2.8. RELIABILITY OF A COMPONENT BY THE P-S-N CURVES APPROACH 55
For the stress level 2 to stress level 3, we have:
ˇ
2
D
ln N
C 2
ln
n
L2eq
ln N
C 2
D
11:01311 ln.27658:8/
0:191
D 3:986858: (d)
n
eq23
D exp
.
9:47966 3:986858 0:195
/
D 6016:27 (e)
n
3eq
D n
L3
C n
eq23
D 2800 C 6016:27 D 8816:27: (f)
e stress level 3 is the last. erefore, the reliability of the component in this example per
Equation (2.49) is
R D ˆ
"
ln N
C 3
ln
n
3eq
ln N
C 3
#
D ˆ
9:47966 ln.8816:27/
0:195
D ˆ.2:02721/ D 0:9787: (g)
In Example 2.14, if we convert the cyclic stress from the stress level 3 to the stress level 2,
and then from the stress level 2 to the stress level 1, we will get the reliability R D ˆ
.
2:07511
/
D
0:9810
. e results are slightly different because it is an approximate estimation with the assump-
tion of the equivalent fatigue damage concept.
2.8.7 RELIABILITY OF A COMPONENT UNDER MODEL #5 CYCLIC
LOADING SPECTRUM
Model #5 cyclic loading spectrum consists of multiple constant stress amplitudes of cyclic load-
ings with corresponding distributed cycle numbers at each cyclic stress level. is section will
discuss how to calculate the reliability of a component under model #5 cyclic loading spectrum.
It is very difficult to create the limit state function of a component under model #5 cyclic
loading spectrum. e author, in 2016, proposed an approach with a modified equivalent fatigue
damage concept to deal with this type of problem [16]. Let us use two stress loading levels with
a distributed number of cycles as an example to explain this approach. e cyclic loading and
corresponding component fatigue life at two different stress levels are listed in Table 2.22. n
Li
is a distributed number of cycles of the fully reversed cyclic loading with a stress amplitude
ai
in the stress level #i. N
Ci
is the distributed component fatigue life at the fully reversed fatigue
strength S
0
f
D
ai
in the stress level #i . e component fatigue life N
Ci
can be determined by
Equations (2.34), (2.35), and (2.36), which have been discussed in Section 2.8.2. Two assump-
tions [16] for this approach are as follows.
Assumption One: e reliability index of the component under cyclic loading is used as an
indirect index for measuring fatigue damage of a component. To transfer a distributed cyclic
number n
Li
at the stress level
ai
to the distributed cyclic number n
Lj
at the stress level
aj
, the
reliability index of the component due to n
Li
at the cyclic stress level
ai
should be equal to