Study of elastoplastic contact of spherical indenter with metals and solid lubricating coatings: Part 2. Contact characteristics

Estimation of characteristics of contact between rough surfaces, one of which has solid lubricating coating

“…The transition from elastic deformation of SLC to elastoplastic proceeds at the exceedance of critical value of stress on indenter. In this case, the indentation would exceed the critical penetra tion a cr , corresponding to this critical load N cr [4]. Let us split all peaks that are in contact by two groups 1 depending on the degree of their penetration ( Fig.…”

“…(2), the total real contact area can be represented as the sum of the areas, which are formed by the peaks of the first and second groups, respectively, at the interaction with SLCs as follows: (4) where and are real contact areas of the peaks of the first and second groups, respectively. …”

“…The equation for the relative penetration of a spherical indenter to the elastoplastic coating fixed with the elastic base can be represented as follows [4]: (7) where d = h/a cr is relative penetration of spherical indenter to elastoplastic coating; h is penetration of spherical indenter; k = P/N cr is relative load on spher ical indenter; and α is the coefficient, which is deter mined by the ratio of real contact area to its section area at the penetration depth.…”

“…We obtain the following from the Eq. (6), with the assumption that ρ = [4]; equilibrate the load on indenter at elastic deformation of coating P to the load on a single peak for the first group and replace the indentation h by the penetration of the single peak as follows: (8) We should note that the transition of load on indenter P to the load on a single peak for the first group N 1i and replacement of indentation h by the penetration of a single peak implies the extension of the solution obtained for indenter to any peak of the considered rough surface if it is modeled by spherical segment and is in an elastic contact interaction with coating.…”

“…The latter [3] considers the discrete contact as the contact problem of elasticity or elastoplasticity problem with the assumption of the mutual effect of individual contacts on strain-stress state of interacting surfaces. The use of the former approach allows the extension of the early studies of the characteristics of elastoplastic contact of spherical indenter with SLCs [4] on the contact interaction of rough surfaces, one of which has an elastoplastically strained coating. The essential characteristics of the contact of rough surfaces are the approach of solids under stress and the real contact area.…”