5.1 Stiffness degradation obtained by extensometer
In Fig. 6, the data from extensometer processed according to the
algorithm of section 4.1, are presented.
Fig. 6a shows E/E0 versus N . At a first
sight, it is possible to see that the entity of stiffness reduction is
the same at each stress level, and the metrics achieves a steady-state
value of 0.80 for each test. At a specific ratio value ofN/Nf , Fig. 6b, all the data exhibits the same
value of E/E0 and present a steady state
condition. The stiffness reduction occurs up toN/Nf of 0.3 according to literature[10], [17].
The stress dependence is appreciable in Fig. 6a, but at fixedN/Nf there is a slight effect on stiffness
reduction.
In this research, the models of literature (Eq. (3) and (4)) have been
considered as a reference for analysing the stiffness loss trend.
Table IIa reports the coefficients A , b , d of Eq.
(3) obtained by the fitting of the data provided by extensometer and the
squared correlation coefficient R2 .
Eq. (4) can be rewritten by indicating the stress dependence of Kcoefficient, Eq. (8):
\(\frac{E}{E_{0}}=\left(C\sigma_{\max}\right)^{a}\left(\frac{N}{N_{f}}\right)^{k}\)(8)
with the coefficients C , a and k experimentally
determined.
Table IIb reports the coefficients of Eq. (8) together with theR2 coefficient. This latter is higher in the
case of the model described by Eq. (8) indicating a better capability of
this model in describing the stiffness degradation of the investigated
material.
Fig. 7 reports graphically for each stress level the comparison between
the two models and experimental data in terms ofE/E0 . The model of Eq. (8) (black dotted line)
fits better than the one of Eq. (3) (black solid line) the experimental
data. However, it is noteworthy to highlight that all the literature
models are not capable of describing all the damage stages of the
materials. In effect, the steady state conditions are not taken into
account in the model even if the stabilisation of the stiffness is an
important stage of the damage [5-15].
The model of Eq. (3) fits very well the behaviour of the material at
initial cycles but in some cases (Fig. 7a and c) it does not model the
major stiffness degradation that occurs between 0-0.4 ofN/Nf . On the other hand, the model of Eq. (8)
seems to be a good compromise for describing all the damage stages. This
latter model will be used as reference to represent stiffness
degradation of the material in the next section.