On the breakdown of the Nix-Gao model for indentation size effect

References

• J.R. Greer and J.T.M. De Hosson, Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog. Mater. Sci. 56 (2011), pp. 654–724.
   Web of Science ®Google Scholar
• E.O. Hall, The deformation and ageing of mild steel. 3. Discussion of results. Proc. Phys. Soc. Lond. Sect. B 64 (1951), pp. 747–753.
   Google Scholar
• N.J. Petch, The cleavage strength of polycrystals. J. Iron Steel Inst. 174 (1953), pp. 25–28.
   Web of Science ®Google Scholar
• Z.C. Cordero, B.E. Knight and C.A. Schuh, Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals. Int. Mater. Rev. 61 (2016), pp. 495–512.
   Web of Science ®Google Scholar
• A.J. Bushby and D.J. Dunstan, Size effects in yield and plasticity under uniaxial and non-uniform loading: experiment and theory. Phil. Mag. 91 (2011), pp. 1037–1049.
   Google Scholar
• N.A. Fleck, G.M. Muller, M.F. Ashby and J.W. Hutchinson, Strain gradient plasticity: theory and experiment. Acta Metal. Mater. 42 (1994), pp. 475–487.
   Google Scholar
• G.M. Pharr, E.G. Herbert and Y. Gao, The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40 (2010), pp. 271–292.
   Web of Science ®Google Scholar
• I. Manika and J. Maniks, Size effects in micro- and nanoscale indentation. Acta Mater. 54 (2006), pp. 2049–2056.
   Web of Science ®Google Scholar
• V.Y. Milman, АА Golubenko and S.N. Dub, Indentation size effect in nanohardness. Acta Mater. 59 (2011), pp. 7480–7487.
   Web of Science ®Google Scholar
• A. Ruiz-Moreno, P. Hähner, L. Kurpaska, J. Jagielski, P. Spätig, M. Trebala, S.-P. Hannula, S. Merino, G. de Diego, H. Namburi, O. Libera, D. Terentyev, T. Khvan, C. Heintze and N.M. Jennett, Round robin into best practices for the determination of indentation size effects. Nanomaterials 10 (2020), pp. 15). doi:10.3390/nano10010130.
   Web of Science ®Google Scholar
• I.J. Spary, A.J. Bushby and N.M. Jennett, On the indentation size effect in spherical indentation. Phil. Mag. 86 (2006), pp. 5581–5593.
   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), pp. 411–425.
   Web of Science ®Google Scholar
• Y. Huang, F. Zhang, K.C. Hwang, W.D. Nix, G.M. Pharr and G. Feng, A model of size effects in nano-indentation. J. Mech. Phys. Solids 54 (2006), pp. 1668–1686.
   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), pp. 681–694.
   Web of Science ®Google Scholar
• K. Durst, B. Backes and M. Göken, Indentation size effect in metallic materials: correcting for the size of the plastic zone. Scr. Mater. 52 (2005), pp. 1093–1097.
   Web of Science ®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), pp. 2547–2555.
   Web of Science ®Google Scholar
• G. Feng and W.D. Nix, Indentation size effect in MgO. Scrip. Mater. 51 (2004), pp. 599–603.
   Web of Science ®Google Scholar
• W.C. Oliver and G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7 (1992), pp. 1564–1583.
   Web of Science ®Google Scholar
• W.C. Oliver and G.M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation, Advances in understanding and refinements to methodology. J. Mater. Res. 19 (2004), pp. 3–20.
   Web of Science ®Google Scholar
• J. Čech, P. Haušild, A. Materna and O. Kovářík, Examination of Berkovich indenter tip bluntness. Mater. Des. 109 (2016), pp. 347–353.
   Web of Science ®Google Scholar
• X. Hou and N.M. Jennett, Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects. Acta Mater. 60 (2012), pp. 4128–4135.
   Web of Science ®Google Scholar
• J.D. Eshelby, F.C. Frank and F.R.N. Nabarro, The equilibrium of linear arrays of dislocations. Phil. Mag. 42 (1951), pp. 351–364.
   Google Scholar
• J. Čech, P. Haušild and A. Materna, Effect of crystallographic orientation on nanoindentation response of Fe3Si single-crystals. Key Eng. Mater. 784 (2018), pp. 44–48.
   Google Scholar
• Z.C. Szkopiak, Yield stress in niobium-nitrogen solid solution. J. Less Common Metals 21 (1970), pp. 383–393.
   Google Scholar
• C.P. Biswas, Strain hardening of titanium by severe plastic deformation, Ph.D. diss., MIT, 1973.
   Google Scholar
• H. Garbacz, I. Semenova, S. Zherebtsov, and M. Motyka, Nanocrystalline Titanium, Elsevier, Amsterdam, 2018.
   Google Scholar
• D. Brunner, Comparison of flow-stress measurements on high-purity tungsten single crystals with the kink-pair theory. Mater. Trans. JIM 41 (2000), pp. 152–160.
   Web of Science ®Google Scholar
• H.G. Sell, G.H. Keith, R.C. Koo, R.H. Schnitzel, and R. Corth, Physical metallurgy of Tungsten and Tungsten base alloys, Tech. Rep. WADD TR 30-37, Westinghouse Electric Corp, Bloomfield N J, 1962.
   Google Scholar
• Y.Y. Zhao, Z.F. Lei, Z.P. Lu, J.C. Huang and T.G. Nieh, A simplified model connecting lattice distortion with friction stress of Nb-based equiatomic highentropy alloys. Mater. Res. Lett. 7 (2019), pp. 340–346.
   Web of Science ®Google Scholar
• J. Amodeo, S. Merkel, C. Tromas, P. Carrez, S. Korte-Kerzel, P. Cordier and J. Chevalier, Dislocations and plastic deformation in MgO. Crystals 8 (2018), pp. 53. doi:10.3390/cryst8060240.
   Web of Science ®Google Scholar
• A. Foitzik, W. Skrotzki and P. Haasen, Correlation between microstructure, dislocation dissociation and plastic anisotropy in ionic crystals. Mater. Sci. Eng. A 113 (1989), pp. 399–407.
   Web of Science ®Google Scholar