Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-jpcp9 Total loading time: 0.32 Render date: 2022-11-30T00:52:53.070Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

Published online by Cambridge University Press:  31 January 2011

W.C. Oliver
Affiliation:
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6116
G.M. Pharr
Affiliation:
Department of Materials Science, Rice University, P. O. Box 1982, Houston, Texas 77251
Get access

Abstract

The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

Type
Articles
Copyright
Copyright © Materials Research Society 1992

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

1.Pethica, J. B., Hutchings, R., and Oliver, W. C., Philos. Mag. A 48, 593 (1983).CrossRefGoogle Scholar
2.Oliver, W. C., Hutchings, R., and Pethica, J. B., in ASTM STP 889, edited by Blau, P. J. and Lawn, B. R. (American Society for Testing and Materials, Philadelphia, PA, 1986), pp. 90108.Google Scholar
3.Doerner, M. F. and Nix, W. D., J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
4.Pethica, J. B., in Ion Implantation into Metals, edited by Ashworth, V., Grant, W., and Procter, R. (Pergamon Press, Oxford, 1982), pp. 147156.CrossRefGoogle Scholar
5.Loubet, J. L., Georges, J. M., Marchesini, O., and Meille, G., J. Tribology 106, 43 (1984).CrossRefGoogle Scholar
6.Newey, D., Wilkens, M. A., and Pollock, H. M., J. Phys. E: Sci. Instrum. 15, 119 (1982).CrossRefGoogle Scholar
7.Stone, D., LaFontaine, W. R., Alexopoulos, P., Wu, T-W., and Li, Che-Yu, J. Mater. Res. 3, 141 (1988).CrossRefGoogle Scholar
8.Gilman, J. J., in The Science of Hardness Testing and Its Research Applications, edited by Westbrook, J. H. and Conrad, H. (American Society for Metals, Metals Park, OH, 1973), pp. 5174.Google Scholar
9.Oliver, W. C., MRS Bulletin XI, 15 (1986).CrossRefGoogle Scholar
10.Oliver, W. C., McHargue, C. J., and Zinkle, S. J., Thin Solid Films 153, 185 (1987).CrossRefGoogle Scholar
11.Boussinesq, J., Applications des Potentiels a I'étude de équilibre et du mouvement des solides élastiques (Gauthier-Villars, Paris, 1885).Google Scholar
12.Hertz, H., reine, J. und angewandte Mathematik 92, 156 (1882).Google Scholar
13.Love, A. E. H., Philos. Trans. A 228, 377 (1929).CrossRefGoogle Scholar
14.Love, A. E. H., Quart. J. Math. 10, 161 (1939).CrossRefGoogle Scholar
15.Johnson, K. L., Contact Mechanics (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
16.Sneddon, I. N., Int. J. Engng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
17.Harding, J. W. and Sneddon, I. N., Proc. Cambridge Philos. Soc. 41, 12 (1945).CrossRefGoogle Scholar
18.Tabor, D., Proc. R. Soc. A 192, 247 (1948).CrossRefGoogle Scholar
19.Stillwell, N. A. and Tabor, D., Proc. Phys. Soc. London 78, 169 (1961).CrossRefGoogle Scholar
20.Ternovskii, A. P., Alekhin, V. P., Shorshorov, M. Kh., Khrushchov, M. M., and Skvortsov, V. N., Zavod. Lab. 39, 1242 (1973).Google Scholar
21.Bulychev, S. I., Alekhin, V. P., Shorshorov, M. Kh., Ternovskii, A. P., and Shnyrev, G. D., Zavod. Lab. 41, 1137 (1975).Google Scholar
22.Bulychev, S. I., Alekhin, V. P., Shorshorov, M. Kh., and Ternovskii, A. P., Prob. Prochn. 9, 79 (1976).Google Scholar
23.Shorshorov, M. Kh., Bulychev, S. I., and Alekhin, V. P., Sov. Phys. Dokl. 26, 769 (1982).Google Scholar
24.Bulychev, S. I. and Alekhin, V. P., Zavod. Lab. 53, 76 (1987).Google Scholar
25.Pharr, G. M., Oliver, W. C., and Brotzen, F. R., J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
26.King, R. B., Int. J. Solids Structures 3, 1657 (1987).CrossRefGoogle Scholar
27.Bhattacharya, A. K. and Nix, W. D., Int. J. Solids Structures 24, 881 (1988).CrossRefGoogle Scholar
28.Pharr, G. M., Oliver, W. C., and Clarke, D. R., Scripta Metall. 23, 1949 (1989).CrossRefGoogle Scholar
29.Pharr, G. M., Oliver, W. C., and Clarke, D. R., J. Elec. Mater. 19, 881 (1990).CrossRefGoogle Scholar
30.Pharr, G. M., Oliver, W. C., and Harding, D. S., J. Mater. Res. 6, 1129 (1991).CrossRefGoogle Scholar
31.Hirth, J. P. and Lothe, J., Theory of Dislocations, 2nd ed. (John Wiley and Sons, New York, 1982), p. 837.Google Scholar
32.Pethica, J. B. and Oliver, W. C., Physica Scripta T19, 61 (1987).CrossRefGoogle Scholar
33.Pethica, J. B. and Oliver, W. C., in Thin Films: Stresses and Mechanical Properties, edited by Bravman, J. C., Nix, W. D., Barnett, D. M., and Smith, D. A. (Mater. Res. Soc. Symp. Proc. 130, 13 (1989).Google Scholar
34.Oliver, W. C. and Pethica, J. B., U.S. Patent No. 4 848141, July 1989.Google Scholar
35.Simmons, G. and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed. (The Press, M. I. T., Cambridge, MA, 1971).Google Scholar
36.Anstis, G. R., Chantikul, P., Lawn, B. R., and Marshall, D. B., J. Am. Ceram. Soc. 64, 533 (1981).CrossRefGoogle Scholar
37. General Electric Fused Quartz Products Technical Data, general catalog number 7705–7725, April 1985.Google Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *