Issue 24

M. Davydova et alii, Frattura ed Integrità Strutturale, 24 (2013) 60-68; DOI: 10.3221/IGF-ESIS.24.05 62 y = 1.5987x - 0.5063 R² = 0.9875 0 1 2 3 4 5 0 1 2 3 Log(L) Log(r) y = -1.0343x + 2.5891 R² = 0.949 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Log(N) Log (S) (a) (b) Figure 2 : a) Scaling law obtained using the relation for crack length (1). b) Cumulative distribution of the fragment size in a log-log plot. There are two types of energy-dependent fragmentation patterns leading to a breakup (Fig. 3). Fig. 3a presents a fragmentation pattern that illustrates the fracture accompanied by radial crack formation. The right fragmentation pattern (Fig. 3b) has two zones corresponding to two different fracture mechanisms. The central zone has a radial crack only. In the second zone, the crack branching process is observed. Suppose that different fracture mechanisms characterize different fractal dimensions, we have ( ) ~ D L S S (2) where ( ) L S is the total crack length inside the square frame with a thickness h (Fig. 3a) , S is the frame area, and D is the fractal dimension. Calculation the fractal dimension using expression (2) shows that for the left fragmentation pattern (Fig. 3a) the data is fitted by a single line, whereas for the right pattern the log-log representation of ( ) L S changes a slope, and the power-law exponent D decreases. A change in the fracture mechanism (from radial crack-to-crack branching) correlates with the qualitative changes in the fractal dimension. y = 1.36x + 0.43 R² = 0.99 4 4.5 5 2.5 3 3.5 Log (S) Log (L) y = 1.13x + 0.98 R² = 0.99 y = 0.78x + 1.99 R² = 0.99 4 4.5 5 2.5 3 3.5 4 Log(S) Log(L) (a) (b) Figure 3 : a) Fragmentation pattern and fractal dimension definition for the fracture accompanied by radial crack formation. b) Fragmentation pattern and fractal dimension definition for the fracture accompanied by a change in the fracture mechanism.