Abstract
AbstractWe consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter (“line contact”) taking the surface tension of the layer into account. First, it is shown that the boundary condition for the surface outside the contact area is given by the constant contact angle—as in the case of fluids in contact with solid surfaces. In the approximation of thin layer and under usual assumptions of small indentation and small inclination angles of the surface, the problem is solved analytically. In the case of a non-adhesive contact, surface tension makes the contact stiffer (at the given indentation depth, the contact half-width becomes smaller and the indentation force larger). In the case of adhesive contact, the influence of surface tension seems to be more complicated: For a flat-ended punch, it increases with increasing the surface tension, while for a wedge, it decreases. Thus, the influence of the surface tension on the adhesion force seems to be dependent on the particular geometry of the contacting bodies.
Highlights
Classical contact mechanics as represented by the works of Hertz [1] or Bussinesq [2], see [3], neglects the surface tension of the contacting solids
We considered a general adhesive contact of a thin elastic body with a rigid indenter
An important conclusion is that at the boundary of the contact area, the surface of the elastic layer meets the surface of the rigid indenter under a fixed contact angle, which is determined uniquely by the specific surface energies of the rigid body, the elastic body and the interface
Summary
Classical contact mechanics as represented by the works of Hertz [1] or Bussinesq [2], see [3], neglects the surface tension of the contacting solids. If the specific surface energy of the surface of elastic body outside the contact area can be neglected, we have an adhesive contact with specific work of separation w = γ2 − γ12. This case was first considered in the classic work by Johnson, Kendall and Roberts [4]. If the surface energy of the elastic body outside the contact area is finite, γ1 = 0, but the work of adhesion, which in the general case is equal to. Let us note that another contact problem with adhesion and surface tension represents a contact of an elastic solid with a fluid [9]. This length plays the role of the “elastocapillary length” in the present problem
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