Mechanics and energetics modeling of ball-milled metal foil and particle structures

The reported research establishes a semi-analytical computational predictive model of fractal microstructure in ball-milled metal foils and powder particulates, with emphasis on its transformation mechanics via an energy-based approach. The evolving structure is composed of reconfigurable warped ellipsoid material domains, subjected to collisions with the ball milling impactors following Brownian motion energetics. In the first step of the model, impacts are assumed to generate ideal Hertzian elastic stress fields, with associated bulk deformations quantified as per Castigliano's strain energy methods. In the second stage of the model, elastic energies are recast to produce frictional slip and plastic yield, thus resulting in surface micro-joints. Only two parameters of the model necessitate experimental calibration, performed by comparison of joint energy with laboratory tensile measurements on ball-milled multilayer Al-Ni foils. Model predictions of evolving internal microstructure are validated against SEM micrographs of Al-Ni powder particulate samples for different ball milling durations. Results demonstrate the capability of the model to accurately capture relevant fractal measures of the microstructure of ball-milled powders.