Issue 53

Y. Saadallah, Frattura ed Integrità Strutturale, 53(2020) 417-425; DOI: 10.3221/IGF-ESIS.53.32 420 σ and ε being respectively the stress and the strain, the parameters are determined by a direct linear regression from the stress-strain curves. In addition, the nonlinear approach states that the behavior is non-linear in all domains. A polynomial of three degrees with four parameters is proposed. 3 2         A B C K (3) where A, B, C and K are positive parameters;  and  are respectively the stress and the strain. Since the polynomial is nonlinear of third order, recourse to numerical computation is necessary for the determination of its parameters. A polomial regression was favored to identify the behavior. Figure 3: Typical stress-strain curve of cork in compression. R ESULTS AND DISCUSSION he discussion of the results consists of a comparative study of the results obtained by the two models proposed. The identified parameters are presented and discussed. Test-model confrontations are put in place to judge the relevance of the results. Stress-strain curves aspect Fig. 4 illustrates the mechanical behavior of a sample of cork in compression in the non-radial direction. There are three domains that will be called elastic domain, buckling domain and densification domain. The elastic domain spreads at a strain of 7% while the buckling domain of the cells is limited to about 55% strain for all densities. Density is one of the parameters that influences cork resistance behavior [8, 15]. It is noted that this influence is apparent especially in buckling and densification levels. It should be emphasized that density is not the only factor to govern the behavior of cork. Other factors, such as porosity, quality [12], also have a significant effect on the strength of the material. Linear model Since the behavior is trilinear, it is governed by three parameters representing the slopes of the lines and two other parameters corresponding to the limit stresses of the elastic and buckling domains as illustrated in Fig. 3. The results of the parameters obtained are summarized in Tab. 1. In sum, the parameters of the least dense sample are small compared to the parameters of the other two samples. It is also noted that the slopes of the buckling domains F and densification D are largest for the densest sample. It should be mentioned that the stress  d . is not a significant parameter because it only corresponds to the end of the test. However, it can provide us with information on the stress corresponding to the final strain of the test which is 66.9%. The injection of these parameters into the trilinear behavior model formulated in Eqn. (2) makes it possible to compare the model test results as illustrated in Fig. 5. Good consistency in the elastic domain is observed. Indeed, the elastic domain is linear for most materials. Linearity is maintained at the beginning of the buckling step or the pace changes to nonlinear moving towards the densification zone. A relatively large gap appeared in the intersection of the buckling and densification T