Contact of an Elastic Body with a Rigid Base Containing Grooves Partially Filled with Nonwetting Liquid
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CONTACT OF AN ELASTIC BODY WITH A RIGID BASE CONTAINING GROOVES PARTIALLY FILLED WITH NONWETTING LIQUID O. P. Kozachok
UDC 539.3
We study the frictionless contact of an elastic half space with a rigid base textured by quasielliptic grooves in the presence of an incompressible liquid that does not wet the surfaces of bodies in the interface gaps. Under the action of surface tension, the liquid forms bridges in the middle parts of the gaps. At the same time, the edges of the gaps are filled with a gas whose pressure is constant. The pressure drops in the liquid and in gas are described by the Laplace formula. The formulated contact problem is reduced to a singular integral equation for the derivative of the height of interface gaps and to a transcendental equation for the width of liquid bridges. The dependences of the width of liquid bridges, contact pressure, shape of the gaps, contact distances, and contact compliance of the half space on the applied load and surface tension in the liquid are analyzed. Keywords: contact interaction, quasielliptic grooves, interface gaps, incompressible liquid, contact approaching of the bodies, plane strain.
Introduction In order to improve the functional characteristics of two-component joints, the researchers often use the socalled texturing of the surfaces [1, 2]. This procedure is reduced to the formation of regularly arranged notches, pits, or grooves on these surfaces. In the course of operation of bodies with textured surfaces, the interface gaps can be partially or completely filled with liquids as a result of various processes (condensation, adsorption, etc.). Due to the small heights of the artificially made inhomogeneities, for the solution of numerous applied and scientific problems, it is necessary to take into account the presence of liquid bridges between them [3–7]. These bridges strongly affect the contact characteristics of joints, including the distribution of contact pressure, the sizes of intercontact gaps, and the contact approach of the bodies. The shape of the meniscus (the lateral surface of liquid bridge neighboring with the gas) depends on the parameters of liquid and the materials of the bodies. If the wetting angle does not exceed 90°, then the liquid wets the surfaces of the bodies (i.e., they are hydrophilic) and is localized, under the action of surface tension, in the narrow parts of the intercontact gaps. The surfaces of liquid bridges formed in this case have the form of concave menisci. If the wetting angle is larger than 90°, then the liquid does not wet the surfaces of the bodies (i.e., they are hydrophobic) and is localized in the parts of gaps with the largest height. In this case, the surfaces of liquid bridges have the form of convex menisci. A survey of works dealing with the interaction of bodies with periodic surface topography and without fillers in the gaps between them can be found in [8, 9]. In [10–14], some contact problems were solved for bodies Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Aca
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