Elastic properties of contacting surfaces under normal and shear loads: 1. Theory

Abstract

A theory of contact between two elastic rough surfaces is presented that predicts, from knowledge of the surface topography, both the normal and shear deformation. The theory was modified from one developed by others in order to properly account for initial overlap of the two surfaces and to allow for calculation of shear stiffnesses under no‐slip conditions. Since the theory is critically dependent on the surface topography, a new method is introduced for the derivation of the real topographic parameters. The result of theoretical calculation shows that the normal closure nonlinearly increases with normal stress and is larger for rougher surfaces and that the shear stiffness also nonlinearly increases with normal stress and is greater for smoother surfaces than rougher ones. The verification of the theory will be made by comparing it with experimental data in a companion paper.

On the Relationship Between Ultrasonic and Micro-Structural Properties of Imperfect Interfaces in Layered Solids

“…Quite different approaches have been developed to model the elasto-plastic behavior of rough surfaces in contact [1,2,5,11,12,13,14,15,16]. In the most sophisticated models the contacts between the rough surfaces are assumed to occur at the surface asperities, and in many cases their interaction is assumed to be purely elastic [1,11,12,13].…”

Ultrasonic Spectroscopy of two Parallel Imperfect Interfaces

“…This result can be explained qualitatively using the theoretical predictions of Yoshioka and Scholtz [18,19]. These authors modeled the individual asperities on the rough surface as headings of spheres of radius R, spherical segment base radius a, and asperity effective height he (close to hrms).…”

“…The interfacial stiffness between two contracted rough surfaces has been measured ultrasonically by several authors [12,14,15]. Also, several studies have been performed to estimate it theoretically [18,19]). …”

“…In the table, the samples are labeled A, B, C, and D. Note that the roughness obtained from the line surface profile is always smaller than the real value because the stylus usually does not go over the summits and valleys but rather traverses the shoulders of individual asperities. Possible corrections are discussed in [18,19). The interfacial stiffness between two contracted rough surfaces has been measured ultrasonically by several authors [12,14,15].…”

Contact analyses and permeability measurements of polished fracture surfaces in Sambagawa metapelitic schists and Ryoke mylonites from the Median Tectonic Line, Japan

“…On the basis of the models presented in these studies, Brown and Scholz [1985] and Yoshioka and Scholz [1989] have generated models that estimate the characteristics of surface topography such as the distribution function of local asperity peaks and their average curvature (from the surface profiling data), and then calculated closures under normal load on the basis of Hertzian theory. They showed good predictions of closures under normal load of a rough surface made from a polished flat surface [e.g., Brown and Scholz, 1985].…”