Scaling of impact fragmentation near the critical point

Abstract

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power-law. The exponent of this power-law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher order moments of the fragment mass distributions, and obtained multi-scaling exponents that agreed with those of the simple biased cascade model.