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A theoretical study based on dimensional analysis and fractal geometry ofcrack profiles is proposed to establish the relation between their fractaldimension D (1<D<2) and the parameters defining the fatigue crack propagationrate. The exponent m of the Paris' law is found to be an increasing function ofthe fractal dimension of the crack profile, m=2D/(2-D). This trend is confirmedby a quantitative analysis of fractographic images of Titanium alloys withdifferent grain sizes (different roughness of crack profiles), by a newexperimental test and by an indirect estimation of D from crack growthequations accounting from crack-size effects in Steel and Aluminum. The presentstudy can be considered as the first quantitative analysis of fractographicimages aiming at relating the morphological features of cracks to theirkinetics in fatigue.

On the dependency of the parameters of fatigue crack growth from the fractal dimension of rough crack profiles