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 $\sigma _{a}(N_{f})$ or $\sigma _{m}(N_{f})$. It is based on empirical results and often represents the median of the data scatter.

Wöhler curves of Steel and Aluminum

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
• $\Delta \sigma _{C}=$ 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: $\Delta \sigma _{C}$.

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.