Spherical indentation on an elastic coating/substrate system : Determining substrate modulus

James A. MILLS, Xi CHEN*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

4 Citations (Scopus)


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. © 2009 ASCE.
Original languageEnglish
Pages (from-to)1189-1197
Number of pages9
Issue number10
Early online date6 Mar 2009
Publication statusPublished - Oct 2009
Externally publishedYes

Bibliographical note

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.


  • Coating
  • Elasticity
  • Errors
  • Sensitivity analysis
  • Substrates


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