Skip to main content
SpringerLink
Log in

Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A steady-state thermo-contact model of a rigid insulated cylinder of radius R sliding on a finite graded elastic layer is studied, whose Young’s modulus, thermal conductivity coefficient and thermal expansion coefficient vary exponentially in the thickness direction. The transfer matrix method and Fourier integral transform technique are used to obtain a Cauchy-type singular integral equation for the contact stresses. Numerical calculation yields the interface traction and temperature distributions below the rigid punch. It shows that crack damage in the finite graded layer due to the frictional sliding can be prevented by several alternative ways, such as decreasing the shear modulus ratio of the surface to the bottom, decreasing the friction coefficient, increasing the thickness of the finite graded layer, increasing the thermal conductivity coefficient ratio of the surface to the bottom or increasing the sliding velocity. The finding should be very useful for the design of novel graded materials with potential applications in aerospace, tribology, coatings, etc.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Guler M.A., Erdogan F.: Contact mechanics of graded coatings. Int. J. Solids Struct. 41, 3865–3889 (2004)

    Article  MATH  Google Scholar 

  2. Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behaviour of Graded Metals and Metal-Ceramic Composites. Book-Institute of Materials 698 (1998)

  3. Suresh S., Giannakopoulos A.E., Alcala J.: Spherical indentation of compositionally graded materials: theory and experiments. Acta Mater. 45, 1307–1321 (1997)

    Article  Google Scholar 

  4. Suresh S., Giannakopoulos A.E., Alcala J.: Spherical indentation of compositionally graded materials: theory and experiments. Acta Mater. 45, 3087 (1997)

    Article  Google Scholar 

  5. Jitcharoen J., Padture N.P., Giannakopoulos A.E., Suresh S.: Hertzian-crack suppression in ceramics with elastic-modulus-graded surfaces. J. Am. Ceram. Soc. 81, 2301–2308 (1998)

    Article  Google Scholar 

  6. Krumova M., Klingshirn C., Haupert F., Friedrich K.: Microhardness studies on functionally graded polymer composites. Compos. Sci. Technol. 61, 557–563 (2001)

    Article  Google Scholar 

  7. Giannakopoulos A.E., Suresh S.: Indentation of solids with gradients in elastic properties. 1. Point force. Int. J. Solids Struct. 34, 2357–2392 (1997)

    Article  MATH  Google Scholar 

  8. Giannakopoulos A.E., Suresh S.: Indentation of solids with gradients in elastic properties. 2. Axisymmetric indentors. Int. J. Solids Struct. 34, 2393–2428 (1997)

    Article  Google Scholar 

  9. Suresh S., Olsson M., Giannakopoulos A.E., Padture N.P., Jitcharoen J.: Engineering the resistance to sliding-contact damage through controlled gradients in elastic properties at contact surfaces. Acta Mater. 47, 3915–3926 (1999)

    Article  Google Scholar 

  10. Pender D.C., Padture N.P., Giannakopoulos A.E., Suresh S.: Gradients in elastic modulus for improved contact-damage resistance. Part I: The silicon nitride-oxynitride glass system. Acta Mater. 49, 3255–3262 (2001)

    Article  Google Scholar 

  11. Pender D.C., Thompson S.C., Padture N.P., Giannakopoulos A.E., Suresh S.: Gradients in elastic modulus for improved contact-damage resistance. Part II: The silicon nitride-silicon carbide system. Acta Mater. 49, 3263–3268 (2001)

    Article  Google Scholar 

  12. Giannakopoulos A.E., Pallot P.: Two-dimensional contact analysis of elastic graded materials. J. Mech. Phys. Solids 48, 1597–1631 (2000)

    Article  MATH  Google Scholar 

  13. Guler M.A., Erdogan F.: Contact mechanics of two deformable elastic solids with graded coatings. Mech. Mater. 38, 633–647 (2006)

    Article  Google Scholar 

  14. Guler M.A., Erdogan F.: The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings. Int. J. Mech. Sci. 49, 161–182 (2007)

    Article  Google Scholar 

  15. Liu T.J., Wang Y.S.: Axisymmetric frictionless contact problem of a functionally graded coating with exponentially varying modulus. Acta Mech. 199, 151–165 (2008)

    Article  MATH  Google Scholar 

  16. Ke L.-L., Wang Y.-S.: Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. Int. J. Solids Struct. 43, 5779–5798 (2006)

    Article  MATH  Google Scholar 

  17. El-Borgi S., Abdelmoula R., Keer L.: A receding contact plane problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 43, 658–674 (2006)

    Article  MATH  Google Scholar 

  18. Elloumi R., Kallel-Kamoun I., El-Borgi S.: A fully coupled partial slip contact problem in a graded half-plane. Mech. Mater. 42, 417–428 (2010)

    Article  Google Scholar 

  19. Choi H.J., Paulino G.H.: Interfacial cracking in a graded coating/substrate system loaded by a frictional sliding flat punch. Proc. R. Soc. A-Math. Phys. Eng. Sci. 466, 853–880 (2010)

    Article  MATH  Google Scholar 

  20. Chen S.H., Yan C., Zhang P., Gao H.J.: Mechanics of adhesive contact on a power-law graded elastic half-space. J. Mech. Phys. Solids 57, 1437–1448 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen S.H., Chen P.J.: Nanoadhesion of a power-law graded elastic material. Chin. Phys. Lett. 27(10), 108102 (2010)

    Article  Google Scholar 

  22. Jin F., Guo X.: Non-slipping adhesive contact of a rigid cylinder on an elastic power-law graded half-space. Int. J. Solids Struct. 47, 1508–1521 (2010)

    Article  MATH  Google Scholar 

  23. Guo X., Jin F., Gao H.J.: Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space. Int. J. Solids Struct. 48, 2565–2575 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Yi Y.B., Barber J., Hartsock D.: Thermoelastic instabilities in automotive disc brakes-finite element analysis and experimental verification. Solid Mech. Appl. 103, 187–202 (2002)

    Google Scholar 

  26. Zagrodzki P.: Analysis of thermomechanical phenomena in multidisc clutches and brakes. Wear 140, 291–308 (1990)

    Article  Google Scholar 

  27. Zagrodzki P., Lam K., Al Bahkali E., Barber J.: Nonlinear transient behavior of a sliding system with frictionally excited thermoelastic instability. J. Tribol. 123, 699 (2001)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. Jang Y.H., Ahn S.: Frictionally-excited thermoelastic instability in functionally graded material. Wear 262, 1102–1112 (2007)

    Article  Google Scholar 

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

    Google Scholar 

  31. Pauk V.: Plane contact problem involving heat generation and radiation. J. Theor. Appl. Mech. 32, 829–839 (1994)

    Google Scholar 

  32. Pauk V.J.: Plane contact problem for a layer involving frictional heating. Int. J. Heat Mass Transf. 42, 2583–2589 (1999)

    Article  MATH  Google Scholar 

  33. Pauk V., Wozniak M.: Frictional heating effects in the plane contact of layer and rigid flat punch. J. Tech. Phys. 44, 237–244 (2003)

    MATH  Google Scholar 

  34. Yevtushenko A.A., Kulchytskyzhyhailo R.D.: Determination of limiting radii of the contact area in axisymmetrical contact problems with frictional heat-generation. J. Mech. Phys. Solids 43, 599–604 (1995)

    Article  MathSciNet  Google Scholar 

  35. 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, 2536–2548 (2011)

    Article  Google Scholar 

  36. Barber J.R.: Some thermoelastic contact problems involving frictional heating. Q. J. Mech. Appl. Math. 29, 1–13 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  37. Hills D.A., Barber J.R.: Steady motion of an insulating rigid flat-ended punch over a thermally conducting half-plane. Wear 102, 15–22 (1985)

    Article  Google Scholar 

  38. Hills D.A., Barber J.R.: Steady sliding of a circular cylinder over a dissimilar thermally conducting half-plane. Int. J. Mech. Sci. 28, 613–622 (1986)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  40. 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 

  41. 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 

  42. Afferrante L., Ciavarella M.: Separated steady state solutions for two thermoelastic half-planes in contact with out-of-plane sliding. J. Mech. Phys. Solids 53, 1449–1475 (2005)

    Article  MATH  Google Scholar 

  43. 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, 1673–1692 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  44. Jaffar M.J.: Frictionless contact between an elastic layer on a rigid base and a circular flat-ended punch with rounded edge or a conical punch with rounded tip. Int. J. Mech. Sci. 44, 545–560 (2002)

    Article  MATH  Google Scholar 

  45. Choi H.J.: On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch. J. Mech. Sci. Technol. 23, 2703–2713 (2009)

    Article  Google Scholar 

  46. Li H., Dempsey J.P.: Axisymmetric contact of an elastic layer underlain by rigid base. Int. J. Numer. Methods Eng. 29, 57–72 (1990)

    Article  MATH  Google Scholar 

  47. Alblas J.B., Kuipers M.: The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer— I. General considerations and thick layer asymptotics. Int. J. Solids Struct. 7, 99–109 (1971)

    Article  MATH  Google Scholar 

  48. Zhou Y.T., Lee K.Y.: Thermo-electro-mechanical contact behavior of a finite piezoelectric layer under a sliding punch with frictional heat generation. J. Mech. Phys. Solids 59, 1037–1061 (2011)

    Article  MathSciNet  Google Scholar 

  49. Nowacki, W.: Thermoelasticity. Pergamon Press Ltd. 566 (1986)

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

    MATH  Google Scholar 

  51. Wang J.H., Chen C.Q., Lu T.J.: Indentation responses of piezoelectric films. J. Mech. Phys. Solids 56, 3331–3351 (2008)

    Article  MATH  Google Scholar 

  52. Joachim-Ajao D., Barber J.R.: Effect of material properties in certain thermoelastic contact problems. J. Appl. Mech. Trans. ASME 65, 889–893 (1998)

    Article  Google Scholar 

  53. Muskhelishvili N.L.: Singular Integral Equations. P. Noordhoff, Groningen (1953)

    MATH  Google Scholar 

  54. Krenk S.: Quadrature formulas for singular integral equations of 1st and 2nd kind. Q. Appl. Math. 33, 225–232 (1975)

    MathSciNet  MATH  Google Scholar 

  55. Barber J., Comninou M.: Thermoelastic contact problems. Thermal Stress. 3, 1–106 (1989)

    Google Scholar 

  56. Davis P.J., Rabinowitz P.: Methods of Numerical Integration. Academic Press, New York (1975)

    MATH  Google Scholar 

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

    Article  Google Scholar 

  58. Shi, Z.: Mechanical and thermal contact analysis in layered elastic solids. Ph.D. Dissertation. University of Minnesota, vol. Ph.D. Dissertation (2001)

Download references

Author information

Authors and Affiliations

  1. LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Peijian Chen, Shaohua Chen & Zhilong Peng

Authors
  1. Peijian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shaohua Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhilong Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaohua Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, P., Chen, S. & Peng, Z. Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer. Acta Mech 223, 2647–2665 (2012). https://doi.org/10.1007/s00707-012-0732-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0732-y

Keywords

Search

Navigation