Does Thermal Expansion Occur Uniformly in All Directions?

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Discussion Overview

The discussion centers on whether thermal expansion occurs uniformly in all directions for isotropic and homogeneous materials. Participants explore the implications of material structure on thermal expansion, including specific cases and formulas related to linear, area, and volume expansion.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that thermal expansion should be equal in all three dimensions for normal materials, while others suggest exceptions may exist, such as in shape-memory metals.
  • Concerns are raised about atomic structure potentially affecting isotropy, with one participant questioning whether consistent bond structure is necessary for isotropic behavior.
  • It is noted that different formulas exist for linear, area, and volume expansion, but some argue that they are derived from the same linear expansion formula.
  • Discussion includes the behavior of polycrystalline materials, which may exhibit isotropic thermal expansion properties, while anisotropic crystals are acknowledged to have directionally-dependent thermal expansion coefficients.
  • Participants highlight practical implications, such as the importance of diametric changes in certain applications, like press fits in mechanical components, which may be critical compared to axial changes.
  • One participant corrects another's assumption about isotropy, emphasizing that if atomic structure varies in different directions, the material cannot be considered isotropic.

Areas of Agreement / Disagreement

Participants express differing views on the uniformity of thermal expansion in isotropic materials, with some asserting it should be uniform while others present counterexamples and conditions where this may not hold true. The discussion remains unresolved regarding the implications of atomic structure on isotropy.

Contextual Notes

Participants reference specific formulas and conditions related to thermal expansion, indicating that assumptions about material behavior may depend on context and specific applications. There is also mention of the need to consider the scale of dimensions when discussing thermal expansion effects.

Cyrus
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Q: For thermal expansion, does the expansion/contraction take place along all directions uniformly, assuming the material is isotropic and homogeneous? I've had some problems in materials where a change in temperature causes axial changes in length and a different problem where it was diametric changes in length on a shrink lock. It was the same equation with length replaced by diameter, so I thought this must be true in any direction.
 
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I'm not really qualified to respond, but it seems to me that in any normal material, both expansion and contraction should be equal in all 3 dimensions. The only way that I can think of that being untrue would be in the case of shape-memory metals, but they're specifically designed to react in a particular way.
 
Im just worried that the structure of the atoms is not the same in all directions, which would mean its not true. But perhaps this consistent bond structure is a part of being isotropic.
 
cyrusabdollahi said:
Q: For thermal expansion, does the expansion/contraction take place along all directions uniformly, assuming the material is isotropic and homogeneous?
Yes. All linear dimensions scale in the same way.

zoobyshoe said:
It appears there's a different formula for linear expansion, expansion of area, and expansion of volume:
Sure, but all are derived from the same linear expansion formula.
 
cyrusabdollahi said:
Q: For thermal expansion, does the expansion/contraction take place along all directions uniformly, assuming the material is isotropic and homogeneous? I've had some problems in materials where a change in temperature causes axial changes in length and a different problem where it was diametric changes in length on a shrink lock. It was the same equation with length replaced by diameter, so I thought this must be true in any direction.

As [tex]\alpha=\frac{1}{L_o}\frac{\partial L}{\partial T}[/tex] is relative to the initial length [tex]L_o[/tex], one may neglect length variations for small initial lengths (i.e. initial diameter) compared with another length variations (i.e. axial length of a thin rod).
 
Thermal expansion for polycrystalline materials where the crystal orientation is relatively random have effectively isotropic thermal expansion properties.

General cubic crystalline materials, e.g. scc, fcc, bcc have equal thermal expansion coefficients in the principal directions. Anisotropic crystals, e.g. hcp, fct, bct and more complex crystals would have directionally-dependent thermal expansion coefficients. Poly-crystalline alloys are often fabricated with 'texture', or preferred crystalline orientation, and there thermal expansion coefficients will be directionally dependent.
 
Clausius2 said:
As [tex]\alpha=\frac{1}{L_o}\frac{\partial L}{\partial T}[/tex] is relative to the initial length [tex]L_o[/tex], one may neglect length variations for small initial lengths (i.e. initial diameter) compared with another length variations (i.e. axial length of a thin rod).


Actually, just the opposite is true in materials. Sometimes the axial length is of no concern, and the diametric change is of critical concern.
 
  • #10
cyrusabdollahi said:
Actually, just the opposite is true in materials. Sometimes the axial length is of no concern, and the diametric change is of critical concern.
You got that right. Calculate the press fit of a pin in a hole at an elevated temperature if you HAVE to maintain a press fit. That is majorly important for things like shaft fits with bearings, seals and pressed on components like turbine discs and compressors...
 
  • #11
and my take home mid term, to mention a few. Thats exactly the problem I had in mind. Shrink fit of two tubes, where [tex]\sigma_a =0[/tex].
 
  • #12
cyrusabdollahi said:
Q: For thermal expansion, does the expansion/contraction take place along all directions uniformly, assuming the material is isotropic and homogeneous?

Im just worried that the structure of the atoms is not the same in all directions

You have a contradiction there. If the structure is not the same in all directions, you do not have isotropicity.
 
  • #13
Sorry, I should have put the word *if* in there, good catch.
 

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