What is the relationship between hardness and elastic modulus? The higher hardness, the higher elastic modulus?  My understanding is that hardness is a local mechanical property, and 
elastic modulus is an averaged global mechanical property.  Am I right about this? 

This model has a simple closed-form analytical expression, matching with finite element results nearly perfectly.

Ref: G. Feng, S. Qu, Y. Huang and W.D. Nix, An analytical expression for the stress field around an elastoplastic indentation/contact, Acta Materialia, V.55, 2007, P2929-2938. http://dx.doi.org/10.1016/j.actamat.2006.12.030

In the recent issue of Science, researchers from UCLA (Chung et al) report on an ambient pressure synthesis (using arc melting) of a compound, namely, rhenium diboride, which is superhard. Apparently, the material leaves scratch marks on the surface of diamond. Here is the abstract of the paper:

The mechanical properties of materials are ascertained by performing carefully designed laboratory experiments that replicate, as nearly as practical, the service conditions.

Factors to be considered include the nature of the applied load(s), its’ duration and the applicable environmental conditions. It is possible for the load to be tensile, compressive, or shear, and its magnitude may be constant with time, or it may fluctuate continuously. Application time may be for only a fraction of a second, or it may extend over a period of many years. Service temperature can also be an important factor.Mechanical properties are of concern to a variety of parties (e.g., producers and material consumers, research organizations and government agencies) that have differing interests.