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Effects of machine stiffness on the loading–displacement curve during spherical nano-indentation

Published online by Cambridge University Press:  27 June 2013

Weidong Li ,
Hongbin Bei ,
Jun Qu  and
Yanfei Gao
Weidong Li
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996
Hongbin Bei*
Affiliation:
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Jun Qu
Affiliation:
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Yanfei Gao*
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996; andMaterials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
*
a)Address all correspondence to these authors. e-mail: [email protected]
b)e-mail: [email protected]
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Abstract

By taking the machine stiffness into the classic Hertzian solution rather than assuming a constant machine stiffness, we developed an approach to simultaneously derive the spherical indenter tip radius and machine stiffness in arbitrary ranges of loads and indenter radii. In contrast, the direct Hertzian fitting method tends to underestimate the radius, especially for larger indenter tips. The success is based on indention tests on two materials with known material stiffness, and the displacement difference under the same load is not affected by the machine stiffness. A total of eight spherical indenter tips with the radii ranging from a few microns to hundreds of microns have been indented on fused silica and single crystal sapphire. Our method gives correct indenter radii for all indenters. The machine stiffness is found to indeed vary with the indentation load and indenter radius. This method has many potential applications in the area of nano-indentation with spherical indenters, such as indentation size effect, modulus and hardness measurement, and micropillar testing.

Keywords

nanoindentationelastic propertieshardness
Type
Articles
Information
Journal of Materials Research , Volume 28 , Issue 14 , 28 July 2013 , pp. 1903 - 1911
Copyright
Copyright © Materials Research Society 2013 

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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
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
Cheng, Y.T. and Cheng, C.M.: Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493 (1999).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).Google Scholar
Bradby, J.E., Williams, J.S., and Swain, M.V.: Pop-in events induced by spherical indentation in compound semiconductors. J. Mater. Res. 19, 380 (2004).Google Scholar
Bei, H., Lu, Z.P., and George, E.P.: Theoretical strength and the onset of plasticity in bulk metallic glasses investigated by nanoindentation with a spherical indenter. Phys. Rev. Lett. 93, 125504 (2004).Google Scholar
Bucaill, 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
Lee, J.S., Jang, J.I., Lee, B.W., Choi, Y., Lee, S.G., and Kwon, D.: An instrumented indentation technique for estimating fracture toughness of ductile materials: A critical indentation energy model based on continuum damage mechanics. Acta Mater. 54, 1101 (2006).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
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
Li, H. and Ngan, A.H.W.: Size effects of nanoindentation creep. J. Mater. Res. 19, 513 (2004).Google Scholar
Goodal, R. and Clyne, T.W.: A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Mater. 54, 5489 (2006).CrossRefGoogle Scholar
Suresh, S. and Giannakopoulos, A.E.: A new method for estimating residual stresses by instrumented sharp indentation. Acta Mater. 46, 5755 (1998).Google Scholar
Swadener, J.G., Taljat, B., and Pharr, G.M.: Measurement of residual stress by load and depth sensing indentation with spherical indenters. J. Mater. Res. 16, 2091 (2001).CrossRefGoogle Scholar
Sebastiani, M., Bemporad, E., Carassiti, F., and Schwarzer, N.: Residual stress measurement at the micrometer scale: Focused ion beam (FIB) milling and nanoindentation testing. Philos. Mag. 91, 1121 (2011).Google Scholar
Swadener, J.G. and Pharr, G.M.: A methodology for the calibration of spherical indenters, in Thin Films–Stresses and Mechanical Properties VIII, edited by Vinci, R., Kraft, O., Moody, N., Besser, P., and Shaffer, E. III (Mater. Res. Soc. Symp. Proc. 594, Warrendale, PA, 2000), p. 525.Google Scholar
Cao, Y.P. and Lu, J.: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52, 4023 (2004).Google Scholar
Herbert, E.G., Oliver, W.C., and Pharr, G.M.: On the measurement of yield strength by spherical indentation. Philos. Mag. 86, 5521 (2006).Google Scholar
Jiang, P., Zhang, T.H., Feng, Y.H., and Liang, N.G.: Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach. J. Mater. Res. 24, 1045 (2009).Google Scholar
Choi, I.C., Yoo, B.G., Kim, Y.J., Seok, M.Y., Wang, Y.M., and Jang, J.I.: Estimating the stress exponent of nanocrystalline nickel: Sharp vs. spherical indentation. Scr. Mater. 65, 300 (2011).Google Scholar
Lee, H., Lee, J.H., and Pharr, G.M.: A numerical approach to spherical indentation techniques for material property evaluation. J. Mech. Phys. Solids 53, 2037 (2005).Google Scholar
Zhao, M.H., Ogasawara, N., Chiba, N., and Chen, X.: A new approach to measure the elastic–plastic properties of bulk materials using spherical indentation. Acta Mater. 54, 23 (2006).Google Scholar
Lee, J.H., Kim, T., and Lee, H.: A study on robust indentation techniques to evaluate elastic-plastic properties of metals. Int. J. Solids Struct. 47, 647 (2010).Google Scholar
Lan, H.Z. and Venkatesh, T.A.: On the sensitivity characteristics in the determination of the elastic properties of materials through multiple indentation. J. Mater. Res. 22, 1043 (2007).Google Scholar
Hyun, H.C., Kim, M., Lee, J.H., and Lee, H.: A dual conical indentation technique based on FEA solutions for property evaluation. Mech. Mater. 43, 313 (2011).Google Scholar
Montagne, A., Tromas, C., Audurier, V., and Woirgard, J.: A new insight on reversible deformation and incipient plasticity during nanoindentation test in MgO. J. Mater. Res. 24, 883 (2009).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(R) (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., Bei, H., Morris, J.R., George, E.P., and Gao, Y.F.: Scale effects in the convoluted thermal/spatial statistics of plasticity initiation in small stressed volumes during nanoindentation. Mater. Sci. Technol. 28, 1055 (2012).Google Scholar
Bei, H., Lu, Z.P., Shim, S., Chen, G., and George, E.P.: Specimen size effects on Zr-based bulk metallic glasses investigated by uniaxial compression and spherical nanoindentation. Metall. Mater. Trans. A 41, 1735 (2010).CrossRefGoogle Scholar
Choi, I.C., Zhao, Y.K., Yoo, B.G., Kim, Y.J., Suh, J.Y., Ramamurty, U., and Jang, J.I.: Estimation of the shear transformation zone size in a bulk metallic glass through statistical analysis of the first pop-in stresses during spherical nanoindentation. Scr. Mater. 66, 923 (2012).Google Scholar
Swadener, J.G., George, E.P., and Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681 (2002).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
Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).Google Scholar
Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985).CrossRefGoogle Scholar
Gao, Y.F. and Pharr, G.M.: Multidimensional contact moduli of elastically anisotropic solids. Scr. Mater. 57, 13 (2007).Google Scholar
Pharr, G.M., Strader, J.H., and Oliver, W.C.: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res. 24, 653 (2009).Google Scholar
Durst, K., Franke, O., Bohner, A., and Gokin, M.: Indentation size effect in Ni-Fe solid solutions. Acta Mater. 55, 6825 (2007).Google Scholar
Yang, Y., Ye, J., Lu, J., Gao, Y.F., and Liaw, P.K.: Metallic glasses: Gaining plasticity from Microsystems. JOM 62(2), 93 (2010).Google Scholar
Barabash, R.I., Bei, H., Gao, Y.F., and Ice, G.E.: Indentation-induced localized deformation and elastic strain partitioning in composites at submicron length scale. Acta Mater. 58, 6784 (2010).Google Scholar