Analysis of long crack lines in paper webs

Salminen, Lauri; Alava, Mikko J.; Niskanen, Kaarlo

doi:10.1140/epjb/e2003-00111-x

Cited by 38 publications

(42 citation statements)

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“…Salminen et al [56] have used remarkably long samples: their profiles contain 160 000 points, each point corresponding to 0.042 mm. With this resolution, they cannot distinguish individual fiber ends sticking out of the crack line and therefore cannot see the small ''overhangs'' that the randomly oriented fiber ends create (see Fig.…”

Section: Fracture Of a Paper Sheetmentioning

confidence: 99%

Failure of heterogeneous materials: A dynamic phase transition?

2011

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Section: Fracture Of a Paper Sheetmentioning

confidence: 99%

Failure of heterogeneous materials: A dynamic phase transition?

2011

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“…Experiments on 2-dimensional samples tend to report scaling exponents in the range ζ ≈ 0.65 ± 0.04 [2,3,4], indicating the existence of positive correlations between successive crack segments.…”

Section: Introductionmentioning

confidence: 99%

Random and correlated roughening in slow fracture by damage nucleation

2006

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We address the role of the nature of material disorder in determining the roughness of cracks which grow by damage nucleation and coalescence ahead of the crack tip. We highlight the role of quenched and annealed disorders in relation to the length scales d and ξc associated with the disorder and the damage nucleation respectively. In two related models, one with quenched disorder in which d ≃ ξc, the other with annealed disorder in which d ≪ ξc, we find qualitatively different roughening properties for the resulting cracks in 2-dimensions. The first model results in random cracks with an asymptotic roughening exponent ζ ≈ 0.5. The second model shows correlated roughening with ζ ≈ 0.66. The reasons for the qualitative difference are rationalized and explained.

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“…Removal of overhangs in the crack profile eliminates apparent multiscaling. Inset shows that normalization of the data leads to collapse of the curves with a local roughness exponent ζ loc = 0.72 et al (2007), and Salminen et al (2003) Fig. 10a shows large deviations away from Gaussian distribution for these small bin sizes.…”

Section: P( H( )) Distributionsmentioning

confidence: 83%

“…This should then imply a constant scaling exponent ζ loc such that the q-th order correlation function C q ( ) = |h(x + ) − h(x)| q 1/q ∼ ζ loc . It should be noted that Gaussian distribution for p( h( )) has been noted in (Alava et al 2006a, b;Bakke et al 2007;Santucci et al 2007;Salminen et al 2003) only above a characteristic scale where self-affine scaling of crack surfaces is observed. In this study, we would like to further investigate whether removing these jumps in the crack profiles extends the validity of Gaussian probability density distribution p( h( )) of the height differences h( ) = [h(x + )−h(x)] of the crack profile to even smaller window sizes .…”

Section: Introductionmentioning

confidence: 88%

“…In two dimensions, the available experimental results, mainly obtained for paper samples, indicate a roughness exponent in the range ζ 0.6 − 0.7 (Alava et al 2006b;Santucci et al 2007;Kertész et al 1993;Engoy et al 1994;Salminen et al 2003;Rosti et al 2001). However, one should note that apparently one can measure for various ordinary, industrial papers values that are significantly higher than ζ = 0.7 (Menezes-Sobrinho et al 2005).…”

Section: Introductionmentioning

confidence: 99%

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Anomalous roughness of fracture surfaces in 2D fuse models

et al. 2008

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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( h( )) of the height differences h( ) = [h(x + )−h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p( h( )) = h 2 ( ) −1/2 f h( ) h 2 ( ) 1/2 , and follows a Gaussian distribution even for small bin sizes . The anomalous scaling can be summarized with the scaling relation h 2 ( ) 1/2 h 2 (L/2) 1/2 1/ζ loc + ( −L/2) 2 (L/2) 2 = 1, where h 2 (L/2) 1/2 ∼ L ζ and L is the system size.

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Analysis of long crack lines in paper webs

Cited by 38 publications

References 0 publications

Failure of heterogeneous materials: A dynamic phase transition?

Failure of heterogeneous materials: A dynamic phase transition?

Random and correlated roughening in slow fracture by damage nucleation

Anomalous roughness of fracture surfaces in 2D fuse models

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