Normal and tangential compliances of interface of rough surfaces with contacts of elliptic shape

The incremental compliances, normal and tangential, of an interface between rough surfaces are considered. Contacts are assumed to be elliptic – the shape of Hertzian contacts between any two locally smooth asperities. The ellipses may have diverse eccentricities and random or non-random orientation distribution; in the latter case, the tangential compliance is anisotropic. It is found that the Hertzian contacts and “welded” zones of the same geometry produce the same incremental compliances. Microstructural characteristics ξ of the interface that controls its incremental compliances is identified. For the circular contacts, ξ   is the sum ∑Ak where Ak is kth contact area; in the more general case of elliptic contacts, each Ak enters in product with its shape factor dependent on the ellipse aspect ratio. The mentioned in-plane tangential anisotropy is relatively mild, even for parallel strongly elongated elliptic contacts. This is due to weakness of the anisotropy for a single elliptic contact (or external elliptic crack). Comparison of the latter to the internal crack of the same elliptic geometry shows that whereas the anisotropy is mild for both crack types, it is weaker for the external crack, in which case it is also less sensitive to Poisson’s ratio.