2.8. RELIABILITY OF A COMPONENT BY THE P-S-N CURVES APPROACH 39
Equation (2.29) can be used to build the limit state function Equation (2.28) of the component
under cyclic stress at the given fatigue life. is result is the second approach to obtain com-
ponent fatigue strength at the given fatigue life. We can assume that the modification factors
will not change the type of distributions, but only change the distribution parameters. So, we
can assume that S
cf
will have the same type of distribution as that of S
0
f
. If S
0
f
follows a normal
distribution with a mean
S
0
f
and a standard deviation
S
0
f
, the normally distributed S
cf
will
have the following mean
S
cf
and standard deviation
S
cf
:
S
cf
D
k
a
k
b
k
c
K
f
S
0
f
(2.30)
S
cf
D
k
a
k
b
k
c
K
f
S
0
f
v
u
u
t
k
a
k
a
2
C
k
c
k
c
2
C
K
f
K
f
!
2
C
S
0
f
S
0
f
!
2
; (2.31)
where
k
a
and
k
a
are the mean and the standard deviation of the surface finish modification
factor k
a
and determined per Equations (2.14), (2.15), and (2.16). k
b
is the size modification
factor and determined per Equation (2.17).
k
c
and
k
c
are the mean and the standard deviation
of the load modification factor k
c
and determined per Equations (2.18), (2.19), and (2.20).
K
f
and
K
f
are the mean and standard deviation of the fatigue stress concentration factor K
f
and
determined per Equations (2.22), (2.23), (2.24), and (2.25).
S
0
f
and
S
0
f
are the mean and the
standard deviation of material fatigue strength S
0
f
at the given fatigue life.
S
cf
and
S
cf
are the
mean and the standard deviation of the component fatigue strength at the given fatigue life.
For the component fatigue life N
c
at the given cyclic stress level, we can use the following
approach to modify the material fatigue life N . In a traditional S-N curve per Equation (2.1),
the component S-N curve will be:
N
k
a
k
b
k
c
K
f
S
0
f
m
D constant: (2.32)
We can rearrange Equation (2.32) as follows:
N
k
a
k
b
k
c
K
f
m
S
0
f
m
D constant: (2.33)
Based on Equation (2.33), we can use N
c
to represent the component fatigue life after the
consideration of all modification factors at the given cyclic stress level:
N
c
D N
k
a
k
b
k
c
K
f
m
: (2.34)
It is assumed that the component fatigue life N
c
has the same type of distribution as that of N .
If N is a lognormal distribution with a log-mean
ln N
and log-standard deviation
ln N
, the