The contact of two elastic semiinfinite bodies one of which has a wavy surface in the presence of real gases in interface gaps is investigated. The state of the gas is described by the van der Waals equation, which makes it possible to consider the gas-liquid phase transition. The posed contact problem is reduced to a singular integral equation (SIE) with Hilbert kernel for the derivative of the height of interface gaps. Then this SIE is transformed into a SIE with Cauchy kernel, which is solved analytically. The condition of existence of a solution of this SIE and the van der Waals equation yield a system of transcendental equations for the width of the gaps and gas pressure. This system is solved numerically. The dependences of the width of the gaps, the pressure and volume of the gas, the average normal displacement, and the contact compliance of the bodies on the applied load and temperature are analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Etsion, “State of the art in laser surface texturing,” ASME J. Tribol., 127, No. 1, 248–253 (2005).
P. Stepien, “Deterministic and stochastic components of regular surface texture generated by a special grinding process,” Wear, 271, Nos. 3–4, 514–518 (2011).
O. P. Datsyshyn and V. V. Panasyuk, “Pitting of the rolling bodies contact surface,” Wear, 251, Nos. 1–2, 1347–1355 (2001).
O. P. Datsyshyn, V. V. Panasyuk, and A. Yu. Glazov, “Modeling of fatigue contact damages formation in rolling bodies and assessment of their durability,” Wear , 271, Nos.1–2, 186–194 (2011).
G. S. Kit, R. M. Martynyak, and I. M. Machishin, “The effect of a fluid in the contact gap on the stress state of conjugate bodies,” Int. Appl. Mech., 39, No. 3, 292–299 (2003).
R. M. Martynyak, “The contact of a half space and an uneven base in the presence of an intercontact gap filled by an ideal gas,” J. Math. Sci., 107, No. 1, 3680–3685 (2001).
R. Martynyak and K. Chumak, “Effect of heat-conductive filler on interface gap on thermoelastic contact of solids,” Int. J. Heat Mass Transfer, 55, No. 4, 1170–1178 (2012).
I. V. Savel’ev, A Course of General Physics [in Russian], Nauka, Moscow (1966).
J. M. Block and L. M. Keer, “Periodic contact problems in plane elasticity,” J. Mech. Mater. Struct., 3, No. 7, 1207–1237 (2008).
I. G. Goryacheva and R. M. Martynyak, “Contact problems for textured surfaces involving frictional effects,” J. Eng. Tribol., 228, No. 7, 707–716 (2014).
A. Kryshtafovych and R. Martynyak, “Frictional contact of two elastic half planes with wavy surfaces,” J. Friction Wear, 21, No. 5, 1–8 (2000).
N. Malanchuk, “Local friction sliding of elastic bodies with wavy topography of the surfaces,” Fiz.-Mat. Model. Inf. Tekh., Issue 17, 112–119 (2013).
I. Ya. Shtaerman, Contact Problem of Elasticity Theory [in Russian], GITTL, Moscow, Leningrad (1949).
B. Slobodian, K. Chumak, and R. Martynyak, “Mechanical and thermal effect of a filler of intercontact gaps on contact between two semiinfinite solids with microtextured surfaces,” Fiz.-Mat. Model. Inf. Tekh., Issue 17, 168–174 (2013).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Interaction of two elastic bodies in the presence of periodically located gaps filled with a real gas,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 1, 103–111 (2015); English translation : J. Math. Sci., 222, No. 2, 131–142 (2017).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Interaction of elastic bodies with periodic topography in the presence of liquid bridges in interface gaps,” Teor. Prikl. Mekh., Issue 7 (53), 45–52 (2013).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Contact of elastic bodies in the presence of gas and incompressible liquid in periodic interface gaps,” Fiz.-Khim. Mekh. Mater., 51, No. 6, 50–57 (2015); English translation : Mater. Sci., 51, No. 6, 804–813 (2016).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Contact of an elastic body and a stiff base with periodic system of quasielliptic grooves partially filled with liquid wetting the surfaces of the bodies,” Mat. Met. Fiz.-Mekh. Polya, 60, No. 1, 132–140 (2017).
I. G. Goryacheva and A. G. Shpenev, “Modeling of the process of sliding of a stamp with regular topography of the base over the viscoelastic support in the presence of a liquid lubricant,” Prikl. Mekh. Mat., 76, Issue 5, 754–763 (2012).
E. A. Kuznetsov, “On the contact of rough bodies in the presence of compressible lubricants,” Prikl. Mekh., 24, No. 12, 85–94 (1988).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Influence of the ideal gas in interface gaps on the contact of two elastic bodies with wavy topography of the surface,” Prikl. Probl. Mekh. Mat., Issue 13, 135–140 (2015).
O. P. Kozachok, “Contact interaction of bodies with wavy topography with regard for the compressible interface liquid,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 26, 45–54 (2017).
O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Influence of interface liquid bridges on the contact interaction of bodies with wavy topography,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 24, 34–46 (2016).
N. I. Muskhelishvili, Singular Integral Equations, Dover, New York (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 54, No. 2, pp. 57–63, March–April, 2018.
Rights and permissions
About this article
Cite this article
Kozachok, O.P., Slobodian, B.S. & Martynyak, R.M. Contact of Two Elastic Bodies with Wavy Topography in the Presence of Gases in Gaps. Mater Sci 54, 194–201 (2018). https://doi.org/10.1007/s11003-018-0173-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-018-0173-4