Are the Paris' law parameters dependent on each other?

Abstract

The question about the existence of a correlation between the parameters C and m of the

Paris' law is re-examined in this paper. 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 the fatigue phenomenon 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 correlation and the experimental data concerning Aluminium, Titanium and steel alloys.