Contact Problems at Nano/Microscale and Depth Sensing Indentation Techniques

Abstract

An overview of development of indentation techniques and connections between contact mechanics and methods of extracting mechanical characteristics from indentation data is given. Observed disagreements between the experimental observations and the models of indentation are discussed. It is shown that this disagreement is often caused by violation of hypotheses that are used in the formulation of the appropriate boundary-value contact problems and strictly speaking one cannot apply directly the solutions of Hertz type contact problems to indentation tests employing the sharp indenters. It is shown that commonly used experimental test involving sharp pyramidal and conical indenters may be applied to study plastic properties of materials while this approach is not very accurate for estimations of elastic modulus of the test solid. The recently proposed by Borodich and Galanov non-direct method that employs data of elastically loading of a spherical indenter is described. It is argued that the non-direct method can be used for determination of both the work of adhesion and elastic modulus of the tested material.

Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation

“…The hardness studies of materials have a long history (see a review by Borodich [6,7]). There were several very important steps in the development of modern hardness techniques.…”

“…Although the BG method is very robust to external noise and it is very fast, the method cannot be employed in its present form for extraction of mechanical characteristics of the components of such highly inhomogeneous materials as coals. On the other hand, although the former approach for determination of E Ã based on the BASh formula has several drawbacks [6], it is generally accepted that the results obtained for bulk material samples have acceptable accuracy. In addition, the use of sharp nanoindenters looks very reasonable taken into account that some microcomponents of tested materials are very small.…”

“…The progress in development of depth-sensing micro/nanoindentation, see, e.g. reviews by Borodich and Keer [10], Bull [11], Chaudhri and Lim [14] and Borodich [6,7], has made it possible to study various homogeneous materials in small volumes. These techniques were also applied to study mechanical properties of thin films and coated materials, i.e.…”

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

“…Currently depth-sensing indentation (DSI) techniques, that is, the continuously monitoring of the P -δ curve where P is the applied load and δ is the displacement (the approach of the distant points of the indenter and the sample), are widely used in materials science [10]. For example, the indentation by sharp pyramidal indenters is used to estimate the elastic modulus of a tested material by measuring the slope S of the unloading branch of the diagram and employing the semi-empirical BASh (Bulychev-Alekhin-Shorshorov) formula or its modifications [11,12] …”

Adhesive Contact Between Silicon-Based Mems Tooth Surfaces Modelled by the Multiscale Multi-Block Model

“…The force of adhesion for one nano-asperity is assumed as the pull-off force according to Boussinesq-Kendall model, corrected with non-slip coefficient ( ) introduced by Borodich [20,21]. Let Fadh1 be the adhesion force of one asperity and n be the number of asperities in contact.…”