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

Abstract

Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann–Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implementation for studying complex systems such as the fracture mechanisms and crack evolution processes that occur in mechanically loaded specimens of brittle materials. In the current work, acoustic emission (AE) data recorded when marble and cement mortar specimens were subjected to three distinct loading protocols until fracture, are discussed in the context of NESM. The NESM analysis showed that the cumulative distribution functions of the AE interevent times (i.e., the time interval between successive AE hits) follow a q-exponential function. For each examined specimen, the corresponding Tsallis entropic q-indices and the parameters βq and τq were calculated. The entropic index q shows a systematic behaviour strongly related to the various stages of the implemented loading protocols for all the examined specimens. Results seem to support the idea of using the entropic index q as a potential pre-failure indicator for the impending catastrophic fracture of the mechanically loaded specimens.

Assessing structural integrity of non-homogeneous systems by means of Acoustic Emissions and Non-Extensive Statistical Mechanics

“…n the present work, the acoustic activity that was developed in two quite different types of marble structures (from the geometrical and the loading points of view) was analyzed, taking advantage of concepts based on the NESM, aiming mainly to detect possible pre-failure indicators. The specific approach, i.e., the analysis of the temporal evolution of the acoustic activity using NESM concepts has been already adopted by the authors' team for the data obtained from previously published experimental protocols, in which homogeneous specimens were tested under various loading schemes [6,8]. In ref.…”

“…In ref. [6] Dionysos marble plates (a marble variety with remarkably high homogeneity [33][34][35]) were submitted to direct tension while in ref. [8] Dionysos marble beams were submitted to three-point bending.…”

“…(a) (b) Figure 14: The entropic index and the applied load versus time-to-failure, for notched marble specimens (a) under three-point bending [8], and (b) under uniaxial tension [6].…”

“…The concepts of NESM were recently applied in the direction of detecting pre-failure indices while brittle building materials (like marble and concrete) are submitted to mechanical loading schemes, including direct tension, three-point bending, compression, and diametral compression etc. [6]. Interesting conclusions were drawn from the temporal evolution of the entropic index q, namely the factor that quantifies the degree of non-additivity of a system according to the founding principles of NESM and the definition of S q .…”

“…According to existing data [7], this tendency of q to re-approach the limiting value of q=1, is an indication that mechanisms leading to intense generation of macrocracks are activated, leading eventually to fatal propagation of these macro-cracks and to macroscopic fracture. Besides materials of almost "perfect" homogeneity like marble, materials with a certain degree of inhomogeneity (fiberreinforced concrete) were tested in that study [6] and, also, in a recently published one [8]. It is interesting to note that for these materials instead of a global maximum the temporal evolution of q at the very last loading stages was characterized by a global minimum which was attributed to the activation of an additional damage mechanism (which does not appear in homogeneous materials), namely the debonding between the concrete mass and the reinforcing fibers.…”