Morphology of two dimensional fracture surface

TL;DR

This paper investigates the morphology of two-dimensional fracture surfaces, comparing experimental observations with numerical models, revealing multiscaling at small scales and self-affine scaling at larger scales, and analyzing different crack models.

Contribution

It demonstrates that the roughness exponent from the random fuse model can be reproduced by a simpler connected crack model, and explores multiscaling behavior across models.

Findings

Data obey multiscaling at small scales

Roughness exponent recovered by a connected crack model

Directed crack behaves like a random walk

Abstract

We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey multiscaling at small scales but cross over to self-affine scaling at larger scales. Next, we show that the roughness exponent of the random fuse model is recovered by a simpler model that produces a connected crack, while a directed crack yields a different result, close to a random walk. We discuss the multiscaling behavior of all these models.