Composite Power Laws in Shock Fragmentation

New Universality Class for the Fragmentation of Plastic Materials

“…At lower impact velocities the power law regime of the distribution is followed by a hump for the largest fragments which gradually disappears and the cutoff becomes exponential as v 0 increases. The most astonishing feature of the experimental results is that the value of the exponent τ pl = 1.2 ± 0.06 of the power law regime is significantly lower than the values τ br ≈ 1.8 − 2.1 typically found in the fragmentation of threedimensional bulk objects consisting of disordered brittle materials [3][4][5][6]12]. The anomalously low value of τ pl is the consequence of the breakup mechanism of plastic materials which has not been considered by the usual theoretical approaches [6,12].…”

“…Fragmentation phenomena are ubiquitous in nature and play a crucial role in numerous industrial processes related to mining and ore processing [1]. A large variety of measurements starting from the breakup of heavy nuclei through the usage of explosives in mining or fragmenting asteroids revealed the existence of a striking universality in fragmentation phenomena [1][2][3][4][5][6][7][8][9][10]: fragment mass distributions exhibit a power law decay, independent on the type of energy input (impact, explosion, ...), the relevant length scales or the dominating microscopic interactions involved. Detailed laboratory experiments on the breakup of disordered solids have revealed that mainly the effective dimensionality of the system determines the value of the exponent, according to which universality classes of fragmentation phenomena can be distinguished.…”

Minimal fragmentation of regular polygonal plates

“…The result for the regular polygon with 64 sides is displayed in Figure 5, where the crossover at µ = µ c (vertical line) is evident, each power-law regime being valid for several decades. Actually, power laws (15) and (18) are very good approximations for the distribution P (n) (µ) in the range of values of µ < 0.1, beyond the upper values of the dust regime. In fact, one can precisely determine the crossover mass by seeking the point where the curves (15) and (18) We see, therefore, that the crossover mass becomes smaller as the number of sides increases, becoming zero for n → ∞ (no crossover for the disk).…”

“…Actually, power laws (15) and (18) are very good approximations for the distribution P (n) (µ) in the range of values of µ < 0.1, beyond the upper values of the dust regime. In fact, one can precisely determine the crossover mass by seeking the point where the curves (15) and (18) We see, therefore, that the crossover mass becomes smaller as the number of sides increases, becoming zero for n → ∞ (no crossover for the disk). For n = 15, e. g., µ c ≈ 9 −4 ≈ 1.5 × 10 −4 , and the dust regime would hardly be observed in a hypothetical experiment.…”

Fragmentation of grains in a two-dimensional packing

“…[2][3][4]). Much interest has been focused on understanding the origin of the fragment-size distribution [2][3][4][5][6][7][8][9][10][11][12][13]. Both log-normal and power-law distributions appear commonly in experimental and theoretical studies.…”