A Study on the Fracture of Brittle Heterogeneous Materials Using Non-Extensive Statistical Mechanics and the Energy Distribution Function.

The fracture process of heterogeneous materials is studied here in the framework of the discipline of Non-Extensive Statistical Mechanics. Acoustic emission data provided by an experimental protocol with concrete specimens, plain or fiber-reinforced, under bending are taken advantage of. This innovation of the study lies in the fact that the analysis of the acoustic activity is implemented in terms of the energy content of the acoustic signals rather than of their interevent time or their interevent distance. The Energy Distribution Functions were properly fitted using the expression proposed by Shcherbakov, Kuksenko and Chmelet. This study reveals that the loading and fracture processes of the specific materials are definitely non-additive and non-extensive. It is concluded that the presence of notches is crucial since it assigns non-additivity and non-extensivity from relatively low loading levels due to the early formation of the fracture process zone around the crown of the notch. The values of the Tsallis entropic index, q, that were determined are in very good agreement with the respective ones obtained in previous studies by means of different analysis tools. Finally, a clear correlation between the index q and the average energy content of the acoustic signals is highlighted for the whole range of values of the energy content of the acoustic signals.