Paris' law
![Schematic plot of the typical relationship between the crack growth rate and the range of the stress intensity factor. In practice, the Paris law is calibrated to model the linear interval around the center.](/Images/godic/202501/06/ParisLaw1437.png")
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