102 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
tion 2.9 such as Examples 2.24, 2.28, and 2.30 use the Monte Carlo method to calculate the
reliability of component under a cyclic loading spectrum.
2.9.12 THE COMPARISON OF RESULTS BY THE K-D MODEL WITH THE
RESULTS BY THE P-S-N CURVES
Both the P-S-N curves and the K-D model are probabilistic fatigue theory and can be used to
describe material fatigue test data, that is, material fatigue strength. Both can be used to calculate
the reliability of a component under cyclic loading spectrums.
Table 2.11 in Section 2.8.1 list fatigue test results of 195 fatigue tests on the 10 gauge
6060-T6 sheet-type flat test specimen under 5 different cyclic axial stress levels. e P-S-N
curves on these set of fatigue data are shown in Table 2.13 and are redisplayed here for conve-
nience. e K-D model on these set of fatigue test data is listed in Table 2.35 and redisplayed
here for conveniences. Now, the following three Examples 2.32–2.34 will be used to compare
the results from both fatigue theories.
Table 2.13: e P-N distribution at different fatigue strength levels
Axial Stress
Level #
σ
a
(ksi) σ
m
(ksi)
Equivalent Stress
σ
a˗eqi
(ksi)
Lognormal Distributed Fatigue Life
μ
lnN
σ
lnN
1 20.833 20.833 35.126 11.4736 0.238106
2 22.083 22.083 38.832 11.0410 0.227320
3 22.5 22.5 40.139 10.9551 0.242377
4 22.917 22.917 41.485 10.7831 0.225735
5 23.333 23.333 42.871 10.716 0.241955
Table 2.35: K
0
with three distribution parameters
Material: 6061-T6
10-Gauge Sheet
Sample Size:
195
Test Conditions: Cyclic Axial Stress, Milled
Machined Sheet-type Flat Specimen
Slope of the Traditional S-N
Curve: m
Log Normally Distributed K
0
Log Mean: μ
lnK
0
Log Standard Deviation: σ
lnK
0
3.8812 25.3014 0.245451
Example 2.32
e aluminum 6061-T6 10 Gauge sheet-type flat fatigue specimen, as shown in Figure 2.8 is
subjected to cyclic axial stress with a stress amplitude 20.833 (ksi) and mean stress 20.833 (kis).
e number of cycles of this cyclic axial loading is 60,000 (cycles). e ultimate tensile strength