Youngs Modulus in case of thermal expansion

[raja24]

We know that youngs modulus(E) is stress/strain. In case of free body thermal expansion, if the material is allowed to expand and contract freely, than there are no stresses in the body. The body has only strains.

That means the stresses are zero in case of free expansion. So in this case youngs modulus E will also be zero because E=stress/strain. But E cannot be zero since it is a material property...so what will be the value of E when stresses are zero? Does E has a value?

 

[AlephZero]

We know that youngs modulus(E) is stress/strain.

That is not quite right. E = stress / elastic strain. There are other things that can create strain, including thermal expansion.

The change of shape or size of the body (the total strain) = elastic strain + thermal strain + plastic strain + etc.

In your example there is a thermal strain, and the elastic strain = 0.

If you fixed the body so it can not expand, and heat it, the total strain = 0, the elastic strain and thermal strain are equal and opposite, and there will stress = E times the elastic strain. (This is sometimes called the "thermal stress", which may be confusing you)

 

[raja24]

Dear AlephZero, Thanks for the reply...You said that stress=E times strain, this is when the body is fixed.

But if the body has free expansion i.e, its is allowed to expand and contract freely...then there will be no stresses in the body, it has only strains (all kinds). Then in this case according to stress-strain relationship...E=stress/strain...since stresses are zero in free expansion...E=0/strain and E will be zero too...

But this cannot be possible because E cannot be zero since it is a material property...so how is this justified...I hope you got my question

 

[Mapes]

So in this case youngs modulus E will also be zero because E=stress/strain.

The equation you're using assumes constant temperature.* If the temperature can change, then the strain is $\epsilon=\sigma/E+\alpha\Delta T$.

*Along with uniaxial elastic loading and negligible lateral stresses.