Trapping and Fracture of Particles in Three-Sphere Ball-Milling Collisions

Ziyi Cui; Qiong Zhang; Suwei Liu; Richard M. Lueptow

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arXiv · 2611.08435

Trapping and Fracture of Particles in Three-Sphere Ball-Milling Collisions

Ziyi Cui·Qiong Zhang·Suwei Liu·Richard M. Lueptow

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Abstract

We numerically investigate the collision and fracture processes of ball milling based on a minimal model of a three-sphere geometry using discrete element method (DEM) simulations combined with Christensen-type and Weibull-type normalized fracture criteria. The outcome of the brittle target particle (ejected versus trapped, fractured versus intact) depends on the impact geometry and velocity. We develop a reduced three-sphere collision description in which trapping is governed by impact geometry and friction, while fracture inside the trapping regime is evaluated from DEM output using stress-based and contact-force-based normalized criteria. The trapping regime follows a closed-form geometric condition, while the critical conditions for fracture vary with impact angle, obliquity angle, impact velocity, and particle size ratio. Head-on collisions with larger size ratios require lower critical impact velocities for fracture.

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Ziyi Cui, Qiong Zhang, Suwei Liu, Richard M. Lueptow. 2026-11-05. Trapping and Fracture of Particles in Three-Sphere Ball-Milling Collisions. https://arxiv.org/abs/2611.08435

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