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 multiscaling exponents that agreed with those of the simple biased cascade model.