Roughness of Brittle Fractures as a Correlated Percolation Problem

Bakke, Jan Øystein Haavig; Bjelland, Johannes; Ramstad, T.A.; Stranden, Torunn; Hansen, Alex; Schmittbuhl, Jean

doi:10.1238/physica.topical.106a00065

Cited by 14 publications

(5 citation statements)

References 37 publications

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“…Breakdown is driven by a voltage difference between two opposing boundaries and the analogy of Kirchhoff 's equations with linear elasticity is the reason why this model is referred to as a scalar model of fracture. In two dimensions results reported for the roughness exponent with the fuse model are ζ = 0.74 (2) [6,7], and more recently ζ = 0.83 (4) [8]. In three dimensions the random fuse model has yielded values in the range 0.4 ζ 0.6, i.e., Batrouni et al obtained ζ = 0.62 (5) [9], Räisänen et al obtained ζ = 0.41 (2) [10,11], and Nukala et al obtained ζ = 0.52(3) [12].…”

Section: Introductionmentioning

confidence: 99%

Discrete element modeling of brittle crack roughness in three dimensions

Skjetne¹,

Helle²,

Hansen³

2014

Front. Phys.

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Crack morphology obtained in the fracture of materials with a disordered micro-structure is studied using numerical simulations. Physical properties are embedded on a regular three dimensional lattice as discrete stochastic elements which conform to the laws of linear elasticity. In this model, also known as the beam lattice, these elements are analogous to beams in that relative displacements between neighboring nodes induce axial, bending, and shearing forces, as in a real elastic solid. The stochastic nature enters via the introduction of random breaking thresholds on the individual elements. Using this model, the exponent characterizing the scaling with system size of the crack roughness perpendicular to the fracture plane is reported. Two different types of disorder have been used to generate the thresholds, i.e., distributions with a tail toward strong elements or with a tail toward weak elements. At weak disorders the self-affine regime seems to lie beyond the system sizes presently included. At stronger disorders a self-affine regime appears, for which we obtain exponents consistent with ζ 0.6 for both types of disorder. The latter result is in fair agreement with the experimental value reported for large length scales, ζ 0.50.

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Section: Introductionmentioning

confidence: 99%

Discrete element modeling of brittle crack roughness in three dimensions

Skjetne¹,

Helle²,

Hansen³

2014

Front. Phys.

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“…In the simplest approximation of a scalar displacement, one recovers the random fuse model (RFM) where a lattice of fuses with random threshold are subject to an increasing external voltage [22]. Using two-dimensional RFM, the estimated crack surface roughness exponents are: ζ = 0.7 ± 0.07 [23], ζ loc = 2/3 [24], and ζ = 0.74 ± 0.02 [25]. Recently, using large system sizes (up to L = 1024) with extensive sample averaging, we found that the crack roughness exhibits anomalous scaling [26].…”

Section: Introductionmentioning

confidence: 99%

Crack roughness in the two-dimensional random threshold beam model

et al. 2008

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We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents ͑ loc and , respectively͒ are equal to each other, and the two-dimensional crack roughness exponent is estimated to be loc = = 0.64Ϯ 0.02. Removal of overhangs ͑jumps͒ in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution p͓⌬h͑l͔͒ of the height differences ⌬h͑l͒ = ͓h͑x + l͒ − h͑x͔͒ of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes ͑l͒.

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“…The most common way of performing these simulations is by using lattice models where a scalar ͑fuse model 13,[24][25][26][27][28][29] ͒ or elastic ͑beam model, 30,31 central force model [32][33][34] ͒ interaction is used. The disorder in the system is usually introduced through a randomly selected threshold distributions for the bonds in the model.…”

Section: Introductionmentioning

confidence: 99%