Anomalous roughness of fracture surfaces in 2D fuse models

Phani K.V.V. Nukala; Stefano Zapperi; Mikko J. Alava; Srdłan Šimunović

doi:10.1007/s10704-008-9298-z

Anomalous roughness of fracture surfaces in 2D fuse models

Phani K.V.V. Nukala, Stefano Zapperi, Mikko J. Alava, Srdłan Šimunović

Multiscale Materials

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Abstract

We study anomalous scaling and multiscaling 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(Δ hℓ)) of the height differences Δ hℓ = [h (x+ℓ) - h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Δ hℓ)) = 〈Δ h²(ℓ)〉 ^-1/2 f(Δ hℓ)〈Δh² (ℓ)^1/2 Δh(ℓ)), and follows a Gaussian distribution even for small bin sizes ℓ. The anomalous scaling can be summarized with the scaling relation [〈h² (L/2)〉^1/2 〈Δh² (ℓ) ^1/2, where ^1/ζloc + (L/2)² (ell; - L/2)²= 1 〈h² (L/2)〉 ^1/2 ∼^Lζand L is the system size.

Original language	English
Pages (from-to)	119-130
Number of pages	12
Journal	International Journal of Fracture
Volume	154
Issue number	1-2
DOIs	https://doi.org/10.1007/s10704-008-9298-z
State	Published - 2008

Funding

Acknowledgements This research is sponsored by the Mathematical, Information and Computational Sciences Division, Office of Advanced Scientific Computing Research, US Department of Energy under contract number DE-AC05-00OR22725 with UT-Battelle, LLC. MJA and SZ gratefully thank the financial support of the European Commissions NEST Pathfinder programme TRIGS under contract NEST-2005-PATH-COM-043386. MJA also acknowledges the financial support from The Center of Excellence program of the Academy of Finland, and the hospitality of the Kavli Institute of Theoretical Physics, China in Beijing.

Funders	Funder number
European Commissions NEST	NEST-2005-PATH-COM-043386
Kavli Institute of Theoretical Physics
US Department of Energy	DE-AC05-00OR22725
Advanced Scientific Computing Research
Academy of Finland

Keywords

Anomalous scaling
Crack roughness
Multi-affine scaling
Stochastic excursions

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10.1007/s10704-008-9298-z

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title = "Anomalous roughness of fracture surfaces in 2D fuse models",

abstract = "We study anomalous scaling and multiscaling 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(Δ hℓ)) of the height differences Δ hℓ = [h (x+ℓ) - h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Δ hℓ)) = 〈Δ h2(ℓ)〉 -1/2 f(Δ hℓ)〈Δh2 (ℓ)1/2 Δh(ℓ)), and follows a Gaussian distribution even for small bin sizes ℓ. The anomalous scaling can be summarized with the scaling relation [〈h2 (L/2)〉1/2 〈Δh2 (ℓ) 1/2, where 1/ζloc + (L/2)2 (ell; - L/2)2= 1 〈h2 (L/2)〉 1/2 ∼Lζand L is the system size.",

keywords = "Anomalous scaling, Crack roughness, Multi-affine scaling, Stochastic excursions",

author = "Nukala, {Phani K.V.V.} and Stefano Zapperi and Alava, {Mikko J.} and Srd{\l}an {\v S}imunovi{\'c}",

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TY - JOUR

T1 - Anomalous roughness of fracture surfaces in 2D fuse models

AU - Nukala, Phani K.V.V.

AU - Zapperi, Stefano

AU - Alava, Mikko J.

AU - Šimunović, Srdłan

PY - 2008

Y1 - 2008

N2 - We study anomalous scaling and multiscaling 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(Δ hℓ)) of the height differences Δ hℓ = [h (x+ℓ) - h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Δ hℓ)) = 〈Δ h2(ℓ)〉 -1/2 f(Δ hℓ)〈Δh2 (ℓ)1/2 Δh(ℓ)), and follows a Gaussian distribution even for small bin sizes ℓ. The anomalous scaling can be summarized with the scaling relation [〈h2 (L/2)〉1/2 〈Δh2 (ℓ) 1/2, where 1/ζloc + (L/2)2 (ell; - L/2)2= 1 〈h2 (L/2)〉 1/2 ∼Lζand L is the system size.

AB - We study anomalous scaling and multiscaling 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(Δ hℓ)) of the height differences Δ hℓ = [h (x+ℓ) - h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Δ hℓ)) = 〈Δ h2(ℓ)〉 -1/2 f(Δ hℓ)〈Δh2 (ℓ)1/2 Δh(ℓ)), and follows a Gaussian distribution even for small bin sizes ℓ. The anomalous scaling can be summarized with the scaling relation [〈h2 (L/2)〉1/2 〈Δh2 (ℓ) 1/2, where 1/ζloc + (L/2)2 (ell; - L/2)2= 1 〈h2 (L/2)〉 1/2 ∼Lζand L is the system size.

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KW - Crack roughness

KW - Multi-affine scaling

KW - Stochastic excursions

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EP - 130

JO - International Journal of Fracture

JF - International Journal of Fracture

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ER -

Anomalous roughness of fracture surfaces in 2D fuse models

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