# Fracture Surfaces as Multiscaling Graphs

Abstract : Fracture paths in quasi-two-dimensional (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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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00156808
Contributor : Loïc Vanel Connect in order to contact the contributor
Submitted on : Friday, June 22, 2007 - 4:30:44 PM
Last modification on : Monday, January 4, 2021 - 2:46:09 PM

### Citation

Eran Bouchbinder, Itamar Procaccia, Stéphane Santucci, Loïc Vanel. Fracture Surfaces as Multiscaling Graphs. Physical Review Letters, American Physical Society, 2006, 96 (5), pp.055509. ⟨10.1103/PhysRevLett.96.055509⟩. ⟨ensl-00156808⟩

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