J. Astrom et al., DYNAMIC FRAGMENTATION OF A 2-DIMENSIONAL BRITTLE MATERIAL WITH QUENCHED DISORDER, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(4), 1997, pp. 4757-4761
Fragmentation of a two-dimensional brittle material caused by a rapid
impact has been analyzed. Computer simulations together with simple ar
guments are used to obtain a qualitative understanding of crack format
ion, which is then used to derive an exponential fragment size distrib
ution valid in the large fragment size limit. In the limit of small fr
agments this distribution is solved numerically, and it is found to be
y a scaling law with the exponent -1.5. These results suggest that two
different mechanisms are operative in the fragmentation process: bran
ching of propagating cracks determines the small fragment size limit,
and merging of the nucleated cracks determines the large size limit. T
he point of crossover between these two regimes is also found to obey
a scaling law.