Closure of random elastic surfaces in contact

Abstract

The physical contact between two rough surfaces is referred to as a “joint,” and the deformation of such a joint under normal stress is called the “joint closure.” Toward better understanding of joint closure, we present a theory of contact between two random nominally flat elastic surfaces. This theory is a more general form of a theory presented previously by others for the elastic contact of a rough surface and a flat surface. In agreement with the previous theory we show that the joint closure property depends as much on the details of the surface topography as on the elastic properties of the material. To apply these results by using linear surface profiles requires mapping of profile information to three dimensions. The mapping techniques described here require the probability density function for the contacting surfaces to be approximated well by either a Gaussian distribution or an inverted chi‐square distribution. Laboratory experiments on ground surfaces of glass samples were done to test the theory. Both joint closure and surface topography were measured. In most cases, experimental results agreed quantitatively with predictions of the theory. However, in experiments on the smoothest surfaces, sample preparation problems often resulted in surfaces with a domed shape. These surfaces did not fit the assumptions of the theory, but the observed deviations from the theory were consistent with this domed shape. Surface topography measurements suggest that many surfaces are statistically similar. This implies that the success of the theory in predicting joint closure does not depend on a particular sample preparation technique. Therefore the theory should be valid for all nominally flat elastic surfaces. The form of the power spectrum implies that the surface topography and thus the joint closure depend on sample size.

Normal stress distribution of rough surfaces in contact

“…The surface is then self affine with a Hurst exponent H. In Figure I The problem we have set out to study is that of two self-affine rough surfaces in full contact. However, assuming that one of the surfaces is rough and infinitely hard, and the other elastic and initially fiat, we find the same normal stress field at the interface as in the original problem within the approximation using the fiat-surface Green function, (3) and using the composite topography introduced by Brown and Scholz [1985b] (i.e. the sum of both topographies).…”

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

“…The heights of the peaks of the composite surface are distributed according to a probability density function, q>(z). Brown and Scholz [11] used the probability density function for the peak height found by Adler and Firman [17]. In this work, a simpler expression for q>(z), that is approached by the exact one when the composite surface contains high frequency components, is used.…”

“…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].…”

“…The models were developed by Brown and Scholz [11] and by Boitnott et al [12] to describe the closure, 8, and the sliding of two rough surfaces against each other when they are subjected to an external normal or transverse load, respectively. The models account for the topography ofthe two rough surfaces through a fictitious composite surface.…”

Micromechanical model for anisotropic rock joints

“…From the viewpoint of modeling interface behavior the geometry of composite topography of contacting surfaces has been found to be more applicable [Francis, 1977;Brown and Scholz, 1985]. For a given resolution the composite topography may be reasonably described via statistics of asperity contact height, curvature, and orientation [Nayak, 1971;Adler and Firman, 1981].…”