Issue 50

D. Triantis et alii, Frattura ed Integrità Strutturale, 50 (2019) 537-547; DOI: 10.3221/IGF-ESIS.50.45 541 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08 0 25 50 75 100 125 150 175 200 225 250 275 300 325 cummulative energy (aJ) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ib-value cummulative energy Ib-value stage A stage C stage D stage B Cu ulative energy [aJ] Ib-value Time [s] Cumulative energ I - alue stage stage B stage D stage C Ib=1 Figure 4: Time evolution of the cumulative energy and the I b -values during the four stages of the loading scheme. during the very last seconds before the macroscopic fracture of the specimen. The as above behaviour could be considered as corresponding to a transitional phase, from the stage of cracks formation to that of the final fracture of the specimen. At the end of this transitional phase preliminary crack-coalescence is possible. Special attention is next paid to the time evolution of the cumulative energy (CE) of the acoustic signals in stages B and D, i.e., the stages of constant stress level. For both stages, it appears that the time evolution of the specific parameter is gov- erned by a power law of the following form:   ( ) m o CE L t t (2) In Eq.(2) L and m are constants while t o corresponds to the time instant of onset of each constant stress stage (see Fig.1). Plotting Eq.(2) on log-log scales (Fig.5a) indicates that the time evolution of the cumulative energy (CE) of the acoustic signals during the constant stress stage B consists, in fact, of two distinct branches of different values of the exponent m. The first branch is of relatively limited duration (t-t o <1 s) and corresponds to an exponent value m=0.70. The second branch (t-t o >1 s), corresponds to an exponent value m=0.31. Attention is drawn to the fact that the starting point for calculating and drawing the time evolution of the cumulative energy is the time instant t o (the beginning of stage B), while the starting point of the horizontal axis (t=t o ) corresponds, also, to the onset of stage B. stage B 1E+03 1E+04 1E+05 1E+06 0.01 0.1 1 10 100 slope=m=0.70 slope=m=0.31 Cumulative energy [aJ] t - t o [s] stage D 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08 0.01 0.1 1 10 100 ( ) slope=m=0.94 slope=m=0.29 40s t - t o [s] Cumulative energy [aJ] m=0.31 m=0.70 m=0.29 m=0.94 40 (a) (b) Figure 5 : Time evolution of the cumulative energy in stages B (a) and D (b).