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Fractals and fractal scaling in fracture mechanics

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Abstract

A review of modern fractal models of fracture in brittle and quasibrittle materials is given. The difference between mathematical and physical fractal approaches is emphasized. The scaling for both a fractal solitary crack and a fractal pattern of microcracks surrounding the main fracture is considered. Some concepts appropriate for fractal description of fracture are discussed. It is shown that if the layer of inelastic deformations in quasibrittle materials has the same order of magnitude as the upper cutoff of the fractal scaling then fractal properties of the main crack surface do not corellate with fracture energy. This observation selects the cases when the concept of the universal roughness exponent may be valid. It is shown that the corellation between fractal properties of fractal pattern of microcracks and the fracture energy of polyphase materials is usually possible. The case of different fractal dimensions for different length scales is also discussed.

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  1. Department of Mathematics, Glasgow Caledonian University, Glasgow, G4 0BA, UK; e-mail

    Feodor M. Borodich

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Borodich, F.M. Fractals and fractal scaling in fracture mechanics. International Journal of Fracture 95, 239–259 (1999). https://doi.org/10.1023/A:1018660604078

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