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.
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