Advertisement

Materials Science

, Volume 46, Issue 4, pp 543–552 | Cite as

Local slip of bodies caused by the inhomogeneous friction coefficient

  • N. I. Malanchuk
Article

We study the problem of contact interaction of two elastic isotropic bodies under the conditions of plane deformation with regard for slip caused by the local inhomogeneity of the friction coefficient under consecutive loading by normal and shear forces. By the method of complex potentials, this contact problem is reduced to a singular integral equation for the relative shift of the boundaries of the bodies in the region of slip whose solution is found in the analytic form. The influence of external loads on the relative shift of the boundaries of the bodies in this region, their length, and contact stresses is analyzed.

Keywords

contact interaction matching surfaces inhomogeneous friction coefficient adhesion slip relative shift 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. A. Hills, D. Nowell, and A. Sackfield, Mechanics of Elastic Contact, Butterworth-Heinemann, Oxford (1993).Google Scholar
  2. 2.
    K. L. Johnson, Contact Mechanics, Cambridge Univ. Press, Cambridge (1985).Google Scholar
  3. 3.
    I. G. Goryacheva, P. T. Rajeev, and T. N. Farris, “Wear in partial slip contact,” J. Tribol., 123, 848–856 (2001).CrossRefGoogle Scholar
  4. 4.
    V. V. Panasyuk, O. P. Datsyshyn, and R. B. Shchur, “Residual durability of solids contacting under conditions of fretting fatigue,” Mater. Sci., 36, No. 2, 153–169 (2000).CrossRefGoogle Scholar
  5. 5.
    O. P. Datsyshyn and V. M. Kadyra, A fracture-mechanics approach to prediction of pitting under fretting fatigue conditions,” Int. J. Fatigue, 28, No. 4, 375–385 (2006).CrossRefGoogle Scholar
  6. 6.
    O. P. Datsyshyn and V. M. Kadyra, “Development of fretting-fatigue edge cracks under the adhesion–slip conditions of contact between the bodies,” Mashynoznavstvo, No. 3, 9–15 (2006).Google Scholar
  7. 7.
    C. Cattaneo, “Sul contatto di due corpi elastici: distribuzione locale degli sforzi.” Rendiconti dell’Accademia Nazionale dei Lincei, 27, 342–348 (1938).Google Scholar
  8. 8.
    V. I. Ostryk and A. F. Ulitko, Wiener–Hopf Method in Contact Problems of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (2006).Google Scholar
  9. 9.
    M. Comninou, D. Schmueser, and J. Dundurs, “Frictional slip between a layer and a substrate caused by a normal load,” Int. J. Eng. Sci., 18, 131–137 (1980).CrossRefGoogle Scholar
  10. 10.
    D. Schmueser, M. Comninou, and J. Dundurs, “Separation and slip between a layer and a substrate caused by a tensile load,” Int. J. Eng. Sci., 18, 1149–1155 (1980).CrossRefGoogle Scholar
  11. 11.
    M. Comninou and J. Barber, “Frictional slip between a layer and a substrate due to a periodic tangential surface force,” Int. J. Solids Struct., 19, No. 6, 533–539 (1983).CrossRefGoogle Scholar
  12. 12.
    R. M. Martynyak, N. I. Malanchuk, and B. E. Monastyrs’kyi, “Shear of two half planes pressed to each other and containing a surface groove. Part 1. Full contact,” Mater. Sci., 41, No. 2, 178–185 (2005).CrossRefGoogle Scholar
  13. 13.
    R. M., Martynyak, N. I. Malanchuk, and B. E Monastyrs’kyi, “Shear of two half planes pressed to each other and containing a surface groove. Part 2. Incomplete contact,” Mater. Sci., 42, No. 4, 551–559 (2006).CrossRefGoogle Scholar
  14. 14.
    R. M., Martynyak, N. I. Malanchuk, and B. E Monastyrs’kyi, “Elastic interaction of two half planes under the conditions of local shift of the boundaries in the region of intercontact gap,” Mat. Met. Fiz.-Mekh. Polya, 48, No. 3, 101–109 (2005).Google Scholar
  15. 15.
    R. Martynyak and A. Kryshtafovych, “Friction contact of two elastic half planes with local recesses in boundary,” J. Friction Wear, 21, No. 4, 6–15 (2000).Google Scholar
  16. 16.
    R. Martynyak and A. Kryshtafovych, “Friction contact of two elastic half planes with wavy surfaces,” J. Friction Wear, 21, No. 5, 1–8 (2000).Google Scholar
  17. 17.
    A. Kryshtafovych and R. Martynyak, “Strength of a system of mated anisotropic half planes with surface recesses,” Int. J. Eng. Sci., 39, 403–413 (2001).CrossRefGoogle Scholar
  18. 18.
    B. E. Monastyrs’kyi, “Axially symmetric contact problem for half spaces with geometrically perturbed surface,” Mater. Sci., 35, No. 6, 777–782 (1999).CrossRefGoogle Scholar
  19. 19.
    B. Monastyrs’kyi and R. Martynyak R, “Contact of two half spaces one of which contains a ring-shaped pit. Part 1. Singular integral equation,” Mater. Sci., 39, No. 2. 206–213 (2003).CrossRefGoogle Scholar
  20. 20.
    R. M. Shvets, R. M. Martynyak, and A. A. Kryshtafovych, “Discontinuous contact of an anisotropic half plane and a rigid base with disturbed surface,” Int. J. Eng. Sci., 34, No. 2, 183–200 (1996).CrossRefGoogle Scholar
  21. 21.
    V. D. Kubenko, “Nonstationary plane elastic contact problem for matched cylindrical surfaces,” Int. Appl. Mech., 40, No. 1, 51–60 (2004).CrossRefGoogle Scholar
  22. 22.
    G. S. Kit, R. M. Martynyak, and I. M. Machishin, “The effect of fluid in the contact gap on the stress state of conjugate bodies,” Int. Appl. Mech., 39, No. 3, 292–299 (2003).CrossRefGoogle Scholar
  23. 23.
    R. M. Martynyak and B. S. Slobodyan, “Contact of elastic half spaces in the presence of an elliptic gap filled with liquid,” Mater. Sci., 45, No. 1, 66–71 (2009).CrossRefGoogle Scholar
  24. 24.
    R. M. Martynyak and K. A. Chumak, “Thermoelastic contact of half spaces with equal thermal distortivities in the presence of a heat-permeable interface gap,” J. Math. Sci., 165, No. 3, 355–370 (2010).CrossRefGoogle Scholar
  25. 25.
    R. M. Martynyak, B. S. Slobodyan, and V. M. Zelenyak, “Pressure of an elastic half space on a rigid base with rectangular hole in the case of a liquid bridge between them,” J. Math. Sci., 160, No. 4, 470–477 (2009).CrossRefGoogle Scholar
  26. 26.
    R. M. Martynyak, “The contact of a half space and an uneven base in the presence of an intercontact gap filled with an ideal gas,” J. Math. Sci., 107, No. 1, 3680–3685 (2001).CrossRefGoogle Scholar
  27. 27.
    R. M. Martynyak and B. S. Slobodyan, “Influence of liquid bridges in the interface gap on the contact of bodies made of compliant materials,” Mater. Sci., 44, No. 2, 147–155 (2008).CrossRefGoogle Scholar
  28. 28.
    R. M. Martynyak, “Mechanothermodiffusion interaction of bodies with regard for the filler of intercontact gaps,” Mater. Sci., 36, No. 2, 300–304 (2000).CrossRefGoogle Scholar
  29. 29.
    R. M. Martynyak, “Instability of thermoelastic interaction between a half space and a rigid base through a thin liquid layer,” J. Math. Sci., 99, No. 5, 1607–1615 (2000).CrossRefGoogle Scholar
  30. 30.
    A. A. Krishtafovich and R. M. Martynyak, “Lamination of anisotropic half spaces in the presence of contact thermal resistance,” Int. Appl. Mech., 35, No. 2, 159–164 (1999).CrossRefGoogle Scholar
  31. 31.
    A. A. Krishtafovich and R. M. Martynyak, “Thermoelastic contact of anisotropic half spaces with thermal resistance,” Int. Appl. Mech., 34, No. 7, 629–634 (1998).CrossRefGoogle Scholar
  32. 32.
    R. M. Martynyak, Kh. I. Honchar, and S. P. Nahalka, “Simulation of thermomechanical closure of an initially open interface crack with heat resistance,” Mater. Sci., 39, No. 5, 672–681 (2003).CrossRefGoogle Scholar
  33. 33.
    R. M. Martynyak, “Thermal opening of an initially closed interface crack under conditions of imperfect thermal contact between its lips,” Mater. Sci., 35, No. 5, 612–622 (1999).CrossRefGoogle Scholar
  34. 34.
    R. M. Martynyak and K. A. Chumak, “Thermoelastic delamination of bodies in the presence of a heat-conducting filler of the intercontact gap,” Mater. Sci., 45, No. 4, 1–10 (2009).CrossRefGoogle Scholar
  35. 35.
    N. Malanchuk, R. Shvets’, and R. Martynyak, “Local slip of bodies caused by surface inhomogeneities under the action of force and thermal loads,” Mashynoznavstvo, No. 7, 15–20 (2007).Google Scholar
  36. 36.
    N. I. Muskheshvili, Singular Integral Equations [in Russian], Fizmatlit, Moscow (1962).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

Personalised recommendations