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

335

6

10000

8.0

200

9000 9

Cumulative count (S1) Cumulative count (S2)

PSC load hits per sec

8000

Power Law (S1) Power Law (S2) Axial force

7000

6.0

150

1000

6000 6

Η its per sec

5000

4.0

100

4000

- 0.41

y S1 = 149.97x

Axial force [kN] PSC [pA]

3000 3

100

Cumulative counts

2.0

50

2000

y S2 = 72.97x 0.46 -0.46

1000

a o =8 cm

10

0.0

0

0

0

0.001

0.1

10

1000

0.00

0.25

0.50

0.75

1.00

t f -t [s]

Normalized (over the test’s duration) time

Fig. 5. Considering comparatively the acoustic activity around the two notches of a specimen with a 0 =8 cm.

Fig. 6. The acoustic activity in juxtaposition to the load induced and the PSC for a specimen with a 0 =4 cm.

position to the time rate of the hits recorded by the respective acoustic sensor and the load applied, for a specimen with a 0 =4 cm. The similarity between the time evolution of the rate of the acoustic hits and that of the PSC is striking. Excluding some weak electric activity at about 10% of the maximum load attained (attributed to parasitic friction pheno mena, inevitably appearing during the self-alignment of the specimen - recall that the load is applied with the aid of pins passing through holes drilled at the vertical symmetry axis of the specimens), the PSC recorded is almost constant or it increases imperceptibly for the whole time period of “ silence ” of the acoustic activity. It is only after the two thirds of the test’s duration that the PSC starts increasing, almost simultaneously with the “ awakening ” of the acoustic activity. Then, following a pattern almost identical to that of the evolution of the time rate of the acoustic hits the PSC starts in creasing “explosively” while the specimen enters into its “ critical ” stage, i.e., the stage of impending fracture. Focusing attention to the stage of impending fracture, the PSCs recorded by the two “electric sensors” attached around the crowns of the two notches of a characteristic specimen with a=6 cm, are plotted in Fig. 7, versus the (t f -t) parameter, for the last 100 seconds of the test’s duration . It is seen that during the last ten to twenty seconds before macroscopic fracture the electric activity obeys, also, a power law (dotted lines), similar to that governing the acoustic activity. In accordance with what was observed for the acoustic activity, the power law starts governing the response of the area around the notch from which crack propagation started (sensor ES1 in Fig. 7) much earlier with respect to the other notch (sensor ES2). The specific characteristics of the PSC at the stage of impending fracture have been recently reported by Triantis et al. (2021) for a wide variety of experimental protocols, including direct tension, uniaxial com pression and three-point bending of specimens made of either marble or cement mortar. In an attempt to further validate the conclusions already drawn, the acoustic activity is here described, also, in terms of the F-function (Triantis and Kourkoulis 2018), which represents the average frequency of appearance of AE hits (within a sliding time window of N successive AE hits) in terms of the inter-event time intervals. The inverse of the average value of these N inter-event time intervals of each group of successive AE hits is paired to the mean va lue, τ, of the time instants t i , i=1…N, at which each one of the N AE hits of the group is recorded. It is highlighted that τ is an “ average ” time instant. The specific manner for interpreting the AE data is already used worldwide by many researchers (e.g., Niu 2019, Wang et al. 2019, Zhang et al. 2019). The time variation of the F-function for the specimen considered in Fig. 7 is plotted in Fig. 8 versus the “time -to- fracture” parameter (properly modified as (t f - τ ) to take into account the mean value of the time instants at which each AE hit is detected), using logarithmic scales, in juxtaposition to the load applied. Once again, it is clearly observed that, within the stage of impending fracture, the acoustic activity is excellently described by a power law (dotted lines) for both notches. The form of this law is similar to that governing the acoustic activity in terms of the cumulative counts and, also, to that describing the electric activity. As it was previous ly concluded, the power law starts prevailing earlier around the notch from which fracture started.