Effect of Disorder and Notches on Crack Roughness

TL;DR

This study investigates how disorder and notches influence crack surface roughness in two-dimensional materials, revealing universal local roughness and independence from initial conditions or material disorder.

Contribution

It demonstrates that both local and global crack roughness exponents are universal and unaffected by initial notches or material disorder in 2D crack simulations.

Findings

Local roughness exponent ζ_loc = 0.71 is universal.

Global roughness exponent ζ = 0.87 is independent of disorder.

Crack profile fluctuations follow a Gaussian distribution.

Abstract

We analyze the effect of disorder and notches on crack roughness in two dimensions. Our simulation results based on large system sizes and extensive statistical sampling indicate that the crack surface exhibits a universal local roughness of $\zeta_{loc} = 0.71$ and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as $\zeta = 0.87$ and is also independent of material disorder. Furthermore, we note that the statistical distribution of crack profile height fluctuations is also independent of material disorder and is described by a Gaussian distribution, albeit deviations are observed in the tails.