Spherical Indentation on a Prestressed Elastic Coating/Substrate System

  • James A. Mills
  • Xi ChenEmail author
Reference work entry


While there have been many studies on the indentation test of thin film/substrate systems, the primary goal has been determining the film properties. However, there was very little effort to probe the properties of both the film and the substrate (the latter may be as important as the film properties). Moreover, a prestress usually exists in the film, typically resulted from mismatched deformation or material properties. In this study, we establish a spherical indentation framework to examine the material properties of both the film and substrate as well as determining the film prestress. An indentation test is performed at two prescribed depths, and functional forms are established between indentation parameters and material variables. An effective reverse analysis algorithm is established to deduce the desired material properties. The potential error sensitivity is also examined in a systematic way. The study on prestressed film/substrate systems has many potential applications in engineering.


Indentation Thin film Substrate Elastic property Film prestress 



The study is supported by the National Natural Science Foundation of China (11172231), DARPA (W91CRB-11-C-0112), the World Class University Program through the National Research Foundation of Korea (R32-2008-000-20042-0), and the National Science Foundation (CMMI-0643726).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil Engineering and Engineering MechanicsColumbia UniversityNew YorkUSA
  2. 2.Department of Earth and Environmental Engineering, Columbia Nanomechanics Research CenterColumbia UniversityNew YorkUSA

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