Crack Roughness in the 2D Random Threshold Beam Model

TL;DR

This study investigates the scaling behavior of two-dimensional crack roughness using beam lattice models, revealing non-anomalous scaling and Gaussian height difference distributions after removing overhangs.

Contribution

It demonstrates that beam lattice models do not exhibit anomalous scaling and that removing overhangs aligns local and global roughness exponents, clarifying previous discrepancies.

Findings

Crack roughness exponent estimated at 0.64 ± 0.02.

Removing overhangs eliminates multiscaling.

Height difference distribution is Gaussian after overhang removal.

Abstract

We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents ($\zeta_{loc}$ and $\zeta$, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be $\zeta_{loc} = \zeta = 0.64 \pm 0.02$. Removal of overhangs (jumps) in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution $p(\Delta h(\ell))$ of the height differences $\Delta h(\ell) = [h(x+\ell) - h(x)]$ of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes ($\ell$).