Modeling and Analysis of High-Energy Ball Milling Through Attritors
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MECHANICAL alloying through high-energy ball milling is presently used to fabricate several commercial oxide dispersion strengthened Ni-, Fe-, and Al-base alloys.[1–3] High-energy ball milling has also been used to produce various metastable materials such as supersaturated solid solutions,[4,5] amorphous phases,[4,6–8] and solid solutions containing two (or more) immiscible components.[9] It has also been utilized to prepare various nanocrystalline solids[6–8,10–12] and compounds.[13–18] It is generally agreed that the fundamental process during high-energy ball milling is repeated elastic and plastic deformation, fragmentation, cold welding, micro-diffusion, recovery, recrystallization, amorphization, crystallization, and/or chemical reactions of powder particles.[1–3,16,19,20] Simulation and modeling have been performed to understand the fundamental process during high-energy ball milling[21–30] and to define the mechanics and major controlling parameters of the ball milling process.[21,22,31–38] Many of the progresses made in the
XUZHE ZHAO and LEON SHAW are with the Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616. Contact e-mail: [email protected] Manuscript submitted February 27, 2017. Article published online July 5, 2017 4324—VOLUME 48A, SEPTEMBER 2017
fundamental understanding and modeling have been nicely summarized in two review articles recently.[39,40] Models to understand the fundamental process during high-energy ball milling have focused on the description of powder deformation, fracture, cold welding, microstructure, and property evolution in response to ball milling conditions.[21–30] The most basic ‘‘event’’ during high-energy ball milling is elastic/plastic deformation and can be approximated as ‘‘mini-forging’’ of the powder trapped between two colliding balls.[21] The local ‘‘mini-forging’’ conditions can be related to global ball milling conditions through classical mechanics, fluid mechanics, experimentally determined motion of balls with estimated collision frequency and intensity, or numerical simulation and modeling.[21,22,25,31–38] Models to define the mechanics and major controlling parameters of the ball milling process have focused on distributions of the velocity, angle and frequency of collisions, mechanical loading experienced by powder particles, energy dissipation rate, interaction duration and force of milling tools, and the torque applied to achieve the desired rotation speed of impellers.[21,22,25,31–38] Among various modeling approaches, discrete element modeling (DEM) has been shown to be an effective method in predicting the motion of individual balls, the interactions of balls, the energy transferred from milling tools to the powder, power consumption, liner and media wear, and mill output.[35–38] In a series
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of studies,[35–38] Dreizin’s group has proposed an energy-based parameter, the milling dose, to define the energy transfer from milling tools to the powder (i.e., e
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