Issue 24

M. Davydova et alii, Frattura ed Integrità Strutturale, 24 (2013) 60-68; DOI: 10.3221/IGF-ESIS.24.05 61 rods under dynamic loading were carried out to test the effect of sample size and variation in loading type. It was found out that the type of distribution function did not change, it remained a power law. The fragment size distribution was determined using a standard sieve analysis technique and electronic balance. In order to investigate temporal scaling, an original method was proposed. The main idea was to measure the kinetic of the appearance of the fracture surface. For a loaded glass sample illuminated with the light source, the newly formed fracture surface produced light impulses, which were registered by Photo Multiplayer Tube connected to the oscilloscope. The temporal variable was the interval between impulses, or in other words, the time between the fracture events. The statistical data processing shows that the distribution of time intervals obeys the power law. In the case of analyzing data corresponding to the initial time of the process the distribution of time interval is governed by the exponential law. The explanation of the fact that fracture kinetics at the initial stage is characterized by another distribution function requires additional investigation. F RAGMENTATION OF THE GLASS PLATES UNDERQUASI - STATIC LOADING uasi-static testing was performed in the experiments with glass plates loaded in a “sandwich” to save the glass fragmentation pictures (Fig. 1a). Using the original software, the images were transformed into schematic pictures corresponding to the fragmentation patterns (Fig. 1b). This allowed us to determine the size and number of fragments and the total length of cracks. We consider two types of scaling. The first type is based on the relation ( ) ~ D L r r (1) where ( ) L r is the total crack length in the boxes of a size r r  centred at the point B (Fig. 1b) , and D is the fractal dimension. The second type is the traditional definition of the cumulative distribution of fragment sizes, in other words, the calculation of the number of fragments ( ) N S with a size larger than S . (a) (b) Figure 1 : a) Photo of typical fragmentation patterns. b) Schematic pictures of the fragmentation patterns used to determine the size and number of fragments and the total length of cracks. The use of expression (1) was discussed by Sornette et al. [10]. However, it should be noted that the fracture pattern [10] does not have a distinct central point. At the same time, the examined fragmentation patterns have a central point, and their configuration is similar to that created with the model of diffusion-limited aggregation (DLA) [11] or the model of dielectric breakdown (DB) [12]. Relation (1) can be used to define the fractal dimension for both these models. In the case of the DB model, ( ) L r is the total length of the discharge branches within the circle of radius r For the DLA model, ( ) L r is the number of particles. By analogy with the DLA and DB models, to determine the fractal dimension of the fragmentation patterns, we use relation (1), where ( ) L r is the total length of cracks in the boxes of a size  r r centred at the point B (Fig. 1b). The minimal number of the boxes used for calculation of the fractal dimension is 200. The scaling law obtained using the relation for the crack length (1) is presented in Fig. 2a. The processing of the fragment sizes shows that the relation between the fragment area and number is also fitted by a power law (Fig. 2b). Q