64 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
2.8.8 RELIABILITY OF A COMPONENT UNDER MODEL #6 CYCLIC
LOADING SPECTRUM
Model #6 cyclic loading spectrum is several distributed cyclic stress amplitudes at specified cycle
numbers, that is, .n
Li
;
ai
; i D 1; 2; : : : /. Here, n
Li
is a constant number of cycles in the cyclic
number level #i. Fully reversed cyclic stress level
ai
in the cyclic number level #i is a distributed
random variable. e corresponding component fatigue strength data will be the component
fatigue strength S
cfi
at the given fatigue life N D n
Li
. e component fatigue strength S
cfi
at
the given fatigue life N D n
Li
can be calculated per Equation (2.29). Its mean and standard
deviation can be calculated through Equations (2.30) and (2.31). is section will discuss how
to calculate the reliability of a component under model #6 cyclic loading spectrum.
It is difficult to establish the limit state function of a component under model #6 cyclic
loading spectrum. It is typically assumed that the influence of the sequence of cyclic loading on
fatigue life or fatigue damage can be negligible. erefore, each loading condition in the model
#6 can be treated as an independent event. e author proposed an approach [17] in 2017 to
estimate the reliability of a component under such cyclic loading spectrum. is approach has
the following two assumptions.
Assumption One: Based on the concepts of the widely accepted Miner rule [7, 10, 18], the
effect of the sequence of cyclic loading on the fatigue damage during the service life of the
component can be ignored, so that each cyclic loading stress condition .n
Li
;
ai
/ can be treated
as an independent random event.
Assumption Two: Since the fatigue damage of the component due to these independent cyclic
stress conditions is assumed to be independent, the estimation of the reliability R of the com-
ponent under Model #6 .n
Li
;
ai
/ is equal to the multiplication of the reliability R
i
of the com-
ponent under each cyclic loading condition .n
Li
;
ai
/.
Assumption One is mainly based on the widely accepted linear cumulative fatigue damage
theory. Assumption Two is a natural extension of Assumption One, but it is the expression of
the reliability computational method. So, according to Assumption Two, the reliability of a
component under the model #6 cyclic loading spectrum can be modeled as a series of reliability
block diagrams, each of which represents the component under each cyclic loading condition.
us, the reliability R of a component under model #6 cyclic loading spectrum is:
R D
L
Y
iD1
R
i
; (2.66)