Three-dimensional contact analysis of elastic-plastic layered media with fractal surface topographies

Three-dimensional rough surfaces were generated using a modified two-variab le Weierstrass-Mandelbrot function with fractal parameters determined from real surface images. The number and size of truncated asperities were assum ed to follow power-law relations. A finite element model of a rigid sphere in normal contact with a semi-infinite elastic-plastic homogeneous medium w as used to obtain a constitutive relation between the mean contact pressure , real contact area, and corresponding representative strain. The contact m odel was extended to layered media by modifying the constitutive equation o f the homogeneous medium to include the effects of the mechanical propertie s of the layer and substrate materials and the layer thickness. Finite elem ent simulations of an elastic-plastic layered medium indented by a rigid sp here validated the correctness of the modified contact model. Numerical res ults for the contact load and real contact area are presented for real surf ace topographies resembling those of magnetic recording heads and smooth ri gid disks. The model yields insight into the evolution of elastic, elastic- plastic, and fully plastic deformation at the contact interface in terms of the maximum local surface interference. The dependence of the contact load and real contact area on the fractal parameters and the carbon overcoat th ickness is interpreted in light of simulation results obtained for a tri-pa d picoslider in contact with a smooth thin-film hard disk.