Elastic-plastic microcontact analysis of a sphere and a flat plate

The elastic-plastic microcontact model of a sphere in contact with a flat plate is developed in the present study to investigate the effect of surface roughness on the total contact area and contact load. From the study done by the finite element method, the dimensionless asperity contact area, average contact pressure, and contact load in the elastoplastic regime are assumed to be a power form as a function of dimensionless interference (δ/δ _ec). The coefficients and exponents of the power form expressions can be determined by the boundary conditions set at the two ends of the elastoplastic deformation regime. The contact pressures evaluated by the present model are compared with those predicted by the Hertz theory, without considering the surface roughness and the reported model, including the roughness effect, but only manipulating in the elastic regime. The area of non-zero contact pressure is enlarged if the surface roughness is considered in the microcontact behavior. The maximum contact pressure is lowered by the presence of surface roughness if the contact load is fixed. Under a normal load, both the contact pressure and the contact area are elevated by raising the plasticity index for the surface of the same surface roughness.