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Summary: May 2007
EPL, 78 (2007) 46006 www.epljournal.org
doi: 10.1209/0295-5075/78/46006
Fracture surfaces of heterogeneous materials:
A 2D solvable model
E. Katzav(a)
, M. Adda-Bedia and B. Derrida
Laboratoire de Physique Statistique de l'Ecole Normale Sup´erieure, CNRS UMR 8550 - 24 rue Lhomond,
75231 Paris Cedex 05, France
received 24 January 2007; accepted in final form 10 April 2007
published online 8 May 2007
PACS 68.35.Ct Interface structure and roughness
PACS 62.20.Mk Fatigue, brittleness, fracture, and cracks
PACS 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
Abstract Using an elastostatic description of crack growth based on the Griffith criterion and
the principle of local symmetry, we present a stochastic model describing the propagation of a
crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks
and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the
nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the
power spectrum of the paths. This result suggests an alternative to the conventional power law
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