The fatigue process involves the initiation and propagation of cracks in the material. The diagram below indicates the nature of the process. The crack starts at a surface flaw

which increases the local stress. In the compression part of the cycle, the stress pushes the crack closed. In the tension part, the crack can extend by an amount Da that is determined by the nature of the material and the amplitude of the tensile stress. As long as a is less than a 'critical' value, the crack is stable and increases in length each cycle. Once the crack reaches the 'critical' length, the material becomes unstable to fast

From: McMahon and Graham, :"The Bicycle and the Walkman," Merion (1992)

fracture at that stress and the sample fails. The critical crack length, c, is related to the surface energy of the crack, g, Young's Modulus, E, and the stress at fracture, s_{cr ,}by:
s_cr = (2 E g / pc)^0.5