Fatigue crack growth

Paris' law (also known as the Paris-Erdogan law) relates the stress intensity factor range to sub-critical crack growth under a fatigue stress regime. As such, it is the most popular fatigue crack growth model used in materials science and fracture mechanics. The basic formula reads

where ${\displaystyle a}$ is the crack length and ${\displaystyle {\rm {d}}a/{\rm {d}}N}$ is the crack growth rate, which denotes the crack growth for a load cycle. On the right hand side, ${\displaystyle C}$ and ${\displaystyle m}$ are constants that depend on the material, environment and stress ratio, and ${\displaystyle \Delta K}$ is the range of the stress intensity factor during the fatigue cycle, i.e.,

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