Bjm. Aikin et Th. Courtney, MODELING OF PARTICLE-SIZE EVOLUTION DURING MECHANICAL MILLING, Metallurgical transactions. A, Physical metallurgy and materials science, 24(11), 1993, pp. 2465-2471
The process of mechanical alloying (MA) involves the repeated deformat
ion, welding, and fracture of powder materials during grinding in high
-energy mills. During MA, the size and size distribution of the partic
les change as a result of the particles' different fracture and weldin
g rates. The evolution of particle volume distributions during such a
combined ''fission-fusion'' process can be described via a differentia
l-integral equation. While analytical solutions are known for systems
in which only fusion takes place, there is apparently no such solution
for the fission-fusion problem. In this article, we describe a discre
tized form of the fission-fusion equation and apply it to modeling of
particle size distributions during milling of elemental powders using
previously determined fracture and welding rates appropriate to the gl
obal system of particles. Predicted particle size distributions mimic
well those determined experimentally.