Fracture Surfaces as Multiscaling Graphs

Details Fracture Surfaces as Multiscaling Graphs Fracture Surfaces as Multiscaling Graphs

2005-08-07

arxiv.org/abs/cond-mat/0508183v2

Phys. Rev. Lett. 96, 055509 (2006)

Physics

Condensed Matter

Materials Science

4 pages, 5 figures

Scientific paper

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.

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