Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

Tribology International

Volumn 42, Issue 2, 2009, Pages 206-212

  Abuzeid, Osama M ^a   Alabed, Taher A ^b  

^a UNIVERSITY OF JORDAN   (Jordan)

^b PHILADELPHIA UNIVERSITY   (Jordan)

Author keywords

Contact deformation; Fractal; Surface roughness

Indexed keywords

ACTIVATION ENERGY; DEFORMATION; FRACTAL DIMENSION; FRACTALS; MAXWELL EQUATIONS; SURFACE MEASUREMENT; SURFACE RELAXATION; SURFACE ROUGHNESS;

ANALYTICAL SOLUTIONS; ARRHENIUS'S EQUATIONS; BULK TEMPERATURES; CONTACT DEFORMATION; CONTACT OF ROUGH SURFACES; DIFFERENT HEIGHTS; EFFECT OF TEMPERATURES; EXPERIMENTAL VERIFICATIONS; FLAT SURFACES; FRACTAL GEOMETRIES; FRACTAL SURFACES; HALF SPACES; MATHEMATICAL MODELING; MAXWELL MODELS; POWER LAWS; ROUGH SURFACES; ROUGHNESS SIZES; SCALING PARAMETERS; SIMPLE MODELS; STRESS RELAXATION BEHAVIORS; THERMAL RELAXATIONS; VISCOELASTIC MATERIALS; WILLIAMSON MODELS;

SURFACES;

EID: 56249110580     PISSN: 0301679X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.triboint.2008.05.017     Document Type: Article

References (37)

1. Johnson K. Contact mechanics. 1st ed. (1985), Cambridge University Press, London
2. Archard J.F. Elastic deformation and the laws of friction. Proc R Soc London A243 (1957) 190-205
3. Greenwood J., and Williamson J. Contact of nominally flat surfaces. Proceeding of the Royal Society of London Series A (1966), The Royal Society, London, UK 300-319 December 6, 1966
4. Handzel-Powierza Z., Klimczak T., and Polijaniuk A. On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces. Wear 154 (1992) 115-124
5. Wu J. The properties of asperities of real surfaces. J Tribol 123 (2001) 872-883
6. Bakolas V. Numerical generation of arbitrary oriented non-Gaussian three-dimensional rough surfaces. Wear 254 5 (2003) 546-554
7. Warren T., Majumdar A., and Krajcinovic D. A fractal model for the rigid-perfectly plastic contact of rough surfaces. J Appl Mech 63 (1996) 47-54
8. Plesha M.E., and Ni D. Scaling of geological discontinuity normal load-deformation response using fractal geometry. Int J Numer Anal Methods Geomechanics 25 (2001) 741-756
9. Borodich F., and Mosolov A. Fractal roughness in contact problems. J Appl Math Mech 5 56 (1992) 681-690
10. Warren T., and Krajcinovic D. Fractal model of elastic-pefectly plastic contact of rough surfaces based on cantor set. Int J Solids Struct 32 (1995) 2907-2922
11. Abuzeid O. Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: Maxwell type medium. Dirasat 30 1 (2003) 22-36
12. Abuzeid O. A linear thermo-viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: Kelvin-Voigt medium. J Qual Maint Eng 9/2 (2003) 202-216
13. Abuzeid O. A linear viscoelastic creep-contact model for of a flat fractal surface: Kelvin-Voigt medium. J Ind Lubr Tribol 56 6 (2004) 334-340
14. Abuzeid O. A viscoelastic creep model for the contact of rough fractal surfaces: Jeffrey's type material. Proceedings of the seventh international conference on production engineering and design for development (2006), Ain shams University, Cairo, Egypt 636-646 February 7-9, 2006
15. Abuzeid O.M., and Eberhard P. Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: standard linear solid (SLS) material. ASME J Tribol 129 (2007) 461-466
16. Alabed T.A., Abuzeid O.M., and Barghash M. A linear viscoelastic relaxation-contact model of a flat fractal surface: Maxwell type medium. Int J Adv Manuf Technol (2007) 10.1007/s00170-007-1234-2
17. Fernandez J.R., and Sofonea M. Numerical analysis of a frictionless viscoelastic contact problem with normal damped response. Comput Math Appl 47 (2004) 549-568
18. Jackson R.L., and Streator J.L. A multi-scale model for contact between rough surfaces. Wear 261 (2006) 1337-1347
19. Majumdar A., and Bhushan B. Fractal model of elastic-plastic contact between rough surfaces. ASME J Tribol 113 1 (1991) 1-11
20. Lee E., and Radok J. The contact problem for viscoelastic bodies. J Appl Mech 27 (1960) 438-444
21. Ting T. Contact stresses between a rigid indenter and a viscoelastic half-space. J Appl Mech 33 4 (1966) 845-854
22. Nghieh G., Rahnejat H., and Jin Z. Contact mechanics of viscoelastic layered surface. Trans Eng Sci 14 (1997) 59-68
23. Wahl V., Stepnowski S., and Unertl W. Viscoelastic effects in nanometer-scale contacts under shear. Tribol Lett 5 (1998) 103-107
24. Graham G. The contact problem in the linear theory of viscoelasticity when the time dependent contact area has any number of maximum and minimum. Int J Eng Sci 5 (1967) 495-514
25. Ezzat M., El-karamany A., Samaan A., and Zakaria M. The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity with thermal relaxation. J Therm Stresses 26 7 (2003) 671-690
26. Ko S., Lee S., and Hsueh C. Viscoelastic stress relaxation in film/substrate systems-Kelvin model. J Appl Phys 93 5 (2003) 2453-2457
27. Borodich F. Fractals and surface roughness in EHL. In: Snidle R., and Evans H. (Eds). IUTAM symposium on elasto-hydrodynamics and micro-elastohydrodynamics (2006) 397-408
28. Mandelbrot B. The fractal geometry on nature. 3rd ed. (1982), W.H Freeman & Company, New York
29. Shames I., and Cozzarelli F. Elastic and inelastic stress analysis. 1st ed. (1992), Prentice-Hall International Inc., New Jersey
30. Sundberg R. Statistical aspects on fitting the Arrhenius equation. Chemometrics Intelligent Lab Syst 41 (1998) 249-252
31. Hashem A. Study on reloading stress relaxation behavior for high temperature bolted steel. Adv Perform Mater 6 2 (1999) 129-140
32. Martin J.W., and Bentz D.P. Fractal-based description of the roughness of blasted steel panels. J Coat Technol 59 745 (1987) 35-41
33. Nowacki W. Thermoelasticity (1962), Pergamon, London p. 547-574
34. Radchik V., Ben-Nissan B., and Müller W. Theoretical modeling of surface asperity depression into an elastic foundation under static loading. ASME J Tribol 124 (2002) 852-856
35. Zhao Y., and Chang L. A model of asperity interactions in elastic-plastic contact of rough surfaces. ASME J Tribol 123 (2001) 857-864
36. Radok J. Viscoelastic stress analysis. Q Appl Math 15 (1957) 198-202
37. Distefano N.J., and Pister K.S. On the identification problem for thermorheologically simple materials. Acta Mech 13 (1972) 179-190