Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T01:52:02.925Z Has data issue: false hasContentIssue false
  • English
  • Français

Error estimation of nanoindentation mechanical properties near a dissimilar interface via finite element analysis and analytical solution methods

Published online by Cambridge University Press:  31 January 2011

Y. Zhao  and
T.C. Ovaert
Y. Zhao
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
T.C. Ovaert*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Nanoindentation methods are well suited for probing the mechanical properties of a heterogeneous surface, since the probe size and contact volumes are small and localized. However, the nanoindentation method may introduce errors in the computed mechanical properties when indenting near the interface between two materials having significantly different mechanical properties. Here we examine the case where a soft material is loaded in close proximity to an interface of higher modulus, such as the case when indenting bone near a metallic implant. The results are derived from both an approximate analytical quarter space solution and a finite element model, and used to estimate the error in indentation-determined elastic modulus as a function of the distance from the apex of contact to the dissimilar interface, for both Berkovich and spherical indenter geometries. Sample data reveal the potential errors in mechanical property determination that can occur when indenting near an interface having higher stiffness, or when characterizing strongly heterogeneous materials. The results suggest that caution should be used when interpreting results in the near-interfacial region.

Keywords

NanoindentationElastic PropertiesSimulation
Type
Articles
Information
Journal of Materials Research , Volume 25 , Issue 12 , December 2010 , pp. 2308 - 2316
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.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987)CrossRefGoogle Scholar
2.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)CrossRefGoogle Scholar
3.Field, J.S., Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993)Google Scholar
4.Hainsworth, S.V., Chandler, H.W., Page, T.F.: Analysis of nanoindentation load displacement loading curves. J. Mater. Res. 11, 1987 (1996)CrossRefGoogle Scholar
5.Cheng, Y.T., Cheng, C.M.: What is indentation hardness? Surf. Coat. Technol. 417, 133 (2000)Google Scholar
6.Lewis, S.G., Beumer, J., Perri, G.R., Hornburg, W.P.: Single tooth implant supported restorations. Int. J. Oral Maxil. Imp. 3, 25 (1988)Google ScholarPubMed
7.Jemt, T.: Modified single and short-span restorations supported by osseointegrated fixtures in the partially edentulous jaw. J. Prosthet. Dent. 55, 243 (1986)CrossRefGoogle ScholarPubMed
8.Branemark, P.T., Adell, R., Albrektsson, T., Lekholm, U., Lundkvist, S., Rockler, B.: Osseointegrated titanium fixtures in the treatment of edentulousness. Biomaterials 4, 25 (1983)CrossRefGoogle ScholarPubMed
9.Chang, M.C., Ko, C.C., Liu, C.C., Douglas, W.H., DeLong, R., Seong, W-J., Hodges, J., An, K-N.: Elasticity of alveolar bone near dental implant-bone interfaces after one month's healing. J. Biomech. 36, 1209 (2003)CrossRefGoogle ScholarPubMed
10.Clark, P.A., Clark, A.M., Rodriguez, A., Hussain, M.A., Mao, J.J.: Nanoscale characterization of bone-implant interface and biomechanical modulation of bone ingrowth. Mater. Sci. Eng., C 27, 382 (2007)CrossRefGoogle Scholar
11.Graf, H.: Occlusal forces during function, Proceedings of Symposium on Occlusion: Research on Form and Function edited by A. Rowe (University of Michigan School of Dentistry, Ann Arbor, MI 1975)90 Google Scholar
12.Chou, H.Y., Jagodnik, J.J., Muftu, S.: Predictions of bone remodeling around dental implant systems. J. Biomech. 41, 1365 (2008)CrossRefGoogle ScholarPubMed
13.Cowin, S.C.: Bone stress adaptation models. J. Biomech. Eng. 115, 528 (1993)Google Scholar
14.Jakes, J.E., Frihart, C.R., Beecher, J.F., Moon, R.J., Stone, D.S.: Experimental method to account for structural compliance in nanoindentation measurements. J. Mater. Res. 23, 1113 (2008)CrossRefGoogle Scholar
15.Uflyand, Ya.S.: Second basic problem of elasticity for a wedge. Trudy Leningr. Politekh. In-ta. 210, 87 (1960)Google Scholar
16.Uflyand, Ya.S.: Some spatial elasticity problems for a wedge, Continuum Mechanics and Related Problems of Analysis (Nauka Moscow 1972)549 Google Scholar
17.Shim, J., Nakamura, H., Ogawa, T.: An understanding of the mechanism that promotes adhesion between roughened titanium implants and mineralized tissue. J. Biomech. Eng. 131, 054503 (2009)CrossRefGoogle ScholarPubMed
18.Popov, G.Ya.: An exact solution of the mixed elasticity problem in a quarter-space. Mech. Solids 38, 23 (2003)Google Scholar
19.Hertz, H.: On the contact of elastic solids. J. Reine Angew. Math 92, 156 (1881)Google Scholar
20.Fischer-Cripps, A.: Nanoindentation (Springer, New York 2002)CrossRefGoogle Scholar
21.Pharr, G.M., Oliver, W.C., Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and the elastic modulus during indentation. J. Mater. Res. 7, 613 (1992)CrossRefGoogle Scholar
22.Love, A.E.H.: Boussinesq's problem for a rigid cone. Q. J. Math. 10, 161 (1939)CrossRefGoogle Scholar
23.Zhang, J., Niebur, G.L., Ovaert, T.C.: Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation. J. Biomech. 41, 267 (2008)Google Scholar