@article{eprints1971,
          volume = {40},
            year = {2009},
          author = {Marco Paggi and Alberto Carpinteri},
           title = {Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue },
         journal = {Chaos, Solitons and Fractals},
           pages = {1136 -- 1145},
          number = {3},
       publisher = {Elsevier},
        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. },
             url = {http://eprints.imtlucca.it/1971/}
}