PSI - Issue 55

Dimos Triantis et al. / Procedia Structural Integrity 55 (2024) 185–192 Triantis et al. / Structural Integrity Procedia 00 (2023) 000 – 000

187

3

n

N





E

E

i

i

, ( ) f E t

( ) i

E t

1

1

i = =

i = =

(1, 2)

n

N

* , i E is then defined as:

The normalized average energy content,

( ) ( ) i f

E t E t

*

*   E

, 0

1

E

=

(3)

i

i

3. Results: analysis of experimental data Data from two experimental protocols are analyzed in this section. The first one included direct tension tests of wide plates made of Dionysos marble. The plates were shaped in the form of Double Edge Notched Tensile specimens. The load was applied quasi-statically and monotonically up to the fracture of the specimens. Details about the specific protocol are provided by Kourkoulis et al. (2018a, 2018b). The fracture force for the typical specimen that will be analyzed here was equal to 2.57 kN. A total of N =85 acoustic events were recorded during the whole duration of the test. Attention is here paid to the very last loading stages. As already mentioned in previous section the temporal evolution of the quantities studied is plotted versus the time-to-failure parameter, t f - t , adopting a logarithmic scale, in order to shed light at the critical stages of the experiment, i.e., the stage during which the load tends to each maximum value, the stage during which the load is almost stabilized and, finally, the stage during which the load starts decreasing until the instant of fracture of the specimen. In this context, the temporal variation of the load applied during the last 250 seconds of the experiment is plotted in Fig.1a together with the energy of each one of the acoustic events recorded.

2.60

1.E+05

1.00

0.75

2.40

1.E+04

0.50

2.20 Load [kN]

1.E+03

0.25

2.00

1.E+02

0.00

0.1

1

10

100

1000

0.1

1

10

100

1000

t f -t [s]

(a) (b) Fig. 1. Direct tension test of wide notched marble plates: (a) The temporal variation of the load applied during the last loading steps of a typical test of the first protocol, together with the energy of each one of the acoustic events recorded; (b) The temporal variation of the normalized load applied in juxtaposition to the respective one of the normalized average energy of the acoustic events. As a next step, the temporal variation of the normalized average energy of the acoustic events is plotted in Fig.1b, together with the respective evolution of the normalized load applied (i.e., L*). It is clearly seen from Fig.1b that as the load tends to attain its maximum value (i.e., at the time instant t f - t ≈18 s, or, equivalently, about 18 seconds before the fracture of the specific specimen) the normalized average energy of the acoustic events exhibits an abrupt increase (from about 0.15 to about 0.60) and then it is trapped within a very narrow and stable “window” ranging in the 0.60< * i E <0.70 interval. In other words, it exhibits a clearly distinguishable plateau, which is terminated at the time instant t f - t ≈0.4 s, i.e., only four tenths of a second before the final catastrophic fracture of the specimen. All specimens of the specific protocol exhibited quite compatible response to that of the specimen just described.