Analytical and experimental elastoplastic spherical indentations of a layered half-space T. Da Silva Botelho * , R. Progri, G. Inglebert, F. Robbe-Valloire LISMMA (Laboratoire d’Ingénierie des Systèmes Mécaniques et des Matériaux), EA 2336, Institut Supérieur de Mécanique de Paris, 3 rue Fernand Hainaut, F-93407 Saint-Ouen Cedex, France article info Article history: Received 11 July 2006 Received in revised form 15 February 2008 Keywords: Analytical model Elastoplastic layer Experimental analysis abstract This paper presents an analytical model for the elastoplastic spherical indentation of smooth coated spheres. In this model, only the coating deforms plastically, while the bulk materials remain elastic. This model takes into account the elastic properties of the spheres and the elastic then elastoplastic behaviour of the coating. Two sets of interface conditions were investigated. In one, the coating is freely laid on its substrate; in the other the coating is bonded to it. The coating was modeled using a thin layer assumption. The model pro- vides a prediction of the contact radius under load. A specifically designed experimental apparatus is then presented and experimental data are analysed. Tests were carried out for silver, copper, aluminium and zinc layers of thicknesses ranging from 20 lm to 500 lm. Spherical indenters radii were 0.5, 1, or 2.5 mm and the interfaces were free or bonded. Comparisons between analytical and experimental results showed a good agree- ment, even for experimental conditions beyond the thin layer assumption. Ó 2008 Elsevier Ltd. All rights reserved. 1. State of the art Point contact is of fundamental interest in many contact mechanics problems. That explains why spherical indenta- tion has been very widely studied, since it is supposed to be the most common contact configuration. Point contact can occur when dealing with thermal and electrical con- ductance problems, powder mechanics problems (Vu-Quoc et al., 2000), contact between rough surfaces... Some rough surface description models assume a spherical shape for single asperities (Greenwood and Williamson, 1966), (Whitehouse and Archard, 1970). Other models are asperity-based, most of those assuming spher- ically shaped asperities, whether the materials are elastic (Greenwood and Williamson, 1966), (Onions and Archard, 1973) or elastoplastic (Hisakado, 1974), (Chang et al., 1987), (Robbe-Valloire et al., 2001). An additional complexity arises when layered media are investigated, due to casual interface discontinuities and non-linear mechanical behaviour. Coated media are of use- ful tribological interest and are in use in many industrial processes and devices (cutting tools, friction enhancement, fatigue, fretting, sealing, etc.). However, relatively few ana- lytical models have been developed, mainly because of dif- ficulties in solving integral equations, especially when elastoplastic behaviour is assumed. Burmister (1945) was a pioneer for the analytical modeling of an elastic layer on a rigid foundation. Chen (1971) extended his work to elastic bulk materials and plane strain/plane stresses prob- lems. A more recent work by Chang (1997) dealt with the analytical modelisation of a soft elastic–plastic metallic coating acting as a solid lubricant (up to 2000 Å thick coatings). With the development of numerical techniques and computational facilities, many numerical models arised (Chen and Engel, 1972), (Polonski and Keer, 2000). Some fi- nite elements modeling were also developed (Tangena and Hurkx, 1985), (Kogut and Komvopoulos, 2004). 0167-6636/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmat.2008.02.007 * Corresponding author. Tel.: +33 149 452 958; fax: +33 149 452 959. E-mail address: tony.dasilva@supmeca.fr (T. Da Silva Botelho). Mechanics of Materials 40 (2008) 771–779 Contents lists available at ScienceDirect Mechanics of Materials journal homepage: www.elsevier.com/locate/mechmat