Self similar solutions to adhesive contact problems with incremental loading

Abstract
The boundary-value problem for axisymmetric distortion of an elastic half space by a rigid indentor is formulated. A dimensional argument is used to infer the form of the distribution of radial displacement within the contact circle in terms of the shape of the body, assuming the load to be applied progressively, with interfacial friction sufficient to prevent any slip taking place between the indentor and the half space. This obviates the need for solving a preliminary integral equation for the boundary conditions, as proposed by Goodman (1962) and Mossakovski (1963). The resulting boundary-value problem is cast in the form of an integral equation of Wiener-Hopf type, which has been solved in a separate paper (Spence 1968, referred to as II). The solution is used to calculate stresses, displacements and contact radii for adhesive indentation by (i) a flat faced cylinder, (ii) an almost flat conical indentor and (iii) a sphere. The results are compared with those for frictionless indentation, for a range of values of Poisson’s ratio (iv). Adhesive indentation of a half space by a sphere of radius R rolling with angular velocity ω and linear velocity V (excluding dynamical effects) is also treated, and a value found for the creep 1 (V/Rω in the absence of torsional or tractive forces.

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