Does Poisson's ratio apply when we have no loadings?

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Discussion Overview

The discussion centers around the applicability of Poisson's ratio in scenarios where no external loadings are applied, specifically in the context of a free rod subjected to temperature changes. Participants explore the relationship between thermal expansion and Poisson's ratio, questioning how to calculate changes in diameter under these conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether Poisson's ratio applies when there are no loadings, specifically in the case of a free rod being heated.
  • Another participant asserts that Poisson's ratio is stress-related and that uniformly heating a free rod does not involve stress.
  • A participant suggests using the formula Δd = α*ΔΤ*d to find the change in diameter due to temperature change.
  • There is a mention that the formula for linear expansion is valid under the condition that the strain is small (##\frac{\delta }{L} \ll 1##).
  • Another participant discusses the practical implications of linear expansion in metals and its importance in applications like bearings, emphasizing the use of coefficients of linear and volumetric expansion.
  • Reference is made to the potential changes in Poisson's ratio under high loads and temperatures, indicating that experimental determination may vary based on conditions.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Poisson's ratio without loadings, and while some agree on the use of thermal expansion formulas, there is no consensus on the broader implications of Poisson's ratio in this context.

Contextual Notes

Participants highlight the need for conditions such as small strain for certain formulas to apply, and there are references to specific contexts where Poisson's ratio may change based on external factors like temperature and mechanical loads.

Who May Find This Useful

This discussion may be of interest to those studying thermal expansion, material science, and the effects of temperature on material properties, particularly in engineering applications.

question4
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Does Poisson's ratio apply when we have no loadings ? For instance if we have a free rod and we increase its temperature, in order to find the change of its diameter should i say :
Δd=-v*ε_x*d, where d is the length of the diameter or Δd= α*ΔΤ*d ?
Thanks in advance.
 
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question4 said:
Does Poisson's ratio apply when we have no loadings ? For instance if we have a free rod and we increase its temperature, in order to find the change of its diameter should i say :
Δd=-v*ε_x*d, where d is the length of the diameter or Δd= α*ΔΤ*d ?
Thanks in advance.
Poisson's Ratio is stress related. If you apply a stress in a given direction causing a strain, it quantifies what happens in lateral directions in terms of expansion/contraction for a given material.

Uniformly heating (i.e. changing the temp of) a free rod is stress free.
 
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erobz said:
Poisson's Ratio is stress related. If you apply a stress in a given direction causing a strain, it quantifies what happens in lateral directions in terms of expansion/contraction for a given material.

Uniformly heating (changing the temp) a free rod is stress free.
So in order to find the change of the diameter is it enough to say that : Δd= α*ΔΤ*d ?
 
question4 said:
So in order to find the change of the diameter is it enough to say that : Δd= α*ΔΤ*d ?
Well, I believe that formula is for ##\frac{\delta }{L} \ll 1##, but basically...yes.
 
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Welcome, @question4 ! :cool:

In practice, the linear expansion of metals is the most calculated due to its negative consequences.
Diameters of solid metal bars also grow with temperature, but that is mainly important for rings that slide tightly into cavities (like a bearing in its housing).

The diametral expansion of those rings are calculated like an unfolded section of metal expanding linearly; therefore, a coefficient of linear expansion is mostly used.

For fluids, a coefficient of volumetric expansion is used instead.

Please, see:
https://pressbooks.bccampus.ca/collegephysics/chapter/thermal-expansion-of-solids-and-liquids/

https://www.engineeringtoolbox.com/volumetric-temperature-expansion-d_315.html

https://www.engineeringtoolbox.com/thin-circular-ring-radius-temperature-change-d_1612.html

https://www.engineeringtoolbox.com/linear-thermal-expansion-d_1379.html

Now, when combining mechanical loads and high temperatures:

Copied from
https://en.wikipedia.org/wiki/Poisson's_ratio

"Most steels and rigid polymers when used within their design limits (before yield) exhibit values of about 0.3, increasing to 0.5 for post-yield deformation which occurs largely at constant volume."

The forging process shown in this video seem to demonstrate that any ratio (determined experimentally for metal in normal conditions) would change depending on sufficiently high applied loads and/or temperatures to the molecular bonds.

 
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