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The mechanics of self-similar and self-affine fractal cracks

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Abstract

In this paper we study the mechanical attributes of the fractal nature of fracture surfaces. The structure of stress and strain singularity at the tip of a fractal crack, which can be self-similar or self-affine, is studied. The three classical modes of fracture and the fourth mode of fracture are discussed for fractal cracks in two-dimensional and three- dimensional solid bodies. It is discovered that there are six modes of fracture in fractal fracture mechanics. The J-integral is shown to be path-dependent. It is explained that the proposed modified J-integrals in the literature that are argued to be path-independent are only locally path-independent and have no physical meaning. It is conjectured that a fractal J-integral should be the rate of potential energy release per unit of a fractal measure of crack growth. The powers of stress and strain singularities at the tip of a fractal crack in a strain-hardening material are calculated. It is shown that stresses and strains have weaker singularities at the tip of a fractal crack than they do at the tip of a smooth crack.

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Authors and Affiliations

  1. School of Engineering and Applied Science, The George Washington University, Washington, DC , 20052, U.S.A

    Arash Yavari (Graduate Research Assistant)

  2. School of Engineering and Applied Science, The George Washington University, Washington, DC , 20052, U.S.A., (E-mail

    Shahram Sarkani (Professor)

  3. Litton/Ingalls Shipbuilding, P.O. Box 149, Pascagoula, MS , 39568, U.S.A.

    E. Thomas Moyer Jr. (Senior Scientist)

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  1. Arash Yavari
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  2. Shahram Sarkani
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  3. E. Thomas Moyer Jr.
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Yavari, A., Sarkani, S. & Moyer, E.T. The mechanics of self-similar and self-affine fractal cracks. International Journal of Fracture 114, 1–27 (2002). https://doi.org/10.1023/A:1014878112730

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