Influence of Partial Filling of the Gaps with Compressible Liquid on the Contact of Elastic Bodies with Wavy Surfaces
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INFLUENCE OF PARTIAL FILLING OF THE GAPS WITH COMPRESSIBLE LIQUID ON THE CONTACT OF ELASTIC BODIES WITH WAVY SURFACES О. P. Kozachok
UDC 539.3
We study the problem of contact of two elastic half planes (plane deformation), one of which has a wavy surface under the conditions of partial filling of the interface gaps with compressible liquid. The formulated contact problem is reduced to a singular integral equation for the derivative of the height of the interface gaps and its analytic solution is obtained. We analyze the contact behavior of this system of bodies for two different levels of loading: on the first level the volume of the gap is larger than the volume of liquid, which does not exert pressure on the surfaces of the bodies, whereas on the second level the load exceeds the threshold value after which the liquid fills the entire space and resists crack closure. Keywords: contact interaction, wavy surface, interface gaps, compressible liquid, contact compliance of the bodies.
Introduction Texturing of the surfaces [1–3], i.e., the formation of regular surface topographies, is used to improve the functional characteristics of two-component joints. In contact between the bodies with textured surfaces, we observe the formation of periodically located gaps. Under the actual operating conditions, these gaps are often filled with liquids or gases, which exert pressure upon the contact surfaces. Moreover, penetrating into the surface defects and cracks, liquids may promote their propagation [4]. Therefore, for the prediction of the contact behavior and strength of bodies with regular surface topographies in gas–liquid media, it is important to study their stress-strain states with regard for the pressure of the filler of the gaps formed between these bodies. A survey of publications devoted to the interaction of bodies with periodic topographies in the absence of filler in the gaps between them can be found in [5, 6]. Contact problems for bodies with periodically located smooth surface grooves or bodies one of which has a wavy surface were solved in [7–18] with regard for the complete filling of interface gaps either with a real gas or with a compressible (incompressible) liquid that wets (or does not wet) the surfaces of the bodies. The contact of an elastic body with a rigid base textured by grooves in the presence of the gas–liquid fillers of interface gaps was investigated in [19, 20]. The problem of stationary motion of a punch with doubly periodic sinusoidal surface topography over a viscoelastic layer described by the Winkler model in the presence of an incompressible liquid in gaps between these bodies was studied in [21]. However, the problem of interaction of two elastic bodies one of which has a wavy surface under the conditions of partial filling of the gaps has not been investigated earlier. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine; e-mail: [email protected]. Translated from Fizyko-Khimichna Mekhanika Materialiv,
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