Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T06:36:33.397Z Has data issue: false hasContentIssue false

An elastic-plastic indentation model and its solutions

Published online by Cambridge University Press:  31 January 2011

Weiping Yu
Affiliation:
Department of Nuclear Engineering and Engineering Physics, The University of Wisconsin at Madison, 1500 Johnson Drive, Madison, Wisconsin 53706
James P. Blanchard
Affiliation:
Department of Nuclear Engineering and Engineering Physics, The University of Wisconsin at Madison, 1500 Johnson Drive, Madison, Wisconsin 53706
Get access

Abstract

An analytical model of hardness has been developed. Four major indentation tests, namely indentation by cones, wedges, spheres, and flat-ended, axisymmetric cylinders have been analyzed based on the model. Analytical relationships among hardness, yield stress, elastic modulus, Poisson's ratio, and indenter geometries have been found. These results enable hardness to be calculated in terms of uniaxial material properties and indenter geometries for a wide variety of elastic and plastic materials. These relationships can also be used for evaluating other mechanical properties through hardness measurements and for converting hardness from one type of hardness test into those of a different test. Comparison with experimental data and numerical calculations is excellent.

Type
Articles
Copyright
Copyright © Materials Research Society 1996

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.Hertz, H., reine, J.und angewandte Mathematik 92, 156 (1882).CrossRefGoogle Scholar
2.Boussinesq, J., Applications des Potentials a l'étude de équilibre et du mouvement des solides élastiques (Gauthier-Villars, Paris, 1885).Google Scholar
3.Sneddon, I. N., Int. J. Engin. Sci., Pergamon Press, 3, 4757 (1965).CrossRefGoogle Scholar
4.Timoshenko, S. and Goodier, J. N., Theory of Elasticity, 2nd ed. (McGraw-Hill, New York, 1951).Google Scholar
5. Prandtl|Göttinger Nachr. Math. Phys. KL. 74, 37 (1920).Google Scholar
6.Hill, R., Lee, E. H., and Tupper, S. J., Proceedings of the Royal Society, London A188, 273289 (1947).Google Scholar
7.Yu, W., Theoretical and Numerical Analysis of Elastic-Plastic and Creeping Solids, Ph.D. Dissertation, University of Wisconsin–Madison (1995).Google Scholar
8.Lockett, F. J., J. Mech. Phys. Solids 11, 345355 (1963).CrossRefGoogle Scholar
9.Ishlinsky, A. J., Appl. Math. Mech. 8, 201 (1944).Google Scholar
10.Ivlev, D. D. and Nepershin, R. I., Izvestiya of U.S.S.R. Akad. Nauk. Solid Mech. 4, 159 (1973).Google Scholar
11.Shield, R. T., Proc. R. Soc. A 233, 267 (1955).Google Scholar
12.Bishop, R. F., Hill, R., and Mott, N. F., Proc. Phys. Soc. 57, 149 (1945).CrossRefGoogle Scholar
13.Marsh, D. M., Proc. R. Soc., London A 279, 420 (1964).Google Scholar
14.Hirst, W. and Howse, M.G.J.W., Proc. R. Soc. A 311, 429444 (1969).Google Scholar
15.Johnson, K. L., J. Mech. Phys. of Solids, 18, 115126 (1970).CrossRefGoogle Scholar