Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T18:44:36.321Z Has data issue: false hasContentIssue false

The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation

Published online by Cambridge University Press:  31 January 2011

J. Alcalá*
Affiliation:
GRICCA-EUETIB, Universitat Politècnica de Catalunya, Barcelona 08036, Spain
D. Esqué-de los Ojos
Affiliation:
GRICCA-EUETIB, Universitat Politècnica de Catalunya, Barcelona 08036, Spain
S.A. Rodríguez
Affiliation:
Surface Phenomena Laboratory, Department of Mechanical Engineering. University of São Paulo, 05508-90 Sao Paulo, Brazil
*
a) Address all correspondence to this author. e-mail: jorge.alcala@upc.es
Get access

Abstract

This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation Phs curve measurements in face-centered cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the Phs curves can be attributed to anisotropy, the variability in the unloading stage of the experiments is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading Phs curve introduces an uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the Phs curves to extract homogenized J2-plasticity-equivalent mechanical properties from single crystals.

Type
Articles
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.Doerner, F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
2.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).CrossRefGoogle Scholar
3.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
4.Mata, M., Anglada, M., and Alcalá, J.: A hardness equation for sharp indentation of elastic-power-law strain-hardening materials. Philos. Mag. A 82, 1831 (2002).CrossRefGoogle Scholar
5.Mata, M. and Alcalá, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).CrossRefGoogle Scholar
6.Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).CrossRefGoogle Scholar
7.Casals, O. and Alcalá, J.: The duality in mechanical property extractions from Vickers and Berkovich instrumented indentation experiments. Acta Mater. 53, 3545 (2005).CrossRefGoogle Scholar
8.Chollacoop, N. and Ramamurty, U.: Robustness of the algorithms for extracting plastic properties from the instrumented sharp indentation data. Mater. Sci. Eng., A 423, 41 (2006).CrossRefGoogle Scholar
9.Chen, X., Ogasawara, N., Zhao, M.H., and Chiba, N.: On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials. J. Mech. Phys. Solids 55, 1618 (2007).CrossRefGoogle Scholar
10.Qian, X., Cao, Y.P., and Lu, J.: Dependence of the representative strain on the hardening functions of metallic materials in indentation. Scr. Mater. 57, 57 (2007).CrossRefGoogle Scholar
11.Lan, H.Z. and Venkatesh, T.A.: On the sensitivity characteristics in the determination of the elastic and plastic properties of materials through multiple indentation. J. Mater. Res. 22, 1043 (2007).CrossRefGoogle Scholar
12.Casals, O. and Alcalá, J.: Analytical and experimental resolutions in the duality of mechanical property extractions from instrumented indentation experiments: Comments on “On determination of material parameters from loading and unloading responses in nanoinden-tation with a single sharp indenter” by L. Wang and S.I. Rokhlin. [J. Mater. Res. 21, 995 (2006)]. J. Mater. Res. 22, 1138 (2007).CrossRefGoogle Scholar
13.Le, M.Q.: Computational study on the instrumented sharp indentations with dual indenters. Int. J. Solids Struct. 45, 2818 (2008).CrossRefGoogle Scholar
14.Swaddiwudhipong, S., Harsono, E., and Hua, J.: Reverse analysis via efficient artificial neural networks based on simulated Berko-vich indentation considering effects of friction. Eng. Comput. 24, 127 (2008).CrossRefGoogle Scholar
15.Luo, J. and Lin, J.: A study on the determination of plastic properties of metals by instrumented indentation using two sharp indenters. Int J. Solids Struct. 44, 5803 (2007).CrossRefGoogle Scholar
16.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, 2106 (2008).CrossRefGoogle Scholar
17.Casals, O., Ocenasek, J., and Alcalá, J.: Crystal plasticity finite element simulations of pyramidal indentation in copper single crystals. Acta Mater. 55, 55 (2007).CrossRefGoogle Scholar
18.Alcalá, J., Casals, O., and Ocenasek, J.: Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis. J. Mech. Phys. Solids 56, 3277 (2008).CrossRefGoogle Scholar
19.Asaro, R.J.: Micromechanics of crystals and polycrystals. Adv. Appl. Mech. 23, 1 (1983).CrossRefGoogle Scholar
20.Bassani, J.L. and Wu, T.Y.: Latent hardening in single crystals. 2. Analytical characterization and predictions. Proc. R. Soc. London A 435, 21 (1991).Google Scholar
21.Alcalá, J.: Instrumented micro-indentation of zirconia ceramics. J. Am. Ceram. Soc. 83, 1977 (2000).CrossRefGoogle Scholar
22.Alcalá, J., Barone, A.C., and Anglada, M.: The influence of plastic hardening on surface deformation modes around Vickers and spherical indents. Acta Mater. 48, 3451 (2000).CrossRefGoogle Scholar
23.Rester, M., Motz, C., and Pippan, R.: Microstructural investigation of the volume beneath nanoindentations in copper. Acta Mater. 55. 6427 (2007).CrossRefGoogle Scholar
24.Alkorta, J., Martninez-Esnaola, J.M., and Sevillano, J.G.: Detailed assessment of indentation size-effect in recrystallized and highly deformed niobium. Acta Mater. 54, 3445 (2006).CrossRefGoogle Scholar
25.Zaafarani, N., Raabe, D., Roters, F., and Zaefferer, S.: On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31 (2008).CrossRefGoogle Scholar
26.Liu, X.H., Gu, J.F., Shen, Y., and Chen, C.: Anisotropy in homogeneous dislocation nucleation by nanoindentation of single crystal Cu. Scr. Mater. 58, 564 (2008).CrossRefGoogle Scholar
27.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
28.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
29.Antunes, J.M., Menezes, L.F., and Fernandes, J.V.: Influence of Vickers tip imperfection on depth-sensing indentation tests. Int. J. Solids Struct. 44, 2732 (2007).CrossRefGoogle Scholar
30.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).CrossRefGoogle Scholar
31.Huang, Y., Zhang, F., and Hwang, K.C.: A model of size effects in nano-indentation. J. Mech. Phys. Solids 54, 1668 (2006).CrossRefGoogle Scholar
32.Xue, Z., Huang, Y., Hwang, K.C., and Li, M.: The influence of indenter tip radius on the micro-indentation hardness. J. Eng. Mater. Technol. 124, 371 (2002).CrossRefGoogle Scholar
33.Qu, S., Huang, Y., Nix, W.D., Jiang, H., Zhang, F., and Hwang, K.C.: Indenter tip radius effect on the Nix-Gao relation in micro- and nanoindentation hardness experiments. J. Mater. Res. 19, 3423 (2004).CrossRefGoogle Scholar
34.Archard, J.F.: Elastic deformation and the laws of friction. Proc. R. Soc. London A 243, 190 (1957).Google Scholar
35.Komvopoulos, K. and Choi, D.H.: Elastic finite element analysis of multi-asperity contacts. J. Tribol. 114, 823 (1992).CrossRefGoogle Scholar
36.Bhushan, B. and Venkatesan, S.: Effective mechanical properties of layered rough surfaces. Thin Solid Films 473, 278 (2005).CrossRefGoogle Scholar
37.Harsono, E., Swaddiwudhipong, S., and Liu, Z.S.: The effect of friction on indentation test results. Model. Simul. Mater. Sci. Eng. 16(065001), (2008).CrossRefGoogle Scholar
38.Komvopoulos, K. and Gong, Z.Q.: Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior. Int. J. Solids Struct. 44, 2109 (2007).CrossRefGoogle Scholar
39.Rodriguez, S.A. and Alcalá, J.: Unpublished results.Google Scholar
40.Mata, M. and Alcalá, J.: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 (2004).CrossRefGoogle Scholar
41.Liu, Y. and Ngan, A.H.W.: Depth dependence of hardness in copper single crystals measured by nanoindentation. Scr. Mater. 44. 237 (2001).CrossRefGoogle Scholar
42.Bahr, D.F., Kramer, D.E., and Gerberich, W.W.: Non-linear deformation mechanisms during nanoindentation. Acta Mater. 46, 3605 (1998).CrossRefGoogle Scholar
43.Xu, Z.H. and Li, X.D.: Effects of indenter geometry and material properties on the correction factor of Sneddon's relationship for nanoindentation of elastic and elastic-plastic materials. Acta Mater. 56, 1399 (2008).CrossRefGoogle Scholar
44.Cao, Y.P., Dao, M., and Lu, J.: A precise correcting method for the study of the superhard material using nanoindentation tests. J. Mater. Res. 22, 1255 (2007).CrossRefGoogle Scholar
45.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).CrossRefGoogle Scholar
46.Vlassak, J.J., Ciavarella, M., Barber, J.R., and Wang, X.: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701 (2003).CrossRefGoogle Scholar