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Single versus successive pop-in modes in nanoindentation tests of single crystals

Published online by Cambridge University Press:  24 May 2016

Yuzhi Xia ,
Yanfei Gao ,
George M. Pharr  and
Hongbin Bei
Yuzhi Xia*
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996
Yanfei Gao
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
George M. Pharr
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
Hongbin Bei
Affiliation:
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

From recent nanoindentation experiments, two types of pop-in modes have been identified: a single pop-in with a large displacement excursion and a number of pop-ins with comparable and small displacement excursions. Theoretical analyses are developed here to study the roles played by indenter tip radius, pre-existing defect density, heterogeneous nucleation source type, and lattice resistance on the pop-in modes. The evolution of dislocation structures in earlier pop-ins provides input to modeling a stochastic, heterogeneous mechanism that may be responsible for the subsequent pop-ins. It is found that when the first pop-in occurs near theoretical shear stress, the pop-in mode is determined by the lattice resistance and tip radius. When the first pop-in occurs at low shear stress, whether the successive pop-in mode occurs depends on how the heterogeneous dislocation nucleation source density increases as compared to the increase of the total dislocation density. The above transitions are found to correlate well with the ratio of indenter tip radius to the mean spacing of dislocation nucleation sources.

Keywords

nanoindentationdefects
Type
Articles
Information
Journal of Materials Research , Volume 31 , Issue 14 , 28 July 2016 , pp. 2065 - 2075
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Copyright
Copyright © Materials Research Society 2016 

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Footnotes

b)

Current address: 3M Company, St. Paul, MN.

Contributing Editor: Jürgen Eckert

c)

This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/editor-manuscripts/.

A previous error in this article has been corrected, see 10.1557/jmr.2017.245.

References

REFERENCES

Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar
Bower, A.F., Fleck, N.A., Needleman, A., and Ogbonna, N.: Indentation of a power law creeping solid. Proc. R. Soc. London, Ser. A 441, 97 (1993).Google Scholar
Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
Bucaille, J.L., Stauss, S., Felder, E., and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).Google Scholar
Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).Google Scholar
Lee, J.H., Gao, Y.F., Johanns, K.E., and Pharr, G.M.: Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials. Acta Mater. 60, 5448 (2012).Google Scholar
Meng, Y., Xia, Y., Young, T.M., Cai, Z., and Wang, S.: Viscoelasticity of wood cell walls with different moisture content as measured by nanoindentation. RSC Adv. 5, 47538 (2015).Google Scholar
Gao, Y.F., Larson, B.C., Lee, J.H., Nicola, L., Tischler, J.Z., and Pharr, G.M.: Lattice rotation patterns and strain gradient effects in face-centered-cubic single crystals under spherical indentation. J. Appl. Mech. 82, 061007 (2015).Google Scholar
Page, T.F., Oliver, W.C., and McHargue, C.J.: The deformation-behavior of ceramic crystals subjected to very low load (nano)indentation. J. Mater. Res. 7, 450 (1992).Google Scholar
Bei, H., Gao, Y.F., Shim, S., George, E.P., and Pharr, G.M.: Strength differences arising from homogeneous versus heterogeneous dislocation nucleation. Phys. Rev. B 77, 060103 (2008).Google Scholar
Shim, S., Bei, H., George, E.P., and Pharr, G.M.: A different type of indentation size effect. Scr. Mater. 59, 1095 (2008).Google Scholar
Li, T.L., Gao, Y.F., Bei, H., and George, E.P.: Indentation Schmid factor and orientation dependence of nanoindentation pop-in behavior of NiAl single crystals. J. Mech. Phys. Solids 59, 1147 (2011).CrossRefGoogle Scholar
Li, T.L., Bei, H., Morris, J.R., George, E.P., and Gao, Y.F.: Scale effects in convoluted thermal/spatial statistics of plasticity initiation in small stressed volumes during nanoindentation. Mater. Sci. Technol. 28, 1055 (2012).Google Scholar
Xia, Y.Z., Bei, H., Gao, Y.F., Catoor, D., and George, E.P.: Synthesis, characterization, and nanoindentation response of single crystal Fe–Cr–Ni alloys with FCC and BCC structures. Mater. Sci. Eng., A 611, 177 (2014).Google Scholar
Venkataraman, S.K., Kohlstedt, D.L., and Gerberich, W.W.: Continuous microindentation of passivating surfaces. J. Mater. Res. 8, 685 (1993).Google Scholar
Corcoran, S.G., Colton, R.J., Lilleodden, E.T., and Gerberich, W.W.: Anomalous plastic deformation at surfaces: Nanoindentation of gold single crystals. Phys. Rev. B 55, R16057 (1997).Google Scholar
Schuh, C.A., Mason, J.K., and Lund, A.C.: Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nat. Mater. 4, 617 (2005).Google Scholar
Morris, J.R., Bei, H., Pharr, G.M., and George, E.P.: Size effects and stochastic behavior of nanoindentation pop-in. Phys. Rev. Lett. 106, 165502 (2011).Google Scholar
Johanns, K.E., Sedlmayr, A., Sudharshan Phani, P., Mönig, R., Kraft, O., George, E.P., and Pharr, G.M.: In-situ tensile testing of single-crystal molybdenum-alloy fibers with various dislocation densities in a scanning electron microscope. J. Mater. Res. 27, 508 (2012).Google Scholar
Sudharshan Phani, P., Johanns, K.E., George, E.P., and Pharr, G.M.: A simple stochastic model for yielding in specimens with limited number of dislocations. Acta Mater. 61, 2489 (2013).Google Scholar
Sudharshan Phani, P., Johanns, K.E., George, E.P., and Pharr, G.M.: A stochastic model for the size dependence of spherical indentation pop-in. J. Mater. Res. 28, 2728 (2013).Google Scholar
Bei, H., Xia, Y.Z., Barabash, R.I., and Gao, Y.F.: A tale of two mechanisms: Strain-softening versus strain-hardening in single crystals under small stressed volumes. Scr. Mater. 110, 48 (2016).Google Scholar
Wang, L., Bei, H., Li, T.L., Gao, Y.F., George, E.P., and Nieh, T.G.: Determining the activation energies and slip systems for dislocation nucleation in body-centered cubic Mo and face-centered cubic Ni single crystals. Scr. Mater. 65, 179 (2011).CrossRefGoogle Scholar
Bei, H., George, E.P., Hay, J.L., and Pharr, G.M.: Influence of indenter tip geometry on elastic deformation during nanoindentation. Phys. Rev. Lett. 95, 045501 (2005).Google Scholar
Bradby, J.E., Williams, J.S., Wong-Leung, J., Swain, M.V., and Munroe, P.: Mechanical deformation of InP and GaAs by spherical indentation. Appl. Phys. Lett. 78, 3235 (2001).Google Scholar
Durst, K., Backes, B., Franke, O., and Göken, M.: Indentation size effect in metallic materials: Modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations. Acta Mater. 54, 2547 (2006).Google Scholar
Ma, Q. and Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853 (1995).Google Scholar
Wang, Z., Bei, H., George, E.P., and Pharr, G.M.: Influences of surface preparation on nanoindentation pop-in in single-crystal Mo. Scr. Mater. 65, 469 (2011).Google Scholar
Gouldstone, A., Koh, H.J., Zeng, K.Y., Giannakopoulos, A.E., and Suresh, S.: Discrete and continuous deformation during nanoindentation of thin films. Acta Mater. 48, 2277 (2000).Google Scholar
Schuh, C.A. and Nieh, T.G.: A nanoindentation study of serrated flow in bulk metallic glasses. Acta Mater. 51, 87 (2003).Google Scholar
Lilleodden, E.T., Zimmerman, J.A., Foiles, S.M., and Nix, W.D.: Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation. J. Mech. Phys. Solids 51, 901 (2003).Google Scholar
Lodes, M.A., Hartmaier, A., Göken, M., and Durst, K.: 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, 4264 (2011).CrossRefGoogle Scholar
Hirth, J.P. and Lothe, J.: Theory of Dislocations (Wiley, New York, 1982).Google Scholar
Cai, W., Bulatov, V.V., Chang, J., Li, J., and Yip, S.: Dislocation core effects on mobility, In Dislocations in Solids, Vol. 12, Nabarro, F.R.N. and Hirth, J.P. eds.; Elsevier, Amsterdam, 2004; pp. 1–90.Google Scholar
Johnson, K.L.: Contact Mechanics (Cambridge University Press, U.K., 1985).Google Scholar
Li, W.D., Bei, H., Qu, J., and Gao, Y.F.: Effects of machine stiffness on the loading–displacement curve during spherical nano-indentation. J. Mater. Res. 28, 1903 (2013).Google Scholar
Gao, Y.F. and Larson, B.C.: Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids. J. Mech. Phys. Solids 83, 104 (2015).Google Scholar
Tada, H., Paris, P.C., and Irwin, G.R.: The Stress Analysis of Cracks Handbook, 3rd ed. (ASME, New York, 2000).Google Scholar
Kwon, J., Brandes, M.C., Sudharshan Phani, P., Pilchak, A.P., Gao, Y.F., George, E.P., Pharr, G.M., and Mills, M.J.: Characterization of deformation anisotropies in an α-Ti alloy by nanoindentation and electron microscopy. Acta Mater. 61, 4743 (2013).Google Scholar
Ziegenhain, G., Urbassek, H.M., and Hartmaier, A.: Influence of crystal anisotropy on elastic deformation and onset of plasticity in nanoindentation: A simulational study. J. Appl. Phys. 107, 061807 (2010).Google Scholar

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