Youngs Modulus in case of thermal expansion

In summary, the conversation discusses the relationship between Young's modulus and stress/strain in materials. It is mentioned that in cases of free body thermal expansion, there are no stresses in the body and only strains. This leads to the question of what the value of Young's modulus would be in this situation, as it cannot be zero. It is explained that in free expansion, the total strain includes both elastic and thermal strain, and the stress is still present but may be referred to as "thermal stress." Therefore, Young's modulus cannot be zero in this case.
  • #1
raja24
2
0
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?
 
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  • #2
raja24 said:
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)
 
  • #3
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
 
  • #4
raja24 said:
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 [itex]\epsilon=\sigma/E+\alpha\Delta T[/itex].

*Along with uniaxial elastic loading and negligible lateral stresses.
 

Related to Youngs Modulus in case of thermal expansion

1. What is Young's Modulus in case of thermal expansion?

Young's Modulus, also known as the elastic modulus, is a measure of a material's stiffness or resistance to deformation. It is defined as the ratio of stress to strain, and in the case of thermal expansion, it refers to the change in length or volume of a material due to changes in temperature.

2. How does temperature affect Young's Modulus?

As temperature increases, the atoms or molecules in a material vibrate more, causing the material to expand. This expansion leads to an increase in strain, which in turn decreases Young's Modulus. Therefore, as temperature increases, Young's Modulus decreases.

3. Is Young's Modulus the same for all materials?

No, Young's Modulus varies among different materials. It is dependent on the type of material, its structure, and its temperature. For example, metals have a higher Young's Modulus than rubber, which is why metals are more resistant to deformation under stress.

4. Can Young's Modulus be negative in case of thermal expansion?

Yes, Young's Modulus can be negative in the case of thermal expansion. This occurs when a material contracts, rather than expands, due to an increase in temperature. Negative Young's Modulus values are typically seen in materials with a high coefficient of thermal expansion, such as certain metals.

5. How is Young's Modulus used in engineering and materials science?

Young's Modulus is a crucial factor in designing and selecting materials for various applications. It helps engineers determine the amount of force a material can withstand before deforming permanently. It is also used to predict how a material will behave under different temperatures and stresses, making it a valuable tool in materials science research.

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