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


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 pages8
Issue number10
Publication statusPublished - 2009
Externally publishedYes


  • Coating
  • Elasticity
  • Errors
  • Sensitivity analysis
  • Substrates


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