Roughness exponent measurements for the central force model

Abstract

We measure the roughness exponent for fracture profiles in the two-dimensional central force lattice model using different measurement methods. We find that the profiles are self-affine for a system with narrow disorders and that broader disorders introduces overhangs in the fracture surface leading to deviation from self-affinity for small length scales and to nontrivial finite size scaling.

Effect of disorder strength on the fracture pattern in heterogeneous networks

“…3 The value of based on the backbone roughness almost coincides with that following from random percolation in a gradient ͑ =8/11=0.73͒. 15 Our results for corresponding to the burning method agree very well with the results of another recent simulation of central-force lattices ͑ = 0.75± 0.03͒, with even stronger disorder ͑␣ = 0.95͒, 31 although there a different assumption has been made about the scaling of the correlation length.…”

“…As explained in our previous paper, 18 the crack path can be defined in at least three ways: averaging, in the direction of load, of the biggest cluster, or identifying the backbone of the biggest cluster by means of the "burning" algorithm, 30 or using the so-called "solid-on-solid approximation." 31 In the latter method, one defines the border of intact material touching the biggest cluster from each side. To avoid artifacts, we consider these methods only above length scales larger than the typical damage width.…”

Anomalous roughness of fracture surfaces in 2D fuse models

“…Anomalous scaling has been noted in the 3D numerical simulations as well (Nukala et al 2006). The origins of anomalous scaling of fracture surfaces is not yet clear although recent studies (Alava et al 2006a, b;Bakke et al 2007;Santucci et al 2007) suggest that the origin of multiscaling and anomalous scaling in numerical simulations may be due to the existence of overhangs (jumps) in the crack profile.…”

“…This should then imply a constant scaling exponent ζ loc such that the q-th order correlation function C q ( ) = |h(x + ) − h(x)| q 1/q ∼ ζ loc . It should be noted that Gaussian distribution for p( h( )) has been noted in (Alava et al 2006a, b;Bakke et al 2007;Santucci et al 2007;Salminen et al 2003) only above a characteristic scale where self-affine scaling of crack surfaces is observed. In this study, we would like to further investigate whether removing these jumps in the crack profiles extends the validity of Gaussian probability density distribution p( h( )) of the height differences h( ) = [h(x + )−h(x)] of the crack profile to even smaller window sizes .…”

“…Recent studies have debated the picture of simple self-affinity, and some evidence has been reporting multi-affine scaling (Bouchbinder et al 2006a, b;Alava et al 2006a, b;Bakke et al 2007;Santucci et al 2007). Bouchbinder et al (2006a, b) argues that a crack line h(x) in two-dimensions is not self-affine; instead, it exhibits a much complicated multi-affine (or multiscaling) structure, with a non-constant scaling exponent ζ q for the q-th order correlation function C q ( ) = |h(x + )−h(x)| q 1/q ∼ ζ q .…”