Analysis of the Effect of Indenter Deformation and Presence of Voids on Silicon Nanoindentation Using Molecular Dynamics Simulation

Document Type : Research Article


Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran


In the present study, a three-dimensional molecular dynamics simulation was carried out to investigate the nanoindentation of single-crystalline Silicon. The simulations were performed using the spherical shape rigid and non-rigid indenters. Subsequently, the effects of the substrate crystalline surfaces were investigated on the force-displacement curve of the indenter. The influence of the indentation force and depth were also studied on the hardness of the substrate. The findings of the simulation were then compared to the force-displacement curve published in the previous studies. The results of comparison between the rigid and non-rigid indenters revealed that the level of the force-displacement and hardness-displacement curves decrease by changing the assumption of the rigid indenter to the non-rigid one. Moreover, the effects of void presence in a silicon substrate (in various sizes at different positions) were investigated on the material hardness. According to the results, the larger the void and the closer it is to the surface of the workpiece, the more it can reduce the hardness. It was also concluded that the presence of voids in silicon substrate could reduce the hardness of the workpiece by 54%. Nevertheless, small voids near the surface may be eliminated during the nanoindentation process.


Main Subjects

[1] B. Poon, D. Rittel, G. Ravichandran, An analysis of nanoindentation in linearly elastic solids, International Journal of Solids and Structures, 45(24) (2008) 6018-6033.
[2] F. Cardarelli, Materials handbook, Springer, 2018.
[3] G. Ziegenhain, A. Hartmaier, H.M. Urbassek, Pair vs many-body potentials: Influence on elastic and plastic behavior in nanoindentation of fcc metals, Journal of the Mechanics and Physics of Solids, 57(9) (2009) 1514-1526.
[4] A.C. Fischer-Cripps, Applications of nanoindentation, in:  Nanoindentation, Springer, 2011, pp. 213-233.
[5] T.-H. Fang, C.-I. Weng, J.-G. Chang, Molecular dynamics analysis of temperature effects on nanoindentation measurement, Materials Science and Engineering: A, 357(1-2) (2003) 7-12.
[6] P. Peng, G. Liao, T. Shi, Z. Tang, Y. Gao, Molecular dynamic simulations of nanoindentation in aluminum thin film on silicon substrate, Applied Surface Science, 256(21) (2010) 6284-6290.
[7] W. Cheong, L. Zhang, Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation, Nanotechnology, 11(3) (2000) 173.
[8] C.-L. Liu, T.-H. Fang, J.-F. Lin, Atomistic simulations of hard and soft films under nanoindentation, Materials Science and Engineering: A, 452-453 (2007) 135-141.
[9] M. Yaghoobi, G.Z. Voyiadjis, Effect of boundary conditions on the MD simulation of nanoindentation, Computational Materials Science, 95 (2014) 626-636.
[10] P. Walsh, A. Omeltchenko, R.K. Kalia, A. Nakano, P. Vashishta, S. Saini, Nanoindentation of silicon nitride: A multimillion-atom molecular dynamics study, Applied physics letters, 82(1) (2003) 118-120.
[11] D. Chocyk, T. Zientarski, Molecular dynamics simulation of Ni thin films on Cu and Au under nanoindentation, Vacuum, 147 (2018) 24-30.
[12] C. Lu, Y. Gao, G. Michal, N.N. Huynh, H.T. Zhu, A.K. Tieu, Atomistic simulation of nanoindentation of iron with different indenter shapes, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 223(7) (2009) 977-984.
[13] T. Fang, W. Chang, Y. Fan, Molecular dynamics of nanoindentation with conical carbon indenters on graphite and diamond, Nano, 5(04) (2010) 231-236.
[14] S. Xu, Q. Wan, Z. Sha, Z. Liu, Molecular dynamics simulations of nano-indentation and wear of the γTi-Al alloy, Computational Materials Science, 110 (2015) 247-253.
[15] S. Goel, N.H. Faisal, X. Luo, J. Yan, A. Agrawal, Nanoindentation of polysilicon and single crystal silicon: Molecular dynamics simulation and experimental validation, Journal of physics D: applied physics, 47(27) (2014) 275304.
[16] A.K. Nair, M.J. Cordill, D. Farkas, W.W. Gerberich, Nanoindentation of thin films: Simulations and experiments, Journal of Materials Research, 24(3) (2009) 1135-1141.
[17] K.V. Reddy, S. Pal, Analysis of deformation behaviour of Al–Ni–Co thin film coated aluminium during nano-indentation: a molecular dynamics study, Molecular Simulation, 44(17) (2018) 1393-1401.
[18] C. Xu, C. Liu, H. Wang, Incipient plasticity of diamond during nanoindentation, RSC Advances, 7(57) (2017) 36093-36100.
[19] L. Yuan, Z. Xu, D. Shan, B. Guo, Atomistic simulation of twin boundaries effect on nanoindentation of Ag(111) films, Applied Surface Science, 258(16) (2012) 6111-6115.
[20] M. Imran, F. Hussain, M. Rashid, S. Ahmad, Dynamic characteristics of nanoindentation in Ni: A molecular dynamics simulation study, Chinese Physics B, 21(11) (2012) 116201.
[21] H. Zhao, P. Zhang, C. Shi, C. Liu, L. Han, H. Cheng, L. Ren, Molecular Dynamics Simulation of the Crystal Orientation and Temperature Influences in the Hardness on Monocrystalline Silicon, Journal of Nanomaterials, 2014 (2014) 365642.
[22] D. Kim, S. Oh, Atomistic simulation of structural phase transformations in monocrystalline silicon induced by nanoindentation, Nanotechnology, 17(9) (2006) 2259.
[23] Y.-H. Lin, T.-C. Chen, P.-F. Yang, S.-R. Jian, Y.-S. Lai, Atomic-level simulations of nanoindentation-induced phase transformation in mono-crystalline silicon, Applied Surface Science, 254(5) (2007) 1415-1422.
[24] P. Zhu, Y. Hu, H. Wang, Atomistic simulations of the effect of a void on nanoindentation response of nickel, Science China Physics, Mechanics and Astronomy, 53(9) (2010) 1716-1719.
[25] P. Zhao, Y. Guo, Z. Deng, Atomic simulation of void effect on the microstructure evolution and internal stress transmission in nanoindentation, Solid State Communications, 301 (2019) 113694.
[26] J. Zimmerman, C. Kelchner, P. Klein, J. Hamilton, S. Foiles, Surface step effects on nanoindentation, Physical Review Letters, 87(16) (2001) 165507.
[27] E. Lilleodden, J. Zimmerman, S. Foiles, W. Nix, Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation, Journal of the Mechanics and Physics of Solids, 51(5) (2003) 901-920.
[28] D. Feichtinger, P. Derlet, H. Van Swygenhoven, Atomistic simulations of spherical indentations in nanocrystalline gold, Physical Review B, 67(2) (2003) 024113.
[29] X.-L. Ma, W. Yang, Molecular dynamics simulation on burst and arrest of stacking faults in nanocrystalline Cu under nanoindentation, Nanotechnology, 14(11) (2003) 1208.
[30] C.M. Tan, Y.R. Jeng, Y.C. Chiou, Atomistic Simulations of Nanoindentation on Cu (111) with a Void, in:  Advanced Materials Research, Trans Tech Publ, 2008, pp. 919-924.
[31] W. Yu, S. Shen, Multiscale analysis of the effects of nanocavity on nanoindentation, Computational Materials Science, 46(2) (2009) 425-430.
[32] S.V. Hosseini, M. Vahdati, A. Shokuhfar, Molecular Dynamics Simulation on Nano-Machining of Single Crystal Copper with a Void, in:  Materials with Complex Behaviour II, Springer, 2012, pp. 661-669.
[33] Y. Yang, Y. Li, G. Zhang, Z. Yang, J. Liu, H. Li, J. Zhao, Molecular dynamics simulation on elastoplastic properties of the void expansion in nanocrystalline copper, Journal of Nanoparticle Research, 20(8) (2018) 1-10.
[34] S. Pathak, S.R. Kalidindi, Spherical nanoindentation stress–strain curves, Materials science and engineering: R: Reports, 91 (2015) 1-36.
[35] S. Pathak, J.L. Riesterer, S.R. Kalidindi, J. Michler, Understanding pop-ins in spherical nanoindentation, Applied Physics Letters, 105(16) (2014) 161913.
[36] Y. Gao, C. Lu, N. Huynh, G. Michal, H. Zhu, A. Tieu, Molecular dynamics simulation of effect of indenter shape on nanoscratch of Ni, Wear, 267(11) (2009) 1998-2002.
[37] S. Vahid Hosseini, M. Vahdati, A. Shokuhfar, Effect of tool nose radius on nano-machining process by molecular dynamics simulation, in:  Defect and Diffusion Forum, Trans Tech Publ, 2011, pp. 977-982.
[38] J. Tersoff, Empirical interatomic potential for silicon with improved elastic properties, Physical Review B, 38(14) (1988) 9902.
[39] M. Papanikolaou, F.R. Hernandez, K. Salonitis, Investigation of the Subsurface Temperature Effects on Nanocutting Processes via Molecular Dynamics Simulations, Metals, 10(9) (2020) 1220.
[40] S. Goel, X. Luo, R.L. Reuben, W.B. Rashid, Atomistic aspects of ductile responses of cubic silicon carbide during nanometric cutting, Nanoscale research letters, 6(1) (2011) 1-9.
[41] S.A. Roncancio, D.F. Arias-Mateus, M.M. Gómez-Hermida, J.C. Riaño-Rojas, E. Restrepo-Parra, Molecular dynamics simulations of the temperature effect in the hardness on Cr and CrN films, Applied Surface Science, 258(10) (2012) 4473-4477.
[42] Q.X. Pei, C. Lu, H.P. Lee, Y.W. Zhang, Study of Materials Deformation in Nanometric Cutting by Large-scale Molecular Dynamics Simulations, Nanoscale Research Letters, 4(5) (2009) 444.
[43] N. Oumarou, J.-P. Jehl, R. Kouitat, P. Stempfle, On the variation of mechanical parameters obtained from spherical depth sensing indentation, International Journal of Surface Science and Engineering, 4(4-6) (2010) 416-428.
[44] S.-P. Ju, C.-T. Wang, C.-H. Chien, J. Huang, S.-R. Jian, The nanoindentation responses of nickel surfaces with different crystal orientations, Molecular Simulation, 33(11) (2007) 905-917.
[45] J. Hass, Thomas' calculus, Pearson Education India, 2008.
[46] F.P. Beer, E. Johnston, J. DeWolf, D. Mazurek, Mechanics of materials, New York,  (1992).