The non-Gaussian nature of fracture and the survival of fat-tail exponents

Ken Tore Tallakstad (1) , Renaud Toussaint (2, 3) , Stéphane Santucci (3, 4) , Knut Jørgen Måløy (3, 1)

1 Department of Physics [Oslo]
2 IPGS-GE - Géophysique expérimentale (IPGS)
3 Centre for Advanced Study at the Norwegian Academy of Science and Letters
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We study the fluctuations of the global velocity Vl(t), computed at various length scales l, during the intermittent Mode-I propagation of a crack front. The statistics converge to a non-Gaussian distribution, with an asymmetric shape and a fat tail. This breakdown of the Central Limit Theorem (CLT), is due to the diverging variance of the underlying local crack front velocity distribution, displaying a power law tail. Indeed, by the application of a generalized CLT, the full shape of our experimental velocity distribution at large scale is shown to follow the stable Levy distribution, which preserves the power law tail exponent under upscaling. This study aims to demonstrate in general for Crackling Noise systems, how one can infer the complete scale dependence of the activity- and extreme event distributions, by measuring only at a global scale.

Mots clés: Levy flights; Crackling Noise; Fracture; Stable distributions; Upscaling; Avalanches

Domaines: Mécanique statistique [cond-mat.stat-mech]; Science des matériaux [cond-mat.mtrl-sci]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Ken Tore Tallakstad, Renaud Toussaint, Stéphane Santucci, Knut Jørgen Måløy. The non-Gaussian nature of fracture and the survival of fat-tail exponents. Physical Review Letters, 2013, 110, pp.145501. ⟨10.1103/PhysRevLett.110.145501⟩. ⟨hal-00816217⟩