%I Elsevier
%P 1136 - 1145
%R 10.1016/j.chaos.2007.08.068
%A Marco Paggi
%A Alberto Carpinteri
%L eprints1971
%D 2009
%V 40
%N 3
%T Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue 
%J Chaos, Solitons and Fractals
%X 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.