[<< wikibooks] 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

σ

a

(

N

f

)

{\displaystyle \sigma _{a}(N_{f})}
or

σ

m

(

N

f

)

{\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

σ

a

m

N
=
C

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

Where

C

{\displaystyle C}
is a constant specific to the test case.
The Basquin relation is often presented in the form

Δ
σ
=
Δ

σ

C

(

N

C

N

)

1
m

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

where

N

C

=
2
⋅

10

6

{\displaystyle N_{C}=2\cdot 10^{6}}
cycles

Δ

σ

C

=

{\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:

Δ

σ

C

{\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

N
=
2
⋅

10

6

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

== Statistical Properties ==