Heterogeneity of material structure determines the stationary surface topography and friction

The character of surface roughness and the force of friction in the stationary state after a sufficiently long run-in process are of key importance for numerous applications, e.g. for friction between road and tire. In the present paper, we study theoretically and experimentally the asymptotic worn state of a bi-phasic material that is arbitrarily heterogeneous in the contact plane, but homogeneous in the direction of the surface normal. Under the assumption of Archard's wear law in its local formulation, the asymptotic shape is found in the closed integral form. Given the surface profile, the coefficient of friction can be estimated, since the coefficient of friction is known to be strongly correlated with the mean square root value of the surface slope. The limiting surface profiles and the corresponding coefficient of friction are determined as functions of size, relative concentration and wear ratio of the phases. The results of numerical calculations are compared to and validated by experiments carried out on simplified model systems. The main conclusion is that the rms value of the surface slope is not influenced by the characteristic linear size of inclusions and depends solely on the relative concentration of phases, as well as the ratio of their wear coefficients.