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

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

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

where

• $N_C = 2 \cdot 10^6$ cycles

## 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: $\Delta\sigma_C$.

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 $N = 2 \cdot 10$ cycles.