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An energy-based method for analyzing instrumented spherical indentation experiments

Published online by Cambridge University Press:  03 March 2011

Wangyang Ni ,
Yang-Tse Cheng ,
Che-Min Cheng  and
David S. Grummon
Wangyang Ni
Affiliation:
Materials and Processes Laboratory, General Motors Research and Development Center, Warren, Michigan 48090, and Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824
Yang-Tse Cheng
Affiliation:
Materials and Processes Laboratory, General Motors Research and Development Center, Warren, Michigan 48090
Che-Min Cheng
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
David S. Grummon
Affiliation:
Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824
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Abstract

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic–plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Keywords

IndentationHardnessMechanical properties
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 1 , January 2004 , pp. 149 - 157
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1.E10-01 Standard Test Method for BRINELL Hardness of Metallic Materials (ASTM International, West Conshohocken, 2003).Google Scholar
2.Tabor, D., The Hardness of Metals (Oxford University Press, London, U.K., 1951); Philosophical Magazine A 74 1207 (1996).Google Scholar
3.Mott, B.W., Micro-indentation Hardness Testing (Butterworths, London, U.K., 1956).Google Scholar
4.Fischer-Cripps, A.C., Nanoindentation (Springer-Verlag, New York, 2002).CrossRefGoogle Scholar
5.Oliver, W.C. and Pharr, G.M., J. Mater. Res. 7 1564 (1992).Google Scholar
6.Field, J.S. and Swain, M.V., J. Mater. Res. 8, 297 1993; J. Mater. Res. 10 101 (1995).CrossRefGoogle Scholar
7.Haggag, F.M. and Lucas, G.E., Metall. Trans. 14A, 1607 (1983).CrossRefGoogle Scholar
8.Taljat, B., Zacharia, T. and Haggaga, F.M., J. Mater. Res. 12, 965 (1997).CrossRefGoogle Scholar
9.Huber, N. and Tsakmakis, C., J. Mech. Phys. Solids 47, 1569 , 1589 (1999).CrossRefGoogle Scholar
10.Alcalá, J., Giannakopoulos, A.E., and Suresh, S., J. Mater. Res. 13, 1390 (1998).Google Scholar
11.Kucharski, S. and Mróz, Z., J. Eng. Mater. Technol. 123 235 (2001).Google Scholar
12.Herbert, G., Pharr, G.M., Oliver, W.C., Lucas, B.N. and Hay, J.L., Thin Solid Films 398–399 331 (2001).CrossRefGoogle Scholar
13.Norbury, A.L. and Samuel, T., J. Iron Steel Inst. 117 673 (1928).Google Scholar
14.Chaudhri, M.M. and Winter, M., J. Phys. D.: Appl. Phys. 21 370 (1988).CrossRefGoogle Scholar
15.Cheng, Y-T. and Cheng, C-M., Philos. Mag. Lett. 78 115 (1998).CrossRefGoogle Scholar
16.Bolshakov, A. and Pharr, G.M., J. Mater. Res. 13 1049 (1998).Google Scholar
17.Cheng, Y-T. and Cheng, C-M., J. Appl. Phys. 84 1284 (1998).CrossRefGoogle Scholar
18.Cheng, Y-T., Li, Z. and Cheng, C-M., Philos. Mag. 82 1821 (2002).Google Scholar
19.Barenblatt, G.I., Scaling, Self-similarity, and Intermediate Asymptotics (Cambridge University Press, Cambridge, 1996).CrossRefGoogle Scholar
20.Ni, W., Cheng, Y-T., Cheng, C-M. and Grummon, D.S., GM Research Publication R&D-9522 (April 23, 2003).Google Scholar
21.Cheng, Y-T. and Cheng, C-M., J. Mater. Res. 14 3493 1999.CrossRefGoogle Scholar
22.Cheng, Y-T. and Cheng, C-M., Appl. Phys. Lett. 73 614 (1998).CrossRefGoogle Scholar
23.Giannakopoulos, A.E. and Suresh, S., Scr. Mater. 40 1191 (1999).Google Scholar
24.Cheng, C-M. and Cheng, Y-T., Appl. Phys. Lett. 71 2623 (1997).CrossRefGoogle Scholar
25.Gschneidner, K.A., Solid State Physics 16 275 (1964).CrossRefGoogle Scholar
26.Simmons, G. and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed. (The M.I.T. Press, Cambridge, MA, 1971).Google Scholar
27. General Electric Fused Quartz Products Technical Data, general catalog number 7705-7725 (April 1985).Google Scholar
28.Hay, J.C., Bolshakov, A. and Pharr, G.M., J. Mater. Res. 14 2296 (1999).CrossRefGoogle Scholar
29.Poole, W.J., Ashby, M.F. and Fleck, N.A., Scr. Mater. 34 559 (1996).Google Scholar
30.McElhaney, K.W., Vlassak, J.J. and Nix, W.D., J. Mater. Res. 13 1300 (1998).CrossRefGoogle Scholar
31.Gerberich, W.W., Tymiak, N.I., Grunlan, J.C., Horstemeryer, M.F. and Baskes, M.I., ASME J. Appl. Mech. 69 433 (2002).CrossRefGoogle Scholar
32.Nix, W.D. and Gao, H., J. Mech. Phys. Solids 46 411 (1998).CrossRefGoogle Scholar
33.Swadener, J.G., George, E.P. and Pharr, G.M., J. Mech. Phys. Solids 50 681 (2002).CrossRefGoogle Scholar