${\displaystyle {\frac {{\rm {d}}a}{{\rm {d}}N}}=C\Delta K^{m}}$

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.