brinell number

ok so it does express hardness in a way... so is it proportional to tensile strength , modulus of elasticity and ductility ???

you should really read the artilcle your answers are in there.

Just in case you are still wondering, no it is not proportional to any of those things all the time. In general, harder things are usually stronger, but that is not always the case. For example, by weight, live wood is one of the strongest substances known to man, but it's not hard at all.

but as the brinel number increases so does the tensile strength
http://www.unified-eng.com/scitech/hardness/hardness.html

did i miss something ?

If you read it carefully, you'll see that it's an approximation based on experimental data. Not all the data fits the function well, but most of it is close.
The most important thing to note is where it says "The conversions are intended for carbon and alloy steels in the annealed, normalized, and quenched-and-tempered conditions."
So in that very specific case, they are somewhat proportional.
I would expect that if you took several types of maple wood and did the same thing, you would find that they are also proportional, but not at all related to the formula for the steel.
So if you restrict yourself to a very limited, specific subset of materials, they may be proportional, but overall they are not.

Hi Tommy ,
thanks for the input... I just have to make a choice between directly proportional and inversely proportional.... so between the two i would choose " directly proportional "...At least they are  for sure NOT inversely proportional , right ?

I would agree with that. In general.

ok , thanks much Tommy for all your help tonight !!