Real-Time Computational Model of Ball-Milled Fractal Structures

Abstract

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.