Hostname: page-component-788cddb947-r7bls Total loading time: 0 Render date: 2024-10-12T20:11:27.585Z Has data issue: false hasContentIssue false

Nonlinear elastic load–displacement relation for spherical indentation on rubberlike materials

Published online by Cambridge University Press:  31 January 2011

D.X. Liu
Affiliation:
Department of Civil and Environmental Engineering, University of California, Irvine, California 92697-2175
Z.D. Zhang
Affiliation:
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
L.Z. Sun*
Affiliation:
Department of Civil and Environmental Engineering, University of California, Irvine, California 92697-2175
*
a)Address all correspondence to this author. e-mail: lsun@uci.edu
Get access

Abstract

Because of the lack of universal contact models for nonlinear strain problems, indentation analysis on rubberlike materials is confined to small deformation in which Hertz's solution is applied. Recognizing that deep indentation may provide more material information, in this paper we propose a nonlinear elastic model for large spherical indentation of rubberlike materials based on the higher-order approximation of spherical function and Sneddon's solution. The effect of limiting network stretch is studied on the initial elastic modulus for lightly cross-linked rubbers. With the comparisons of the finite-element simulation and the experimental result, the proposed model is verified to predict the large indentation of rubberlike materials over the indentation depth of 0.8 times the indenter radius.

Type
Articles
Copyright
Copyright © Materials Research Society 2010

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.Oliver, W.C., 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)Google Scholar
2.ISO 14577 Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters (International Organization for Standardization, Geneva, Switzerland 2002)Google Scholar
3.Pharr, G.M., Cheng, Y-T., Hutchings, I.M., Sakai, M., Moody, N.R., Sundararajan, G., Swain, M.V.: Focus issue on indentation methods in advanced materials research. J. Mater. Res. 24, (3)579 (2009)Google Scholar
4.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, UK 1985)CrossRefGoogle Scholar
5.Tan, J., Chao, Y.J., Van Zee, J.W., Li, X., Wang, X., Yang, M.: Assessment of mechanical properties of fluoroelastomer and EPDM in a simulated PEM fuel cell environment by microindentation test. Mater. Sci. Eng., A 496, 464 (2008)CrossRefGoogle Scholar
6.Lin, D.C., Dimitriadis, E.K., Horkay, F.: Elasticity of rubber-like materials measured by AFM nanoindentation. eXPRESS Polym. Lett. 9, 576 (2007)CrossRefGoogle Scholar
7.Fisher-Cripps, A.C.: Nanoindentation (Springer Press, New York 2002)Google Scholar
8.Ward, I.M., Sweeney, J.: An Introduction to the Mechanical Properties of Solid Polymers 2nd ed (Wiley Press, Chichester, UK 2004)3236Google Scholar
9.VanLandingham, M.R., Villarrubia, J.S., Guthrie, W.F., Meyers, G.F.: Nanoindentation of polymer: An overview. Macromol. Symp. 167, 167 (2001)3.0.CO;2-T>CrossRefGoogle Scholar
10.Lin, D.C., Horkay, F.: Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond. Soft Mater. 4, 669 (2008)CrossRefGoogle ScholarPubMed
11.Rivlin, R.S.: Large elastic deformations of isotropic materials: IV. Future developments of the general theory. Philos. Trans. R. Soc. London, Ser. A 241, 379 (1948)Google Scholar
12.Sabin, G.C.W., Kaloni, P.N.: Contact problem of a rigid indenter with notational friction in second order elasticity. Int. J. Eng. Sci. 27, 203 (1989)Google Scholar
13.Giannakopoulos, A.E., Triantafyllou, A.: Spherical indentation of incompressible rubber-like materials. J. Mech. Phys. Solids 55, 1196 (2007)CrossRefGoogle Scholar
14.Sneddon, 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)Google Scholar
15.Arruda, E.M., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41, 389 (1993)Google Scholar
16.Kang, I., Panneerselvam, D., Panoskaltsis, V.P., Eppell, S.J., Marchant, R.E.: Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-α. Biophys. J. 94, 3273 (2008)CrossRefGoogle ScholarPubMed
17.Yin, H., Sun, L.Z., Wang, G., Yamada, T., Wang, J., Vannier, M.: ImageParser: A tool for finite element generation from three-dimensional medical images. Biomed. Eng. Online 3, 31 (2004)Google Scholar
18.Pharr, G.M., Oliver, W.C., Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613 (1992)Google Scholar