Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces: Approximate Closed-Form Equations Available to Purchase

Approximate closed-form (closure) equations governing the shoulder-shoulder contact of asperities are derived based on a generalization of Chang, Etsion and Bogy (CEB). The work entails the consideration of asperity shoulder-shoulder contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact gives rise to a slanted contact force comprising tangential and normal components. Each force component comprises elastic and elastic-plastic terms, which upon statistical summation yields the force component for the elastic and elastic-plastic force for the contact of two rough surfaces. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction. Two sets of closure equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within nine percent (9%). The second set of closure equations are closed form equations of more complicated form but with accuracy to within 0.2 percent (0.2%).