Ball milling (BM) offers a flexible process for nanomanufacturing of reactive bimetallic multiscale particulates (nanoheaters) for self-heated microjoining engineering materials and biomedical tooling. This paper introduces a mechanics-based process model relating the chaotic dynamics of BM with the random fractal structures of the produced particulates, emphasizing its fundamental concepts, underlying assumptions, and computation methods. To represent Apollonian globular and lamellar structures, the simulation employs warped ellipsoidal (WE) primitives of elasto-plastic strain-hardening materials, with Maxwell–Boltzmann distributions of ball kinetics and thermal transformation of hysteretic plastic, frictional, and residual stored energetics. Interparticle collisions are modeled via modified Hertzian contact impact mechanics, with local plastic deformation yielding welded microjoints and resulting in cluster assembly into particulates. The model tracks the size and diversity of such particulate populations as the process evolves via sequential collision and integration events. The simulation was shown to run in real-time computation speeds on modest hardware, and match successfully the fractal dimension and contour shape of experimental ball-milled Al–Ni particulate micrographs. Thus, the model serves as a base for the design of a feedback control system for continuous BM.
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 ballmilled 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.
Ball milling motion has been previously studied through computationally expensive, off-line experimental video processing and numerical simulations by the discrete element method. This research establishes a more efficient formulation of the ball energetics and kinetics similar to the Brownian kinetic theory of statistical mechanics. Based on assumptions of thermomechanical equilibrium, negligible gravitational, aerodynamic and surface condition effects, and decoupled impact interaction among balls and with milled particulates, this model proposes mono-parametric spectral energy and velocity probability density functions akin to Maxwell-Boltzmann statistics, along with uniformly distributed impact directionality. The model predictions are calibrated and validated by comparison with published experimental measurements and computationally derived spectra. This descriptive Brownian-like motion model enables effective simulation of contact and impact, material deformation and micro-joining of ball milled bimetallic powders. A comprehensive simulation of the evolving internal fractal microstructure of the processed particulates is implemented at real-time computation speed, and its predictions are compared with experimental micrographs of ball milled Ni-Al particulates.
Nanostructured bimetallic reactive multilayers can be conveniently produced by ball milling of elemental powders. This research explores the non-equilibrium microscale conductive thermal transport in ball-milled particulate fractal structures during fabrication, arising from heat dissipation by bulk plastic deformation and surface friction. Upon impactor collisions, temperature increments are determined at interface joints and domain volumes using Green's functions, mirrored by source images with respect to warped ellipsoid domain boundaries. Heat source efficiency is calibrated via laboratory data to compensate for thermal expansion and impactor inelasticity, and the thermal analysis is coupled to a dynamic mechanics model of the particulate fracture. This thermomechanical model shows good agreement with the fractal dimensions of the observed microstructure from ball milling experiments. The model is intended to provide a comprehensive physical understanding of the fundamental process mechanism. In addition, the model could serve as a real-time thermal observer for closed-loop process control, as well as for interfacial diffusion and reaction analysis during ball milling.
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