13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- degrees of freedom corresponding to the set of blow-up dissipative structures of different complexity that can be responsible for different scenario of fragmentation statistics and failure under dynamic and shock wave loading. 0 20 40 400 , M Pa σ 60 , / V m s B V C V S V Figure 1: Stress pattern for steady-state С V V< , branching C V V> and fragmenting B V V> scenario of crack dynamics. Figure 2: Crack velocity V versus stress σ. 0 -2 2 10 20 , / MPa s σ μ & ,MPa σ 0 -5 5 20 40 , / MPa s σ μ & , MPa σ a b Figure 3: Stress phase portraits: σ σ ~& : a - V m s/ 200 = , b - V m s/ 615 = 3. 1 f -fragmentation statistics Fundamental properties of failure are central in determining the temporal scenario of fragmentation statistics and fragment size distribution. Fragment size distributions can range from the relatively tight exponential functions to power-law relations spanning a number of decades in fragment size. Onset of fracture asymptotes to a range of length scales in which fragmentation is self-similar requiring that failure temporal sequences and the fragment size distributions exhibit a power-law dependence [3]. The linkage of scenario of crack propagation and symmetry properties of dynamic system “solid with defects” allowed us to propose the interpretation of temporal and spatial fragmentation statistics depending on the energy density imposed. A large number of the fragmentation statistics were proposed: log-normal, power-law, exponential, combination of exponential and power laws. These theories have focused on the prediction of mean fragment size
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