2.8. RELIABILITY OF A COMPONENT BY THE P-S-N CURVES APPROACH 47
Table 2.16: e iterative results of Example 2.11 by the H-L method
Iterative #
k
a
*
k
f
*
S
'
*
f
β
*
|∆β
*
|
1 0.9053 1.5932 21.8117 1.508306
2 0.87095 1.718111 24.4495 1.559894 0.051589
3 0.865776 1.721417 24.64291 1.561837 0.001942
4 0.865396 1.721634 24.65684 1.561987 0.00015
5 0.865369 1.72165 24.65787 1.561999 1.18E-05
2.8.4 RELIABILITY OF A COMPONENT UNDER MODEL #2 CYCLIC
LOADING SPECTRUM
Model #2 cyclic loading is one constant cyclic stress level
a
with a distributed number of cycles
n
L
. When a component is subjected to model #2 cyclic loading and if the component fatigue
life N
C
at the cyclic stress level
a
is provided, we will have the following limit state function:
g
.
N
c
; n
L
/
D N
c
n
L
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure;
(2.41)
where N
c
is the component fatigue life at the fatigue strength S
0
f
D
a
.
If the component fatigue life N
C
at the cyclic loading stress loading level
a
is obtained
per Equation (2.34), the limit state function of a component under the model #2 cyclic loading
spectrum will be:
g
k
a
; k
c
; K
f
; N; n
L
D N
k
a
k
b
k
c
K
f
m
n
L
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure;
(2.42)
where k
a
, k
b
, k
c
, and K
f
are the surface finish modification factor, the size modification factor,
the loading modification factor, and the fatigue stress concentration factor, respectively. k
a
, k
c
,
and K
f
will be normally distributed random variables. k
b
will be treated as a deterministic con-
stant. N is a distributed material fatigue life at the fatigue strength S
0
f
D
a
. n
L
is a distributed
number of cycles of the cyclic stress loading
a
.
Both limit state function (2.41) and (2.42) can be used to calculate the reliability of a
component under model #2 cyclic loading spectrum by the H-L, R-F, or Monte Carlo method.
We will use the limit state function (2.41) to demonstrate an example.