PSI - Issue 33

Dimos Triantis et al. / Procedia Structural Integrity 33 (2021) 330–336 Dimos Triantis et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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3. Focusing attention at the stage of impending fracture The time evolution of the load applied and that of the hits-per-second recorded by the acoustic sensors at the crowns of the two notches are plotted in Fig. 3a, again for a typical specimen. It is seen that the acoustic activity is strongly intensified only during the very last instants before fracture. At this time interval the experimental data are packed very closely to each other and therefore it is quite possible that important information remains hidden. To enlighten better what happens during this critical interval many researchers adopt an alternative approach for the representation of the experimental data recorded by the acoustic sensors. This approach is based on the so-called “ time to-fracture ” parameter, i.e., on the (t f -t) variable, where t f is the time instant at which macroscopic catastrophic fracture is observed. In fact, according to this approach, the experimental data are plotted along an “inverse” time arrow , usually in logarithmic scale. Plotting the data of Fig. 3a according to this alternative representation one obtains Fig. 3b. It is obvious that the specific representation offers a much clearer insight to what happens during the very last loading steps. Moreover, it permits clear distinction between the data recorded by each sensor. For the specific test, for example, it is indicated that the sensor S2 detects stronger acoustic activity with respect to that detected by sensor S1. 0 20 40 0 1 2 0 500 1000 1500 Load [kN] t [s] Load ch1 ch4 ch1 ch4

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(a) (b) Fig. 3. The load applied and the hits-per-second recorded by both acoustic sensors, for a typical experiment, versus (a) time; (b) “ time-to- fracture” parameter (adopting semi-logarithmic scales). The blue lines correspond to the notch from which fracture started. Adopting the above-described representation, an attempt is now undertaken to explore the acoustic activity recorded during the very last loading steps, i.e., while fracture is impending. It is well known that the acoustic activity is studied by means of quite a few parameters, including, for example, the energy of the acoustic waves, the rise time and the amplitude of the respective pulses, the Ib-value, the time rate of the hits recorded, the recently introduced F-function (Triantis et al. 2018), the cumulative counts etc. Each parameter offers specific advantages enlightening specific aspects of the phenomenon studied. The choice among these parameters depends mainly on the targets of each protocol. In this study, the acoustic activity is analysed, initially, in terms of the cumulative counts and then of the F-function. Along this direction, the time evolution of the cumulative counts is plotted in Fig. 4 against the “time -to- fracture” (t f -t) parameter, for characteristic specimens of all four classes of experiments (i.e., for specimens with a 0 =2 cm, a 0 =4 cm, a 0 =6 cm, a 0 =8 cm). For all graphs logarithmic scales are adopted for both the cumulative counts and the (t f -t) variable. The same scale is adopted for all four plots for comparison reasons. The data used to plot Fig. 4 are those recorded by the sensors attached at the crown of the notch from which fracture started. In addition, the load applied is, also, plotted, using again the same scale for all experiments considered. It is clearly seen that, for all cases, during the very last seconds of the experiments’ duration the acoustic activity is described by a power law of the form y=cx - m , where c and m are numerical constants, determined by proper curve fitting to the experimental data of each experiment. The time interval, during which this power law governs the response of the specimens, varies between three and twelve seconds before their macroscopic fracture. Concerning the numerical values of the exponent m, it is observed that they vary within a relatively narrow interval, ranging between m=0.30 and m=0.47, at least for the specimens and the material of the specific experimental protocol. On the contrary, the numerical values of the constant c vary between extremely broad limits. 0 25 50 75 0 1 2 3 1 10 100 1000 Hits per second Load [kN] t f -t [s] Load ch1 ch4