Elsevier

Acta Materialia

Volume 123, 15 January 2017, Pages 305-316
Acta Materialia

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

https://doi.org/10.1016/j.actamat.2016.10.041Get rights and content

Abstract

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.

Section snippets

Introduction and prior work

Over the past three decades the materials community has made groundbreaking progress in mechano-chemistry research addressing mechanical alloying (MA) of metals and non-metallic materials. On the one hand, this has enabled a variety of transformative and impactful applications, as e.g. in ball milling (BM) fabrication of bimetallic and multi-material micro- and nano-structures, such as of nickel, iron and titanium aluminides etc., used for self-propagating high-temperature synthesis [1]. Such

Model framework and assumptions

Morphological observation of ball-milled bimetallic particulate sections reveals a multi-scale self-similar microstructure (Fig. 1a) composed of lamellar network (branching tree) formations, which have evolved by deformation of globular agglomerates (Apollonian packs) of the original metal powders (Fig. 1b). This fractal microstructure transformation during the BM process can be described by the deformation and joining of these individual monometallic particle domains as warped ellipsoid (WE)

Calibration tests on foils

Laboratory testing of the model is performed on a low-energy planetary BM system (Fritsch Mono Mill Pulverisette 6) in nitrogen inert atmosphere, with five balls of Rball = 5 mm radius in a rounded cylindrical 80 ml vial rotating at 300 rpm and made of stainless steel. The bimetallic Al-Ni reactive system is employed for model calibration and validation, with material properties shown in Table 1 [45], and with ball energetics described by s = 1 m/s in Eq. (1) (Fig. 5). In addition, the contact

Conclusions

The computational model established in this article introduces several original contributions to the wealthy literature of MA simulation. These include: the warped ellipsoid (WE) as universal domain primitive, from spheroidal powders to lamellar particulate layers; implementation of experimentally calibrated kinetic theory-based motion of the ball impactors; ideal elastic-to-inelastic dissipative energetic material transformations of surface friction slip and bulk Castigliano deformation;

Acknowledgment

This research was supported in part by a Khalifa University Internal Research Fund (Level 1) award and by the US Department of Energy, National Nuclear Security Administration under Award Number DENA0002377. KU students Khatera Farzanah, Mira Hassan and Rauda Al Mheiri are gratefully acknowledged for laboratory work in calibration tests. The authors also wish to thankfully acknowledge particularly constructive suggestions on this article context and references by one anonymous reviewer.

References (48)

  • S. Garroni et al.

    Mesostructural refinement in the early stages of mechanical alloying

    Scr. Mater

    (2014)
  • S. Garroni et al.

    Reduction of grain size in metals and metal mixtures processed by ball milling

    Scr. Mater

    (2014)
  • H. Kruggel-Emden et al.

    Review and extension of normal force models for the Discrete Element Method

    Powder Technol.

    (2007)
  • C.C. Doumanidis et al.

    Brownian-like kinematics of ball milling for particulate structural modeling

    Powder Technol.

    (2016)
  • A.S. Rogachev et al.

    Influence of the high energy ball milling on structure and reactivity of the Ni+Al powder mixture

    J. Alloys Compd.

    (2013)
  • J. Jamari et al.

    Plastic deformation and contact area of an elastic-plastic contact of ellipsoid bodies after unloading

    Tribol. Int.

    (2007)
  • J.C. Chung

    Elastic-plastic contact analysis of an ellipsoid and a rigid flat

    Tribol. Int.

    (2010)
  • Q.J. Zheng et al.

    Contact forces between viscoelastic ellipsoidal particles

    Powder Technol.

    (2013)
  • J.L. Liou et al.

    A microcontact model developed for sphere- and cylinder-based fractal bodies in contact with a rigid flat surface

    Wear

    (2010)
  • I.C. Sinka

    A model for the deformation of an ellipsoid subject to a large number of successive impacts with special reference to spheronisation

    Powder Technol.

    (2015)
  • D. Healy

    Elastic field in 3D due to a spheroidal inclusion—MATLAB™ code for Eshelby's solution

    Comput. Geosci.

    (2009)
  • A. Hadjiafxenti et al.

    The influence of structure on thermal behavior of reactive Al-Ni powder mixtures formed by ball milling

    J. Alloys Compd.

    (2010)
  • A.S. Rogachev et al.

    Combustion of heterogeneous nanostructural systems (review)

    Combust. Explos. Shock Waves

    (2010)
  • K.V. Manukyan et al.

    Tailored reactivity of Ni+Al nanocomposites: microstructural correlations

    J. Phys. Chem. C

    (2012)
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