Role of fractal geometry in roughness characterization and contact mechanics of surfaces

Journal of Tribology

Volumn 112, Issue 2, 1990, Pages 205-216

  Majumdar, A ^a   Bhushan, B ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MECHANICS;

CONTACT MECHANICS; ELASTIC CONTACT THEORY; FRACTAL GEOMETRY; WEIERSTRASS-MANDELBROT FUNCTION;

SURFACES;

EID: 0025414841     PISSN: 07424787     EISSN: 15288897     Source Type: Journal    
DOI: 10.1115/1.2920243     Document Type: Article

References (40)

1. Berry, M. V., and Lewis, Z. V., 1980, “On the Weierstrass-Mandelbrot Fractal Function,” Proceedings of the Royal Society of London, Vol. A 370, pp. 459-484.
2. Bhushan, B., 1984a, “Prediction of Surface Parameters in Magnetic Media,” Wear, Vol. 95, pp. 19-27.
3. Bhushan, B., 1984b, “Analysis of the Real Area of Contact between a Polymeric Magnetic Medium and a Rigid Surface,” ASME Journal of Tribology, Vol. 106, pp. 26-34.
4. Bhushan, B., 1985, “The Real Area of Contact in Polymeric Magnetic Media-II: Experimental Data Analysis,” ASLE Transactions, Vol. 28, pp. 181-197.
5. Bhushan, B., Wyant, J. C., and Meiling, J., 1988, “A New Three-Dimensional Non-Contact Digital Optical Profiler,” Wear, Vol. 122, pp. 301-312.
6. Bhushan, B., 1989a, Tribology and Mechanics of Magnetic Storage Devices, Springer-Verlag, New York.
7. Bhushan, B., and Dugger, M. T., 1989b, “Real Contact Area Measurements on Magnetic Rigid Disks,” submitted for publication to Wear.
8. Bhushan, B., and Doerner, M. F., 1989c, “Role of Mechanical Properties and Surface Texture in the Real Area of Contact of Magnetic Rigid Disks,” Journal of Tribology, in press.
9. Brown, S. R., and Scholz, C. H., 1985, “Closure, of Random Elastic Surfaces in Contact,” Journal of Geophysical Research, Vol. 90, No. B7, pp. 5531-5545.
10. Feder, J., 1988, Fractals, Plenum Press, New York.
11. Gupta, P. K., and Cook, N.H., 1972, “Junction Deformation Modes for Asperities in Sliding Interactions,” Wear, Vol. 20, pp. 73-87.
12. Greenwood, J. A., and WIIIiamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proceedings of the Royal Society of London, Vol. A 295, pp. 300-319.
13. Korcak, J., 1938, “Deux types fondamentaux de distribution statistique,” Bulletin de I’lnstitut International de Statistique, III, pp. 295-299.
14. Ling, F. F., 1987, “Scaling Law for Contoured Length of Engineering Surfaces,” Journal of Applied Physics, Vol. 62, pp. 2570-2572.
15. Ling, F. F., 1988, “The Possible Role of Fractal Geometry in Tribology,” presented at the STLE-ASME Tribology Conference, to appear in Tribology Transactions, Vol. 32, 1989.
16. Majumdar, A., 1989a, “Fractal Surfaces and their Applications to Surface Phenomena,” Ph.D. thesis, Department of Mechanical Engineering, University of California, Berkeley.
17. Majumdar, A., and Tien, C. L., 1989b, “Fractal Characterization and Simulation of Rough Surfaces,” submitted for publication to Wear.
18. Majumdar, A., and Tien, C. L., 1989c, “Fractal Network Model for Contact Conductance,” to be presented at the ASME/AIChE 26th National Heat Transfer Conference, Philadelphia, Aug. 6-9.
19. Mandelbrot, B. B., 1967, “How Long is the Coast of Britain? Statistical SelfSimilarity and Fractional Dimension,” Science, Vol. 155, pp. 636-638.
20. Mandelbrot, B. B., and van Ness, J. W., 1968, “Fractional Brownian Motions, Fractional Noises and Applications,” SIAM Review, Vol. 10, pp. 422-437.
21. Mandelbrot, B. B., 1975, “Stochastic Models for the Earth’s Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands,” Proceedings of the National Academy of Science, USA, Vol. 72, pp. 3825-3828.
22. Mandelbrot, B. B., 1982, The Fractal Geometry of Nature, W. H. Freeman, New York.
23. Mandelbrot, B. B., Passoja, D. E., and Paullay, A. J., 1984, “Fractal Character of Fracture Surfaces of Metals,” Nature, Vol. 308, pp. 1571-1572.
24. Mandelbrot, B. B., 1985, “Self-Affine Fractals and Fractal Dimension,” Physiea Scripta, Vol. 32, pp. 257-260.
25. McCool, J. I., 1986, “Comparison of Models for the Contact of Rough Surfaces,” Wear, Vol. 107, pp. 37-60.
26. McCool, J. I., 1987, “Relating Profile Instrument Measurements to the Functional Performances of Rough Surfaces,” ASME Journal of Tribology, Vol. 109, pp. 264-270.
27. Meakin, P., 1987, “Fractal Scaling in Thin Film Condensation and Material Surfaces,” CRC Critical Reviews in Solid State and Materials Science, Vol. 13, pp. 143-189.
28. Nayak, P. R., 1971, “Random Process Model of Rough Surfaces,” ASME Journal of Lubrication Technology, Vol. 93, pp. 398-407.
29. Nayak, P. R., 1973a, “Random Process Model of Rough Surfaces in Plastic Contact,” Wear, Vol. 26, pp. 305-333.
30. Nayak, P. R., 1973b, “Some Aspects of Surface Roughness Measurements,” Wear, Vol. 26, pp. 165-174.
31. Peitgen, H. O., and Saupe, D., 1988, The Science of Fractal Images, Springer-Verlag, New York.
32. Sayles, R. S., and Thomas, T. R., 1978, “Surface Topography as a Nonsta-tionary Random Process,” Nature, Vol. 271, pp. 431-434.
33. Termonia, Y., and Meakin, P., 1986, “Formation of Fractal Cracks in a Kinetic Fracture Model,” Nature, Vol. 320, pp. 429-431.
34. Thomas, T. R., 1982a, “Defining the Microtopography of Surfaces in Thermal Contact,” Wear, Vol. 79, pp. 73-82.
35. Thomas, T. R., 1982b, Rough Surfaces, Longman Inc., New York.
36. Vicsec, T., 1986, “Formation of Solidification Patterns in Aggregation Models,” in Fractals in Physics, eds. L. Pietronero and E. Tossati, pp. 247-250.
37. Voss, R. F., 1985, “Random Fractal Forgeries,” in Fundamental Algorithms for Computer Graphics, ed. R. A. Earnshaw, pp. 805-835.
38. Whitehouse, D. J., and PhIIIips, M. J., 1978, “Discrete Properties of Random Surfaces,” Philosophical Transactions of Royal Society of London, Vol. A 290, pp. 267-298.
39. Wyant, J. C., Koliopoulos, C. L., Bhushan, B., and Basila, D., 1986, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” ASME Journal of Tribology, Vol. 108, pp. 1-8.
40. Yovanovich, M. M., 1987, “Theory and Applications of Constriction and Spreading Resistance Concepts for Microelectronic Thermal Management,” Keynote Address, Proceedings of the International Symposium on Cooling Technology for Electronic Equipment, Honolulu.