Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Crack Initiation/The Wöhler Curve
The Wöhler curve, also referred to as the S-N curve, describes the function or . It is based on empirical results and often represents the median of the data scatter.
A significant interval of the curve can be approximated by the Basquin relation
Where is a constant specific to the test case.
The Basquin relation is often presented in the form
- is the so called detail category number.
Detail Category Number 
The fatigue detail number defines the Basquin relation and specifies a Wöhler curve. The property is often denoted FAT, C, or in mathematical expressions: .
If there are more than one FAT tied to a geometry-type, they refer to different specifics such as weld quality, loading direction etc. Moreover, the FAT normally corresponds to a fatigue life of cycles.