A generalized mechanics theory of idealized rough surfaces under dry and liquid-mediated plastic contact conditions

Abstract

An upper-bound plasticity analysis based on volume conservation and presumed uniform surface rise of noncontact regions was used to develop analytical models of a rigid-perfectly plastic half-space with a flat surface indented by a sinusoidal rigid surface and a rigid-perfectly plastic half-space with a sinusoidal surface compressed by a rigid flat surface. The hydrodynamic effect of lubricant fluid pressurized in the surface grooves of the deformed half-space on the deformation process was analyzed by solving the Reynolds equation of a squeezed film using a perturbation method. Analytical solutions of the fractional contact area, normal approach, average surface rise, cavity volume, and surface roughness were obtained after plastic contact deformation. Numerical results of a finite element analysis of relatively compliant and stiff elastic-nearly perfectly plastic materials are shown to be in good agreement with analytical results. The hypothesis of uniform surface rise of noncontact regions is shown to be a reasonable assumption, leading to a good approximation of global deformation quantities and providing an accurate description of changes in the surface profile for relatively large contact areas. The results of the present study provide a basis for explaining the full plastic merger of asperity contacts in multi-scale rough (fractal) surfaces and elucidate the role of surface roughness in metal-working processes.