Some Applications of Fractal Fracture Mechanics to Describe the Fatigue Behaviour of Materials

Article Preview

Abstract:

As is well-known, fatigue limit, threshold stress intensity range and fatigue crack growth rate are influenced by the specimen or structure size. Limited information on size effect is available in the literature. In the present paper, by employing some concepts of fractal geometry, new definitions of fatigue limit, fracture energy and stress intensity factor, based on physical dimensions different from the classical ones, are discussed. Then, size-dependent laws for fatigue limit, threshold stress intensity range and fatigue crack growth rate are proposed. Some experimental results are examined in order to show how to apply such theoretical scaling laws.

You might also be interested in these eBooks

Info:

Periodical:

Key Engineering Materials (Volumes 378-379)

Pages:

355-370

Citation:

Online since:

March 2008

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2008 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] A.A. Griffith: The phenomenon of rupture and flow in solids (Philosophical Trans Royal Soc. A221, 1921).

Google Scholar

[2] R.E. Peterson: Jnl Applied Mechanics Vol. 1 (1933), p.79.

Google Scholar

[3] W. Weibull: A statistical theory for the strength of materials (Swedish Royal Institute for Engineering Research, Stockholm 1939).

Google Scholar

[4] Al. Carpinteri: Int. J. Solids Struct. Vol. 25 (1989), p.407.

Google Scholar

[5] Al. Carpinteri: Int Jnl Solids Struct. Vol. 31 (1994), p.291.

Google Scholar

[6] G.P. Cherepanov, A.S. Balankin, V.S. Ivanova: Engng Fracture Mechs Vol. 51 (1995), p.997.

Google Scholar

[7] Al. Carpinteri, B. Chiaia: Int Jnl of Fract. Vol. 76 (1996), p.327.

Google Scholar

[8] Al. Carpinteri, B. Chiaia: Chaos, Solitons & Fractals Vol. 8 (1997), p.135.

Google Scholar

[9] B.B. Mandelbrot: The fractal geometry of nature (W.H. Freeman and Company, New York 1982).

Google Scholar

[10] K. Falconer: Fractal geometry: mathematical foundations and applications (Wiley, Chichester 1990).

Google Scholar

[11] K.G. Wilson: Phys Rev. B4 (1971), p.3174.

Google Scholar

[12] G.I. Barenblatt: Similarity, self-similarity and intermediate asymptotics (Consultants Bureau, New York 1979).

DOI: 10.1007/978-1-4615-8570-1

Google Scholar

[13] H.J. Herrmann, S. Roux (Editors): Statistical models for the fracture of disordered media (North-Holland, Amsterdam 1990).

Google Scholar

[14] G.I. Barenblatt, L.R. Botvina: Fatigue Fract. Engng Mater. Struct. Vol. 3 (1980), p.193.

Google Scholar

[15] An. Carpinteri, A. Spagnoli, S. Vantadori: Fatigue Fracture Engng Maters Structs Vol. 25 (2002), p.619.

Google Scholar

[16] An. Carpinteri, A. Spagnoli: Int. J. Fatigue Vol. 26 (2004), p.125.

Google Scholar

[17] A. Spagnoli: Chaos, Solitons & Fractals Vol. 22 (2004), p.589.

Google Scholar

[18] K. Hatanaka, S. Shimizu, A. Nagae: Bulletin of JSME Vol. 26 (1983), p.1288.

Google Scholar

[19] N.E. Frost, in: Proceedings of the First International Conference on Fracture, edited by T. Yokobori/The Japan Society for Strength and Fracture of Materials, Sendai (1966).

Google Scholar

[20] Y. Murakami, M. Endo, in: Publication 1 of the European Group of Fracture, Mechanical Engineering Publications, London (1986).

Google Scholar

[21] Z.P. Bazant, K. XU: ACI Maters Jnl. Vol. 88 (1991), p.390.

Google Scholar

[22] Z.P. Bazant, J. Planas: Fracture and size effect in concrete and other quasibrittle materials (CRC Press, New York 1998).

Google Scholar

[23] Z.P. Bazant, W.F. Shell: ACI Mater Jnl. Vol. 90 (1993), p.472.

Google Scholar

[24] B.B. Mandelbrot, D.E. Passoja, A.J. Paullay: Nature Vol. 308 (1984), p.721.

Google Scholar

[25] J. Weiss: Engng Fracture Mechs Vol. 68 (2001), p. (1975).

Google Scholar

[26] W.N. Findley: J. Mech. Engng Sci. Vol. 14 (1972), p.424.

Google Scholar

[27] H.M. Westergaard: Jnl Applied Mechanics Vol. 6 (1939), p.49.

Google Scholar

[28] G.R. Irwin: Jnl Applied Mechanics Vol. 24 (1957), p.109.

Google Scholar

[29] M.H. El Haddad, T.H. Topper, K.N. Smith: Engng Fracture Mechs Vol. 11 (1979), p.573.

Google Scholar

[30] P.C. Paris and F. Erdogan: Jnl Basic Engrg 85D (1963), p.528.

Google Scholar