Issue 50

D. Triantis et alii, Frattura ed Integrità Strutturale, 50 (2019) 537-547; DOI: 10.3221/IGF-ESIS.50.45 542 A similar pattern prevails in stage D with exponent values m=0.94 and m=0.29, respectively (Fig.5b). Deviation from the law of Eq.(2) is only observed in this stage for t-t o >40 s with the cumulative energy increasing quite rapidly. This deviation is obviously correlated to the fact that at this time instant the average rate of strain growth starts increasing rapidly (see Fig.3) indicating entrance of the system (specimen) into a state of impending failure, and providing thus a potentially inter- esting pre-failure indicator. Frequency of occurrence of AE hits - Analysis in terms of the F-function [7] In this section, a new way of exploring details of the acoustic activity is employed, based on the recently introduced F- function, which represents an average frequency of the AE hits, in a window of N successive hits [7]. To compute and plot the F-function the inter-event times of a sufficient number of Ν (Ν>10) consecutive hits are used, in conjunction to the “sliding window” technique. Each value of the F-function is paired to an average time instant of the time instants of the N successive hits used to calculate the specific value of the F-function. Analytic description of how the F-function is determined can be found in refs. [7, 19]. This approach appears to be advantageous, since it allows for a continuous repre- sentation of the acoustic activity in a given time period rather than for a quantized presentation of the respective data, which characterizes the familiar plots of hits per second. This presentation is particularly useful when intense AE activity is recorded within a very short time interval. It offers, also, valuable information concerning the time evolution of the acoustic activity just before the failure of the samples, providing direct information on the frequency of micro-cracking activity within the specimen. Quite a few research teams worldwide are already using the F-function to study various aspects of the acoustic activity, especially in brittle materials [20-23]. The way according to which the F-function varies throughout the experiment discussed in previous sections is shown in Fig.6. The first significant and abrupt increase of the value of the F-function is observed in stage A and, in particular, after the 125 th second (denoted from here on as t * ). This time instant corresponds to the transition phase from the linear to the non-linear response of the material (see point K, Fig.1). Moreover, at the beginning of stage C, the F-function increases, also, considerably. At the beginning of stages B and D (stages of constant stress level), the F-function exhibits a rapid de- crease and re-establishes low values, due to the sparse occurrence of AE. In particular, in stage D, the F-function, after a short period with low values, shows a gradual increase attaining a maximum value just a few seconds prior to the macro- scopic fracture of the specimen, providing another interesting pre-failure indicator. Due to its increased importance the behaviour of the F-function during the last seconds of stage D will be discussed thoroughly in next paragraphs. 0 20 40 60 0 50 100 150 200 250 300 time (sec) stress (MPa) 0 50 100 150 F-function (1/sec) stress F function stage A stage B stage C stage D t* F-function [s -1 ] Time [s] Axial stress [MPa] Axial stress [MPa] Figure 6 : Time evolution of F-function during the experiment. The time evolution of the F-function and the respective one of the I b -values exhibit several qualitative similarities, as it is shown in Fig.7. More specifically, the sharp decrease of the I b -values observed at the end of stages A and D, as well as during stage C, is combined with the corresponding intense increase of the acoustic activity expressed by the F-function. Furthermore, the intense decrease of the F-function at the beginning of stages B and D is combined with the gradual in- crease of the I b -values. Special attention must be paid to the last seconds of stage D, at which an abrupt decrease of the I b -values, to levels approaching 1, is observed. At the same time, as far as the F-function is concerned, a strong increase is recorded, leading to a local peak, which designates and presages the upcoming failure of the specimen [7].