Crack roughness in the two-dimensional random threshold beam model

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 ͑ loc and , respectively͒ are equal to each other, and the two-dimensional crack roughness exponent is estimated to be loc = = 0.64Ϯ 0.02. Removal of overhangs ͑jumps͒ 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 p͓⌬h͑l͔͒ of the height differences ⌬h͑l͒ = ͓h͑x + l͒ − h͑x͔͒ of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes ͑l͒.

Failure of heterogeneous materials: A dynamic phase transition?

“…The origin of this anomalous scaling remains unclear. It seems to be intrinsic to the scalar character of RFM since it disappears in Random Beam Models [163]. Experimentally, as discussed in Section 3, anomalous scaling was observed only within transient regimes where roughness has to develop from a straight notch [81,82,85].…”

“…However, recent simulations on a beam model supposed to be equivalent to tensorial mode I elasticity [163] show that in this case also, 2D cracks have a roughness index close to: β 2D ≃ 0.64. These cracks do not exhibit anomalous scaling, and when overhangs are removed, they are nowhere multi-affine, and the probability distribution of their height differences is a Gaussian for all window sizes.…”

Intermittency and roughening in the failure of brittle heterogeneous materials

“…The origin of this anomalous scaling remains unclear. It seems to be intrinsic to the scalar dimensionality of RFM since it disappears in Random Beam Models [112].…”

Anomalous roughness of fracture surfaces in 2D fuse models

“…This is in contrast to e.g. the beam model (Nukala et al 2008), where the global and local exponents are equal. The difference of the global and local exponents arises due to an additional lengthscale, which scales as a power-law of the system size L. We further investigated whether anomalous scaling of roughness is an artifact of presence of large jumps in the tails of p( h( )) distribution.…”