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.

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.