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Balankin, Alexander S.; Morales, Daniel A.; Gómez-Mancilla,; Susarrey, Orlando; Campos, Irma Manrique; Sandoval, F.; Bravo, António; García, A.; Galicia, Marco

doi:10.1023/a:1022670017422

International Journal of Fracture

2000

DOI: 10.1023/a:1022670017422

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Alexander S. Balankin

Daniel A. Morales

Gómez-Mancilla Gómez-Mancilla

et al.

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Cited by 16 publications

(18 citation statements)

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“…All these regimes have been observed in experiments using paper as a model twodimensional inhomogeneous medium. In particular, the self-a ne invariance of saturated interfaces was observed in paper wetting experiments (BarabaÂ si and Stanley 1995, Balankin et al 2000a), the crossover scaling regime was noted for ®re front roughening in paper-burning experiments (Amaral and Makse 1998), whereas cracks along the ®bre direction in paper possess intrinsic anomalous roughness (Balankin et al 2000b), while rupture lines formed by multiple fracture of some kinds of paper display super-rough scaling behaviour (Balankin and Susarrey 2000).…”

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confidence: 97%

“…Introduction The scaling properties of interfaces formed in disordered media have attracted much attention in recent years (BarabaÂ si and Stanley 1995, Balankin 1997, Meakin 1998, Balankin et al 2000a. Interface roughening presents us with an architecture problem with direct impact on various natural phenomena, ranging from growth of bacterial colonies to a forest ®re.…”

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confidence: 99%

“…In this work we study the scaling properties of¯ame and burning fronts in slow combustion of Secant paper, which was used early in paper-wetting experiments (Balankin et al 2000a). …”

mentioning

confidence: 99%

“…Experimental details Commercial Secant paper is available in sheets of size 1:20 m £ 0:96 m. The thickness a and areal density a of paper sheets from the same lot vary in accordance with a normal distribution with mean values aˆ0:34 § 0:02 mm and aˆ2 00 § 10 g m ¡2 , respectively (Balankin et al 2000a). Electron microscope analysis of paper has shown that the ®bre and the pore structures are not random but possess statistical auto-similarity within a considerable range of length scale.…”

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confidence: 99%

“…The Secant paper possesses a well-pronounced mechanical anisotropy associated with the preferred orientation of ®bres in the so-called machine direction (Balankin et al 2000a). Nevertheless in the paper-wetting experiments it was found that the roughness exponentˆˆHˆ0:63 § 0:02 does not depend on the interface orientation with respect to the preferred ®bre direction, despite the fact that H depends on the paper structure (Balankin et al 2000a).…”

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confidence: 99%

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Unconventional anomalous roughening in the slow combustion of paper

Balankin

Matamoros²

2001

Philosophical Magazine Letters

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The height¯uctuations in the¯ame front during slow combustion of paper display an unconventional anomalous scaling behaviour, whereas the burning front roughness is statistically self-a ne. The anomalous roughness is characterized by diOE erent scaling exponents in the local ( 1) and the global ( > 1 ) length scales. Furthermore, we ®nd that the local roughness exponent, as well as the power spectrum S (structure factor of¯ame front), decrease as the sheet width W increases as 1 / S / W ¡ , where > 0, despite the fact that the global roughness exponent does not depend on W. This distinguishes the unconventional anomalous roughening from the scaling behaviour expected in the cases of super-roughening and intrinsic anomalous roughening. The physical implications of these points are discussed.

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mentioning

confidence: 97%

mentioning

confidence: 99%

“…In this work we study the scaling properties of¯ame and burning fronts in slow combustion of Secant paper, which was used early in paper-wetting experiments (Balankin et al 2000a). …”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Unconventional anomalous roughening in the slow combustion of paper

Balankin

Matamoros²

2001

Philosophical Magazine Letters

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Fractal dimension of metallic fracture surface

Kotowski

2006

Int J Fract

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In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a "fractal map" of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to 270 P. Kotowski the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges ...

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Fractal pattern of δ-hydride with stress-state

Das

2024

Chaos, Solitons & Fractals

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Untitled

Cited by 16 publications

References 8 publications

Unconventional anomalous roughening in the slow combustion of paper

Unconventional anomalous roughening in the slow combustion of paper

Fractal dimension of metallic fracture surface

Fractal pattern of δ-hydride with stress-state

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