Abstract
We investigate the normal contact stiffness in a contact of a rough sphere with an elastic half-space using 3D boundary element calculations. For small normal forces, it is found that the stiffness behaves according to the law of Pohrt/Popov for nominally flat self-affine surfaces, while for higher normal forces, there is a transition to Hertzian behavior. A new analytical model is derived describing the contact behavior at any force.
Highlights
Since Bowden and Tabor [1], it has been known that surface roughness plays a decisive role in contact, adhesion, friction, and wear
The main understanding of the contact mechanics of nominally flat rough surfaces was achieved in the middle of the 20th century due to works by Archard [2] and Greenwood and Williamson [3]
For small normal forces, the system is dominated by the roughness and the stiffness approaches the asymptotic dependence with the slope (H + 1)−1 characteristic for nominally flat fractal surfaces [12]
Summary
Since Bowden and Tabor [1], it has been known that surface roughness plays a decisive role in contact, adhesion, friction, and wear. The main understanding of the contact mechanics of nominally flat rough surfaces was achieved in the middle of the 20th century due to works by Archard [2] and Greenwood and Williamson [3]. A first analysis of the contact problem including a curved but rough surface was given by Greenwood and Tripp [7]. They applied the Greenwood/Williamson (GW) model [3] of independent asperities with a Gaussian distribution to a parabolic shape. In this model, the roughness can be seen as an additional compressible layer.
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