Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-18T02:31:22.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic–plastic materials

Published online by Cambridge University Press:  31 January 2011

Sara Aida Rodríguez Pulecio ,
María Cristina Moré Farias  and
Roberto Martins Souza
Sara Aida Rodríguez Pulecio*
Affiliation:
Surface Phenomena Laboratory, Department of Mechanical Engineering, University of São Paulo, 05508-900 São Paulo - SP. Brazil
María Cristina Moré Farias
Affiliation:
Surface Phenomena Laboratory, Department of Mechanical Engineering, University of São Paulo, 05508-900 São Paulo - SP. Brazil
Roberto Martins Souza
Affiliation:
Surface Phenomena Laboratory, Department of Mechanical Engineering, University of São Paulo, 05508-900 São Paulo - SP. Brazil
*
a) Address all correspondence to this author. e-mail: sara.pulecio@poli.usp.br
Get access

Abstract

In this work, the effects of indenter tip roundness on the load–depth indentation curves were analyzed using finite element modeling. The tip roundness level was studied based on the ratio between tip radius and maximum penetration depth (R/hmax), which varied from 0.02 to 1. The proportional curvature constant (C), the exponent of depth during loading (α), the initial unloading slope (S), the correction factor (β), the level of piling-up or sinking-in (hc/hmax), and the ratio hmax/hf are shown to be strongly influenced by the ratio R/hmax. The hardness (H) was found to be independent of R/hmax in the range studied. The Oliver and Pharr method was successful in following the variation of hc/hmax with the ratio R/hmax through the variation of S with the ratio R/hmax. However, this work confirmed the differences between the hardness values calculated using the Oliver–Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (Wp/Wt) was found to be independent of the ratio R/hmax, which demonstrates that the methods for the calculation of mechanical properties based on the indentation energy are potentially not susceptible to errors caused by tip roundness.

Keywords

NanoindentationSimulation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 1037 - 1044
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2.Antunes, J.M., Cavaleiro, A., Menezes, L.F., Simões, M.I., and Fernandes, J.V.: Ultra-microhardness testing procedure with Vickers indenter. Surf. Coat. Technol. 149, 27 (2002).CrossRefGoogle Scholar
3.VanLandingham, M.R., Juliano, T.F., and Hagon, M.J.: Measuring tip shape for instrumented indentation using atomic force microscopy. Meas. Sci. Technol. 16, 2173 (2005).CrossRefGoogle Scholar
4.Chen, W., Li, M., Zhang, T., Cheng, Y.T., and Cheng, C.M.: Influence of indenter tip roundness on hardness behavior in nanoin-dentation. Mater. Sci. Eng. A, 445–446, 323 (2007).CrossRefGoogle Scholar
5.Ma, D., Ong, C.W., and Wong, S.F.: New relationship between Young's modulus and nonideally sharp indentation parameters. J. Mater. Res. 19(7), 2144 (2004).Google Scholar
6.Ma, D., Ong, C.W., and Zhang, T.: An improved energy method for determining Young's modulus by instrumented indentation using a Berkovich tip. J. Mater. Res. 23(8), 2106 (2008).Google Scholar
7.Bouzakis, K.D., Michailidis, N., Hadjiyiannis, S., Skordaris, G., and Erkens, G.: The effect of specimen roughness and indenter tip geometry on the determination accuracy of thin hard coatings stress-strain laws by nanoindentation. Mater. Char. 49, 149 (2003).Google Scholar
8.Meza, J.M. and Cruz, E.J.: Tip roundness effect in mechanical properties measured by instrumented indentation. Sci. Teach. 36, 613 (2007).Google Scholar
9.Antunes, J.M., Menezes, L.F., and Fernandes, J.V.: Three-dimensional numerical simulation of Vickers indentation tests. Int. J. Solids Struct. 43, 784 (2006).CrossRefGoogle Scholar
10.Meza, J.M., Abbes, F., and Troyon, M.: Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements. J. Mater. Res. 23, 725 (2008).Google Scholar
11.Troyon, M. and Huang, L.: Correction factor for contact area in nanoindentation measurements. J. Mater. Res. 20, 610 (2005).Google Scholar
12.Troyon, M. and Lafaye, S.: About the importance of introducing a correction factor in the Sneddon relationship for nanoindentation measurements. Philos. Mag. 86, 5299 (2006).Google Scholar
13.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
14.Bucaille, J.L., Stauss, S., Felder, E., and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenter. Acta Mater. 51, 1663 (2003).CrossRefGoogle Scholar
15.Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R, 44. 91 (2004).Google Scholar
16.Casals, O. and Alcalá, J.: The duality in mechanical property extractions from Vickers and Berkovich instrumented indentation experiments. Acta Mater. 53, 3545 (2005).Google Scholar
17.Cheng, Y.T. and Cheng, C.M.: Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements. J. Mater. Res. 13, 1059 (1998).CrossRefGoogle Scholar
18.Chen, J. and Bull, S.J.: On the relationship between plastic zone radius and maximum depth during nanoindentation. Surf. Coat. Technol. 201, 4289 (2006).CrossRefGoogle Scholar
19.Mata, M. and Alcalá, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18(7), 1705 (2003).CrossRefGoogle Scholar
20.Suresh, S. and Giannakopoulos, A.E.: A new method for estimating residual stresses by instrumented sharp indentation. Acta Mater. 46, 5755 (1998).CrossRefGoogle Scholar
21.Sneddon, I.N.: The relationship between load and penetration in the axisimetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
22.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 12 (1987) 1657.Google Scholar
23.Hay, J.C., Bolshakov, A., and Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14(6), 2296 (1999).CrossRefGoogle Scholar
24.Li, M., Chen, W.M., Liang, N.G., and Wang, L.D.: A numerical study of indentation using indenters of different geometry. J. Mater. Res. 19, 73 (2004).Google Scholar
25.Mata, M. and Alcalá, J.: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 (2004).CrossRefGoogle Scholar
26.Swaddiwudhipong, S., Hua, J., Tho, K.K., and Liu, Z.S.: Equivalency of Berkovich and conical load-indentation curves. Modell. Simul. Mater. Sci. Eng. 14, 71 (2006).CrossRefGoogle Scholar
27. Theory Manual 5.1–1, Abaqus, Version 6.7.Google Scholar
28.Sun, Y., Zheng, S., Bell, T., and Smith, J.: Indenter tip radius and load frame compliance calibration using nanoindentation loading curves. Philos. Mag. Lett. 79, 649 (1999).CrossRefGoogle Scholar
29.Taljat, B. and Pharr, G.M.: Development of pile-up during spherical indentation of elastic–plastic solids. Int. J. Solids Struct. 41, 3891 (2004).Google Scholar
30.Bolshakov, A. and Pharr, G.M.: Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).CrossRefGoogle Scholar
31.Cheng, Y.T. and Cheng, C.M.: Effects of “sinking in” and “piling up” on estimating the contact area under load in indentation. Philos. Mag. Lett. 78, 115 (1998).Google Scholar
32.Cheng, Y.T. and Cheng, C.M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).Google Scholar
33.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).CrossRefGoogle Scholar