Some fractal models of fracture

Journal of the Mechanics and Physics of Solids

Volumn 45, Issue 2, 1997, Pages 239-259

  Borodich, F M ^a,b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b GLASGOW CALEDONIAN UNIVERSITY   (United Kingdom)

Author keywords

A. fracture; A. microcracking; B. ceramic material; B. concrete; B. rock; C. optical microscopy

Indexed keywords

BRITTLENESS; CERAMIC MATERIALS; CONCRETES; CRACK INITIATION; ENERGY ABSORPTION; FRACTALS; GEOMETRY; MATHEMATICAL MODELS; MICROCRACKS; OPTICAL MICROSCOPY; ROCK MECHANICS;

FRACTAL GEOMETRY METHODS; QUASI BRITTLE MATERIALS;

FRACTURE MECHANICS;

EID: 0031061907     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(96)00080-4     Document Type: Article

References (48)

1. Anifrani, J.-C., Le Floc'h, C., Sornette, D. and Souillard, B. (1995) Universal log-periodic correction to renormalization group scaling for rupture stress prediction from acoustic emissions. J. Phys. I. France 5, 631-638.
2. Aviles, C. A., Scholz, C. H. and Boatwright, J. (1987) Fractal analysis applied to characteristic segments of the San Andreas fault. J. Geophys. Res. 92, 331-344.
3. Baran, G. R., Roques-Carmes, C., Wehbi, D. and Degrange, M. (1992) Fractal characteristics of fracture surfaces. J. Am. Ceram. Soc. 75, 2687-2691.
4. Barenblatt, G. I. (1987) Dimensional Analysis. Gordon and Breach, New York.
5. Barenblatt, G. I. (1993) Micromechanics of fracture. Theoretical and Applied Mechanics 1992, ed. S. R. Bodner, J. Singer, A. Solan and Z. Hashin, pp. 25-52. Elsevier.
6. Barenblatt, G. I. and Botvina, L. R. (1983) Self-similarity of the fatigue fracture ; the damage accumulation. Mech. Solids 18, 88-92.
7. Barenblatt, G. I. and Botvina, L. R. (1986) Similarity methods in mechanics and physics of fracture. Fiz.-Khim. Mekh. Mater. 1, 57-62.
8. Barenblatt, G. I. and Monin, A. S. (1983) Similarity principles for the biology of pelagic animals. Proc. Natl. Acad. Sci. USA 80, 3540-3542.
9. Bažant, Z. P. and Kazemi, M. T. (1990) Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length. J. Am. Cer. Soc. 73, 1841-1853.
10. Bažant, Z. P. (1995a) Scaling theories for quasibrittle fracture: Recent advances and new directions. Fracture Mechanics of Concrete Structures, Proc., 2nd Int. Conf. on Fracture Mech. of Concrete and Concrete Structures (FraMCoS-2), ETH, Zürich, July 1995, ed. F. H. Wittmann, pp. 515-534. Aedificatio Publishers, Freiburg.
11. Bažant, Z. P. (1995b) Scaling of quasi-brittle fracture and the fractal question. ASME J. Mater. Technol. 117, 361-367.
12. Bažant, Z. P. (1995c) Scaling in nonlinear fracture mechanics. Proc. IUTAM Symp. on Non-linear Analysis of Fracture, University of Cambridge, 3-7 September 1995, ed. J. R. Willis (to be published).
13. Blumenfeld, R. and Ball, R. C. (1991) Onset of scale-invariant pattern in growth processes: the cracking problem. Physica A 177, 407-415.
14. Borodich, F. M. (1992) Fracture energy in a fractal crack propagating in concrete or rock. Doklady Akademii Nauk (Russia) 325, 1138-1141 (English translation: Transactions (Doklady) of the Russian Akademy of Sciences: Earth Science Section 327, 36-40.)
15. Borodich, F. M. (1992) Fracture energy in a fractal crack propagating in concrete or rock. Doklady Akademii Nauk (Russia) 325, 1138-1141 (English translation: Transactions (Doklady) of the Russian Akademy of Sciences: Earth Science Section 327, 36-40.)
16. Borodich, F. M. (1994a) Fracture energy of brittle and quasi-brittle fractal cracks. IFIP Transactions: A. Computer Science and Technology 41, 61-68.
17. Borodich, F. M. (1994b) Some applications of the fractal parametric-homogeneous functions. Fractals 2, 311-314.
18. Borodich, F. M. (1995) Parametric-homogeneous functions, similarity, and fractal function graphs. Technical Report TR/MAT/FMB/95-35, Glasgow Caledonian University, Glasgow, 1-55.
19. Borodich, F. M. and Fradkin, L. Ju. (1995) Evaluation of fractal dimension of patterns in multiple fracture (unpublished).
20. Botvina, L. R., Fradkin, L. Ju. and Bridge, B. (1995) Power laws and generalised dimensional analysis in ultrasonic NDE. Nondestr. Test. Eval. 12, 103-118.
21. Bouchaud, E., Lapasset, G. and Planès, J. (1990) Fractal dimension of fractured surfaces: a universal value? Europhys. Lett. 13, 73-79.
22. Brameshuber, W. and Hilsdorf, H. K. (1990) Influence of ligament length and stress state on fracture energy of concrete. Engng Fracture Mech. 35, 95-106.
23. Carpinteri, A. (1994) Scaling laws and renormalization groups for strength and toughness of disordered materials. Int. J. Solids Structures 31, 291-302.
24. Chelidze, T., Reuschlé, T. and Guéguen, Y. (1994) A theoretical investigation of the fracture energy of heterogeneous brittle materials. J. Phys.: Condens. Matter. 6, 1857-1868.
25. Chudnovsky, A. and Wu, S. (1992) Evaluation of energy release rate in the crack-microcrack interaction problem. Int. J. Solids Structures 29, 1699-1709.
26. Dauskardt, R. H., Haubensak, F. and Ritchie, R. O. (1990) On the interpretation of the fractal character of fracture surfaces. Acta Metall. Mater. 38, 143-159.
27. Davy, P., Sornette, A. and Sornette, D. (1990) Some consequences of a proposed fractal nature of continental faulting. Nature 348, 56-58.
28. Falconer, K. J. (1990) Fractal Geometry: Mathematical Foundations and Applications. John Wiley, Chichester.
29. Griffith, A. A. (1920) The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. (London) Ser. A 221, 163-198.
30. Hirata, T. (1989) Fractal dimension of fault systems in Japan - fractal structure in rock fracture geometry at various scales. Pure and Appl. Geophys. 131, 157-170.
31. Nolen-Hoeksema, R. C. and Gordon, R. B. (1987) Optical detection of crack patterns in the opening-mode fracture of marble. Int. J. Rock Mech. Min. Sci. 24, 135-144.
32. Inghels, E., Heuer, A. H. and Steinbrech, R. W. (1990) Fracture mechanics of high-toughness magnesia-partially-stabilized zirconia. J. Am. Ceram. Soc. 73, 2023-2031.
33. Kershtein, I. M., Klushnikov, V. D., Lomakin, E. V. and Shesterikov, S. A. (1989) Foundations of Experimental Mechanics of Fracture. Moscow University Press, Moscow.
34. Mandelbrot, B. B. (1982) The Fractal Geometry of Nature. W. H. Freeman, San Francisco.
35. Mandelbrot, B. B., Passoja, D. E. and Paullay, A. J. (1984) Fractal character of fracture surfaces of metals. Nature 308, 721-722.
36. Mecholsky, J. J., Passoja, D. E. and Feinberg-Ringel, K. S. (1989) Quantitative analysis of brittle fracture profiles using fractal geometry. J. Am. Ceram. Soc. 72, 60-65.
37. Milman, V. Y., Stelmashenko, N. A. and Blumenfeld, R. (1994) Fracture surfaces : a critical-review of fractal studies and novel morphological analysis of scanning tunneling microscopy measurements. Progress in Mater. Sci. 38, 425-474.
38. Mosolov, A. B. (1993) Mechanics of fractal cracks in brittle solids. Europhys. Lett. 24, 673-678.
39. Newman, W. I., Turcotte, D. L. and Gabrielov, A. M. (1995) Log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation. Phys. Rev. E 52, 4827-4825.
40. Okubo, P. G. and Aki, K. (1987) Fractal geometry in the San Andreas fault system. J. Geophys. Res. 92, 345-355.
41. Sakellariou, M., Nakos, B. and Mitsakaki, C. (1991) On the fractal character of rock surfaces. Int. J. Rock Mech. Min. Sci. 28, 527-533.
42. Saouma, V. E., Barton, C. C. and Gamaleldin, N. A. (1990) Fractal characterization of fracture surfaces in concrete. Engng Fracture Mech. 35, 47-53.
43. Saouma, V. E. and Barton, C. C. (1994) Fractals, fractures, and size effects in concrete. J. Engng Mech. 120, 835-854.
44. Schmittbuhl, J., Roux, S. and Berthaud, Y. (1994) Development of roughness in crack propagation. Europhys. Lett. 28, 585-590.
45. Sornette, A., Davy, P. and Sornette, D. (1990) Growth of fractal fault patterns. Phys. Rev. Lett. 65, 2266-2269.
46. Turcotte, D. L. (1992) Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge.
47. Yokobori, T. (1978) Scientific Foundations for Strength and Fracture of Materials. Naukova Dumka, Kiev.
48. Zhao, Y., Huang, J. and Wang, R. (1993) Fractal characteristics of mesofractures in compressed rock specimens. Int. J. Rock Mech. Min. Sci. 30, 877-882.