Issue 50

D. Triantis et alii, Frattura ed Integrità Strutturale, 50 (2019) 537-547; DOI: 10.3221/IGF-ESIS.50.45

4

150

3

50 F-function [s -1 ] 100

2

Ib-value Ib-value

F function Ib-value

1

F-function (1/sec)

0

0

0

50

100

150

200

250

300

Time [s]

Figure 7: Time evolution of the F-function in juxtaposition to that of the I b -value.

Considering now the systematic reduction exhibited by the F-function at stages B and D, further analysis of the experi mental results was undertaken, indicating that during the first two (2) seconds after the stabilization of the stress level, the F-function decreases following a power law of the form:

      t 



F t

A

( )

exp

(3)

The above law is plotted in Fig.8 for both stages B (Fig.8a) and D (Fig.8b) using logarithmic scale for the values of the F function. In this figure, the origin of the time scale (i.e., t=0) corresponds to the time instant t o (for each stage) at which the stress attains its maximum value and is then stabilized, practically corresponding to the time instant at which the maximum values of the F-function are attained. The values of the parameter A and the time constant τ of Eq.(3), as obtained by means of proper curve fitting, are equal to A=128.7 s -1 , τ=0.98 s for stage B and A=141.6 s -1 , τ=1.23 s, for stage D. As it is expected, the highest value of the time constant τ is observed in stage D due to the considerably increased acoustic activity that is recorded in this stage (recall that, after a while, fracture of the specimen occurred).

1000

1000

stage B

stage D

y = 141.56e -0.81x

y = 128.71e -1.02x

100

100

10 F-function [ -1 ]

10 F-function [s -1 ]

F - function (1/sec)

F - function (1/sec)

1

1

0

2

4

6

8

0

2

4

6

8

time (sec)

time (sec) Time [s]

Time [s]

(a) (b) Figure 8 : Restoration of the F-function during the first seconds following stress stabilization in stages B (a) and D (b). As a last step, it is worth studying the time evolution of the F-function during the very last seconds prior to the failure of the specimen (i.e., the very last time interval of stage D). In a recent paper by Triantis and Kourkoulis [7], it was indicated that the F-function exhibits a peak just before the fracture, while before the occurrence of this peak there is a sharp increase of the F-function, which in terms of the time-to-failure parameter, t f -t, is governed by a power law of the form:

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