The cross sections formed by the contact asperities of two rough surfaces at an interference are island-shaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, 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 (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N).

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