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Greenwood Williamson model
Table of Contents
Introduction
In general, it is assumed that the real area of contact between two nominally flat metal surfaces is determined by the plastic deformation of their highest asperities. This assumption leads to the conclusion that the real area of contact is directly proportional to the applied load and independent of the apparent contact area. However, Greenwood Williamson provides a new theory of elastic contact, which is more closely related to real surfaces than earlier theories. This theory demonstrates how contact deformation depends on the surface topology and establishes a criterion for distinguishing between surfaces that come in contact elastically and plastically. The theory also introduces the concept of “elastic contact hardness,” a composite quantity that depends on both the elastic properties and topography of the surfaces. This quantity plays a similar role in elastic contact as conventional hardness does in plastic contact.
Explanation
If the two surfaces come together until a distance d separates their reference planes, then there will be contacted at any asperity whose height was initially greater than d. Thus, the probability of making contact at any given difficulty of height z is
Where, z is standard deviation of asperity peaks and d is probability of contact on asperity peaks.
The following equations were used to calculate the real contact area and total load.
Where, N is number of asperities, E is elastic moduli, σ is difference in asperity height (z-d), and R is radius of curvature.
Gaussian distribution of asperity height
The following experimental results show that the height distribution is Gaussian to an excellent approximation for many surfaces. We have, therefore,
We can merge the above equations to attain equations for load and total contact area, assuming the Gaussian distribution of asperity heights.
Important points from the GW model:
The theory provides relationships that describe the total real area of contact, number of microcontacts, load, and conductance between two surfaces based on the separation of their mean planes.
- Dependence on Load: While the separation depends on the nominal pressure (load divided by the nominal area), the number of microcontacts and the total area of contact depend solely on the load.
- Separation Insensitivity to Pressure: The separation between the surfaces is not highly sensitive to pressure. It is typically 1 to 2 times the standard deviation, or roughly the centre line average.
- Average Gap Between Surfaces: The average gap between two surfaces in contact is approximately 20 nm for a wide range of loads.
- Difficulty in Gastight Seals: The above factors explain the challenge in creating metal-to-metal gastight seals, as the average gap remains significant even under various loading conditions.
- Elastic Hardness: The concept of “elastic hardness” is introduced, where the area of contact can be predicted from the load, similar to how plastic contact is predicted using conventional hardness.
- Plasticity Index: A criterion called the “plasticity index” is introduced, which is the ratio of elastic hardness to real hardness. This index helps determine whether the contact will be elastic or plastic.
- Deformation Mode: The deformation mode (elastic or plastic) is not significantly affected by changes in load. If the plasticity index is low, the contact will be elastic; if it is high, it will be plastic.
- Misconception About Load and Contact: The idea that contact is elastic at low loads and becomes plastic as the load increases is incorrect. The plasticity index, given by is a more accurate determinant.
- Generalized Surface Texture Parameter: The plasticity index can be viewed as a generalized surface texture parameter, combining both material and topographic properties.
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