Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Crack Initiation/The Wöhler Curve

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Wöhler curves of Steel and Aluminum
Wöhler curves of Steel and Aluminum

The Wöhler curve, also referred to as the S-N curve, describes the function  \sigma_a(N_f) or  \sigma_m(N_f) . 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

\sigma_a^m N = C

Where  C is a constant specific to the test case.

The Basquin relation is often presented in the form

\Delta \sigma = \Delta \sigma_C (\frac{N_C}{N})^\frac{1}{m}


  •  N_C = 2 \cdot 10^6 cycles

Detail Category Number[edit]

The fatigue detail number defines the Basquin relation and specifies a Wöhler curve. The property is often denoted FAT, C, or in mathematical expressions: \Delta\sigma_C.

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  N = 2 \cdot 10^6 cycles.

Statistical Properties[edit]