Fracture Surfaces as Multiscaling Graphs

TL;DR

This paper demonstrates that fracture surfaces in 2D media exhibit multiscaling behavior, challenging existing universality class assumptions, and validates a recent fracture model through this multiscaling property.

Contribution

It reveals the multiscaling nature of 2D fracture surfaces and tests the validity of a new fracture model against this property.

Findings

Fracture paths are multiscaling graphs with nonlinear exponents.

2D fracture does not belong to known universality classes like directed polymers.

A recent fracture model successfully reproduces the multiscaling behavior.

Abstract

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.