relation: http://eprints.imtlucca.it/1971/
title: Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue 
creator: Paggi, Marco
creator: Carpinteri, Alberto
subject: TJ Mechanical engineering and machinery
description: 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. 
publisher: Elsevier
date: 2009
type: Article
type: PeerReviewed
identifier:   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)  
relation: http://www.sciencedirect.com/science/article/pii/S0960077907007035
relation: 10.1016/j.chaos.2007.08.068