Non-adhesive Contact Between Rough Surfaces
When two bodies with rough surfaces are pressed into each other, the true contact area is much smaller than the apparent contact area . In contact between a "random rough" surface and an elastic half-space, the true contact area is related to the normal force by
with equal to the root mean square (also known as the quadratic mean) of the surface slope and . The median pressure in the true contact surface
can be reasonably estimated as half of the effective elastic modulus multiplied with the root mean square of the surface slope .
For the situation where the asperities on the two surfaces have a Gaussian height distribution and the peaks can be assumed to be spherical, the average contact pressure is sufficient to cause yield when where is the uniaxial yield stress and is the indentation hardness. Greenwood and Williamson defined a dimensionless parameter called the plasticity index that could be used to determine whether contact would be elastic or plastic.
The Greenwood-Williamson model requires knowledge of two statistically dependent quantities; the standard deviation of the surface roughness and the curvature of the asperity peaks. An alternative definition of the plasticity index has been given by Mikic. Yield occurs when the pressure is greater than the uniaxial yield stress. Since the yield stress is proportional to the indentation hardness, Micic defined the plasticity index for elastic-plastic contact to be
In this definition represents the micro-roughness in a state of complete plasticity and only one statistical quantity, the rms slope, is needed which can be calculated from surface measurements. For, the surface behaves elastically during contact.
In both the Greenwood-Williamson and Mikic models the load is assumed to be proportional to the deformed area. Hence, whether the system behaves plastically or elastically is independent of the applied normal force.
Read more about this topic: Contact Mechanics
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