PSI - Issue 26

Andronikos Loukidis et al. / Procedia Structural Integrity 26 (2020) 277–284 Loukidis et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3. The applied stress and the corresponding recorded PSC values during the loading protocol for a) the amphibolite specimen and b) the marble specimen. 4. Results and discussion Figures 3a) and 3b) depict the applied stress and the corresponding recorded PSC values for the amphibolite and the marble specimen respectively. As one can notice, the failure of both specimens occurred after the application of eight loading cycles. The amphibolite specimen had a failure stress of 44.1MPa f  and it was observed during the eighth loading step ( 8 f    ), while the corresponding value for the marble specimen was 47.5MPa f  , with the value 8  being slightly lower than f  .The study of the temporal relaxation of PSCs for mi t t  , shows that the function * ( ) t  obeys the functional form of Eq.3. (see Fig.4). By fitting Eq.3, the values for the entropic index q and the time parameter q  are derived. Figures 4a) and 4b) show the function * ( ) t  in the case of the amphibolite specimen which for depicting reasons were split in two graphs. Similarly, Figs.4c) and 4d) present the function ξ * (t) values, along with their corresponding q -exponential fitting curves for the marble specimen. Table1 presents the values of q and q  for each loading step, in the case of both classes of specimens as well as the stress i  . Figure 5 (a) shows the Tsallis’ q parameter versus the normalised stress i f   for both the marble and amphibolite specimens, plotted in blue and grey lines respectively. Notice, that up to 0.85 of the specimens’ uniaxial strength , the q parameter increases systematically, reaching a maximum value of approximately 1.4. Subsequently, for the last two loading steps as the total applied mechanical stress exceeds 0.9 of the compressive axial strength the q parameter shows a slight decrease It is noted that the increase of q manifests the fact that subadditivity is dominant and strongly affects the total entropy of the system manifesting the influence of the pre-existing status of the specimen to each next one. On the other hand, the drop of the entropic index q manifests initiation of dynamic processes that take place before failure leading the specimen-load system in criticality indicating the upcoming fracture.