A modified fractal microcontact model developed for asperity heights with variable morphology parameters

Jeng Luen Liou, Jen-Fin Lin

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


The cross-sections formed by the contact asperities of two rough surfaces at an interference are actually island-shaped, rather than having the commonly assumed circular or elliptic contour. These island-shaped contact area contours show fractal behavior with fractal dimension Ds of the two-dimensional profile. The three-dimensional surface fractal dimension for the topography of asperity heights is defined as D and the topothesy is defined as G. In Mandelbrot's study, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformation regimes are derived and the inceptions of the elastoplastic and fully plastic deformation regimes are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). A revised elastic-plastic contact model of a single fractal asperity is also proposed. The revised model shows that a fractal asperity behaves according to classical contact mechanics, but not those predicted by the MB model. The contact parameters, including the total force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing mean separation.

Original languageEnglish
Pages (from-to)133-144
Number of pages12
Issue number1
Publication statusPublished - 2010 Jan 4

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films
  • Materials Chemistry

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