Thomas Industrial Library

12.2 MATING SURFACES

When two surfaces are pressed together under load, their apparent area of contact Aa is easily calculated from geometry, but their real area of contact Ar is affected by the asperities present on their surfaces and is more difficult to accurately determine. Figure 12-4 shows two parts in contact. The tops of the asperities will initially contact the mating part and the initial area of contact will be extremely small. The resulting stresses in the asperities will be very high and can easily exceed the compressive yield strength of the material. As the mating force is increased, the asperity tips will yield and spread until their combined area is sufficient to reduce the average stress to a sustainable level, i.e., some compressive penetration strength of the weaker material.

We can get a measure of a material’s compressive penetration strength from conventional hardness tests (Brinell, Rockwell, etc.), that force a very smooth stylus into the material and deform (yield) the material to the stylus’ shape. The penetration strength Sp is easily calculated from these test data and tends to be of the order of 3 times the compressive yield strength Syc of most materials.[3]

The real area of contact can then be estimated from

where F is the force applied normal to the surface and the strengths are as defined in the above paragraph, taken for the weaker of the two materials. Note that the contact area for a material of particular strength under a given load will be the same regardless of the apparent area of the mating surfaces.