Spherical Indentation on an Elastic Coating/Substrate System: Determining Substrate Modulus
Publication: Journal of Engineering Mechanics
Volume 135, Issue 10
Abstract
A vast amount of indentation studies on coating/substrate systems focused on extracting the mechanical properties of the film, by either avoiding or subtracting off the substrate effect. However, in engineering and biomedical applications, very often the substrate properties, in particular the substrate modulus, need to be measured from an indentation test and the protective layer cannot be removed. For the model system of an elastic film deposited on an elastic substrate, we establish the general approach of spherical indentation focusing on the substrate property determination. Indentation data are taken from different indentation depths which reflect different degrees of film and substrate effects. An effective reverse analysis algorithm is established such that, from an indentation test if either the film modulus or film thickness is known, the other variable can be measured along with the substrate modulus. Error sensitivity of the proposed formulation is analyzed in a systematic way.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work is supported in part by the National Science Foundation under Grant Nos. NSFCMS-0407743 and NSFCMMI-0643726, and in part by the Department of Civil Engineering and Engineering Mechanics, Columbia University.
References
ABAQUS. (2007). ABAQUS 6.7 user’s manual, ABAQUS Inc., Pawtucket, R.I.
Bucaille, J. L., Stauss, S., Felder, E., and Michler, J. (2003). “Determination of plastic properties of metals by instrumented indentation using different sharp indenters.” Acta Mater., 51(6), 1663–1678.
Chen, X., Ogasawara, N., Zhao, M., and Chiba, N. (2007). “On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials.” J. Mech. Phys. Solids, 55(8), 1618–1660.
Chen, X., and Vlassak, J. J. (2001). “Numerical study on the measurement of thin film mechanical properties by means of nanoindentation.” J. Mater. Res., 16(10), 2974–2982.
Chen, X., Xiang, Y., and Vlassak, J. J. (2006). “A novel technique to measure mechanical properties of porous materials by nanoindentation.” J. Mater. Res., 21(3), 715–724.
Cheng, Y. T., and Cheng, C. M. (2004). “Scaling, dimensional analysis, and indentation measurements.” Mater. Sci. Eng. R., 44(4–5), 91–149.
Dintwa, E., Tijskens, E., and Ramon, H. (2008). “On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres.” Granular Matter, 10(3), 209–221.
Doerner, F., and Nix, W. D. (1986). “A method for interpreting the data from depth-sensing indentation instruments.” J. Mater. Res., 1(4), 601–609.
Gao, H., Chiu, C.-H., and Lee, J. (1992). “Elastic contact versus indentation modeling of multi-layered materials.” Int. J. Solids Struct., 29(20), 2471–2492.
Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A. M., and Shen, Y. -L. (2007). “Indentation across size scales and disciplines: Recent developments in experimentation and modeling.” Acta Mater., 55(12), 4015–4039.
Hu, X. Z., and Lawn, B. R. (1998). “A simple indentation stress-strain relation for contacts with spheres on bilayer structures.” Thin Solid Films, 322(1–2), 225–232.
Pharr, G. M. (1998). “Measurement of mechanical properties by ultra-low load indentation.” Mater. Sci. Eng., A, 253(1), 151–159.
Saha, R., and Nix, W. D. (2002). “Effects of the substrate on the determination of thin film mechanical properties by nanoindentation.” Acta Mater., 50(1), 23–38.
Saha, R., Xue, Z., Huang, Y., and Nix, W. D. (2001). “Indentation of a soft metal on a hard substrate: Strain gradient hardening effects.” J. Mech. Phys. Solids, 49(9), 1997–2014.
Swadener, J. G., George, E. P., and Pharr, G. M. (2002). “The correlation of the indentation size effect measured with indenters of various shapes.” J. Mech. Phys. Solids, 50(4), 681–694.
Tsui, T. Y., Vlassak, J. J., and Nix, W. D. (1999). “Indentation plastic displacement field. Part I: The case of soft films on hard substrates.” J. Mater. Res., 14(6), 2196–2203.
Zhao, M., Chen, X., Ogasawara, N., Razvan, A. C., Chiba, N., Lee, D., and Gan, Y. X. (2006a). “A new sharp indentation method of measuring the elastic-plastic properties of soft and compliant materials by using the substrate effect.” J. Mater. Res., 21(12), 3134–3151.
Zhao, M., Chen, X., Xiang, Y., Vlassak, J. J., Lee, D., Ogasawara, N., Chiba, N., and Gan, Y. X. (2007). “Measuring elastoplastic properties of thin films on an elastic substrate using sharp indentation.” Acta Mater., 55(18), 6260–6274.
Zhao, M., Ogasawara, N., Chiba, N., and Chen, X. (2006b). “A new approach to measure the elastic-plastic properties of bulk materials using spherical indentation.” Acta Mater., 54(1), 23–32.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Jul 1, 2008
Accepted: Feb 9, 2009
Published online: Mar 6, 2009
Published in print: Oct 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.