PSI - Issue 10

D. Triantis / Procedia Structural Integrity 10 (2018) 11–17 D. Triantis / Structural Integrity Procedia 00 (2018) 000 – 000

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5

(2010)). In RILEM TC 212-ACD, the classification of cracks in Mode I and Mode II types of damage, the quantities used are RA and AF. In order to study the variability of the average frequency (AF) of the AE hits and the RA values throughout the experimental procedure, the moving average was calculated for 100 sequential hits, to allow the variability monitoring. It is recalled that it is recommended to calculate the RA and AF from the moving average of more than 50 hits (Ohtsu (2010)).

80

40

(C) (D)

(B)

60

30

stress

40

20

(A)

20 RA (μs/mV)

10

(kHz)

stress (MPa)

0

0

0 25 50 75 100 125 150 175 200 225 250 275 300 325 time (s)

Fig. 4. Stress, RA and AF history.

The average frequency of the AE hits shows a similar behavior with that of the Ib – values (see Fig.4 and Fig.1). A sharp drop of the values is observed when the stress in stage A exceeds 57 MPa (t>120 s), as well as while entering stage C, whereas, in stage D, 30 s prior to the final failure the values start to drop. During the last 3 s prior to the fracture of the specimen, the AF values decline rapidly from 20 to 10 kHz. Taking into consideration that low AF values indicate shear type of cracking, it can be concluded that while microcracks cluster to create macrocracks, frictional phenomena appear. Also, observing the temporal variation of the RA values (Fig.4), strong peaks with high RA greater than 60 μ s/mV appear, in the ranges where the applied stress is higher than 96% of the failure stress. This constitutes another indication of the existence of shear phenomena, which could be either due to Mode II cracking or due to friction between the bases of the specimens and the loading platens or due to friction between the material fragments already formed (see Fig.2a). The latter is unavoidable, even in case of “perfectly” smooth contact of the specimens and the loading platens, as it was observed by Vardoulakis et al. (1997) during axial com pression of cylindrical marble specimens which split axially when the formation of the familiar Mohr‟s cones was totally suppressed. In order to study the relation between the RA value and the AF for various crack types, diagrams are plotted, in which the vertical axis corresponds to the AF in kHz, while the horizontal corresponds to the RA in μ s/mV. Α straight line starting from (0,0) and of slope m=0.5 kHz ∙ mV/ μ s is drawn and the AE with m<0.5 kHz ∙ mV/ μ s, are considered to be related to shear type of cracking (mode II) or friction. The determination of the appropriate value for the slope m is an open issue for research since there is not a rule generally accepted. However, it is accepted that it should be determined depending on the type of the material and the type of the experiment (Aggelis (2011)).

Table 2. Proportion of AE corresponding to Mode-II cracking for two different values of the parameter m. stage A1 A2 Β C D1

D2

(σ/σf)≈1 hits for last 3 s

stress

0.7≤(σ/σf)≤0.9

0 .9<(σ/σf)≤0.96

(σ/σf)≈0.96

0.96<(σ/σf)≤1 (σ/σf)≈1 total hits

% hits for m≤0.5 (mode II) % hits for m≤0.2 (mode II)

6%

53%

13%

33%

40%

53%

28%

33%

8%

19%

20%

33%