Fatigue is the deterioration of a structure's ability to sustain normal operating stresses. This deterioration occurs gradually over time, and is caused by cracks growing within the material of the structure. Examples of such failures in an engineering context include cracking in the skin of an aircraft, engine blocks on cars, cranks and forks in bicycles, ships propellers and bridges. In all these cases, the cause of structural failure is the growth of one dominant crack.
While it is possible to model lifetime in more general terms, the key to structural failure is cracking within the material under stress, and when modelling fatigue, this is a good place to start.