Nanoindentation near the edge of a viscoelastic solid with a rough surface

Highlights: • The mechanics of nanoindentation near the edge of a small object with a rough surface was investigated. • A novel data analysis method that can be applied to an embedded, finite-volume viscoelastic solid was developed. • The method accounts for the structural compliance and effective contact point of an embedded sample with a rough surface. • The method was experimentally validated for a cross-sectional acrylic paint sample embedded in a ~10 times stiffer medium. -- Abstract: We have developed a method to address problems associated with the use of nanoindentation near the edge of a small object with a rough surface, encountered in a variety of research fields including heritage conservation. The method consists of determining the structural compliance of an embedded material system based on the definition of reduced modulus that takes into account the effective contact point of the indenter with a rough sample surface. The method does not require the ratio of mean contact stress to reduced modulus squared to remain constant with penetration depth so as to be applicable to an embedded material system with a sharp elastic discontinuity. When applied to the dynamic indentation data of a viscoelastic paint film embedded in a ~10 times stiffer medium, the proposed method correctly predicted the flat modulus profile of the film across the thickness, in contrast to existing methods that significantly overestimated the modulus near the sample edge.