Elastic deformation of coating/substrate composites in axisymmetric indentation
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Elastic deformation of coating/substrate composites was examined for axisymmetric indentations with three different geometries of flat-ended cylinder, sphere, and cone. Intensive theoretical considerations were made for the Boussinesq problems not only in its Fredholm integral equation of the second kind, but also in its Green function using the principle of superposition for the approximated contact stress distribution. The agreement and the disagreement between these two different numerical/analytical assessments for elastic surface deformations are discussed. Along with these theoretical considerations, experimental scrutiny was conducted for the theoretical predictions for spherical indentation by the use of a sol-gel-derived MeSiO3/2 film coated on a soda-lime glass plate. A novel technique is also proposed for estimating in a simultaneous manner the elastic moduli of both the coating film and of the substrate or the elastic modulus of the film and its thickness in spherical indentation tests. I. INTRODUCTION
The growing importance of microelectromechanical systems (MEMS), ceramic-coated metal composites, solgel-derived organic/inorganic hybrid materials, compositionally graded materials, etc. has led to intense interest in the science and engineering of thin-films coated on a solid substrate. Micro- and nano-indentation techniques have been intensively as well as extensively utilized for characterizing the mechanical properties of coating/ substrate composites.1–9 In the determination of the mechanical properties including the elastic modulus and the indentation contact hardness of thin films on a substrate, it has been well known that the experimental results obtained for coatings by indentation are highly dependent on the properties of the substrate. There is a rule of thumb; the measurement of “film-only” properties is limited to the penetration depth less than “ten-percent” or “one-tenth” of the thickness of coating film.10 However, this rule yields only a rough estimate for the penetration depth, being a non-scientific rule, and strongly dependent on the geometry and the dimension of the indenter used.7,11 Furthermore, this rule is not practical as the thickness of coating films in many advanced engineering applications progressively decreases to several tens of a)
Address all correspondence to this author. e-mail: [email protected] This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs .org/publications/JMR/policy/html/ DOI: 10.1557/JMR.2005.0270 J. Mater. Res., Vol. 20, No. 8, Aug 2005
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nanometers or less. Accordingly, an appropriate method with a sound scientific basis must be incorporated into the micro-/nano-indentation tests for thin films, which allows the intrinsic film properties to be singled out of the indentation data affected with substrate properties. Numbers of analytical studies have been rep
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