Youngs Modulus in case of thermal expansion

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Discussion Overview

The discussion revolves around the implications of thermal expansion on Young's modulus (E) and its relationship with stress and strain. Participants explore the conditions under which E can be defined, particularly in scenarios of free thermal expansion versus constrained conditions.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant asserts that in the case of free thermal expansion, the stresses are zero, leading to the conclusion that Young's modulus E would also be zero, which raises questions about its definition as a material property.
  • Another participant clarifies that Young's modulus is defined as stress divided by elastic strain, and that thermal expansion introduces thermal strain, which complicates the relationship.
  • A later reply emphasizes that if the body is fixed and heated, the total strain is zero, and thus elastic and thermal strains are equal and opposite, resulting in stress being defined as E times the elastic strain.
  • One participant reiterates the concern that if stresses are zero in free expansion, then E would also be zero, which contradicts its nature as a material property.
  • Another participant notes that the equation for Young's modulus assumes constant temperature, suggesting that temperature changes must be considered in the analysis of strain and stress.

Areas of Agreement / Disagreement

Participants express disagreement regarding the implications of free thermal expansion on Young's modulus, with some arguing that E must be zero under certain conditions while others challenge this notion by emphasizing the role of different types of strain.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about temperature constancy and the definitions of strain types, which are not fully resolved.

raja24
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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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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)
 
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
 
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.
 

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