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

Paggi, Marco and Carpinteri, Alberto Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue. Chaos, Solitons and Fractals, 40 (3). 1136 - 1145. ISSN 0960-0779 (2009)

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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.

Item Type: Article
Identification Number: 10.1016/j.chaos.2007.08.068
Subjects: T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Prof Marco Paggi
Date Deposited: 29 Nov 2013 11:55
Last Modified: 09 Oct 2014 09:20
URI: http://eprints.imtlucca.it/id/eprint/1971

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