Conditions for crack propagation in pre-notched concrete beams by means of non-Gaussian distributions of Acoustic Emissions time series

• The acoustic activity in pre-notched concrete specimens under 3 PB is studied. • The analysis is realized within the frame of Non-Extensive Statistical Mechanics. • The “Variable Returns” parameter of the counts of the hits is employed. • q-Gaussian distributions fit almost perfectly the Probability Distribution Function. • The entropic index q provides signals designating onset of crack propagation. The conditions governing crack propagation in prismatic, concrete specimens, are explored, taking advantage of the Acoustic Emissions recorded during an experimental protocol comprising of standardized bending tests. The time series of the Acoustic Emissions are modelled adopting the concepts of Non-Extensive Statistical Mechanics, as formulated by means of Tsallis entropy and entropic index. The innovation of the present approach lies in the fact that the acoustic data are analyzed using a parameter exhibiting transient characteristics and strong fluctuations, namely, the “Variable Returns” of the “counts” of the acoustic hits. Moreover, the evolution of this parameter is modelled using q-Gaussian- rather than Gaussian-distributions, since the processes that take place while brittle materials are loaded up to fracture are characterized by memory effects and, also, long-range interactions, rendering the traditional Boltzmann-Gibbs Statistical Thermodynamics inadequate for proper modelling. The analysis reveals that Tsallis formalism for the Non-Extensive Statistical Mechanics, models quite satisfactorily the mechanical response of the loaded system and, also, that the q-Gaussian distribution fits almost perfectly the respective Probability Distribution Functions. Deviations are observed only for the tails of the experimental distributions, which correspond to an extremely small portion of the overall number of the acoustic hits that were recorded. In addition, it is revealed that the temporal variation of the entropic index is characterized by a global maximum, which designates entrance into the stage of impending macroscopic fracture and provides a Structural Health Monitoring tool that, under certain conditions, could be interesting from the engineering point of view.