20 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
• the fatigue strength S
0
f
D 31:89 ksi at the fatigue life N D 6:5 10
5
(cycles) under a fully
reversed cyclic stress, that is, (S
0
f
D 31:89 ksi, N D 6:5 10
5
cycles).
2.6 THE FATIGUE STRESS CONCENTRATION FACTOR
e fatigue stress-concentration factor K
f
will be used to multiply the nominal stress amplitude
and can be treated as a normally distributed random variable. Its mean
K
f
can be calculated
by the following equation [7]:
K
f
D
K
t
1 C
2
p
r
K
t
1
K
t
p
a
; (2.22)
where K
t
is static stress concentration factor which can be obtained through any design hand-
book and some websites. r is the notch radius in the unit of inch.
p
a is defined as the Neuber
constant and can be calculated through the following equation:
p
a D
8
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
:
5
S
ut
For a transverse hole
4
S
ut
For a shoulder
5
S
ut
For a groove;
(2.23)
where S
ut
is material tensile ultimate strength in the unit of ksi.
e coefficient of variance of the fatigue stress concentration factor K
f
can be estimated
by the following equation:
K
f
D
8
ˆ
ˆ
<
ˆ
ˆ
:
0:11 For a transverse hole
0:08 For a shoulder
0:13 For a groove:
(2.24)
e standard deviation of the fatigue stress concentration factor K
f
will be:
K
f
D
K
f
K
f
: (2.25)