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This research introduces dynamic modeling and real-time control of fractal structure in particulate materials fabricated by the ball milling process, specifically addressing challenges of unavailable real-time non-destructive and non-invasive imaging measurements in the enclosed rotating vials. A description of the internal temperature dynamics in the container is established along with a thermal regulator based on external temperature feedback. The fractal dimension is introduced as a structural measure, and its dynamics is established via an analytical formulation through a lumped model, along with a full thermostructural computational model of the ball milling particulate microstructure. These models are used as real-time observers of inaccessible internal states during the process. In addition, they are used as model references in an adaptive control system, regulating the fractal structure with adaptation via external temperature measurements, available experimentally via an infrared thermocouple. The controller is designed on the basis of the dynamic models and is tested experimentally. The controller is demonstrated to command the duration of the process at steady conditions to obtain the necessary thermal exposure yielding the desired microstructure for the ball-milled particulates. Keywords: Ball milling, Adaptive control, Aluminum alloys, Fractal dimension

This work establishes a computationally efficient model of temperature and diffusion dynamics in ball milled bimetallic Ni-Al particulates. Mechanical contact conditions between adjacent bimetallic domains and temperature fields generated upon impact define the diffusive fluxes through the domains' interfaces. The concentration distributions are studied via Green's function methods, by defining mirror images which reflect the boundary diffusive resistance conditions. Predictions of the model are validated against experimental open-loop scanning electron micrographs and X-ray diffraction spectra at steady-state. Dynamic models of diffusion saturation and internal temperature are developed for the design of closed-loop controller via simulation. This feedback controller is implemented on a laboratory device, equipped with infrared thermometry for external vial temperature measurement, as a self-tuning regulator. The controller adapts an efficiency parameter of the model that thus serves as a real-time observer for internal temperature and diffusion saturation, which are physically inaccessible during processing. Experimental open-loop results are employed to set thresholds of diffusion penetration to avoid early exothermic reaction during fabrication. By controlling the process duration, the regulation system successfully reproduces the material composition of the open-loop reference tests, to ensure desired thermodynamic properties of the ball milled products and safety of the operation. Keywords: Ball milling, Diffusion control, Thermal dynamics, Green's function, Self-tuning regulation

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. 123 305 316 305-316