Fragmentation of a Circular Disc by Impact on a Frictionless Plate

TL;DR

This study uses molecular dynamics simulations to analyze how a circular disc breaks upon impact on a frictionless plate, revealing a critical velocity that determines whether the disc is damaged, cleaved, or shattered into fragments.

Contribution

It introduces a detailed simulation model showing impact velocity's role in fragmentation patterns and identifies a universal crack pattern dependent only on the normal impact component.

Findings

Crack patterns depend solely on the normal impact velocity component.

A critical velocity separates damage, cleavage, and fragmentation regimes.

Fragment mass distribution follows a velocity-independent power law.

Abstract

The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. It is found that for both normal and oblique impacts the crack patterns are the same and depend solely on the normal component of the impact velocity. Analysing the pattern of breakage, amount of damage, fragment masses and velocities, we show the existence of a critical velocity which separates two regimes of the impact process: below the critical point only a damage cone is formed at the impact site (damage), cleaving of the particle occurs at the critical point, while above the critical velocity the disc breaks into several pieces (fragmentation). In the limit of very high impact velocities the disc suffers complete disintegration (shattering) into many small fragments. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc.