  The paper uses the spring potential to present interaction between the
coarse-grained interfacial particles of the $\alpha$-Al2O3/$\alpha$-Al2O3 and
$\alpha$-Fe2O3/$\alpha$-Fe2O3 contacts in the sliding friction study of these
micron-scale oxides by smoothed particle hydrodynamics simulations. The spring
constants of the potential for the particle systems are converted from those of
the atomic oxide systems that are yielded by the second order polynomial fits
of the probed surface potentials in molecular dynamics simulations, and are
dependent on the particle coarse-graining. It is founded that at micron-scale
the friction properties of the oxides are almost independent of the
coarse-graining and are the same in the different sliding directions. Even the
hardness contacts friction coefficient shows a decrease with increasing
intensity of normal component of the interfacial interaction, originating from
stability of friction force and growth of normal force. This result is as an
implementation for the previous observations of sliding friction of various
materials that showed that a drop of friction coefficient with increasing
externally applied normal load has originated from deformation of interfaces or
occurrence of debris at contact, indicating an unsteady contact.
