Issue 10

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 10 (2009) 3-11; DOI: 10.3221/IGF-ESIS.10.01 8 specimen volume V . The fractal criterion predicts a volume-effect on the maximum number of acoustic emission events N max , that, in a bilogarithmic diagram, would appear as: max log log logV 3 AE D N    (4) with a slope equal to D /3, where Γ AE is the critical value of fractal acoustic emission density and D is the fractal exponent, comprised between 2 and 3 [37] . Experiments carried out by Carpinteri et al. [36] on concrete specimens tested in compression confirm the soundness of the proposed approach. For all the tested specimens, the critical number of acoustic emissions N max was evaluated in correspondence to the peak-stress  u . The compression tests show an increase in AE cumulative event number by increasing the specimen volume. More in detail, subjecting the average experimental data to a statistical analysis, the parameters D and Γ AE in eq. (4) were quantified. From the best-fitting, reported graphically in Fig. 5, the estimated value of the slope was computed as D /3 = 0.766, so that, as predicted by the fragmentation theories, 2  D  3. This result is a confirmation of the fact that the energy dissipation, measured by the number of acoustic emissions N , occurs over a fractal domain. Interestingly, the criticality of the cracking phenomena does appear not only in space, but also in time. A scaling relation of the type of eq. (4) can be written for the time t , allowing one to define the damage parameter  , which can be expressed [9, 37] as a function of different parameters, i.e., stress σ, strain ε or time t : σ ε t β β β max max max max σ ε η σ ε N t N t                       (5) where the exponents β can be obtained from the AE data of a reference specimen. The fractal multiscale criterion of Eq. (5) is a fundamental result, since it allows to predict the damage evolution also in large concrete structural elements. Monitoring the damage evolution by AE, it is therefore possible to evaluate the damage level as well as the time to the final collapse [9]. Figure 5 : Volume effect on the maximum number of acoustic emissions. R OUTE TOWARDS CHAOS IN THE DYNAMICS OF CRACKED BEAMS he fourth and last topic is concerned with the dynamical behaviour of cracked beams (Carpinteri and Pugno [40, 10,11 ]. Dealing with the presence of a crack in the structure, previous studies have demonstrated that a transverse crack can change its state (from open to closed and vice versa) when the structure, subjected to an external load, vibrates. As a consequence, a nonlinear dynamic behavior is introduced. This phenomenon has been detected during experimental testing performed by Gudmundson [41], in which the influence of a transverse breathing crack upon the natural frequencies of a cantilever beam was investigated. T