Research Papers: Fractal Engineering and Biomedicine

Real-Time Computational Model of Ball-Milled Fractal Structures

[+] Author and Article Information
Constantine C. Doumanidis

Pankyprion Gymnasion,
Nicosia 1060, Cyprus
e-mail: kdoumani98@gmail.com

I. E. Gunduz

School of Mechanical Engineering,
Purdue University,
West Lafayette, IL 47907
e-mail: igunduz@purdue.edu

Claus Rebholz

Department of Mechanical and
Manufacturing Engineering,
University of Cyprus,
Nicosia 1678, Cyprus
e-mail: claus@ucy.ac.cy

Charalabos C. Doumanidis

Department of Mechanical Engineering,
Khalifa University,
Abu Dhabi 127788, UAE
e-mail: haris.doumanidis@kustar.ac.ae

Manuscript received July 29, 2015; final manuscript received July 31, 2015; published online March 8, 2016. Assoc. Editor: Abraham Quan Wang.

J. Nanotechnol. Eng. Med 6(3), 031001 (Mar 08, 2016) (6 pages) Paper No: NANO-15-1056; doi: 10.1115/1.4031276 History: Received July 29, 2015; Revised July 31, 2015; Accepted August 03, 2015

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.

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Fig. 1

Fractal globular Apollonian packing of ellipsoid particles

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Fig. 2

Scanning electron microscope (SEM) micrographs of ball-milled Al (dark phase)–Ni (bright) particulates after 2, 4, 6, and 8 hrs [1]

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Fig. 3

Three-dimensional WE primitive

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Fig. 4

Two-dimensionalWE parameters and loads

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Fig. 5

Particulate assembly of deformed WE particles (bold) with an additional cluster rolling to contact on its bottom surface and an impactor

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Fig. 6

Strain-hardening elastoplastic particle behavior

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Fig. 7

Experimental (bar, Ref. [17]) and theoretical (dashed) PDF of cascading BM particulate velocities

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Fig. 8

Contact conditions between two impacting parts 1 and2

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Fig. 9

Boundary conditions of particulate deformation from adjacent contacts

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Fig. 10

Simulated sections of ball-milled Al (dark phase)–Ni (bright) particulates after 2, 4, 6 and 8 hrs



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