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question4

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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

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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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- #2

erobz

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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.question4 said:

Δd=-v*ε_x*d, where d is the length of the diameter or Δd= α*ΔΤ*d ?

Thanks in advance.

Last edited:

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question4

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So in order to find the change of the diameter is it enough to say that : Δd= α*ΔΤ*d ?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.

Uniformlyheating (changing the temp) a free rod is stress free.

- #4

erobz

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Well, I believe that formula is for ##\frac{\delta }{L} \ll 1##, but basically...yes.question4 said:So in order to find the change of the diameter is it enough to say that : Δd= α*ΔΤ*d ?

- #5

Lnewqban

Homework Helper

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Welcome, @question4 !

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.

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.

Last edited:

- #6

FEAnalyst

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This video can be helpful:

Poisson's ratio is a measure of the deformation behavior of a material when it is subjected to loading. It is defined as the negative ratio of transverse strain to axial strain. Essentially, it describes how much a material will expand or contract in directions perpendicular to the direction of loading.

No, Poisson's ratio is inherently a property that describes the material's response to stress. Without any applied loadings, there are no strains to measure, and thus Poisson's ratio does not have a practical application in this context.

Poisson's ratio itself cannot predict material behavior in the absence of loading because it is specifically a measure of the relationship between strains under stress. However, it is a fundamental material property that helps in understanding how a material will behave when loads are applied.

In theoretical studies, Poisson's ratio is relevant as a fundamental material property. It can be used in simulations and models to predict how materials will behave under various loading conditions, but it does not describe the state of the material when it is unloaded.

Poisson's ratio cannot be determined without applying loadings. It is measured by applying a known stress to a material, observing the resulting strains in both the axial and transverse directions, and then calculating the ratio of these strains.

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