We study anomalous scaling and multi-scaling of two-dimensional crack profiles in the random fuse model using both periodic and open boundary conditions. Our large scale and extensively sampled numerical results reveal the importance of crack branching and coalescence of microcracks, which induce jumps in the solid-on-solid crack profiles. Removal of overhangs (jumps) in the crack profiles eliminates the multiscaling observed in earlier studies and reduces anomalous scaling. We find that the probability density distribution p(Delta h(l)) of the height differences Delta h(l) = [h(x+l)-h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Delta h(l)) = (Delta h(2)(l)>(-1/2) f(Delta h(l)/(Delta h(2)(l)>(1/2)), and follows a Gaussian distribution even for small bin sizes l. The anomalous scaling can be summarized with the scaling relation [(1/2)/(Delta h(2)(L/2)>(1/2)](1/zeta loc)+(l-L/2)(2)/(L/2)(2) = 1, where (1/2) similar to L-zeta and L is the system size.

Anomalous roughness of fracture surfaces in 2D fuse models / P.K.V.V. Nukala, S. Zapperi, M.J. Alava, S. Simunovic. - In: INTERNATIONAL JOURNAL OF FRACTURE. - ISSN 0376-9429. - 154:1-2(2008 Nov), pp. 119-130. ((Intervento presentato al convegno Conference on Physical Aspects of Fracture Scaling and Size Effect tenutosi a Ascona nel 2008.

Anomalous roughness of fracture surfaces in 2D fuse models

S. Zapperi;
2008

Abstract

We study anomalous scaling and multi-scaling of two-dimensional crack profiles in the random fuse model using both periodic and open boundary conditions. Our large scale and extensively sampled numerical results reveal the importance of crack branching and coalescence of microcracks, which induce jumps in the solid-on-solid crack profiles. Removal of overhangs (jumps) in the crack profiles eliminates the multiscaling observed in earlier studies and reduces anomalous scaling. We find that the probability density distribution p(Delta h(l)) of the height differences Delta h(l) = [h(x+l)-h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Delta h(l)) = (Delta h(2)(l)>(-1/2) f(Delta h(l)/(Delta h(2)(l)>(1/2)), and follows a Gaussian distribution even for small bin sizes l. The anomalous scaling can be summarized with the scaling relation [(1/2)/(Delta h(2)(L/2)>(1/2)](1/zeta loc)+(l-L/2)(2)/(L/2)(2) = 1, where (1/2) similar to L-zeta and L is the system size.
Crack roughness; Anomalous scaling; Multi-affine scaling; Stochastic excursions
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Settore FIS/03 - Fisica della Materia
nov-2008
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/658344
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