22 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
2.7 RELIABILITY OF A COMPONENT WITH AN
INFINITE LIFE
For a component with infinite life, the component endurance limit
S
e
will be used for the com-
ponent fatigue design. e limit state function of a component with an infinite life will be:
g
S
e
; K
f
;
eqa
D S
e
K
f
eqa
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure;
(2.26)
where S
e
is the component endurance limit at the critical section, which is defined by Equa-
tion (2.12). K
f
is the fatigue stress concentration factor at the critical section and is defined by
Equations (2.22)–(2.25).
eqa
is the component’s equivalent fully reversed cyclic stress ampli-
tude at the critical section and is determined by Equation (2.21).
e limit state function Equation (2.26) can be used to calculate the reliability of a com-
ponent with infinite life. e H-L, R-F, or Monte Carlo method, which were discussed in
Chapter 3 of Le [8], can be used to calculate its reliability. e concise description of proce-
dures of three methods is presented in Appendix A of this book. We will use three examples to
demonstrate how to calculate the reliability of a component with infinite life. e corresponding
MATLAB programs will be displayed in Appendix B for a reference.
Example 2.6
A machined constant circular bar with a diameter d D 1:250 ˙ 0:005
00
is subjected a cyclic axial
loading. e mean axial loading F
m
of the cyclic axial loading is a constant and equal to 12 (klb).
e loading amplitude F
a
of the cyclic loading follows a normal distribution with a mean
F
a
D
8:5 (klb) and a standard deviation
F
a
D 1:2 (klb). e ultimate material strength is 61.5 (ksi).
Its endurance limit S
0
e
follows a normal distribution with a mean
S
0
e
D 24:7 (ksi) and a standard
deviation
S
0
e
D 2:14 (ksi), which are based on fatigue tests under fully reversed bending stress.
is bar is designed to have an infinite life. (1) Establish the limit state function of this problem.
(2) Calculate the reliability of the bar under the cyclic axial loading.
Solution:
(1) Establish the limit state function of this problem.
We can use Equation (2.26) to establish the limit state function for this problem.
Per Equation (2.12), the component endurance limit will be:
S
e
D k
a
k
b
k
c
S
0
e
: (a)