Issue 10

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 10 (2009) 3-11 ; DOI: 10.3221/IGF-ESIS.10.01 7 interpreted the size effects on the tensile strength and the fracture energy by fractal geometry. Fitting the experimental results, they found the values d σ = 0.14 and d G = 0.38. Some of the  –ε (stress vs. strain) and  – w diagrams are reported respectively in Fig. 4b and 4c, where w is the displacement localized in the damaged band. Eq. (3) yields d ε = 0.48, so that the fractal cohesive laws can be plotted in Fig. 4d. As expected, all the curves related to the single sizes tend to merge in a unique, scale-independent cohesive law. The overlapping of the cohesive laws for the different sizes proves the soundness of the fractal approach to the interpretation of concrete size effects. Figure 4 : Tensile test on dog-bone shaped specimens (a) by Carpinteri and Ferro [28] ; stress-strain diagrams (b), cohesive law diagrams (c), fractal cohesive law diagrams (d). T HE FRACTAL INTERPRETATION OF MULTISCALE CRACKING PHENOMENA he third topic deals with the criticality of the complex multiscale cracking phenomena in heterogeneous and disordered materials, evaluated by means of the Acoustic Emission (AE) technique. Acoustic Emission (AE) is represented by the class of phenomena whereby transient elastic waves are generated by the rapid release of energy from localized sources within a material. All materials produce AE during both the generation and propagation of cracks. The elastic waves move through the external solid surface, where they are detected by sensors. In this way, information about the existence and location of possible damage sources is obtained. This is similar to seismicity, where seismic waves reach the station placed on the earth surface (Richter [28]) . With regard to the basis of AE research in concrete, the early scientific papers were published in the 1960s. Particularly interesting are the contributions by Rusch [29], L'Hermite [30] and Robinson [31]. They discussed the relation between fracture process and volumetric change in the concrete under uniaxial compression. The most important applications of AE to structural concrete elements started in the late 1970s [32]. Regarding the determination of the defects position and orientation in the material, research has been growing at a fast rate in the last decade (Shah & Zongjing [33] and Ohtsu [34]) . In the last few years the AE technique has been applied to identify defects and damage in reinforced concrete structures and masonry buildings (Carpinteri & Lacidogna [35,36]) . By means of this technique, a particular methodology has been put forward for crack propagation monitoring and crack stability assessment in structural elements under service conditions. This technique permits to estimate the amount of energy released during fracture propagation and to obtain information on the criticality of the ongoing proces s [9, 37] . Without entering the details, recent developments in fragmentaron theories (Carpinteri & Pugno [38,39]) have shown that the energy dissipation E during microcrack propagation occurs in a fractal domain comprised between a surface and the T