Issue 50

D. Triantis et alii, Frattura ed Integrità Strutturale, 50 (2019) 537-547; DOI: 10.3221/IGF-ESIS.50.45 544      n f F c t t (4) where t f is the time instant corresponding to the fracture of the sample and t, n are numerically obtained constants. A similar response is observed in the present experimental protocol. This is clearly seen in Fig.9, in which the F-function is plotted versus the (t f -t) parameter on log-log scales. Plotting the F-function versus the specific parameter offers a “magnified” pic- ture of what happens during the very last instants before macroscopic fracture. It is observed from Fig.9 that from the critical time instant at which the F-function starts increasing (i.e., about 40 s before the specimen’s macroscopic fracture) the law of Eq.(4) prevails, with an exponent value equal to n=1.4, close enough to the value of n=1.2 determined in the protocol described in ref. [7] for marble specimens under monotonic uniaxial compression. From this time instant on, i.e., for (t f -t)<5 s, the F-function exhibits a stabilisation trend at relatively high values. Finally, during the very last tenths of a second before macroscopic fracture (i.e., (t f -t)<0.7 s) the values of the F-function are reduced, as a consequence of the high values of the respective inter-event times, due to the fact that long-duration acoustic hits are recorded (again in ac- cordance with the behaviour observed in ref. [7]). y = 1042.10x -1.44 1 10 100 1000 0.1 1 10 100 tf - t (sec) F - function (1/sec) 100 100 10 1 F-function [s -1 ] 0.1 1 10 100 y=1042.10x - 1. t f - t [s] Figure 9 : The F-function versus the (t f -t) parameter on a log-log scale, during the last seconds before the sample failure (i.e., during the last time interval of stage D). Classification of the cracking modes by correlating Average Frequency and RA values to the values of the F-function The AE technique is already widely used to classify the cracking modes according to the RILEM TC 212-ACD Recommend- ation, with very satisfactory results, for example in concrete [24]. According to the specific recommendation, the classifica- tion of micro-cracking in Mode-I or Mode-II is achieved through the correlation of the parameter RA (Rise Time/Ampli- tude) of the acoustic signals to their Average Frequency (AF). In order to investigate how the average values of RA and AF are correlated in the various loading stages of the experimental protocol considered here, in which both high and low acoustic activity is observed, the following procedure is followed: As a first step, the maximum value F max of the F-function is determined. For the specific experiment, considered in previous sections, the time instant at which the F-function was maximized was found equal to about t=319 s and the corresponding value of the F-function was F max =145.7 s -1 . For each one of the four stages of the loading protocol the acoustic hits were classified into three categories: The first one includes the hits that are recorded when the acoustic activity is low or, equival- ently, the normalized function f=F/F max varies in the 0<f<0.1 range. The second category includes the hits recorded when 0.1≤f<0.5 (i.e., the acoustic activity is of moderate intensity), and the third one includes the hits recorded when f≥0.5 (i.e., the acoustic activity is intense). As a second step, for each one of these three categories and for each stage of the loading protocol the average values of RA and AF are calculated. In Fig.10 the mean value of the AF is plotted against the respective mean value of the RA for all three categories and all four stages. Α straight line of slope equal to k=0.5 kHz·mV/μs is plotted, starting from point (0, 0), in order to study the ratio between the RA and AF values and properly classify the cracking modes within the marble volume. It is noted here that the appropriate slope of this line is an open issue for research, as there is not a generally accepted rule. In general, it is believed that this slope is to be determined taking into account the type of the material and the type of the experiment [25].