Hardness measurements are indications to tensile strength, e.g. Brinell hardness, HB, is used as a measure of strength. For steel the yield strength, YS, is YS~0.3HB and the ultimate tensile strength , UTS is UTS~0.35 HB. For details see the book of David Tabor
The Hardness of Metals, Clarendon Press, Oxford (1951), Oxford Classics Series 2000.
For short details you can see also at
http://en.wikipedia.org/wiki/Brinell_scale
As the Vickers Hardness, Hv is proportional to HB, similar relation might hold in that case too. For example see papers of Brian Lawns, e.g. the one in
J. Amer. Ceram. Soc., 79[10] 2609-18 (1996)
And finally there might be a relation between 4 point bending, MOR, and fracture strength, Sf, say MOR~0.4-0.6Sf, then you can roughly estimate what the tensile strength will be. For example in some cases MOR~0.7 Sf see this article: