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Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue

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  • Paggi, Marco
  • Carpinteri, Alberto

Abstract

The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris’ constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.

Suggested Citation

  • Paggi, Marco & Carpinteri, Alberto, 2009. "Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1136-1145.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1136-1145
    DOI: 10.1016/j.chaos.2007.08.068
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    1. Carpinteri, Alberto & Paggi, Marco, 2009. "A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 540-546.
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    Cited by:

    1. Carpinteri, A. & Lacidogna, G. & Niccolini, G., 2009. "Fractal analysis of damage detected in concrete structural elements under loading," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2047-2056.
    2. Carpinteri, Alberto & Lacidogna, Giuseppe & Puzzi, Simone, 2009. "From criticality to final collapse: Evolution of the “b-value” from 1.5 to 1.0," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 843-853.

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    2. Carpinteri, A. & Lacidogna, G. & Niccolini, G., 2009. "Fractal analysis of damage detected in concrete structural elements under loading," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2047-2056.
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