Dynamic modelling of hardness changes of aluminium nanostructure during mechanical ball milling process

Document Type : Research Paper


1 Young Researchers and Elite Club, Quchan Branch, Islamic Azad University, Quchan, Iran

2 Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

3 Department of Chemical Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran


In this research, the feasibility of using mathematical modelling in the ball milling process has been evaluated to verify the hardness changes of an aluminium nanostructure. Considering the model of normal force displacement (NFD), the radius of elastic-plastic and normal displacement of two balls were computed by applying analytical modelling and coding in MATLAB. Properties of balls and aluminium powder were entered into the software as input data. The impact radius and then the hardness of powder were calculated accordingly. The changes of aluminium powder hardness resulting from the collision of two spherical balls during the synthesis of an aluminium nanostructure were analytically derived and compared with experimental data obtained from the literature. Calculation of results accuracy shows the model has a better agreement with the experimental data at the beginning than the results from Maurice et al. (R2= 0.68 in this model).This research innovation is to combine the NFD model with hardness formulation to calculate final hardness.


  • Elastic and plastic deformation effects during collision were investigated.
  • The combination of NFD and powder hardness model shows better results.
  • This model is compared to Maurice et.al. The results show a 35% increase in model accuracy.


[1] M. Sopicka-Lizer, High-energy ball milling: Mechanochemical processing of nanopowders, Woodhead, New York, 2010.
[2] A. Nazari, M. Zakeri, Modeling the mean grain size ofsynthesized nanopowders produced by mechanical alloying, Ceram. Int. 39 (2013) 1587-1596.
[3] B. Nasiri-Tabrizi, A. Fahami, R. EbrahimiKahrizsangi, J. Ind. Eng. Chem. 20 (2014) 245-258.
[4] M. Abdellahi, M. Bahmanpour, A novel technology for minimizing the synthesis time of nanostructured powders in planetary mills, Mater. Res. 17 (2014) 781-791.
[5] M.S. Khoshkhoo, S. Scudino, T. Gemming, J. Thomas, J. Freudenberger, M. Zehetbauer, C. Koch, , J. Eckert, Nanostructure formation mechanism during in-situ consolidation of copper by room temperature ball milling, Mater. Desgin 65 (2015) 1083-1090.
[6] J.S. Benjamin, Mechanical alloying-A perspective, Metal Powder Report. 45 (1990) 122-127.
[7] M.S. El-Asfoury, M.N. Nasr, A. Abdel-Moneim, Effect of Friction on Material Mechanical Behaviour in Non-equal Channel Multi Angular Extrusion (NECMAE), in Book of Abstracts, 2015, pp. 364.
[8] T.P. Yadav, R.M. Yadav, D.P. Singh, Mechanical Milling: a Top Down Approach for the Synthesis of Nanomaterials and Nanocomposites, Nanosci. Nanotech. 2 (2012) 22-48.
[9] M. Zandrahimi, M.D. Chermahini, M. Mirbeik, The effect of multi-step milling and annealing treatments on microstructure and magnetic properties ofnanostructured Fe-Si powders, J. Mag. Mag. Mater. 323 (2011) 669-674.
[10] J. Ding, P. McCormick, R. Street, Structure and magnetic properties of mechanically alloyed SmxFe100-x nitride, J. Alloy. Compd. 189 (1992) 83-86. 
[11] J. Ding, W.F. Miao, P.G. McCormick, R. Street, Mechanochemical synthesis of ultrafine Fe powder, Appl. Phys. lett. 67 (1995) 3804-3806.
[12] M. Abdellahi, H. Bahmanpour, M. Bahmanpour, The best conditions forminimizing the synthesis time of nanocomposites during high energy ball milling: Modeling and optimizing, Ceram. Int. 40 (2014) 9675-9692.
[13] A. Canakci, S. Ozsahin, T. Varol, Modeling the influence of a process control agent on the properties of metal matrix composite powders using artificial neural networks, Powder Technol. 228 (2012) 26-35.
[14] L. Vu-Quoc, X. Zhang, L. Lesburg, A normal force-displacement model for contacting spheres accounting for plastic deformation force-driven formulation, J. Appl. Mech. 67 (2000) 363-371.
[15] H. Hertz, Uber die Beruhrung fester elastische Korper and uber die Harts (On the contact of rigid elastic solids and on hardness), Verhandlunger des Vereins zur Beforderung des Gewerbefleisses, Leipzig, Nov. 1882.
 [16] R.D. Mindlin, H. Deresiewica, Elastic spheres in contact under varying oblique forces, J. Appl. Mech. 20 (1953) 327-344.
[17] L. Vu-Quoc, X. Zhang, L. Lesburg, Contact force-displacement relations for spherical particles accounting for plastic deformation, Int. J. Solids Struct. 38 (2001) 6455-6490.
[18] O.R. Walton, R.L. Braun, Viscosity, granulartemperature, and stress calculations for shearing assemblies of inelastic, frictional disks, J. Rheol. 30 (1986) 949-980.
[19] W. Goldsmith, Impact, the theory and physical behavior of colliding solids, Edward Arnold Pub., 1960.
[20] C. Thornton, Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres, J. Appl. Mech. 64 (1997) 383-386.
[21] D. Maurice, T.H. Courtney, Modeling of mechanical alloying: Part I. deformation, coalescence, bdand fragmentation mechanisms, Metall. Mater. Trans. A, 25 (1994) 147–158.
[22] D. Maurice, T.H. Courtney, Modeling of mechanical alloying: Part II. development of computational modeling programs, Metall. Mater. Trans. A 26 (1995) 2431-2435.
[23] D. Maurice, T.H. Courtney, Modeling of mechanical alloying: Part III. Applications of computational programs, Metall. Mater. Trans. A 26 (1995) 2437-2444.
[24] H. Mio, J. Kano, F. Saito, K. Kaneko, Effects of rotational direction and rotation-to-revolution speed ratio in planetary ball milling, Mater. Sci. Eng. A 332 (2002) 75-80.
[25] E. Hryha, P. Zubko, E. Dudrova, L. Pešek, S. Bengtsson, An application of universal hardness test to metal powder particles, J. Mater. Process. Tech. 209 (2009) 2377-2385.
[26] J. Walkenbach, Excel 2013 Formulas, John Wiley & Sons Publisher, 2013, pp. 483.
[27] K. Velten, Mathematical Modeling and Simulation: Introduction for Scientists and Engineers, John Wiley & Sons Publisher, 2009, pp. 69.
Volume 3, Issue 1
March 2017
Pages 25-32
  • Receive Date: 19 August 2016
  • Revise Date: 04 June 2017
  • Accept Date: 11 July 2017
  • First Publish Date: 11 July 2017