PSI - Issue 26

Andronikos Loukidis et al. / Procedia Structural Integrity 26 (2020) 277–284 Loukidis et al. / Structural Integrity Procedia 00 (2019) 000 – 000

282

6

i  for each loading step, along with the

Table 1. The values of the applied mechanical stress calculated values of the q -index and the time parameter q  for both specimens

amphibolite

marble

step









  q s 

  q s 

i MPa 

i MPa 

q

q

1 2 3 4 5 6 7 8

12.2 15.3 20.5 25.9 31.3

1.17 1.18 1.25 1.31 1.40 1.45 1.40 1.34

0.81 0.92 1.05 1.29 1.74 2.21 2.77 4.15

8.9

1.13 1.14 1.21 1.31 1.37 1.44 1.42 1.36

0.68 0.83 1.02 1.29 1.52 1.80 1.97 2.41

13.8 24.1 29.9 34.7 40.6 44.3 46.1

38.20

40.7 44.1

Under cracking and damaging terms, it should be stressed that cracking generation and growth forming crack networks and paths is a well-known process and can be easily determined knowing the stress field. Such phenomena are expected up to the near failure regions (i.e. 0.90  of the of the specimens’ uniaxial strength). Beyond the stress level, crack propagation and damage growth can no longer be estimated using local stress fields since the dimensions of the reacting mechanically active specimen become too small, making size effect and specimen microstructure (i.e. inclusion, composition) dominate fracture. This behaviour is projected as a dynamic condition (drop of index q ) that precedes the upcoming failure. Regarding the q  parameter that represents a time quantity, as can be seen in Fig.5(b) for both specimen cases, parameter q  exhibits a wide region of mild increase until the applied mechanical stress reaches approximately 0.85 of the maximum applied stress, followed by a steep increase for 0.9 i f    . Figure 5(c) shows the recorded background PSC values B I for both specimens. It can be seen that the B I values for 0.9 i f    are increasing almost linearly, while for 0.9 i f    a steep increase is observed.

amphibolite (b)

amphibolite (a)

1

1

0.1

0.1

step8 fit q=1.34 step6 fit q=1.45 step4 fit q= 1.31 step2 fit q= 1.18

step7 fit q= 1.40 step5 fit q= 1.40 step3 fit q = 1.25 step1 fit q= 1.17

ξ * (t)

ξ * (t)

0.01

0.01

0.001

0.001

0.1

1

10

100

0.1

1

10

100

t-t mi (s)

t-t mi (s)

marble (a)

marble (b)

1

1

0.1

0.1

step7 fit q= 1.42 step5 fit q= 1.37 step3 fit q= 1.21 step1 fit q= 1.13

step8 fit q= 1.36 step6 fit q= 1.44 step4 fit q= 1.31 step2 fit q= 1.14

ξ * (t)

ξ * (t)

0.01

0.01

0.001

0.001

0.1

1

10

100

0.1

1

10

100

t-t mi (s)

t-t mi (s)

* ( ) t  values (open circles) in respect to the time scale

mi t t  for both classes of specimens, along with their

Fig. 4. The relaxation function

corresponding q-exponential fitting for Eq.3 (solid lines). Legend shows the q -index values for each loading step.