Skip to main content
SpringerLink
Log in

A Thermodynamic Approach for Prediction of Wear Coefficient Under Unlubricated Sliding Condition

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

During a sliding process, the surface asperities tend to undergo fatigue fracture, break off, and form wear debris. This article applies the principles of continuum damage mechanics (CDM) to predict the appropriate adhesive wear coefficient. Using the CDM approach, we predict the number of cycles before crack nucleation sets in, evaluate the probability that an asperity forms a wear particle, and use this information to derive an expression for the wear coefficient. Experimental wear coefficient results for Aluminum 6061 sliding against stainless steel support the validity of the analytical expression for wear coefficient. A series of results are presented for the variation of wear coefficient as a function of friction coefficient for SAE 4340, Aluminum 6061, Aluminum 2024, and Titanium 6ALV4.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

A :

Area of an asperity involved (m2)

A r :

Real area of contact (m2)

dA :

Elementary area (m2)

D :

Damage variable

D i :

Damage after i cycles

D c :

Critical damage value

E :

Modulus of elasticity of an undamaged material (GPa)

E′:

Effective modulus of elasticity (GPa)

H :

Cyclic hardening modulus (MPa)

k :

Wear coefficient

k w :

Stress-raising effects factor

L :

Normal force (N)

M :

Cyclic hardening exponent

n :

Number of asperities

n :

Normal to an elemental cross section

N :

Number of cycles to failure

P :

Probability of wear particle formation

p :

Material flow pressure (MPa)

S :

Total distance of sliding (m)

S e :

Endurance limit (MPa)

T i :

Boundary traction (MPa)

V :

Wear volume (m3)

∆ε oi :

Threshold strain of damage increment in cycle i

∆εpli :

Initial plastic strain in ith cycle

∆εpmi :

Final plastic strain in ith cycle

∆εpoi :

Threshold plastic strain of damage increment in cycle i

∂R 1 :

Part of system boundary on which traction is applied

ε :

Strain

μ :

Friction coefficient

σ :

Stress (MPa)

σ′ :

Effective stress (MPa)

σ f :

True failure stress (MPa)

σ ∞ :

Far-field stress (MPa)

σ max :

Maximum normal stress (MPa)

τ :

Shear stress (MPa)

ψ D :

Partial derivative of Helmholtz free energy with respect to D (MPa)

References

  1. Rabinowicz, E.: Friction and Wear of Materials. Wiley, New York, NY (1995)

    Google Scholar 

  2. Bayer, R.G., Engel, P.A., Sirico, S.L.: Impact wear testing machine. Wear 19, 343–354 (1972)

    Article  Google Scholar 

  3. Halling, J.: Principles of Tribology. Macmillan, London, UK (1975)

    Google Scholar 

  4. Suh, N.P.: Tribophysics. Prentice Hall, Englewood Cliffs, NJ (1986)

    Google Scholar 

  5. Kragelskii, I.V.: Friction and Wear. Butterworths, London, UK (1965)

    Google Scholar 

  6. Rozeanu, L.: Fatigue wear as a rate process. Wear 6, 337–340 (1963)

    Article  Google Scholar 

  7. Kimura, Y.: The role of fatigue in sliding wear. In: Rigney, D.A. (ed.) Fundamentals of Friction and Wear of Materials, pp. 187–219. ASM Materials Science Seminar, Metal Parks, OH (1981)

    Google Scholar 

  8. Arnell, R.D., Davies, P.B., Halling, J., Whomes, T.L.: Tribology: Principles and Design Applications, 1st edn, pp. 11–17. Macmillan, Pittsburgh, PA (1991)

    Google Scholar 

  9. Suh, N.P., Saka, N., Jahanmir, S.: Implications of the delamination theory on wear minimization. Wear 44, 127–134 (1977)

    Article  CAS  Google Scholar 

  10. Soda, N., Kimura, Y., Tanaka, A.: Wear of some F.C.C. metals during unlubricated sliding—part IV. Wear 43, 165–174 (1977)

    Article  CAS  Google Scholar 

  11. Challen, J.M., Oxley, P.L.B., Hockenhull, B.S.: Prediction of Archard’s wear coefficient for metallic sliding friction assuming a low-cycle fatigue mechanism. Wear 111, 275–288 (1983)

    Article  Google Scholar 

  12. Halling, J.: A contribution to the theory of friction and wear and the relationship between them. Proc. Inst. Mech. Eng. 34, 291–299 (1975)

    Google Scholar 

  13. Yamada, K., Takeda, N., Kagami, J., Naoi, T.: Analysis of the mechanism of steady wear by the fatigue theory as a stochastic process. Wear 54, 217–233 (1979)

    Article  Google Scholar 

  14. Finkin, E.F.: An explanation of the wear of metals. Wear 47, 107–117 (1978)

    Article  Google Scholar 

  15. Jain, V.K., Bahadur, S.: Development of a wear equation for polymer–metal sliding in terms of the fatigue and topography of the sliding surfaces. Wear 60, 237–248 (1980)

    Article  Google Scholar 

  16. Omar, M.K., Atkins, A.G.: The adhesive-fatigue wear of metals. Wear 107, 279–285 (1986)

    Article  Google Scholar 

  17. Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24, 981–988 (1953)

    Article  ADS  Google Scholar 

  18. Archard, J.F., Hirst, W.: The wear of metals under unlubricated conditions. Proc. R. Soc. Lond. Ser. A A236, 397–410 (1956)

    ADS  Google Scholar 

  19. Kragelskii, I.V.: Friction and Wear, Calculation Methods. Pergamon Press, London, UK (1982)

    Google Scholar 

  20. Peterson, M.B., Winer, W.O.: Wear Control Handbook. ASME publication, New York, NY (1981)

    Google Scholar 

  21. Fatemi, A., Yang, L.: Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. Int. J. Fatigue 20(1), 9–34 (1998)

    Article  CAS  Google Scholar 

  22. Feinberg, A.A.: Connecting parametric aging to catastrophic failure through thermodynamics. IEEE Trans. Reliab. 45(1), 28–33 (1996)

    Article  MathSciNet  Google Scholar 

  23. Bryant, M.D., Khonsari, M.M., Ling, F.F.: On the thermodynamics of degradation. Proc. R. Soc. A 464, 2001–2014 (2008)

    Article  MATH  CAS  ADS  Google Scholar 

  24. Lamaitre, J.: Continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol. 107(1), 83–89 (1985)

    Article  Google Scholar 

  25. Bhattacharya, B., Ellingwood, B.: A new CDM-based approach to structural deterioration. Int. J. Solids Struct. 36, 1757–1779 (1999)

    Article  MATH  Google Scholar 

  26. Hansen, N.R., Schreyer, H.L.: A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids Struct. 31(3), 359–389 (1994)

    Article  MATH  Google Scholar 

  27. Quraishi, S.M., Khonsari, M.M., Baek, D.K.: A thermodynamic approach for predicting fretting fatigue life. Tribol. Lett. 19(3), 169–175 (2005)

    Article  Google Scholar 

  28. Kachanov, L.M.: On the Creep fracture time. Izv Akad. Nauk USSR Otd. Tekh. 8, 26–31 (1958)

    Google Scholar 

  29. Bhattacharya, B., Ellingwood, B.: Continuum damage mechanics analysis of fatigue crack initiation. Int. J. Fatigue 20(9), 631–639 (1998)

    Article  CAS  Google Scholar 

  30. Bhattacharya, B.: A damage mechanics based approach to structural deterioration and reliability. Ph. D. thesis, John Hopkins University, Baltimore, MD (1997)

  31. Krajcinovic, D.: Continuum damage mechanics. Appl. Mech. Rev. 37(1), 1–6 (1984)

    MathSciNet  Google Scholar 

  32. Simo, J.C., Ju, J.W.: Strain and stress-based continuum damage models: I. Int. J. Solids Struct. 23(7), 821–840 (1987)

    Article  MATH  Google Scholar 

  33. Hult, J.: Introduction and general overview. In: Krajcinovic, D., Lemaitre, J. (eds.) Continuum Damage Mechanics: Theory and Applications, pp. 1–36. Springer, Berlin (1987)

    Google Scholar 

  34. Voyiadjis, G.Z., Kattan, P.I.: Advances in Damage Mechanics: Metals and Metal Matrix Composites, 1st edn. Elsevier, Oxford (1999)

    MATH  Google Scholar 

  35. Lamaitre, J.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin (2005)

    Google Scholar 

  36. Lamaitre, J.: A Course in Damage Mechanics. Springer, New York (1992)

    Google Scholar 

  37. DeVree, J.H.P., Brekelmans, W.A.M., Van Gils, M.A.J.: Comparison of nonlocal approaches in continuum damage mechanics. Comput. Struct. 55(4), 581–588 (1995)

    Article  ADS  Google Scholar 

  38. Chow, C.L., Wei, Y.: A damage mechanics model of fatigue crack initiation in notched plates. Theor. Appl. Fract. Mech. 16, 123–133 (1991)

    Article  Google Scholar 

  39. Rosenfield, A.R.: Wear and fracture mechanics. In: Rigney, D.A. (ed.) Fundamentals of Friction and Wear of Materials, pp. 221–234. ASM Materials Science Seminar, Metal Parks, OH (1981)

    Google Scholar 

  40. Nishioka, K., Hirakawa, K.: Fundamental investigations of fretting fatigue—part 2. Bull. JSME 12(50), 180–187 (1969)

    Google Scholar 

  41. Boller, C., Seeger, T.: Materials Data for Cyclic Loading. Elsevier, Amsterdam, The Netherlands (1987)

    Google Scholar 

  42. Endo, T., Morrow, J.: Cyclic stress–strain and fatigue behavior of representative aircraft metals. J. Mater. (JMLSA) 4(1), 159–175 (1969)

    Google Scholar 

  43. Wong, W.A.: Monotonic and Cyclic Fatigue Properties of Automotive Aluminum Alloys. Kaiser Aluminum & Chemical Corp, Pleasanton, CA (1984)

    Google Scholar 

  44. Baumel Jr., A., Seeger, T.: Materials Data for Cyclic Loading, Supplement 1. Elsevier, Amsterdam (1990)

    Google Scholar 

  45. Amiri, M., Naderi, M., and Khonsari, M. M.: An experimental approach to evaluate the critical damage. Int. J. Damage Mech. doi:10.1177/1056789509343082 (2010)

  46. Ming, Q., Yougzhen, Z., Jun, Z., Jianheng, Y.: Dry friction characteristics of Ti-6Al-4V alloy under high sliding velocity. J. Wuhan Univ. Technol. 22(4), 582–585 (2007)

    Article  Google Scholar 

  47. Niebuhr, D.: Friction and wear behavior of engineering materials in a simulated Martian (CO2) environment, a preliminary study. Wear 263, 88–92 (2007)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Louisiana State University, 2508 Patrick Taylor Hall, Baton Rouge, LA, 70803, USA

    Ali Beheshti & M. M. Khonsari

Authors
  1. Ali Beheshti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Khonsari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Khonsari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beheshti, A., Khonsari, M.M. A Thermodynamic Approach for Prediction of Wear Coefficient Under Unlubricated Sliding Condition. Tribol Lett 38, 347–354 (2010). https://doi.org/10.1007/s11249-010-9614-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-010-9614-4

Keywords

Search

Navigation