation length exponent nu = 1.7 ± 0.3

No sign of anomalous scaling

Abstract

We measure the roughness exponent and the correlation length exponent of a stress-weighted percolation process in the central force model in 2D. The roughness exponent is found to be zeta = 0.75 \pm 0.03 and the correlation length exponent is found to be nu = 1.7 \pm 0.3. This result supports a conjecture that the fracture roughness for large scales is controlled by a stress weighted percolation process, and the fracture roughness can by calculated from the correlation length exponent by zeta = 2*nu/(1+2*nu). We also compare global and local measurements of the fracture roughness and do not find sign of anomalous scaling in the central force model.