Self-similarity and crack growth instability in the correlation between the Paris’ constants

In this note the question about the existence of a correlation between the parameters C and m of the Paris’ law is re-examined. According to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter C to m and to the governing variables of fatigue is derived. Then, from the observation that the Griffith–Irwin instability must coincide with the Paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. A fair good agreement is found between the proposed theory and extensive experimental data.