2.9. THE PROBABILISTIC FATIGUE DAMAGE THEORY (THE K-D MODEL) 73
In this approach, a probabilistic distribution function is used to describe the fatigue test data at
the same cyclic stress level. If fatigue tests are at several cyclic stress levels such as seven stress
levels, there will be seven different probabilistic distribution functions if there are big enough
number of tests in each stress levels. However, the P-S-N curve approach has the following four
issues in its implementation for fatigue reliability design.
1. Since fatigue tests are time-consuming, there are only a few fatigue test data at each stress
levels, which are common cases, as shown in the fatigue data book [21]. In such a situation,
the P-S-N curve cannot be constructed due to the small sample size.
2. In some available fatigue test data, the total number of fatigue test might be more than
30 even though the number of fatigue tests in the same stress level is small, which is the
common case in the fatigue data book [21]. e P-S-N curve approach cannot use such
data to construct the P-S-N curves.
3. When the cyclic stress level in cyclic loading is not equal to the fatigue test stress level,
the probabilistic distribution function at this level is not available in the P-S-N curves,
which is a typical case in reality for fatigue design. So the P-S-N curves cannot be used
to solve this type of issue. e P-S-N curve approach could use the interpolation method
to obtain the probabilistic distribution function at the required stress level for reliability
fatigue design. However, this distribution function is not directly obtained from or based
on the test data, and it might induce some big error.
4. In fatigue tests, actual dimensions of fatigue specimen will be slightly different. erefore,
the actual stress level for the same nominal stress level fatigue test might be different; even
the nominal stress level is the same. However, the P-S-N curve approach ignores these
differences and use the nominal stress level to create the P-S-N curves.
e fatigue damage mechanism, which has been discussed in Section 2.2, shows that the
fatigue damage is mainly caused by cyclic loading and randomly distributed defects inside a
component such as voids and dislocations and or on the surface of a component such as man-
ufacturing scratches. is result strongly suggests that the fatigue damage mechanism for the
same type of material specimen under different cyclic test stress levels should be the same. ere-
fore, we can use all test data from every stress level to construct a probabilistic fatigue damage
model for presenting material strength, which is the topic in this Section 2.9.
2.9.2 THE MATERIAL FATIGUE STRENGTH INDEX K
0
In the traditional fatigue design, the S-N curve is typically plotted in a logarithmetic axis with
a fatigue strength S
0
f
verse the fatigue life N . S
0
f
is equal to a fully reversed stress amplitude
a
.
e fatigue life N is the number of cycles to failure at the stress level
a
. is traditional S-N
curve in logarithmic axes will typically be treated as a straight lineper Equation (2.1):
N.S
0
f
/
m
D Constant: (2.1)