  A theoretical study based on dimensional analysis and fractal geometry of
crack profiles is proposed to establish the relation between their fractal
dimension D (1<D<2) and the parameters defining the fatigue crack propagation
rate. The exponent m of the Paris' law is found to be an increasing function of
the fractal dimension of the crack profile, m=2D/(2-D). This trend is confirmed
by a quantitative analysis of fractographic images of Titanium alloys with
different grain sizes (different roughness of crack profiles), by a new
experimental test and by an indirect estimation of D from crack growth
equations accounting from crack-size effects in Steel and Aluminum. The present
study can be considered as the first quantitative analysis of fractographic
images aiming at relating the morphological features of cracks to their
kinetics in fatigue.
