Tensile Strength

In ferrous materials mild carbon steel of <0.25% carbon does not exhibit any significant change in the tensile strength whereas materials of higher carbon content exhibit increased tensile strength by heating & quenching. The metallurgical change of grain structure from Austenite region results in ferritic and pearlitic structure (with alternate stripes of Ferrite and Cementite) in slow cooling but results in martensitic structure during quenching. Here carbon atoms are trapped while migrating to a stable structure which causes the increase in tensile strength. Increase in tensile strength causes proportionate increase in hardness value.

The effect is akin to when a bundle of bamboo sticks are kept arranged in an orderly stack it is easy to pull out one of them, while it is much more difficult to pull out one from a bundle that is randomly laid bunched together interlocked in all directions.

It is basics of metallurgy and heattreatment. I would rather that you go through some good physical metallurgy books. The theory will be quite elaborate and would start from the lattice to grain structure phase diagrams....

On most materials, tensile strength and hardness go parallel: If you make some heat treatment (or mechanical such us cold forming) use to modify both in the same direction, both increase or decrease, but If you are not quite expert on the matter, I would recommend you to select a standardized treatment and do not play with that as some other important properties are also involved (i.e toughness).

Kind regards