Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-17T06:28:07.216Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling Relationships in Conical Indentation in Elastic-Plastic Solids with Work-Hardening

Published online by Cambridge University Press:  10 February 2011

Yang-Tse Cheng  and
Che-Min Cheng
Yang-Tse Cheng
Affiliation:
Physics and Physical Chemistry Department, General Motors Global Research and Development Operations, Warren, Michigan 48090, USA, YangT._Cheng@notes.gmr.com
Che-Min Cheng
Affiliation:
Laboratory for Non-Linear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China, zhengzm@lnm.imech.ac.cn
Get access

Abstract

We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work-hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 522: Symposium T – Fundamentals of Nanoindentation & Nanotribology , 1998 , 139
Copyright
Copyright © Materials Research Society 1998

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 Tabor, D., Phil. Mag. A 74, 1207 (1996).Google Scholar
2. Pethica, J. B., Hutchings, R., and Oliver, W. C., Phil. Mag. A48, 593 (1983).Google Scholar
3. Oliver, W. C., and Pharr, G. M., J. Mat. Res. 7, 1564 (1992).Google Scholar
4. Doemer, M. F., and Nix, W. D., J. Mat. Res. 1, 601 (1986).Google Scholar
5. Myers, S. M., Knapp, J. A., Follstaedt, D. M., and Dugger, M. T., J. Appl. Phys. 83, 1256 (1998).Google Scholar
6. Cheng, Y.-T., and Cheng, C.-M., Phil. Mag. Lett. 77, 39 (1998).Google Scholar
7. Cheng, Y.-T., and Cheng, C.-M., “Scaling laws in conical indentation of elastic-perfectly plastic solids,” GM Research and Development Center Publication R&D-8689 (June 23, 1997); Int. J. Solids and Structures (in press).Google Scholar
8. Cheng, Y.-T., and Cheng, C.-M., “A scaling approach to conical indentation in elastic-plastic solids with work-hardening,” GM Research and Development Center Publication R&D-8741 (November 18, 1997).Google Scholar
9. Lubliner, J., Plasticity Theory (Macmillan, New York), (1990).Google Scholar
10. Dieter, G., Mechanical Metallurgy, Second Edition (McGraw-Hill, New York, 1976).Google Scholar
11. ABAQUS, version 5.6, Hibbitt, Karlsson & Sorensen, Inc. (Pawtucket, RI, 02860, USA).Google Scholar
12. Sneddon, I. N., Int. J. Eng. Sci. 3, 47 (1963).Google Scholar
13. Lockett, F. J., J. Mech. Phys. Solids 11, 345 (1963).Google Scholar
14. Tabor, D., The Hardness of Metals (Oxford, London, 1951).Google Scholar
15. Chaudhri, M. M., and Winter, M., J. Phys. D: Appl. Phys. 21, 370 (1988).Google Scholar
16. Bec, S., Tonck, A., Georges, J.-M., Georges, E., and Loubet, J.-L., Phil. Mag. A74, 1061 (1996).Google Scholar
17. Cheng, Y.-T., and Cheng, C.-M., Phil. Mag. Lett. (in press).Google Scholar