123 Int J Fract (2007) 145:223–228 DOI 10.1007/s10704-007-9122-1 © Springer Science+Business Media B.V. 2007 CONTACTING ROUGH SURFACES: HERTZIAN CONTACTS VERSUS WELDED AREAS Igor Sevostianov 1 and Mark Kachanov 2 1 Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88001, USA; e-mail: igor@nmsu.edu 2 Department of Mechanical Engineering, Tufts University, Medford, MA 02155, USA; e-mail: mark.kachanov@tufts.edu Abstract. For two rough plates pressed against one another, two types of contacts can be distinguished: Hertzian ones and “welded” areas. We find that the two types produce the same effect on the incremental stiffness of the interface and on the effective conductivity across it if their contact areas are the same. Keywords: rough surface, contact, elasticity, conductivity, cross-property. 1. Introduction. In the problem of contacting rough surfaces, the exact morphology of contacts is usually unknown. While rich variety of microgeometries may occur, two types of contacts appear to attract most attention in the literature: Hertzian contacts (sometimes called “kissing bonds”, Nagy, 1992), and “welded” areas (external cracks), see Figure 1. In some sense, these two types of contact can be considered as two limiting cases - for Hertzian contact, the plane tangential to the contact at the edge of the contact zone coincides with the plane of contact, while for the welded areas these two planes are perpendicular, as illustrated in Figure 1. We examine and compare the effects produced by the two contact types on the overall compliance and the overall conductivity. Such a comparison is important, for example, in the context of extraction of information on the interface microgeometry from the data on transmission of waves across the interface (as noted, for example, by Nagy, 1992). Besides, in materials science applications, the type of contacts may be uncertain, and both types may be present. The effect of this uncertainty on quantitative modeling needs to be understood. Plane of contact Tangential to the contact Figure 1. Two types of contacts between rough surfaces: (a) Hertzian and (b) welded. Note that the plane tangential to the contact at the edge of the contact area coincides with the plane of contact in the case (a) and is normal it in the case (b). LETTERS IN FRACTURE AND MICROMECHANICS