On the role of surface forces in contact interaction between elastic sphere and hard surface

Abstract

The works preformed earlier were reviewed briefly, and the new problem of the contact interaction between the elastic sphere and hard surface was formulated. The solution of a problem to the generalized surface force and its contact and noncontact components was obtained. The specific case of the obtained solution, when the separation α = 0, was considered. The existence of two states of contact interaction between the elastic sphere and hard plane was revealed at α = 0: (i) the stable state, at contact with the “neck” of radius a1= \(\sqrt[3]{{2{\pi}^2 R^2 {\theta}\phi {(\varepsilon)}}}\), where Ris the sphere radius, θ = (1 – η)/(πE), Eis the modulus of elasticity of the sphere, η is its Poisson's coefficient, and ϕ(e) is the specific energy of adhesion of the surfaces at the lowest possible separation e between these surfaces; and (ii) the unstable (metastable) state, at contact with radius a2= 0, i.e., at the point contact between the sphere and the plane. In this case, however, the stable contact with the neck at θ → 0 when the modulus of elasticity E→ ∞, i.e., at the interaction between the hard sphere and hard plane, is also degenerated into the point contact. It was shown that at the point contact, the contact component Fs"of the generalized surface force Fsvanishes, whereas the noncontact component Fs""acquires the value Fs""= Fs= 2πRϕ(e) equal to the force of adhesion.