Fragment-size distribution in disintegration by maximum-entropy formalism

Abstract

By maximizing the information entropy under appropriate constraints, we obtain the distribution of fragment sizes when either the whole or part of the volume of a material disintegrates as the result of some dynamic process (for example, blasting, impact). The energy constraint involves a realistic fragment energy to which one adds, when the fragmented volume is fixed, a volume constraint. The prior probability distribution has been chosen to be a uniform function of the linear fragment size. Agreeing with a broad range of experiments, the fragment number distribution derived in this work follows an inverse power law, a ^−θ (a is linear in fragment size, θ∼2–5), except for large sizes when it decreases exponentially. The weight distribution is maximum at (5γ/ρε²)^1/3 (γ is the surface energy density, ρ is the mass density and εέ is the volumetric dilution rate) in agreement with several experiments and Grady's prediction, and is independent of the stored elastic energy.