Understanding the linear relation between pop-in excursion length and critical force for spherical nanoindentation

References

• Y. Sato, S. Shinzato, T. Ohmura, T. Hatano and S. Ogata, Unique universal scaling in nanoindentation pop-ins. Nat Commun 11 (2020), p.4177.
   PubMed Web of Science ®Google Scholar
• Y. Sato, S. Shinzato, T. Ohmura and S. Ogata, Atomistic prediction of the temperature- and loading-rate-dependent first pop-in load in nanoindentation. Int J Plasticity 121 (2019), p. 280.
   Web of Science ®Google Scholar
• J.L. Bassani and V. Racherla, From non-planar dislocation cores to non-associated plasticity and strain bursts. Prog Mater Sci 56 (2011), p. 852.
   Web of Science ®Google Scholar
• T. Zhu and J. Li, Ultra-strength materials. Prog Mater Sci 55 (2010), p. 710.
   Web of Science ®Google Scholar
• H. Nili, K. Kalantar-zadeh, M. Bhaskaran and S. Sriram, In situ nanoindentation: probing nanoscale multifunctionality. Prog Mater Sci 58 (2013), p. 1.
   Web of Science ®Google Scholar
• J. Li, K.J.V. Viiet, T. Zhu, S. Yip and S. Suresh, Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418 (2002), p. 307.
   PubMed Web of Science ®Google Scholar
• C.A. Schuh, J.K. Mason and A.C. Lund, Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nat Mater 4 (2005), p. 617.
   PubMed Web of Science ®Google Scholar
• A.M. Minor, S.A. Asif, Z. Shan, E.A. Stach, E. Cyrankowski, T.J. Wyrobek and O.L. Warren, A new view of the onset of plasticity during the nanoindentation of aluminium. Nat Mater 5 (2006), p. 697.
   PubMed Web of Science ®Google Scholar
• Q. Yu, M. Legros and A.M. Minor, In situ TEM nanomechanics. Mrs Bull 40 (2015), p. 62.
   Web of Science ®Google Scholar
• K. Xiong, H. Lu and J. Gu, Atomistic simulations of the nanoindentation-induced incipient plasticity in Ni 3 Al crystal. Comp Mater Sci 115 (2016), p. 214.
   Web of Science ®Google Scholar
• W. Zhang, Y. Gao, Y. Xia and H. Bei, Indentation Schmid factor and incipient plasticity by nanoindentation pop-in tests in hexagonal close-packed single crystals. Acta Mater 134 (2017), p. 53.
   Web of Science ®Google Scholar
• D. Lorenz, A. Zeckzer, U. Hilpert, P. Grau, H. Johansen and H.S. Leipner, Pop-in effect as homogeneous nucleation of dislocations during nanoindentation. Phys Rev B 67 (2003), p. 172101.
   Web of Science ®Google Scholar
• T.L. Li, Y.F. Gao, H. Bei and E.P. George, Indentation Schmid factor and orientation dependence of nanoindentation pop-in behavior of NiAl single crystals. J Mech Phys Solids 59 (2011), p. 1147.
   Web of Science ®Google Scholar
• C. Caër, E. Patoor, S. Berbenni and J.S. Lecomte, Stress induced pop-in and pop-out nanoindentation events in CuAlBe shape memory alloys. Mater Sci Eng A 587 (2013), p. 304.
   Web of Science ®Google Scholar
• Z. Zhang, S. Yang, C. Xu, B. Wang and N. Duan, Deformation and stress at pop-in of lithium niobate induced by nanoindentation. Scripta Mater 77 (2014), p. 56.
   Web of Science ®Google Scholar
• S.R. Jian, Pop-in effects and dislocation nucleation of c-plane single-crystal ZnO by Berkovich nanoindentation. J Alloy Compd 644 (2015), p. 54.
   Web of Science ®Google Scholar
• S.R. Jian, C.H. Tasi, S.Y. Huang and C.W. Luo, Nanoindentation pop-in effects of Bi2Te3 thermoelectric thin films. J Alloy Compd 622 (2015), p. 601.
   Web of Science ®Google Scholar
• P.M. Derlet and R. Maaß, The stress statistics of the first pop-in or discrete plastic event in crystal plasticity. J Appl Phys 120 (2016), p. 225101.
   Web of Science ®Google Scholar
• Y. Xia, Y. Gao, G.M. Pharr and H. Bei, Single versus successive pop-in modes in nanoindentation tests of single crystals. J Mater Res 31 (2016), p. 2065.
   Web of Science ®Google Scholar
• M. Dietiker, R.D. Nyilas, C. Solenthaler and R. Spolenak, Nanoindentation of single-crystalline gold thin films: correlating hardness and the onset of plasticity. Acta Mater 56 (2008), p. 3887.
   Web of Science ®Google Scholar
• A.M. Minor, J.W. Morris and E.A. Stach, Quantitative in situ nanoindentation in an electron microscope. Appl Phys Lett 79 (2001), p. 1625.
   Web of Science ®Google Scholar
• L. Zhang, T. Ohmura, K. Seikido, K. Nakajima, T. Hara and K. Tsuzaki, Direct observation of plastic deformation in iron–3% silicon single crystal by in situ nanoindentation in transmission electron microscopy. Scripta Mater 64 (2011), p. 919.
   Web of Science ®Google Scholar
• D. Bufford, Y. Liu, J. Wang, H. Wang and X. Zhang, In situ nanoindentation study on plasticity and work hardening in aluminium with incoherent twin boundaries. Nat Commun 5 (2014), p. 4864.
   PubMed Web of Science ®Google Scholar
• Y. Liu, H. Wang and X. Zhang, In situ TEM nanoindentation studies on stress-induced phase transformations in metallic materials. Jom 68 (2015), p. 226.
   Web of Science ®Google Scholar
• H. Bei, Y.F. Gao, S. Shim, E.P. George and G.M. Pharr, Strength differences arising from homogeneous versus heterogeneous dislocation nucleation. Phys Rev B 77 (2008), p. 060103.
   Web of Science ®Google Scholar
• S. Shim, H. Bei, E.P. George and G.M. Pharr, A different type of indentation size effect. Scripta Mater 59 (2008), p. 1095.
   Web of Science ®Google Scholar
• C. Begau, A. Hartmaier, E.P. George and G.M. Pharr, Atomistic processes of dislocation generation and plastic deformation during nanoindentation. Acta Mater 59 (2011), p. 934.
   Web of Science ®Google Scholar
• D. Feichtinger, P.M. Derlet and H. Van Swygenhoven, Atomistic simulations of spherical indentations in nanocrystalline gold. Phys Rev B 67 (2003), p. 024113.
   Web of Science ®Google Scholar
• C.J. Ruestes, A. Stukowski, Y. Tang, D.R. Tramontina, P. Erhart, B.A. Remington, H.M. Urbassek, M.A. Meyers and E.M. Bringa, Atomistic simulation of tantalum nanoindentation: effects of indenter diameter, penetration velocity, and interatomic potentials on defect mechanisms and evolution. Mater Sci Eng A 613 (2014), p. 390.
   Web of Science ®Google Scholar
• G.Z. Voyiadjis and M. Yaghoobi, Large scale atomistic simulation of size effects during nanoindentation: dislocation length and hardness. Mater Sci Eng A 634 (2015), p. 20.
   Web of Science ®Google Scholar
• X. Zhou, B. Ouyang, W.A. Curtin and J. Song, Atomistic investigation of the influence of hydrogen on dislocation nucleation during nanoindentation in Ni and Pd. Acta Mater 116 (2016), p. 364.
   Web of Science ®Google Scholar
• A. Ukwatta and A. Achuthan, A molecular dynamics (MD) simulation study to investigate the role of existing dislocations on the incipient plasticity under nanoindentation. Comp Mater Sci 91 (2014), p. 329.
   Web of Science ®Google Scholar
• K. Sun, W. Shen and L. Ma, The influence of residual stress on incipient plasticity in single-crystal copper thin film under nanoindentation. Comp Mater Sci 81 (2014), p. 226.
   Web of Science ®Google Scholar
• V. Gaspard, G. Kermouche, D. Delafosse and A. Barnoush, Hydrogen effect on dislocation nucleation in a ferritic alloy Fe–15Cr as observed per nanoindentation. Mater Sci Eng A 604 (2014), p. 86.
   Web of Science ®Google Scholar
• P. Sudharshan Phani, K.E. Johanns, E.P. George and G.M. Pharr, A simple stochastic model for yielding in specimens with limited number of dislocations. Acta Mater 61 (2013), p. 2489.
   Web of Science ®Google Scholar
• A. Montagne, V. Audurier and C. Tromas, Influence of pre-existing dislocations on the pop-in phenomenon during nanoindentation in MgO. Acta Mater 61 (2013), p. 4778.
   Web of Science ®Google Scholar
• J.J. Zhang, T. Sun, A. Hartmaier and Y.D. Yan, Atomistic simulation of the influence of nanomachining-induced deformation on subsequent nanoindentation. Comp Mater Sci 59 (2012), p. 14.
   Web of Science ®Google Scholar
• I. Salehinia and D.F. Bahr, The impact of a variety of point defects on the inception of plastic deformation in dislocation-free metals. Scripta Mater 66 (2012), p. 339.
   Web of Science ®Google Scholar
• A. Barnoush, M. Asgari and R. Johnsen, Resolving the hydrogen effect on dislocation nucleation and mobility by electrochemical nanoindentation. Scripta Mater 66 (2012), p. 414.
   Web of Science ®Google Scholar
• Z. Wang, H. Bei, E.P. George and G.M. Pharr, Influences of surface preparation on nanoindentation pop-in in single-crystal Mo. Scripta Mater 65 (2011), p. 469.
   Web of Science ®Google Scholar
• J.K. Mason, A.C. Lund and C.A. Schuh, Determining the activation energy and volume for the onset of plasticity during nanoindentation. Phys Rev B 73 (2006), p. 054102.
   Web of Science ®Google Scholar
• D. Wu and T.G. Nieh, Incipient plasticity and dislocation nucleation in body-centered cubic chromium. Mater Sci Eng A 609 (2014), p. 110.
   Web of Science ®Google Scholar
• G. Liu, M. Song, X. Liu, S. Ni, S. Wang, Y. He and Y. Liu, An investigation of the mechanical behaviors of micro-sized tungsten whiskers using nanoindentation. Mater Sci Eng A 594 (2014), p. 278.
   Web of Science ®Google Scholar
• A. Barnoush, Correlation between dislocation density and nanomechanical response during nanoindentation. Acta Mater 60 (2012), p. 1268.
   Web of Science ®Google Scholar
• Y. Shibutani, T. Tsuru and A. Koyama, Nanoplastic deformation of nanoindentation: crystallographic dependence of displacement bursts. Acta Mater 55 (2007), p. 1813.
   Web of Science ®Google Scholar
• T.H. Fang, W.Y. Chang and J.J. Huang, Dynamic characteristics of nanoindentation using atomistic simulation. Acta Mater 57 (2009), p. 3341.
   Web of Science ®Google Scholar
• J.E. Bradby, J.S. Williams and M.V. Swain, Pop-in events induced by spherical indentation in compound semiconductors. J Mater Res 19 (2004), p. 380.
   Web of Science ®Google Scholar
• M.J. Cordill, W.W. Gerberich and N.R. Moody, Size effects on yield instabilities in nickel. Mater. Res Soc Symp Proc 976 (2007), p. 0976.
   Google Scholar
• W.W. Gerberich, W.M. Mook, M.D. Chambers, M.J. Cordill, C.R. Perrey, C.B. Carter, R.E. Miller, W.A. Curtin, R. Mukherjee and S.L. Girshick, An energy balance criterion for nanoindentation-induced single and multiple dislocation events. J Appl Mech 73 (2006), p. 327.
   Web of Science ®Google Scholar
• M.J. Cordill, N.R. Moody and W.W. Gerberich, The role of dislocation walls for nanoindentation to shallow depths. Int J Plasticity 25 (2009), p. 281.
   Web of Science ®Google Scholar
• D. Catoor, Y.F. Gao, J. Geng, M.J.N.V. Prasad, E.G. Herbert, K.S. Kumar, G.M. Pharr and E.P. George, Incipient plasticity and deformation mechanisms in single-crystal Mg during spherical nanoindentation. Acta Mater 61 (2013), p. 2953.
   Web of Science ®Google Scholar
• M.A. Lodes, A. Hartmaier, M. Göken and K. Durst, Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: experiments and molecular dynamics simulations. Acta Mater 59 (2011), p. 4264.
   Web of Science ®Google Scholar
• S. Qu, Y. Huang, G.M. Pharr and K.C. Hwang, The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity. Int J Plasticity 22 (2006), p. 1265.
   Web of Science ®Google Scholar
• J.G. Swadener, E.P. George and G.M. Pharr, The correlation of the indentation size effect measured with indenters of various shapes. J Mech Phys Solids 50 (2002), p. 681.
   Web of Science ®Google Scholar
• M. Yaghoobi and G.Z. Voyiadjis, Atomistic simulation of size effects in single-crystalline metals of confined volumes during nanoindentation. Comp Mater Sci 111 (2016), p. 64.
   Web of Science ®Google Scholar
• N.M. Pugno, A general shape/size-effect law for nanoindentation. Acta Mater 55 (2007), p. 1947.
   Web of Science ®Google Scholar
• W.D. Nix and H. Gao, Indentation size effects in crystalline materials : a law for strain gradient plasticity. J Mech Phys Solids 46 (1998), p. 411.
   Web of Science ®Google Scholar
• Y. Gao, C.J. Ruestes, D.R. Tramontina and H.M. Urbassek, Comparative simulation study of the structure of the plastic zone produced by nanoindentation. J Mech Phys Solids 75 (2015), p. 58.
   Web of Science ®Google Scholar
• Y. Gao, C.J. Ruestes and H.M. Urbassek, Nanoindentation and nanoscratching of iron: atomistic simulation of dislocation generation and reactions. Comp Mater Sci 90 (2014), p. 232.
   Web of Science ®Google Scholar
• L. Zhang, T. Ohmura, S. Emura, N. Sekido, F. Yin, X. Min and K. Tsuzaki, Evaluation of matrix strength in ultra-fine grained pure Al by nanoindentation. J Mater Res 24 (2011), p. 2917.
   Web of Science ®Google Scholar
• L. Zhang and T. Ohmura, Plasticity initiation and evolution during nanoindentation of an iron-3% silicon crystal. Phys Rev Lett 112 (2014), p. 145504.
   PubMed Web of Science ®Google Scholar
• M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun and M. Asta, Development of new interatomic potentials appropriate for crystalline and liquid iron. Phil Mag 83 (2003), p. 3977.
   Google Scholar
• S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117 (1995), p. 1.
   Web of Science ®Google Scholar
• T. Tsuru, Y. Kaji, D. Matsunaka and Y. Shibutani, Incipient plasticity of twin and stable/unstable grain boundaries during nanoindentation in copper. Phys Rev B 82 (2010), p. 024101.
   Web of Science ®Google Scholar
• D. Mordehai, M. Kazakevich, D.J. Srolovitz and E. Rabkin, Nanoindentation size effect in single-crystal nanoparticles and thin films: a comparative experimental and simulation study. Acta Mater 59 (2011), p. 2309.
   Web of Science ®Google Scholar
• S. Roy and D. Mordehai, Annihilation of edge dislocation loops via climb during nanoindentation. Acta Mater 127 (2017), p. 351.
   Web of Science ®Google Scholar
• R. Kositski and D. Mordehai, Depinning-controlled plastic deformation during nanoindentation of BCC iron thin films and nanoparticles. Acta Mater 90 (2015), p. 370.
   Web of Science ®Google Scholar
• M. Yaghoobi and G.Z. Voyiadjis, Size effects in fcc crystals during the high rate compression test. Acta Mater 121 (2016), p. 190.
   Web of Science ®Google Scholar
• B. Wang, Y. Gao and H.M. Urbassek, Microstructure and magnetic disorder induced by nanoindentation in single-crystalline Fe. Phys Rev B 89 (2014), p. 104105.
   Web of Science ®Google Scholar
• P. Hansson, Influence of surface roughening on indentation behavior of thin copper coatings using a molecular dynamics approach. Comp Mater Sci 117 (2016), p. 233.
   Web of Science ®Google Scholar
• A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Model Simul Mater Sc 18 (2010), p. 015012.
   Web of Science ®Google Scholar
• F. Javaid, E. Bruder and K. Durst, Indentation size effect and dislocation structure evolution in (001) oriented SrTiO3 Berkovich indentations: HR-EBSD and etch-pit analysis. Acta Mater 136 (2017), p. 1.
   Web of Science ®Google Scholar
• R.W.K. Honeycombe, Plastic Deformation of Metals, 2nd ed., Edward Arnold, London, 1984.
   Google Scholar
• E.K. Njeim and D.F. Bahr, Atomistic simulations of nanoindentation in the presence of vacancies. Scripta Mater 62 (2010), p. 598.
   Web of Science ®Google Scholar
• N. Zhou, K.I. Elkhodary, X. Huang, S. Tang and Y. Li, Dislocation structure and dynamics govern pop-in modes of nanoindentation on single-crystal metals. Phil Mag 100 (2020), p. 1585.
   Google Scholar
• A. Gouldstone, K.J.V. Vliet and S. Suresh, Simulation of defect nucleation in a crystal. Nature 411 (2001), p. 656.
   PubMed Web of Science ®Google Scholar
• G. Ziegenhain, A. Hartmaier and H.M. Urbassek, Pair vs many-body potentials: influence on elastic and plastic behavior in nanoindentation of fcc metals. J Mech Phys Solids 57 (2009), p. 1514.
   Web of Science ®Google Scholar
• G.I. Taylor, Plastic strain in metals. J Inst Metals 62 (1938), p. 307.
   Google Scholar
• K. Durst, B. Backes, O. Franke and M. Göken, Indentation size effect in metallic materials: modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations. Acta Mater 54 (2006), p. 2547.
   Web of Science ®Google Scholar
• X. Qiu, Y. Huang, W.D. Nix, K.C. Hwang and H. Gao, Effect of intrinsic lattice resistance in strain gradient plasticity. Acta Mater 49 (2001), p. 3949.
   Web of Science ®Google Scholar