Please note that "interlocking asperities" was discarded as a model for
friction a long time ago. The term "asperities" is now used in the sense
of iregularities in a surface, but the general mechanism is a welding
(atomic bonding) between the irregularities in contact. The number of
bonds formed is proportional to the actual area of welding, which in turn
depends on the distribution of asperities over the surfaces, their deformation
under load (area of contact increases as two asperities are forced into
closer contact) and the normal force between the surfaces.
Also note that the surface layers are not the same as the bulk material,
there being oxides and adsorbed atmospheric gases as well as grease, etc.