Predictive stochastic modeling of mechanically alloyed particle size and shape

Mechanical alloying of bimetallic materials by ball milling produces particulate products where, aside from internal structure, the size and shape of particles is of importance for various applications. This article introduces real-time modeling tools for the particle species demographics of size and aspect ratio, their dynamic evolution and dependence on processing conditions. Its highlight is a simple, analytical stochastic model of external particle features based on statistical formulations of impact energetics, friction and plastic deformation effects, as well as bonding and fracture transformations of the particles during the process. The model is calibrated and validated experimentally by measurements on laboratory micrographs and literature data in low- and high-energy ball milling of Al-Ni powders at different molar ratios. Its size and shape predictions offer insights to population growth of particles through mechanical alloying phenomena for material design and optimization and process observation for real-time feedback control.