Surface roughness influences the stiffness behaviour at 'very low' displacements (of the same order as roughness itself) that is near the origin of the force/displacement curve.
roughness is related to the topology state of the surface, however hardness is the resistance to penetration which means the reasistance of the bulk (the whole) matrix to deformation under indentation. I think these two properties are far away from each other. Regards
The question is not well posed. If you mean the intrinsic stiffness of the material (normally, elastic modulus is understood), it is regardless of roughness. However, you might mean the APPARENT stiffness when you compress the material through an ideally planar layer of another material. In the latter case the upper material will immediately interact with less area (surficial "peaks") of the lower one and the measured response ("stiffnes") will get lesser.
Dr. Zisman, thats exactly what I was looking for! Thank you!
However, I still don't know how to calculate these "interaction responses". Can the apparent stiffness (in kPa range) be a couple of magnitudes smaller than the intrinsic stiffness of the material (in GPa range)?
It depends on a specific relief. If your machine is adapted to control very low loads, you will see first a low stiffness (dF/du, ..force / displacement or rel. strain) that will then increase and finally (if the machine is strong enough) reach the "intrinsic" value (slope of F(u) dependence). You may also apply a moderate force to series of sections with various roughness, or successively repolish the sample after each next compression. Of course, there is a risk of plasticity since the deformation is too localized on "peaks", however this apparent effect should be isolated when analyzing loading diagrams.