The application of dimensional analysis and similarity methods to the study of the speed of fatigue crack growth is considered. It is shown that the Paris range of the crack propagation diagram is an intermediate-asymptotic stage of the crack growth process. Over this stage the influence of the initial conditions on the process of fatigue crack growth has disappeared but the influence of the instability has not yet intruded. So-called incomplete self-similarity prevails at this stage with respect to a basic similarity parameter, equal to the ratio of the stress intensity factor amplitude to the fracture toughness. It is shown that for a certain material under fixed external loading conditions the exponent in the Paris power law is a universal function of the ratio of specimen thickness to the ultimate size of the cyclic plastic zone. Processing of available experimental data confirmed the results obtained by this approach. Nomenclaturegrain size hK range of the stress intensity factor specimen thickness N number of loading cycles length of a fatigue crack static yield strength C, m constants in the Paris equation cyclic yield strength z similarity parameter cyclic fracture toughness t time plane strain fracture toughness ultimate size of cyclic plastic zone dlldN rate of fatigue cmck growth R asymmetry ratio of the loading cycle

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