Non-Extensive Statistical Analysis of Acoustic Emissions Recorded in Marble and Cement Mortar Specimens Under Mechanical Load Until Fracture

Abstract

Non-extensive statistical mechanics (NESM), which is a generalization of the traditionalBoltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating theirreversible damage evolution processes and fracture mechanisms occurring when materials aresubjected to mechanical loading. In this study, NESM is used for the analysis of the acousticemission (AE) events recorded when marble and cement mortar specimens were subjected tomechanical loading until fracture. In total, AE data originating from four distinct loading protocolsare presented. The cumulative distribution of inter-event times (time interval between twoconsecutive AE events) and the inter-event distances (three-dimensional Euclidian distance betweenthe centers of successive AE events) were examined under the above concept and it was found thatNESM is suitable to detect criticality under the terms of mechanical status of a material. This wasconducted by evaluating the fitting results of the q-exponential function and the corresponding qindicesof Tsallis entropy qδτ and qδ r , along with the parameters τδτ and dδ r . Results supportthat qδτ + qδ r ≈ 2 for AE data recorded from marble and cement mortar specimens of this work,which is in good agreement with the conjecture previously found in seismological data and AE datarecorded from Basalt specimens.Keywords: non-extensive statistical physics

Non-Extensive Statistical Analysis of Acoustic Emissions: The Variability of Entropic Index q during Loading of Brittle Materials Until Fracture

“…, based on Equation 7, obeys a q-exponential distribution proposed by ref [36] for AE data recorded from basalt specimens subjected to mechanical loading until fracture and verified in the cases of AE data recorded from mechanically loaded marble, sandstone and cement mortar specimens [37][38][39][40][41][42]:…”

“…In the case of sub-additivity when 1 q > , a power law tail appears, whereas in the case of super-additivity when 0 1 q < < the q-exponential function presents a cut-off [26,27]. According to refs [36][37][38][39][40][41][42], the quantity that should be compared with the distribution the system under study is not the original ( )…”

“…Non-extensive statistical mechanics (NESM) introduced by Tsallis [21][22][23][24][25], based on the principle of entropy have been proven a reliable statistical framework for analysing intricate dynamical systems such as the fracture mechanisms responsible for the generation of earthquakes and AEs. NESM has been applied in a variety of fields [23]; here, the authors focus mainly on NESM applications of seismology [26][27][28][29], plate tectonics [30][31][32][33][34][35] and fracture mechanics [36][37][38][39][40][41][42]. Taking into account the similarities between seismicity and AE activity, as already mentioned, the application of NESM in fracture mechanics concerning stressed rocks is valid.…”

“…Taking into account the similarities between seismicity and AE activity, as already mentioned, the application of NESM in fracture mechanics concerning stressed rocks is valid. As such, several works have been conducted, attempting to study the fracture processes occurring in mechanically loaded brittle materials (e.g., rocks, cement mortar) through the recorded AEs under the scope of NESM [36][37][38][39][40][41][42]. Vallianatos et al [36] studied the recorded AE activity in terms of NESM, when basalt specimens were subjected to diametral compression until fracture.…”

Acoustic Emission Signal Entropy as a Means to Estimate Loads in Fiber Reinforced Polymer Rods

“…Studies have shown that acoustic emission (AE) signal analysis is a promising non-destructive technique for studying failure in concrete, e.g., within non-extensive statistical mechanics framework [ 4 , 5 , 6 ], damage localization in composite structures [ 7 , 8 ] and for damage monitoring in FRP materials [ 9 , 10 ]. When damage occurs in FRP materials, the sudden change in stress produces AE signal.…”