Fragmentation of brittle plates by localized impact

TL;DR

This paper presents a geometric statistical model for brittle plate fragmentation due to high-velocity impacts, successfully matching experimental mass distributions and analyzing crack fractal dimensions.

Contribution

It introduces a novel probabilistic approach to model crack patterns and fragment distributions in brittle materials under impact.

Findings

Mass distribution follows a power law with exponent 0.1<α<0.3.

Model predictions agree with experimental data.

Crack fractal dimension correlates with the mass distribution exponent.

Abstract

In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over the surface. The specific probabilities employed to place the fractures come from an analysis of how the energy input propagates and dissipates over the material. The cumulative mass distributions $F(m)$ we obtain are in excellent agreement with the experimental data produced by T. Kadono [Phys. Rev. Lett. {\bf 78}, 1444 (1997)]. Particularly, in the small mass regime we get $F(m)\sim m^{-\alpha}$, with $0.1<\alpha<0.3$ for a quite broad range of dissipation strengths and total number of fragments. In addition we obtain the fractal dimension of the set of cracks and its correlation to the exponent $\alpha$ that account for the experimental results given by Kadono and Arakawa [Phys. Rev. E {\bf 65}, 035107(R) (2002)].