Question

AMONG YOUNG BULK AND RIGIDITY MODULUS WHICH IS GREATER WITH REASON

Answer 1

I would go with Youngs modulus, normally has values in GPa, they are interelated. as for the reason why, find the relationship formula

Answer 2

These are measures of different elastic properties and they are the so-called "elastic" moduli. They only work therefore if you are still working in the range where the materials spring back when the stress is removed.

Young's M (E) is a measure of linear elastic behaviour. How much does a linear thing stretch or compress under stress. Build a cable suspension bridge and you will want to know the YM of the steel in the support cables.

Bulk Modulus (K) is a measure of how much a thing compresses under uniform compression - ie in all three dimensions. An example would be how much the hull of a submarine compresses when you take it deep down into the ocean where pressure would squish it. And submarines do shrink quite a lot, BTW.

Rigidity Modulus (G) is about shearing. That is how much displacement takes place when material is stressed across itself by two opposing forces. When you cut a sheet of tin with tin-snips, you are shearing the metal.

You would use these measures for different applications. Interestingly, if you know two of the above, you can work out the third because

E = 2G (1 + PR) = 3K (1 - 2PR) where PR is Poisson's ratio (don't ask!)

PR is less than 0.5 for most materials you need to worry about. FOr steel it is 0.3 or thereabouts

So, crudely!

E = 2.6G = 1.2 K

So for steel E > K > G, and this is the case for most sensible engineering materials.

(BTW, pls treat this with care. It is all a gross simplification.)

Answer 3

BTW the submarine example is an analogy for you. It's to give you the idea of the pressure being in all three dimensions. Calculating the hull stresses in a submarine is a hugely complex set of sums.