An elastoplastic fractal model for cylinder in contact with a smooth plane

Abstract

A mechanical model of which a cylinder-based fractal body in contact with a rigid plat surface presented based on fractal theory. The generalized Weierstrass-Mandelbrot function is employed to derive the formulae of fractal surface asperities formed a smooth cylindrical surface. The existing conditions of which a single asperity is in elastic, elastoplastic or full plastic deformation are derived. When the cylinder-based fractal rough is uniformly divided into N subdivisions, a relation between the N subdivisions and the asperity geometric dimensioning is obtained. A modified size distribution function is adopted to obtain the relation between the dimensionless contact load and the real contact area. The results show: the critical areas of a single asperity are scale dependent. With an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. The mechanical properties of the cylindrical rough surface are related to the range of the asperity frequency indexes. When the first six asperity frequency indexes are less than critical elastic frequency index n ec, the rough surface appears to be elastic property under contact load. When the first six asperity frequency indexes are between the critical elastic frequency index n ec and critical plastic frequency index n pc, the rough surface appears to be elastic property and elastoplastic property, otherwise the rough surface appears to be of inelastic property.