Instability of Thermoelastic Contact

  • J. R. Barber
Part of the International Centre for Mechanical Sciences book series (CISM, volume 457)


The thermal boundary conditions in thermoelastic contact problems are typically coupled to the mechanical boundary conditions. For static thermoelastic contact, surface roughness effects causes a thermal contact resistance which is dependent on local contact pressure. The effects of this thermomechanical coupling are illustrated in a simple one-dimensional rod model, which exhibits instability if the transmitted heat flux is sufficiently large. The stability problem is analyzed using a linear perturbation method which is then extended to problems in two and three dimensions. An important application concerns the development of non-uniformities in the nominally one-dimensional solidification of a metal in contact with a plane mould.

Related instabilities are obtained when two bodies slide together causing frictional heating that is proportional to the local contact pressure. The stability of idealized geometries such as half-planes and layers can be investigated by analytical methods, but the perturbation problem must be solved numerically for practical geometries, such as those arising in brakes and transmission clutches. Results for such cases are compared with experimental observations of thermal damage under industrial test conditions.


Contact Pressure Critical Speed Heat Conduction Problem Thermal Contact Resistance Migration Speed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, A.E. and Knapp, R.A. (1989). Hot spotting in automotive friction systems, International Conference on Wear of Materials, Vol. 2, 673–680.Google Scholar
  2. Azarkhin, A. and Barber, J.R. (1985). Transient thermoelastic contact problem of two sliding half-planes, Wear 102: 1–13.CrossRefGoogle Scholar
  3. Azarkhin, A. and Barber, J.R. (1986). Thermoelastic instability for the transient contact problem of two sliding half-planes, ASME J. Appl. Mech. 53: 565–572.ADSCrossRefzbMATHGoogle Scholar
  4. Barber, J.R. (1969). Thermoelastic instabilities in the sliding of conforming solids, Proc. Roy.Soc. A312: 381–394.ADSCrossRefGoogle Scholar
  5. Barber, J.R. (1973). Indentation of the semi-infinite elastic solid by a hot sphere, Int.J.Mech.Sci. 15: 813–819.CrossRefGoogle Scholar
  6. Barber, J.R. (1987). Stability of thermoelastic contact, International Conference on Tribology, Institution of Mechanical Engineers, London, 981–986.Google Scholar
  7. Barber, J.R., Beamond, T.W., Waring, J.R. and Pritchard, C. (1985). Implications of thermoelastic instability for the design of brakes, ASME J. Tribology 107: 206–210.CrossRefGoogle Scholar
  8. Barber, J.R., Dundurs, J. and Comninou, M. (1980). Stability considerations in thermoelastic contact, ASME J.Appl.Mech. 47: 871–874.ADSCrossRefzbMATHGoogle Scholar
  9. Barber, J.R. and Hector, L.G. (1999). Thermoelastic contact problems for the layer, ASME J.Appl.Mech. 66: 806–808.ADSCrossRefGoogle Scholar
  10. Barber, J.R. and Zhang, R. (1988). Transient behaviour and stability for the thermoelastic contact of two rods of dissimilar materials, Int. J. Mech. Sci. 30: 691–704.CrossRefzbMATHGoogle Scholar
  11. Berry, G.A. (1976). The Division of Frictional Heat - A Guide to the Nature of Sliding Contact, PhD Dissertation, University of Newcastle upon Tyne.Google Scholar
  12. Borri-Brunetto, M., Carpinteri, A. and Chiaia, B. (1998). Contact, closure and friction behaviour of rough crack concrete surfaces, in Framcos 3, Fracture of Concrete Structures, Mikashi, H. ed., Gifu, Japan, Aedificato Publ., Freiburg.Google Scholar
  13. Burton, R.A. (1973). The role of insulating surface films in frictionally excited thermoelastic instabilities, Wear 24: 189–198.CrossRefGoogle Scholar
  14. Burton, R.A., Nerlikar V. and Kilaparti, S.R. (1973). Thermoelastic instability in a seal-like configuration, Wear 24: 177–188.CrossRefGoogle Scholar
  15. Clausing, A.M. (1963). Thermal Contact Resistance in a Vacuum Environment, Ph.D. Thesis, University of Illinois.Google Scholar
  16. Clausing A.M. and Chao, B.T. (1965). Thermal contact resistance in a vacuum environment, ASME J.Heat Transfer 87: 243–251.CrossRefGoogle Scholar
  17. Comninou, M. and Dundurs, J. (1979). On the Barber boundary conditions for thermoelastic contact, ASME J.Appl.Mech. 46: 849–853.ADSCrossRefzbMATHGoogle Scholar
  18. Cooper, M.G., Mikic B.B. and Yovanovich, M.M. (1969). Thermal contact conductance, Int.J.Heat Mass Transfer 12: 279–300.CrossRefGoogle Scholar
  19. Dow, T.A. and Burton, R.A. (1972). Thermoelastic instability of sliding contact in the absence of wear, Wear 19: 315–328.CrossRefGoogle Scholar
  20. Du, S., Zagrodzki, P., Barber, J.R. and Hulbert, G.M. (1997). Finite element analysis of frictionally-excited thermoelastic instability, J. Thermal Stresses 20: 185–201.CrossRefMathSciNetGoogle Scholar
  21. Duvaut, G. (1979). Free boundary problem connected with thermoelasticity and unilateral contact, Free Boundary Problems, Vol 11, Pavia.Google Scholar
  22. Hector, L.G., Kim, W.S. and Richmond, O. (1996). Freezing range on shell growth instability during alloy solidification, ASME J.Appl.Mech. 63: 594–602.ADSCrossRefzbMATHGoogle Scholar
  23. Ho, K. and Pehlke, R.D. (1985). Metal-mold interfacial heat transfer, Metall. Trans. 16B: 585–594.CrossRefGoogle Scholar
  24. Joachim-Ajao, D. and Barber, J.R. (1998). Effect of material properties in certain thermoelastic contact problems, ASME J.Appl.Mech. 65: 889–893.ADSCrossRefGoogle Scholar
  25. Kennedy, F.E. and Ling, F.F. (1974). A thermal, thermoelastic and wear simulation of a high energy sliding contact problem, ASME J.Lub.Tech. 96: 497–507.CrossRefGoogle Scholar
  26. Lee, K. and Barber, J.R. (1993). Frictionally-excited thermoelastic instability in automotive disk brakes, ASMEJ.Tribology 115: 607–614.CrossRefGoogle Scholar
  27. Lee, K. and Dinwiddie, R.B. (1998). Conditions of frictional contact in disk brakes and their effects on brake judder. SAE 980598.Google Scholar
  28. Li, C. and Barber, J.R. (1997). Stability of thermoelastic contact of two layers of dissimilar materials, J.Thermal Stresses 20: 169–184.CrossRefMathSciNetGoogle Scholar
  29. Parker, R.C. and Marshall, P.R. (1948). The measurement of the temperature of sliding surfaces, with particular reference to railway blocks, Proc.Inst.Mech.Eng. 158: 209–229.CrossRefGoogle Scholar
  30. Richmond, O. and Huang, N.C. (1977). Interface stability during unidirectional solidifcation of a pure metal, Proceedings of the Sixth Canadian Congress of Applied Mechanics, Vancouver, 453–454.Google Scholar
  31. Richmond, O. and Tien, R.H. (1971). Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold, J.Mech.Phys.Solids 19: 273–284.ADSCrossRefGoogle Scholar
  32. Shlykov, Yu.P. and Ganin, Ye.A. (1964). Thermal resistance of metallic contacts, Int.J.Heat Mass Transfer 7: 921–929.CrossRefGoogle Scholar
  33. Srinivasan, M.G. and France, D.M. (1985). Non-uniqueness in steady-state heat transfer in prestressed duplex tubes–Analysis and case history, ASME J.Appl.Mech. 52: 257–262.ADSCrossRefGoogle Scholar
  34. Thomas T.R. and Probert, S.D. (1970). Thermal contact resistance: The directional effect and other problems, Int.J.Heat Mass Transfer 13: 789–807.CrossRefGoogle Scholar
  35. Thorns, E. (1988). Disc brakes for heavy vehicles, Institution of Mechanical Engineers, International Conference on Disc Brakes for Commercial Vehicles, C464 /88, 133–137.Google Scholar
  36. Wray, P.J. (1981). Geometric features of chill-cast structures, Metall. Trans. 12B: 167.CrossRefGoogle Scholar
  37. Yavuz, G. (1995). Instability Problems in Unidirectional Solidification Process, Ph.D. Thesis, University of Michigan.Google Scholar
  38. Yeo, T. and Barber, J.R. (1994). Finite element analysis of thermoelastic contact stability, ASME J.Appl. Mech. 61: 919–922.ADSCrossRefGoogle Scholar
  39. Yeo, T. and Barber, J.R. (1996). Finite element analysis of the stability of static thermoelastic contact, J.Thermal Stresses 19: 169–184.CrossRefGoogle Scholar
  40. Yi, Y-B., Du, S., Barber, J.R. and Fash, J.W. (1999). Effect of geometry on thermoelastic instability in disk brakes and clutches, ASME J.Tribology 121: 661–666.CrossRefGoogle Scholar
  41. Yi, Y-B., Barber, J.R. and Zagrodzki, P. (2000). Eigenvalue solution of thermoelastic instability problems using Fourier reduction, Proc. Roy.Soc. A456: 2799–2821.ADSCrossRefzbMATHGoogle Scholar
  42. Yigit, F. (1998). Effect of mold properties on thermo-elastic instability in unidirectional planar solidification, J.Thermal Stresses 21: 55–81.CrossRefGoogle Scholar
  43. Yigit, F. and Barber, J.R. (1994). Effect of Stefan number on thermoelastic instability in unidirectional solidification, Int.J.Mech.Sci.. 36: 707–723.zbMATHGoogle Scholar
  44. Yu, C.C. and Heinrich, J.C. (1987). Petrov-Galerkin method for multidimensional time-dependent convective diffusion equations, Int.J.Numer.Meth.Engng. 24: 2201–2215.CrossRefzbMATHGoogle Scholar
  45. Zagrodzki, P. (1990). Analysis of thermomechanical phenomena in multidisc clutches and brakes, Wear 140: 291–308.CrossRefGoogle Scholar
  46. Zagrodzki, P., Lam, K.B., Al-Bahkali, E. and Barber, J.R. (1999). Simulation of a sliding system with frictionally-excited thermoelastic instability, Thermal Stresses ‘89, Cracow, Poland.Google Scholar
  47. Zhang, R. and Barber, J.R. (1993). Transient thermo-elastic contact and stability of two thin-walled cylinders, J.Thermal Stresses 16: 31–54.ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • J. R. Barber
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

Personalised recommendations