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.
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