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.