PSI - Issue 26

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

279

3

Fig. 1. The PSC relaxation phase after a steep increase from a lower stress level

i  to a higher

1 i  

1 i   , produces an electrical current (PSC) whose form can be seen in Fig.1. From the moment mi t , where the stress is maintained at the higher level of each step 1 i   , the PSC follows a descending trend until it relaxes back to a background level ( B I ). The PSC relaxation function   i t  is defined as the difference:   i i PSC t I   , while * ( ) t  represents the normalised PSC relaxation function defined as:

    mi t t

*

i 

  t

*

(2)

i 



*

i 

  * i t  is the maximum value of   * i t 

  mi

  i mi PSC t is the peak value of the PSC signal

The

, where

PSC t

I





i

i



(see Fig.1). When the applied mechanical load reaches the high level 1 i   of each step, the normalized PSC relaxation signal * ( ) t  decreases monotically with time, in a standard exponential manner. Based on this observation one can assume that * ( ) t  is of the exponential type and would satisfy the following equation: 1 d dt      hence 1 t e     , where 1  is a constant. Since multifractality is involved, a more general equation holds: q q d dt      (Tsallis, 2009a) leading to the generalized q -exponential function (Vallianatos et al., 2011; Vallianatos and Triantis, 2013; Christopoulos and Sarlis, 2015):

1

 1 1 1 q            q  t 

1

q



  t

(3)

*



where

, expresses a q -relaxation property.

1/

q 



q 

2. The materials and the specimens used For the purpose of this study, amphibolite and Dionysos marble specimens were used. The amphibolite specimens were cut from cores extracted from the drilling site of the German Continental Deep Drilling program (KTB)