Investigación

Ultrasonic determination of real contact area of randomly rough surfaces in elastoplastic contact

A. Baltazar*, J–Y. Kim**, S.I. Rokhlin***

* Instituto Tecnológico de Hermosillo, División de Estudios de Posgrado e Investigación Hermosillo, Sonora, México
Corresponding author.

** Georgia Institute of Technology, George W. Woodruff School of Mechanical Engineering Atlanta, Georgia, U.S.A.

*** The Ohio State University, Laboratory for Multiscale Materials Processing and Characterization, Edison Joining Technology Center Columbus, Ohio, U.S.A.

Recibido el 15 de junio de 2005
Aceptado el 12 de octubre de 2005

Abstract

Micromechanical characterization of interfacial properties of non–conforming rough surfaces in contact was performed by a method based on ultrasonic waves. The method to estimate the interfacial properties is based on ultrasonic spectroscopy of signals reflected from the interface. Ultrasonic results are complemented with probabilistic contact mechanics to model the normal and tangential interfacial stiffness (K_N and K_T) constants for different degrees of closure. The results show that a single set of stiffness constants K_N and K_T is sufficient to describe the dynamic response of the interface independently of the incident angle of the ultrasonic waves. Plastic deformation of the rough interface is studied using the same ultrasonic method. Experimental results indicate that the hysteretic effect observed by repetitive loading cycles is an indication of plastic deformation at the asperity summits with greater height values. The phenomenon is explained using micromechanical and probabilistic models. The results show the possibility of using the method to estimate the interfacial stiffness, presence of plastic deformation, and the real contact area, which in the past have been impossible to measure accurately.

Keywords: Interfacial stiffness; ultrasound; rough surfaces.

Resumen

Caracterizacion micromecánica de propiedades interfaciales de superficies rugosos no–conformantes fue realizado mediante un método basado en ondas ultrasonicas. El método para estimar las propiedades interfaciales hace uso de espectroscopia ultrasónica de señales reflejadas desde la interfase. Resultados de las pruebas con ultrasonidos se complementan con analisis probabilístico y mecanica del contacto para modelar las constantes de rigidez normal y tangencial de (K_N y K_T) para diferentes grados de acercamiento de las superficies. Los resultados muestran que un par unico de constantes de rigidez K_N y K_T son suficientes para describir la respuesta dinamica de la interfase independientemente del angulo de incidencia de la onda ultrasónica. Se estudió la deformación plástica de la interfase rugosa usando el mismo metodo ultrasónico. Los resultados experimentales indican que el efecto histerético observado durante la aplicación de cargas repetitivas es un indicador de la deformacion plástica en las crestas de las asperezas con valores de alturas mayores. El fenómeno se explica usando modelos probabilísticos y micromecanicos. Los resultados muestran la posibilidad de usar el método para estimar el área de contacto real, el cual hasta ahora ha sido imposible de medir.

Descriptores: Rigidez interfacial; ultrasonido superficies rugosas.

PACS: 43.35.+d; 46.55.+d; 81.70.Cv

DESCARGAR ARTÍCULO EN FORMATO PDF

References

1. R.J. Adler and D. Firman, Philos. Trans. R. Soc. London. Ser. A 303 (1981) 433.        [ Links ]

2. M. Aronowich and R.J. Adler, Adv. Appl. Prob. 17 (1985) 280.        [ Links ]

3. J.M. Baik and R.B. Thompson, J. Non–Destruct. Eval. 4 (1984) 177.        [ Links ]

4. A. Baltazar, S.I. Rokhlin, and C. Pecorari, On the Relationship Between Ultrasonic and Micro–structural Properties of Imperfect Interfaces in Layered Solids, in Review of Progress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti, eds. (American Institute of Physics, New York, 1999) Vol. 18B p. 1463.        [ Links ]

5. A.Baltazar, S.I. Rokhlin, and C. Pecorari, J. Mech. Phys. Solids 50 (2002) 1397.        [ Links ]

6. A. Baltazar, L. Wang, B. Xie, and S.I. Rokhlin, The Journal of the Acoustical Society of America 114 (2003) 424.        [ Links ]

7. B. Bhushan, Modern tribology handbook (CRC Press LLC, 2001).        [ Links ]

8. G.N. Boitnott, R.L. Biegel, C.H. Scholz, N. Yoshioka, and W. Wang, J. Geoph. Res. 97 (1992) 8965.        [ Links ]

9. S.R.Brown and C.H. Sholtz, J. Geophys. Res. 90 1985 5531.        [ Links ]

10. A.W. Bush, R.D. Gibson, and G.P Keogh, Mech. Res. Commun. 3 (1976) 169.        [ Links ]

11. W.R. Chang, I. Etsion, and D.B. Bogy, ASME J. Tribol 109 (1987) 257.        [ Links ]

12. C.–M. Cheng and Y.–T. Cheng, Appl. Phys. Lett. 71 (1997) 2623.        [ Links ]

13. S.K. Chilamakuri and B. Bhushan, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol 212 (1998) 19.        [ Links ]

14. B.Drinkwater, R. Dwyer–Joyce, and P. Cawley, J. Acoust. Soc. Am. 101 (1997) 970.        [ Links ]

15. R.S. Dwyer–Joyce, B.W. Drinkwater, and A.M. Quinn, ASME Trans. J. Tribol. 123 (2001) 8.        [ Links ]

16. A.C. Fisher–Cripps, Nanoindentation (Springer, New York, 2002).        [ Links ]

17. R.E. Goodman, "Methods of Geological Engineering" in (Discontinuous Rocks, West Publishing, New York, 1976).        [ Links ]

18. J.A. Greenwood and J. Williamson, Proc. R. Soc., London, Ser. A 295(1966)300.        [ Links ]

19. Haines, N. F., 1980. The theory of sound transmission and reflection at contacting surfaces, CEGB Report RD–B–N4744, Berkeley Nuclear Laboratories.        [ Links ]

20. I.M. Huchings, Tribology; Friction and wear of engineering materials (St. Edmundsbury Press, Cornwell, 1992).        [ Links ]

21. Johnson, K. L., Contact mechanics. Cambridge University Press, Cambridge,1985.        [ Links ]

22. K.L.Johnson, Modelling the indentation hardness of solids. Proceedings of the First Royal Society–Unilevel Indo–Uk Forum in material Science and Engineering, Solid–Solid interactions (Imperial College Press, 1996) p. 16.        [ Links ]

23. K. Kendall and D. Tabor, Proc. Roy. Soc. Lond. A 323 (1971) 321.        [ Links ]

24. J.–Y.Kim, A. Baltazar, and S.I. Rokhlin, J. Mech. Phys. Solids 52 (2000) 1911–1934.        [ Links ]

25. Kogut, and I. Etsion, J. Appl. Mech. 69 (2002) 657.        [ Links ]

26. A.I. Lavrentyev and S.I. Rokhlin, J. Acoust. Soc. Am. 103 (1998) 657.        [ Links ]

27. L.–Y. Li, C.–Y. Wu, and C. Thornton, Proc. Instn. Mech. Engrs. C 216 (2002) 421.        [ Links ]

28. F.J. Margetan, R.B. Thompson, J.H. Rose, and T.A. Gray, J. Non–Destruct. Eval. 11 (1992) 109.        [ Links ]

29. S. Dj. Mesarovic and K.L. Johnson, J. Mech. Phys. Solids 48 (2000) 2009.        [ Links ]

30. Mesarovic, S. Dj., Fleck, N.A., 2000. Frictionless indentation of elastic–plastic solids. Int. J. Solids Struct. 37, 7071–7091.        [ Links ]

31. P.B. Nagy, J. Non–Destruct. Eval. 11 (1992) 127.        [ Links ]

32. P. Nayak, J. Lubr. Tech. 93 (1971) 398.        [ Links ]

33. P.R.Nayak, Wear 25 (1973) 305.        [ Links ]

34. W.C. Oliver and G.M. Pharr, J. Mater. Res. 7 (1992) 1564.        [ Links ]

35. C. Thornton, J. Appl. Mech. 64 (1997) 383.        [ Links ]

36. L. Vu–Quoc and X. Zhang, Proc. R. Soc. (Lond) A 455 (1999) 4013.        [ Links ]

37. M. Webster and R.S. Sayles, Trans. ASME–J. Tribol. 108 (1986) 314.        [ Links ]

38. N. Yoshioka, J. Geophys. Res. B 99 (1994) 15561.        [ Links ]

39. N. Yoshioka and C.H. Scholz, Theory. J. Geophys. Res. 94 (1989) 17681.        [ Links ]

40. D. Zhao, M. Maietta, and L. Chang, J. Tribol. ASME 122 (2000) 86.        [ Links ]