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multiaxial and multivariable loading conditions, in which factors of stress ratios and
on-axis/off-axis orientations are taken into account and treated in simultaneously.
To introduce and implement new perspective and ef
cient approach based upon
arti
field of composite
materials lifetime assessment are the main motivation and objective of the present
study. It is preferred to handle the fatigue life assessment in such a way that fatigue
lives of different stress ratio and on-axis/off-axis orientation values are predicted
based upon fatigue data from, if possible, just limited number of stress ratio(s) and
on-axis/off-axis orientation(s) as the basis of training data.
In this study, the multilayer perceptron (MLP)-NARX and radial basis functions
NN (RBFNN)-NARX models were developed and further applied for composite
materials lifetime assessment application. Rational of the use of the NARX structure
in the application was emphasized and linked to the concept of CLD as described in
Sect. 2 . Fatigue life assessment was then performed and realized as one-step ahead
prediction with respect to each stress level corresponding to stress ratio values
arranged in such a way that transition took place from a fatigue region to another one
in the CLD. As a result, material lifetime assessment can be fashioned for a wide
spectrum of loading in an ef
cial intelligence and system identi
cation technique in the
cient manner. Such an analysis constitutes to a variable
amplitude or spectrum fatigue loading (Vassilopoulos et al. 2010 ).
2 Constant Life Diagrams (CLD)
Constant life diagrams (CLD) are graphical representations of the safe regime of
constant amplitude loading for a given speci
ed life, e.g. the endurance limit or
in
nite life (Sendeckyj 2001 ; Vassilopoulos et al. 2010 ). CLD also serves as a
convenient way in fatigue life assessment analysis under spectrum loading. CLD is
also another way to represent the S-N curve, with which design engineers are very
familiar. Stress ratio R, which is a ratio between minimum and maximum alter-
nating stresses, now in CLD also indicates what fatigue region the stress ratio value
belongs to. Figure 1 represents the CLD schematic.
The points along each radial line are the points of S-N curve for a speci
c stress
ratio. Moreover, as one can see in Fig. 1 , fatigue region moves from tensile-tensile
to compressive-compressive sector in CCW direction forming a spectrum of
loading conditions and all points with the same fatigue life N are connected with
lines in a plane of amplitude stress (S a )
mean stress (S m ) axes. The transition
regions are marked by stress ratio values of R = 1 (ultimate static strength), R =0
(minimum alternating stress equals zero), R =
-
1 (maximum alternating stress
equals the absolute value of minimum alternating stress) and R =
± *
(the absolute
value of minimum alternating stress is much higher than the value of maximum
alternating stress, which can be either positive or negative).
Dynamic nature of both the CLD and the NARX model to result in the
rst
application of the NARX model in spectrum fatigue analysis will be explored in the
developed NN architectures and procedures in the subsequent sections.
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