Effect of adhesion energy on the contact stiffness in nanoindentation

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The effect of surface interaction on nanoindentation testing using a rigid conical indenter is analyzed. A relation between the indentation depth and the indentation load is established as a function of the adhesion energy between the indenter and the surface of an elastic material. A closed-form solution of the contact stiffness for adhesive contact is obtained. The contact stiffness in the presence of surface interaction is always less than that for contact without surface interaction at the same indentation depth, while it is always larger than that for adhesion-less contact subjected to the same indentation load. A lower bound is established, which determines the working zone to operate to avoid the effect of surface interaction in the characterization of the contact modulus.

I. INTRODUCTION

The adhesive contact problem between two elastic spheres was first solved by Johnson et al.1 in 1971. The Johnson–Kendall–Roberts (JKR) theory was derived based on the Hertzian contact theory2 for frictionless contact between two elastic solid spheres. Applying fracture mechanics to the adhesion problem between spherical particles, Maugis and Barquins3 obtained the same relation between force and contact area as that of the JKR theory. Yang et al.4 evaluated the effect of infinite interfacial friction (sticky condition) on adhesive contact between a rigid sphere and an elastic half-space and found that the adhesive contact depends on the Poisson’s ratio of the elastic sphere. Recently, Yang5 analyzed the size effects associated with the adhesive contact between a rigid sphere and an elastic thin film deposited on a rigid substrate and obtained a relation between the pull-off force and surface energy. From the theory of adhesive contact, Yang6 found that the nominal contact stiffness depends on the interfacial energy between the indenter and the surface of sample. For indenters of large size and small indentation load, the interfacial energy controls the contact process. In nanoindentation testing, cubic and Berkovich indenters have been widely used in determining the nearsurface mechanical properties of nanoscaled materials.7

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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0331 J. Mater. Res., Vol. 21, No. 10, Oct 2006

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Both cubic and Berkovich indenters have been approximated as conical indenters with different included angles in the community of nanoindentation testing7 to analyze the indentation loading–unloading curves, since it is unreasonable to use the solutions of spherical indenters. However, no analysis has been done to assess the adhesive contact between a rigid conical indenter and an elastic half-space and its effect on the indentation behavior. The purpose of this work is to analyze the adhesive contact between a rigid conical indenter and an elastic half space, assuming that the contact between the indenter and the elastic half space is sticky. II. ADHESION OF A RIGID CONICAL INDENTER TO AN ELASTIC HALF

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