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Stress field in the thermoelastic rolling contact of graded coatings

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Abstract

The thermoelastic rolling contact problem for an FGM-coated half plane under the plane strain deformation is studied in this paper. A rigid roller rolls over the surface of coating with constant translational velocity generating frictional heating in the slip zones of the contact patch. The material properties of the FGM vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique are used to achieve a system of two Cauchy singular integral equations. The coupling effect of tangential traction is eliminated by adapting the conventional Goodman approximation. The associated governing equations are discretized by applying the Gauss–Chebyshev integration method gaining a system of linear algebraic equations. The effects of moving velocity, thermal conductivity and expansion coefficients’ ratios on through the thickness stress distribution are studied.

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References

  1. Alinia, Y., Guler, M.A., Adibnazari, S.: The effect of material property grading on the rolling contact stress field. Mech. Res. Commun. 55, 45–52 (2014)

    Article  Google Scholar 

  2. Barik, S.P., Kanoria, M., Chaudhuri, P.K.: Steady state thermoelastic contact problem in a functionally graded material. Int. J. Eng. Sci. 46(8), 775–789 (2008)

    Article  MathSciNet  Google Scholar 

  3. Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids, 2nd edn. Oxford University Press, Oxford (1959)

    MATH  Google Scholar 

  4. Choi, H.J., Paulino, G.H.: Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation. J. Mech. Phys. Solids 56(4), 1673–1692 (2008)

    Article  MathSciNet  Google Scholar 

  5. Chudzikiewicz, A., Myslinski, A.: Thermoelastic wheel–rail contact problem with elastic graded materials. Wear 271(1–2), 417–425 (2011)

    Article  Google Scholar 

  6. Chudzikiewicz, A.: Thermoelastic Rolling Contact Problems for a Multi-Layer Structure. Nonlinear Anal.: Real World Appl. 22(August), 1–2 (2011)

    Google Scholar 

  7. Comez, I., Erdol, R.: Frictional contact problem of a rigid stamp and an elastic layer bonded to a homogeneous substrate. Arch. Appl. Mech. 83(1), 15–24 (2013)

    Article  Google Scholar 

  8. Comez, I.: Frictional moving contact problem for a layer indented by a rigid cylindrical punch. Arch. Appl. Mech. 87(12), 1993–2002 (2017)

    Article  Google Scholar 

  9. Dag, S., Yildirim, B., Sarikaya, D.: Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads. Int. J. Solids Struct. 44(24), 7816–7840 (2007)

    Article  Google Scholar 

  10. Erdogan, F., Gupta, G.D., Cook, T.S.: Numerical solution of singular integral equations BT. In: Methods of Analysis and Solutions of Crack Problems: Recent Developments in Fracture Mechanics Theory and Methods of Solving Crack Problems

  11. Goodman, L.E.: Contact stress analysis of normally loaded rough spheres. J. Appl. Mech. 29(3), 515–522 (1962)

    Article  MathSciNet  Google Scholar 

  12. Guler, M.A., Adibnazari, S., Alinia, Y.: Tractive rolling contact mechanics of graded coatings. Int. J. Solids Struct. 49(6), 929–945 (2012)

    Article  Google Scholar 

  13. Guo, L.C., Noda, N.: Dynamic investigation of a functionally graded layered structure with a crack crossing the interface. Int. J. Solids Struct. 45(1), 336–357 (2008)

    Article  Google Scholar 

  14. Hills, D.A., Nowell, D., Sackfield, A.: Mechanics of Elastic Contacts. Butterworth-Heinemann, London (1993)

    MATH  Google Scholar 

  15. Jin, Z.H., Noda, N.: Transient thermal stress intensity factors for a crack in a semi-infinite plate of a functionally gradient material. Int. J. Solids Struct. 31(2), 203–218 (1994)

    Article  Google Scholar 

  16. Johnson, K.L.: Contact Mechanics. Cambridge University Press, London (1985)

    Book  Google Scholar 

  17. Krenk, S.: On quadrature formulas for singular integral equations of the first and the second kind. Q. Appl. Math. 33(3), 225–232 (1975)

    Article  MathSciNet  Google Scholar 

  18. Krenk, S.: On the use of the interpolation polynomial for solutions of singular integral equations. Q. Appl. Math. 32(4), 479–484 (1975)

    Article  MathSciNet  Google Scholar 

  19. Li, W., Wen, Z., Jin, X., Wu, L.: Numerical analysis of rolling-sliding contact with the frictional heat in rail. Chin. J. Mech. Eng. 27(1), 41–49 (2014)

    Article  Google Scholar 

  20. Liu, T.J., Wang, Y.S., Zhang, C.: Axisymmetric frictionless contact of functionally graded materials. Arch. Appl. Mech. 78(4), 267–282 (2008)

    Article  Google Scholar 

  21. Liu, J., Ke, L.L., Wang, Y.S.: Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating. Int. J. Solids Struct. 48(18), 2536–2548 (2011)

    Article  Google Scholar 

  22. Liu, J., Ke, L.L., Wang, Y.S., Yang, J., Alam, F.: Thermoelastic frictional contact of functionally graded materials with arbitrarily varying properties. Int. J. Mech. Sci. 63(1), 86–98 (2012)

    Article  Google Scholar 

  23. Matysiak, S.J., Pauk, V.J.: Plane contact problem for periodic laminated composite involving frictional heating. Arch. Appl. Mech. 66, 82–89 (1995)

    Article  Google Scholar 

  24. Munisamy, R., Hills, D.A., Nowell, D.: Brief note on the tractive rolling of dissimilar elastic cylinders. Int. J. Mech. Sci. 33(3), 225–228 (1991)

    Article  Google Scholar 

  25. Myslinski, A.: Thermoelastic Rolling contact problems for multilayer materials. Nonlinear Anal.: Real World Appl. 78(April), 619–631 (2015)

    Article  MathSciNet  Google Scholar 

  26. Nowell, D., Hills, D.A.: Tractive rolling of dissimilar elastic cylinders. Int. J. Mech. Sci. 30(6), 427–439 (1988)

    Article  Google Scholar 

  27. Pauk, V., Zastrau, B.: 2D rolling contact problem involving frictional heating. Int. J. Mech. Sci. 44(12), 2573–2584 (2002)

    Article  Google Scholar 

  28. Shi, Z.: Mechanical and thermal contact analysis in layered elastic solids. Ph.d. dissertation, University of Minnesota (2001)

  29. Shodja, H.M., Ghahremaninejad, A.: An FGM coated elastic solid under thermomechanical loading: a two dimensional linear elastic approach. Surf. Coat. Technol. 200(12–13), 4050–4064 (2006)

    Article  Google Scholar 

  30. Suresh, S., Mortensen, A., Needleman, A.: Fundamentals of Metal-Matrix Composites: Materials Processing and Thermomechanical Behavior of Graded Metals and Metallic Ceramic Composites. IOM Communications Ltd., London (1998)

    Google Scholar 

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Nili, A., Adibnazari, S. & Karimzadeh, A. Stress field in the thermoelastic rolling contact of graded coatings. Arch Appl Mech 88, 1805–1814 (2018). https://doi.org/10.1007/s00419-018-1405-7

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