Scaling of impact fragmentation near the critical point

TL;DR

This study experimentally explores impact-induced fragmentation near the critical point, revealing universal power-law fragment distributions and multi-scaling behavior inconsistent with percolation theory.

Contribution

It demonstrates that fragmentation transition universality differs from percolation and introduces a scaling approach using weighted mean mass near the critical point.

Findings

Fragment mass distribution follows a power-law with exponent 0.5.

Fragmentation data collapse into a universal scaling function.

Multi-scaling exponents match a biased cascade model.

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.