Hostname: page-component-f554764f5-sl7kg Total loading time: 0 Render date: 2025-04-09T11:58:54.465Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of the spherical indentation cycle for elastic–perfectly plastic solids

Published online by Cambridge University Press:  01 December 2004

L. Kogut  and
K. Komvopoulos
L. Kogut
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720
K. Komvopoulos*
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

A finite element analysis of frictionless indentation of an elastic–plastic half-space by a rigid sphere is presented and the deformation behavior during loading and unloading is examined in terms of the interference and elastic–plastic material properties. The analysis yields dimensionless constitutive relationships for the normal load, contact area, and mean contact pressure during loading for a wide range of material properties and interference ranging from the inception of yielding to the initiation of fully plastic deformation. The boundaries between elastic, elastic–plastic, and fully plastic deformation regimes are determined in terms of the interference, mean contact pressure, and reduced elastic modulus-to-yield strength ratio. Relationships for the hardness and associated interference versus elastic–plastic material properties and truncated contact radius are introduced, and the shape of the plastic zone and maximum equivalent plastic strain are interpreted in light of finite element results. The unloading response is examined to evaluate the validity of basic assumptions in traditional indentation approaches used to measure the hardness and reduced elastic modulus of materials. It is shown that knowledge of the deformation behavior under both loading and unloading conditions is essential for accurate determination of the true hardness and reduced elastic modulus. An iterative approach for determining the reduced elastic modulus, yield strength, and hardness from indentation experiments and finite element solutions is proposed as an alternative to the traditional method.

Keywords

HardnessIndentationTheory
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 12 , December 2004 , pp. 3641 - 3653
Copyright
Copyright © Materials Research Society 2004

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

1Vu-Quoc, L., Zhang, X. and Lesburg, L.: A normal force-displacement model for contacting spheres accounting for plastic deformation: Force-driven formulation. J. Appl. Mech. 67, 363 (2000).CrossRefGoogle Scholar
2Komvopoulos, K. and Ye, N.: Three-dimensional contact analysis of elastic–plastic layered media with fractal surface topographies. J. Tribol. 123, 632 (2001).CrossRefGoogle Scholar
3Komvopoulos, K. and Yan, W.: Three-dimensional elastic–plastic fractal analysis of surface adhesion in microelectromechanical systems. J. Tribol. 120, 808 (1998).CrossRefGoogle Scholar
4Chang, W.R., Etsion, I. and Bogy, D.B.: Static friction coefficient model for metallic rough surfaces. J. Tribol. 110, 57 (1988).CrossRefGoogle Scholar
5Sahoo, P. and Chowdhury, S.K. Roy: A fractal analysis of adhesive friction between rough solids in gentle sliding. Proc. Inst. Mech. Engrs. J. 214, 583 (2000).Google Scholar
6Bhushan, B.: Contact mechanics of rough surfaces in tribology: Single asperity contact. J. Appl. Mech. Rev. 49, 275 (1996).CrossRefGoogle Scholar
7Bhushan, B.: Contact mechanics of rough surfaces in tribology: Multiple asperity contact. Tribol. Lett. 4, 1 (1998).CrossRefGoogle Scholar
8Liu, G., Wang, Q. and Lin, C.: A survey of current models for simulating the contact between rough surfaces. Tribol. Trans. 42, 581 (1999).CrossRefGoogle Scholar
9Adams, G.G. and Nosonovsky, M.: Contact modeling – Forces. Tribol. Int. 33, 431 (2000).CrossRefGoogle Scholar
10Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, U.K., 1951)Google Scholar
11Herbert, E.G., Pharr, G.M., Oliver, W.C., Lucas, B.N. and Hay, J.L.: On the measurement of stress-strain curves by spherical indentation. Thin Solid Films 398–399, 331 (2001).CrossRefGoogle Scholar
12Huber, N., Konstantinidis, A. and Tsakmakis, C.: Determination of Poisson’s ratio by spherical indentation using neural networks – Part I: Theory. J. Appl. Mech. 68, 218 (2001).CrossRefGoogle Scholar
13Nayebi, A., Abdi, R. El, Bartier, O. and Mauvoisin, G.: New procedure to determine steel mechanical parameters from the spherical indentation technique. Mech. Mater. 34, 243 (2002).CrossRefGoogle Scholar
14Oliver, 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
15Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985), pp. 90–95 and 170–184CrossRefGoogle Scholar
16Hill, R., Storåkers, B. and Zdunek, A.B.: A theoretical study of the Brinell hardness test. Proc. R. Soc., London Ser. A 423, 301 (1989).Google Scholar
17Biwa, S. and Storåkers, B.: An analysis of fully plastic Brinell indentation. J. Mech. Phys. Solids 43, 1303 (1995).CrossRefGoogle Scholar
18Fischer-Cripps, A.C.: Elastic–plastic behavior in materials loaded with a spherical indenter. J. Mater. Sci. 32, 727 (1997).CrossRefGoogle Scholar
19Hardy, C., Baronet, C.N. and Tordion, G.V.: The elasto-plastic indentation of a half-space by a rigid sphere. Int. J. Numer. Meth. Eng. 3, 451 (1971).CrossRefGoogle Scholar
20Follansbee, P.S. and Sinclair, G.B.: Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere. Part 1: Analysis. Int. J. Solids Struct. 20, 81 (1984).CrossRefGoogle Scholar
21Kral, E.R., Komvopoulos, K. and Bogy, D.B.: Elastic–plastic finite element analysis of repeated indentation of a half-space by a rigid sphere. J. Appl. Mech. 60, 829 (1993).CrossRefGoogle Scholar
22Giannakopoulos, A.E.: Strength analysis of spherical indentation of piezoelectric materials. J. Appl. Mech. 67, 409 (2000).CrossRefGoogle Scholar
23Kucharski, S. and Mroz, Z.: Identification of plastic hardening parameters of metals from spherical indentation tests. Mater. Sci. Eng. A 318, 65 (2001).CrossRefGoogle Scholar
24Mesarovic, S.D. and Fleck, N.A.: Spherical indentation of elastic– plastic solids. Proc. R. Soc., London Ser. A 455, 2707 (1999).CrossRefGoogle Scholar
25Ye, N. and Komvopoulos, K.: Indentation analysis of elastic– plastic homogeneous and layered media: Criteria for determining the real material hardness. J. Tribol. 125, 685 (2003).CrossRefGoogle Scholar
26Johnson, K.L.: Correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).CrossRefGoogle Scholar
27Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
28Thurn, J., Morris, D.J. and Cook, R.F.: Depth-sensing indentation at macroscopic dimensions. J. Mater. Res. 17, 2679 (2002).CrossRefGoogle Scholar
29Marsh, D.M.: Plastic flow in glass. Proc. R. Soc., London Ser. A 279, 420 (1964).Google Scholar
30Chaudhri, M.M.: Strain hardening around spherical indentations. Phys. Status Solidi A 182, 641 (2000).3.0.CO;2-U>CrossRefGoogle Scholar
31Mesarovic, S.D. and Johnson, K.L.: Adhesive contact of elastic– plastic spheres. J. Mech. Phys. Solids 48, 2009 (2000).CrossRefGoogle Scholar
32Park, Y.J. and Pharr, G.M.: Nanoindentation with spherical indenters: Finite element studies of deformation in the elastic–plastic transition regime. Thin Solid Films 447, 246 (2004).CrossRefGoogle Scholar