Skip to main content
Log in

The coupled thermoelastic instability of FGM coatings with arbitrarily varying properties: in-plane sliding

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The hot spot caused by frictional heat and thermal contact resistance is one of the most important reasons for hot-cracks and brake failure in brake systems. This paper simulates the brake system as a functionally graded material (FGM) coated half-plane sliding against a homogeneous half-plane. The motivation of using the FGM coating is to improve the coupled thermoelastic instability (TEI) of the brake system due to the thermal contact resistance and frictional heat. The thermoelastic properties of the FGM coating are assumed to vary arbitrarily along the thickness direction. The homogeneous multi-layered model is employed to simulate arbitrary properties of the coating. The perturbation method and transfer matrix method are used to derive the characteristic equation of the coupled TEI problem. The effects of the thermal contact resistance, friction coefficient, heat generation factor and different gradient types of the FGM coating on the stability boundaries are discussed in detail. The results show that the stability boundary is sensitive to the varying thermal parameters of the FGM coating, and an appropriate gradient type can adjust the coupled TEI of the sliding system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barber, J.R.: Thermoelastic instabilities in the sliding of comforming solids. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, vol. 312, pp. 381–394 (1969)

  2. Dow, T.A., Burton, R.A.: Thermoelastic instability of sliding contact in the absence of wear. Wear 19, 315–28 (1972)

    Article  Google Scholar 

  3. Bryant, M.D., Wang, J.P., Lin, J.W.: Thermal mounding in high speed dry sliders: experiment, theory and comparison. Wear 181, 668–677 (1995)

    Article  Google Scholar 

  4. Burton, R.A., Nerlikar, V., Kilaparti, S.R.: Thermoelastic instability in a seal-like configuration. Wear 24, 177–188 (1973)

    Article  Google Scholar 

  5. Lee, K., Barber, J.R.: Frictionally excited thermoelastic instability in automotive disk brakes. J. Tribol. 115, 607–614 (1993)

    Article  Google Scholar 

  6. Lee, K.: Frictionally excited thermoelastic instability in automotive drum brakes. J. Tribol. 122, 849–855 (2000)

    Article  Google Scholar 

  7. Decuzzi, P., Ciaverella, M., Monno, G.: Frictionally excited thermoelastic instability in multi-disk clutches and brakes. J. Tribol. 123, 865–871 (2001)

    Article  Google Scholar 

  8. Du, S., Zagrodzki, P., Barber, J.R., Hulbert, G.M.: Finite element analysis of frictionally excited thermoelastic instability. J. Therm. Stresses 20, 185–201 (1997)

    Article  MathSciNet  Google Scholar 

  9. Yi, Y.B., Du, S., Barber, J.R., Fash, J.W.: Effect of geometry on thermoelastic instability in disk brakes and clutches. J. Tribol. 121, 661–666 (1999)

    Article  Google Scholar 

  10. Yi, Y.B., Barber, J.R., Zagrodzki, P.: Eigenvalue solution of thermoelastic instability problems using Fourier reduction. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, vol. 456, pp. 2799–2821 (2000)

  11. Panier, S., Dufrenoy, P., Bremond, P.: Infrared characterization of thermal gradients on disc brakes. Aero Sense 5073, 295–302 (2003)

    Google Scholar 

  12. Johansson, L.: Model and numerical algorithm for sliding contact between two elastic half-planes with frictional heat generation and wear. Wear 160, 77–93 (1993)

    Article  Google Scholar 

  13. Ciavarella, M., Johansson, L., Afferrante, L., Klarbring, A., Barber, J.R.: Interaction of thermal contact resistance and frictional heating in thermoelastic instability. Int. J. Solids Struct. 40, 5583–5597 (2003)

    Article  MATH  Google Scholar 

  14. Afferrante, L., Ciavarella, M.: Frictionally excited thermoelastic instability in the presence of contact resistance. Int. J. Solids Struct. 39, 351–357 (2004)

    MATH  Google Scholar 

  15. Afferrante, L., Ciavarella, M.: Instability of thermoelastic contact for two half-planes sliding out-of-plane with contact resistance and frictional heating. J. Mech. Phys. Solids 52, 1527–1547 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ciavarella, M., Barber, J.R.: Stability of thermoelastic contact for a rectangular elastic block sliding against a rigid wall. Eur. J. Mech. A Solids 24, 371–376 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Xue, Z.N., Yu, Y.J., Tian, X.G.: Transient responses of multi-layered structures with interfacial conditions in the generalized thermoelastic diffusion theory. Int. J. Mech. Sci. 131, 63–74 (2017)

    Article  Google Scholar 

  18. Chumak, K.: The thermoelastic contact problem for wavy surfaces with a heat-conducting medium in interface gaps. Math. Mech. Solids . (2017). https://doi.org/10.1177/1081286517726369

  19. Shao, Z.S., Wang, T.J.: Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads. Int. J. Solids Struct. 43, 3856–3874 (2006)

    Article  MATH  Google Scholar 

  20. Ke, L.L., Wang, Y.S.: Two-dimensional sliding fractional contact of functionally graded materials. Eur. J. Mech. A Solids 26, 171–88 (2007)

    Article  MATH  Google Scholar 

  21. Shao, Z.S., Ang, K.K., Reddy, J.N., Wang, T.J.: Nonaxisymmetric thermomechanical analysis of functionally graded hollow cylinders. J. Therm. Stresses 31, 515–536 (2008)

    Article  Google Scholar 

  22. Zhong, Z., Shang, E.: Closed-form solutions of three-dimensional functionally graded plates. Mech. Adv. Mater. Struct. 15, 355–363 (2008)

    Article  Google Scholar 

  23. Jin, X., Wu, L.Z., Guo, L.C., Yu, H.J., Sun, Y.G.: Experimental investigation of the mixed-mode crack propagation in ZrO\(_{2}\)/NiCr functionally graded materials. Eng. Fract. Mech. 76, 1800–1810 (2009)

    Article  Google Scholar 

  24. Sharma, J.N., Sharma, D., Kumar, S.: Stress and strain analysis of rotating FGM Thermoelastic circular disk by using FEM. Int. J. Pure Appl. Math. 74, 339–352 (2012)

    MATH  Google Scholar 

  25. Bouderba, B., Houari, M.S.A., Tounsi, A.: Thermomechanical bending response of FGM thick plates resting on Winkler–Pasternak elastic foundations. Steel Compos. Struct. 14, 85–104 (2013)

    Article  Google Scholar 

  26. Van, T.H., Duc, N.D.: Nonlinear response of shear deformable FGM curved panels resting on elastic foundations and subjected to mechanical and thermal loading conditions. Appl. Math. Model. 38, 2848–2866 (2014)

    Article  MathSciNet  Google Scholar 

  27. Shen, H.S., Wang, H.: Nonlinear vibration of shear deformable FGM cylindrical panels resting on elastic foundations in thermal environments. Compos. B Eng. 60, 167–177 (2014)

    Article  Google Scholar 

  28. Suresh, S., Mortensen, A.: Functionally graded metals and metal-ceramic composites: part 2. Thermomechanical behaviour. Int. Mater. Rev. 42, 85–116 (1997)

    Article  Google Scholar 

  29. Suresh, S.: Graded materials for resistance to contact deformation and damage. Science 292, 2447–2451 (2001)

    Article  Google Scholar 

  30. Chen, P.J., Chen, S.H., Peng, Z.L.: Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer. Acta Mech. 223, 2647–2465 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chen, P.J., Chen, S.H.: Partial slip contact between a rigid punch with an arbitrary tip-shape and an elastic graded solid with a finite thickness. Mech. Mater. 59, 24–35 (2013)

    Article  Google Scholar 

  32. Liu, T.J., Xing, Y.M.: Analysis of graded coatings for resistance to contact deformation and damage based on a new multi-layer model. Int. J. Mech. Sci. 81, 158–164 (2014)

    Article  Google Scholar 

  33. Liu, T.J., Ke, L.L., Wang, Y.S., Xing, Y.M.: Stress analysis for an elastic semispace with surface and graded layer coatings under induced torsion. Mech. Based Des. Struct. Mach. 43, 74–94 (2015)

    Article  Google Scholar 

  34. Aizikovich, S.M., Galybin, A.N., Krenev, L.I.: Semi-analytical solution for mode I penny-shaped crack in a soft inhomogeneous layer. Int. J. Solids Struct. 53, 129–137 (2015)

    Article  Google Scholar 

  35. Liu, T.J., Zhang, C., Wang, Y.S., Xing, Y.M.: The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties. Int. J. Solids Struct. 96, 229–239 (2016)

    Article  Google Scholar 

  36. Chen, P.J., Chen, S.H., Yin, Y.: Nonslipping contact between a mismatch film and a finite-thickness graded substrate. J. Appl. Mech. 83, 021007 (2016)

    Google Scholar 

  37. Eshraghi, I., Dag, S., Soltani, N.: Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading. Compos. Struct. 137, 196–207 (2016)

    Article  Google Scholar 

  38. Dag, S.: Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials. ZAMM 96, 121–36 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  39. Çömez, İ., El-Borgi, S., Kahya, V., Erdöl, R.: Receding contact problem for two-layer functionally graded media indented by a rigid punch. Acta Mech. 227, 2493–2504 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Alinia, Y., Beheshti, A., Guler, M.A., El-Borgi, S., Polycarpou, A.A.: Sliding contact analysis of functionally graded coating/substrate system. Mech. Mater. 94, 142–155 (2016)

    Article  Google Scholar 

  41. Guler, M.A., Ozturk, M., Kucuksucu, A.: The frictional contact problem of a rigid stamp sliding over a graded medium. Key Eng. Mater. 681, 155–174 (2016)

    Article  Google Scholar 

  42. Hein, J., Kuna, M.: 3D J-integral for functionally graded and temperature dependent thermoelastic materials. Proc. Struct. Integr. 2, 2246–2254 (2016)

    Article  Google Scholar 

  43. Aizikovich, S.M., Mitrin, B.I., Seleznev, N.M., Wang, Y.C., Volkov, S.S.: Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation. Struct. Eng. Mech. 58(4), 613–625 (2016)

    Article  Google Scholar 

  44. Balci, M.N., Dag, S., Yildirim, B.: Subsurface stresses in graded coatings subjected to frictional contact with heat generation. J. Therm. Stresses 40, 517–534 (2017)

    Article  Google Scholar 

  45. Güler, M.A., Kucuksucu, A., Yilmaz, K.B., Yildirim, B.: On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium. Int. J. Mech. Sci. 120, 12–29 (2017)

    Article  Google Scholar 

  46. Chen, P., Chen, S., Peng, J.: Frictional contact of a rigid punch on an arbitrarily oriented gradient half-plane. Acta Mech. 226, 4207–4221 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  47. Chen, P., Chen, S., Peng, J.: Interface behavior of a thin-film bonded to a graded layer coated elastic half-plane. Int. J. Mech. Sci. 115–116, 489–500 (2016)

    Article  Google Scholar 

  48. Chen, P., Chen, S., Peng, J.: Sliding contact between a cylindrical punch and a graded half-plane with an arbitrary gradient direction. J. Appl. Mech. Trans. ASME 82, 041008 (2015)

    Article  Google Scholar 

  49. Chen, P., Peng, J., Yu, L., Yang, Y.: The interfacial analysis of a film bonded to a finite thickness graded substrate. Int. J. Solids Struct. 120, 57–66 (2017)

    Article  Google Scholar 

  50. Zhang, W.: Global and chaotic dynamics for a parametrically excited thin plate. J. Sound Vib. 239, 1013–1036 (2001)

    Article  Google Scholar 

  51. Hao, Y.X., Chen, L.H., Zhang, W., Lei, J.G.: Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate. J. Sound Vib. 312, 862–892 (2008)

    Article  Google Scholar 

  52. Zhang, W., Li, S.B.: Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations. Nonlinear Dyn. 62, 673–686 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  53. Guo, X.Y., Zhang, W., Zhao, M.H., He, Y.C.: A new kind of energy transfer from high-frequency mode to low-frequency mode in a composite laminated plate. Acta Mech. 224, 2937–2953 (2013)

    Article  MATH  Google Scholar 

  54. Zhang, W., Zhao, M.H.: Nonlinear vibrations of a composite laminated cantilever rectangular plate with one-to-one internal resonance. Nonlinear Dyn. 70, 295–313 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  55. Zhang, W., Hao, Y.X., Guo, X.Y., Chen, L.H.: Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations. Meccanica 47, 985–1014 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  56. Zhang, W., Zhao, M.H., Guo, X.Y.: Nonlinear responses of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations. Compos. Struct. 100, 554–565 (2013)

    Article  Google Scholar 

  57. Kim, J.W., Liu, L., Zhang, Y.: Improving the resistance to sliding contact damage of zirconia using elastic gradients. J. Biomed. Mater. Res. B Appl. Biomater. 94, 347–52 (2010)

    Google Scholar 

  58. Kulchytsky-Zhyhailo, R., Bajkowski, A.S.: Axisymmetrical problem of thermoelasticity for halfspace with gradient coating. Int. J. Mech. Sci. 106, 62–71 (2016)

    Article  Google Scholar 

  59. Lee, S.W., Jang, Y.H.: Effect of functionally graded material on frictionally excited thermoelastic instability. Wear 266, 139–146 (2009)

    Article  Google Scholar 

  60. Lee, S.W., Jang, Y.H.: Frictionally excited thermoelastic instability in a thin layer of functionally graded material sliding between two half-planes. Wear 267, 1715–1722 (2009)

    Article  Google Scholar 

  61. Mao, J.J., Ke, L.L., Wang, Y.S.: Thermoelastic instability of functionally graded materials in frictionless contact. Acta Mech. 226, 2295 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  62. Mao, J.J., Ke, L.L., Wang, Y.S., Liu, J.: Frictionally excited thermoelastic instability of functionally graded materials sliding out-of-plane with contact resistance. J. Appl. Mech. 83, 021010 (2016)

    Article  Google Scholar 

  63. Mao, J.J., Ke, L.L., Yang, J., Kitipornchai, S., Wang, Y.S.: Thermoelastic instability of functionally graded materials with interaction of frictional heat and contact resistance. Mech. Based Des. Struct. Mach., 46, 139–156 (2018)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Liao-Liang Ke.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, JJ., Ke, LL., Yang, J. et al. The coupled thermoelastic instability of FGM coatings with arbitrarily varying properties: in-plane sliding. Acta Mech 229, 2979–2995 (2018). https://doi.org/10.1007/s00707-018-2150-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-018-2150-2

Navigation