2.9. THE PROBABILISTIC FATIGUE DAMAGE THEORY (THE K-D MODEL) 81
2.9.5 THE PROBABILISTIC FATIGUE DAMAGE THEORY (THE K-D
MODEL)
Based on the definitions of the component fatigue strength index K and the component fatigue
damage index D, the general limit state function of a component under cyclic loading is:
g
.
K; D
/
D K D D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(2.86)
If the material fatigue strength index K
0
is given, the limit state function of a component under
model #1, model #2, or model #3 cyclic loading spectrum is:
g
.
K; D
/
D K D D
.
k
a
k
b
k
c
/
m
K
0
n
L
K
f
a
m
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(2.87)
All variables in Equation (
2.87) have the same meanings as those in Equations (2.79) and (2.84).
If the material fatigue strength index K
0
is given, the limit state function of a component
under model #4, model #5, or model #6 cyclic loading spectrum is:
g
.
K; D
/
D K D D
.
k
a
k
b
k
c
/
m
K
0
L
X
iD1
n
Li
K
f
ai
m
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(2.88)
All variables in Equation (2.88) have the same meanings as those in Equations (2.79) and (2.85).
When this probabilistic fatigue damage model (the K-D model) is used, the reliability of a
component under any cyclic loading spectrum can be calculated per Equations (2.87) or (2.88).
2.9.6 RELIABILITY OF A COMPONENT UNDER CYCLIC AXIAL
LOADING
Per Equations (2.87) or (2.88), we can establish the limit state function of a component under
any type of cyclic axial loading spectrum. After the limit state function of a component under
cyclic axial loading is established, we can use the H-L method, R-F method, or Monte Carlo
method to calculate its reliability. In this section, we will use two examples to demonstrate how
to calculate the reliability of a component under cyclic axial loading spectrum.
Example 2.22
A constant round bar with a diameter 0:850 ˙ 0:005
00
is subjected to model #1 cyclic axial loading
spectrum as listed in Table 2.37. e ultimate material strength S
u
is 75 (ksi). ree parameters