Dynamic fragmentation of a two-dimensional brittle material with quenched disorder

Fragmentation of a two-dimensional brittle material caused by a rapid impact has been analyzed. Computer simulations together with simple arguments are used to obtain a qualitative understanding of crack formation, which is then used to derive an exponential fragment size distribution valid in the large fragment size limit. In the limit of small fragments this distribution is solved numerically, and it is found to bey a scaling law with the exponent -1.5. These results suggest that two different mechanisms are operative in the fragmentation process: branching of propagating cracks determines the small fragment size limit, and merging of the nucleated cracks determines the large size limit. The point of crossover between these two regimes is also found to obey a scaling law.