eprintid: 1971
rev_number: 6
eprint_status: archive
userid: 56
dir: disk0/00/00/19/71
datestamp: 2013-11-29 11:55:29
lastmod: 2014-10-09 09:20:25
status_changed: 2013-11-29 11:55:29
type: article
metadata_visibility: show
creators_name: Paggi, Marco
creators_name: Carpinteri, Alberto
creators_id: marco.paggi@imtlucca.it
creators_id: 
title: Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue 
ispublished: pub
subjects: TJ
divisions: CSA
full_text_status: none
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. 
date: 2009
date_type: published
publication: Chaos, Solitons and Fractals
volume: 40
number: 3
publisher: Elsevier
pagerange: 1136 - 1145
id_number: 10.1016/j.chaos.2007.08.068
refereed: TRUE
issn: 0960-0779
official_url: http://www.sciencedirect.com/science/article/pii/S0960077907007035
citation:   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)