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

Andronikos Loukidis,Dimos Triantis,Ilias Stavrakas

doi:10.3390/e22101115

Andronikos Loukidis, Dimos Triantis + Show 1 more

Open Access

https://doi.org/10.3390/e22101115

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Journal: Entropy	Publication Date: Oct 2, 2020
Citations: 5	License type: CC BY 4.0

Affiliation: University of West Attica

Abstract

Non-extensive statistical mechanics (NESM), which is a generalization of the traditional Boltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating the irreversible damage evolution processes and fracture mechanisms occurring when materials are subjected to mechanical loading. In this study, NESM is used for the analysis of the acoustic emission (AE) events recorded when marble and cement mortar specimens were subjected to mechanical loading until fracture. In total, AE data originating from four distinct loading protocols are presented. The cumulative distribution of inter-event times (time interval between two consecutive AE events) and the inter-event distances (three-dimensional Euclidian distance between the centers of successive AE events) were examined under the above concept and it was found that NESM is suitable to detect criticality under the terms of mechanical status of a material. This was conducted by evaluating the fitting results of the q-exponential function and the corresponding q-indices of Tsallis entropy and , along with the parameters and . Results support that 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 data recorded from Basalt specimens.

Highlights

Assessing the accumulated damage and understanding the physical mechanisms behind fractures, which lead to critical failures in mechanically loaded specimens or structures, is important for the scientific and engineering community working in situ
Results support that qδτ + qδr ≈ 2 for acoustic emission (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 data recorded from Basalt specimens
It should be stressed that the probability density function P(> X) of the q-exponential distribution given by Equation (11) and the normalized cumulative distribution functions of the AE inter-event times P(> δτ) and the AE

Summary

Introduction

Assessing the accumulated damage and understanding the physical mechanisms behind fractures, which lead to critical failures in mechanically loaded specimens or structures, is important for the scientific and engineering community working in situ. Acoustic activity data can provide information about the crack evolution processes that take place inside the material [1] In this context, specific AE related parameters have been used as pre-failure indicators, allowing the estimation of the overall accumulated damage and remaining loading carrying capacity of specimens or full-scale structures [2,3,4,5,6,7]. They analyzed seismic data from Japan and southern California and found that the cumulative distributions of the three-dimensional Euclidean distances and the time interval between consecutive earthquakes obey the modified Zipf-Mandelbrot law [20], characterized by the q-exponential distributions with q = qδr < 1 [18] and q = qδτ > 1 [19], respectively They estimated that qδτ + qδr ≈ 2, where qδτ and qδr , represent the calculated values of the q-parameter for the temporal and spatial distributions, respectively [18]. It is for first time experimentally verified in a small scale laboratory environment the validity of the relation qδτ + qδr ≈ 2 of the calculated entropic q-indices

Theoretical Background

Specimens and Experimental Protocol

Results and Discussion

Conclusions