Issue 72

S. K. Kourkoulis et al., Fracture and Structural Integrity, 72 (2025) 179-192; DOI: 10.3221/IGF-ESIS.72.13

1000

34 kPa/sec 140 kPa/sec

Loading rate:

100

10

F [s -1 ]

1

0.1

0.94

0.88

0.01

0.00

0.25

0.50

0.75

1.00

τ /t f

Figure 6: The F-functions of the two representative experiments discussed, plotted in juxtaposition to each other along a logarithmic scale, versus the normalized (over the duration of each experiment) “average time” parameter, τ /t f . Criticality by means of the acoustic activity in terms of the Cumulative Energy of the Acoustic Emissions An additional Acoustic Emissions parameter, which is quite often used in the direction of detecting signs warning about impending approach of the loaded system (specimen) to the stage of accelerated damage processes (which will lead to the catastrophic fracture), is the Cumulative Energy of the Acoustic Emissions (CE) AE . An abrupt increase of the temporal rate of the (CE) AE is usually conceived as a pre-failure index designating entrance into the stage of impending failure [29]. The temporal evolution of the (CE) AE for the two experiments analyzed here are plotted in Fig.7a, in juxtaposition to each other, in terms of the normalized (over the duration of each test) time. Attention is paid to the time interval t/t f > 0.7, i.e., after a significant amount of acoustic energy is accumulated in the specimens. In Fig.7a the Cumulative Energies are plotted along logarithmic scale. It is observed from this figure that during the early loading steps (i.e., while the response of the specimens’ material is still linear) the (CE) AE increases obeying, for both specimens, a power law of the following form:

μ

f t        t β

  CE

(1)

AE

In Eq.(1) β is an energy constant and μ is an exponent related mainly to the level of the cumulative energy of the Acoustic Emissions of each test and the respective background level of the cumulative energy at lower stress levels. It is seen from Fig.7 that for the specimen loaded at high rate the values of the (CE) AE are systematically higher. This is well attributed to the

4.0

1E+07

Loading rate Exp. data Power law 34 [kPa/s] C(t/t f ) 5.6 140 [kPa/s] C(t/t f ) 2.3  

3.0

1E+06

1.0 R = (CE) AE,140 / (CE) AE,34 2.0

1E+05

1E+04

0.90

0.87

Cumulative Energy of AEs [aJ]

0.0

1E+03

0.70

0.80

0.90

1.00

0.70

0.80

0.90

1.00

t/t f

t/t f

(a) (b) Figure 7: (a) The Cumulative Energy of the Acoustic Emissions, (CE) AE , plotted in juxtaposition to each other along a logarithmic scale, versus the normalized (over the duration of each experiment) “average time” parameter, t/t f . (b) The ratio of the two (CE) AE .

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