16 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
will have a different surface finish, different dimension, and different types of cyclic loading.
Different surface finish will have quite different initial defects or cracks on the surfaces. A com-
ponent with a bigger dimension means that it will have a much higher likelihood of more initial
defects inside components. e maximum stress’ area of a component due to bending, torsion,
and axial loading are quite different. For a component under bending, the maximum stress will
happen on the uppermost and lowermost layers. For a component under torsion, the maximum
stress will appear on the outer surface. However, a component under axial loading, the maxi-
mum stress will appear on the whole cross-section. erefore, component fatigue strength will
be different from the material fatigue strength obtained from fatigue specimen tests. is differ-
ence of fatigue strength between fatigue test specimen and a component is typically considered
by several Marin modification factors [2, 6, 7]. ose modifications on the material fatigue test
data are based on the rotating-beam bending fatigue test under a fully reversed cyclic bending
stress. e following equation can calculate component endurance limit S
e
at the critical section:
S
e
D k
a
k
b
k
c
S
0
e
; (2.12)
where S
0
e
is the material endurance limit obtained from fatigue test on the fatigue test spec-
imen. k
a
is the surface finish modification factor. k
b
is the size modification factor. k
c
is the
loading modification factor. A mechanical component might have several different component
endurance limits at different critical section due to the different size modification factors.
Component fatigue strength S
f
at a given fatigue life N can be obtained through the
following equation:
S
f
D k
a
k
b
k
c
S
0
f
; (2.13)
where S
0
f
is material fatigue strength at the fatigue life N , which is the number of cycles at
failure in the fatigue test. For fatigue design, the component fatigue strength S
f
is not one value
and will have a different value at different given fatigue life N . e rests in Equation (2.13) are
the same as those in Equation (2.12).
e surface finish modification factor k
a
can be treated as a normally distributed random
variable. Its mean
k
a
[7] will be calculated by the following equations:
k
a
D
8
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
:
16:45
.
S
ut
/
0:7427
For hot-rolled component
39:9
.
S
ut
/
0:995
For as-forged component
2:7
.
S
ut
/
0:2653
For machined surface component
1:34
.
S
ut
/
0:0848
For ground surface component;
(2.14)
where S
ut
is material ultimate tensile strength in the unit of ksi.