Abstract
A model for determining the fractal dimension of the fracture surface profile of a cylindrical sample with standard tension characteristics is developed. Analytical dependences relating the fractal dimension to standard tension characteristics of the material and lateral strain coefficient are derived. Qualitative and quantitative consistency of the calculated dependences with experimental data is tested. The estimated and experimental values of the fractal dimension are found to be in satisfactory agreement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Z. Q. Mu and C. W. Lung, “Studies on the fractal dimension and fracture toughness of steel,” J. Appl. Phys., 21, No. 5, 848–850 (1988).
L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).
R. H. Dauskardt, F. Haubensak, and R. O. Ritchie, “On the interpretation of the fractal character of fracture surfaces,” Acta Metal. Mater., 38, No. 2, 143–150 (1990).
B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York (1983).
O. N. Romaniv, Fracture Viscosity of Structural Steels [in Russian], Metallurgiya, Moscow (1979).
N. A. Shaposhnikov, Mechanical Testing of Metals [in Russian], Mashgiz, Moscow-Leningrad (1951).
A. Y. Ishlinskii, “Eulerian description of deformation of an isotropic medium,” in: Applied Problems of Mechanics, Vol. 1: The Mechanics of Viscoelastic and Slightly Elastic Bodies [in Russian], Nauka, Moscow (1986), pp. 333–336.
V. S. Ivanova, Synergetics: Strength and Fracture of Metallic Materials [in Russian], Nauka, Moscow (1992).
V. A. Kuz’menko, “Variation laws of the lateral strain coefficient,” Probl. Prochn., No. 8, 48–53 (1971).
I. I. Cherkasov, “On the relation between Poisson’s ratio and plastic properties of the material,” Zh. Tekh. Fiz., 22, No. 11, 1834–1837 (1952).
A. S. Balankin, V. S. Ivanova, and V. P. Breusov, “Collective effects in fracture kinetics and spontaneous change in the fractal dimension of a dissipative structure during the viscous-brittle transition,” Dokl. Ross. Akad. Nauk, 322, No. 6, 1080–1085 (1992).
V. S. Ivanova, A. S. Balankin, I. J. Bunin, and A. A. Oksogoev, Synergetics and Fractals in Material Science [in Russian], Nauka, Moscow (1994).
A. V. Kudrya, E. A. Sokolovskaya, and A. M. Arsenkin, “Effectiveness of application of observation devices of various dimensions to analyze the morphology of viscous fractures of upgradable steels,” Deform. Razr. Mater., No. 1, 38–44 (2010).
K. J. Malay, A. Hansen, and E. L. Hinrichen, “Experimental measurements of the roughness of brittle cracks,” Phys. Rev. Lett., 68, No. 2, 213–215 (1992).
V. Y. Milman, N. A. Stelmashenko, and R. Blumenfeld, “Fracture surfaces: A critical review of fractal studies and a novel morphological analysis of scanning tunneling microscopy measurements,” Progr. Mater. Sci., 38, 425–474 (1994).
E. Bouchaud, “Scaling properties of cracks,” J. Phys. Condens. Matter., 9, 4319–4344 (1997).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 6, pp. 177–184, November–December, 2011.
Rights and permissions
About this article
Cite this article
Savenkov, G.G., Barakhtin, B.K. Relation of the fractal dimension of the fracture surface with a set of standard tension characteristics of the material. J Appl Mech Tech Phy 52, 997–1003 (2011). https://doi.org/10.1134/S0021894411060186
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894411060186