# 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 ${\displaystyle \sigma _{a}(N_{f})}$ or ${\displaystyle \sigma _{m}(N_{f})}$. 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

${\displaystyle \sigma _{a}^{m}N=C}$

Where ${\displaystyle C}$ is a constant specific to the test case.

The Basquin relation is often presented in the form

${\displaystyle \Delta \sigma =\Delta \sigma _{C}({\frac {N_{C}}{N}})^{\frac {1}{m}}}$

where

• ${\displaystyle N_{C}=2\cdot 10^{6}}$ cycles
• ${\displaystyle \Delta \sigma _{C}=}$ 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: ${\displaystyle \Delta \sigma _{C}}$.

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 ${\displaystyle N=2\cdot 10^{6}}$ cycles.