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.
Similar content being viewed by others
References
W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7 1564 (1992)
ISO 14577 Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters (International Organization for Standardization, Geneva, Switzerland 2002)
G.M. Pharr, Y-T. Cheng, I.M. Hutchings, M. Sakai, N.R. Moody, G. Sundararajan, M.V. Swain: Focus issue on indentation methods in advanced materials research. J. Mater. Res. 24, (3) 579 (2009)
K.L. Johnson: Contact Mechanics (Cambridge University Press, Cambridge, UK 1985)
J. Tan, Y.J. Chao, J.W. Van Zee, X. Li, X. Wang, M. Yang: 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)
D.C. Lin, E.K. Dimitriadis, F. Horkay: Elasticity of rubber-like materials measured by AFM nanoindentation. eXPRESS Polym. Lett. 9 576 (2007)
A.C. Fisher-Cripps: Nanoindentation (Springer Press, New York 2002)
I.M. Ward, J. Sweeney: An Introduction to the Mechanical Properties of Solid Polymers 2nd ed (Wiley Press, Chichester, UK 2004) 32–36
M.R. VanLandingham, J.S. Villarrubia, W.F. Guthrie, G.F. Meyers: Nanoindentation of polymer: An overview. Macromol. Symp. 167 167 (2001)
D.C. Lin, F. Horkay: Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond. Soft Mater. 4 669 (2008)
R.S. Rivlin: Large elastic deformations of isotropic materials: IV. Future developments of the general theory. Philos. Trans. R. Soc. London, Ser. A 241 379 (1948)
G.C.W. Sabin, P.N. Kaloni: Contact problem of a rigid indenter with notational friction in second order elasticity. Int. J. Eng. Sci. 27 203 (1989)
A.E. Giannakopoulos, A. Triantafyllou: Spherical indentation of incompressible rubber-like materials. J. Mech. Phys. Solids 55 1196 (2007)
I.N. Sneddon: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3 47 (1965)
E.M. Arruda, M.C. Boyce: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 389 (1993)
I. Kang, D. Panneerselvam, V.P. Panoskaltsis, S.J. Eppell, R.E. Marchant: Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-α. Biophys. J. 94 3273 (2008)
H. Yin, L.Z. Sun, G. Wang, T. Yamada, J. Wang, M. Vannier: ImageParser: A tool for finite element generation from three-dimensional medical images. Biomed. Eng. Online 3 31 (2004)
G.M. Pharr, W.C. Oliver, F.R. Brotzen: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7 613 (1992)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, D.X., Zhang, Z.D. & Sun, L.Z. Nonlinear elastic load–displacement relation for spherical indentation on rubberlike materials. Journal of Materials Research 25, 2197–2202 (2010). https://doi.org/10.1557/jmr.2010.0285
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2010.0285