English: ${\displaystyle {\frac {{\rm {d}}a}{{\rm {d}}N}}=C\Delta K^{m}}$ (Paris' law)

For a typical fatigue crack growth process, the crack growth rate is plotted over the range of the stress intensity factor (in red). Paris' law is fitted to quasi-linear part of this curve (in black). The crack growth rate, da/dN, denotes the change in crack length, a, with increasing number of load cycles, N. The range of the stress intensity factor, ${\displaystyle \Delta }$K, depends on the magnitude of the loading, the geometry, and the crack length. Both quantities (i.e., da/dN and ${\displaystyle \Delta }$K) evolve during the fatigue process until the specimen fails.

On a log-log plot, the two Paris law model parameters, C and m, can be determined graphically as the y-axis intersect at x=1 and the slope, respectively. The values of the model shown here, i.e., C=10^-12 and m=2.85, are typical for, e.g., aluminum.