The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation

Abstract

Connections between the Hertz-type contact problems and depth-sensing indentation of materials are studied. Formulations of Hertz-type contact problems with various boundary conditions within the contact area are discussed in detail. The problems under investigations can be subdivided into two large groups: self-similar problems for anisotropic materials with various rheological properties and adhesive contact problems for arbitrary bodies of revolution or for power-law shaped blunt indenters. Specific features of indentation problems are described and the common methods for extracting elastic and adhesive properties of materials are briefly reviewed. The basic formulae are extended to the case of nonslipping boundary conditions between a probe and the material. The main formulae of the JKR theory of adhesion are extended to any material with rotational symmetry of the elastic properties. These materials include not only isotropic or transversely isotropic elastic solids but also homogeneously prestressed isotropic or transversely isotropic nonlinear elastic materials. The BG method introduced for extracting adhesive and elastic properties of isotropic elastic materials from depth-sensing diagrams of spherical indenters, is described and extended to linear or linearized materials with rotational symmetry of the elastic properties.