Does Thermal Expansion Occur Uniformly in All Directions?

[Cyrus]

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.

 

[Danger]

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.

 

[Cyrus]

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.

 

[zoobyshoe]

It appears there's a different formula for linear expansion, expansion of area, and expansion of volume:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html

 

[Doc Al]

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.

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.

 

[Clausius2]

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 $$\alpha=\frac{1}{L_o}\frac{\partial L}{\partial T}$$ is relative to the initial length $$L_o$$, 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).

 

[zoobyshoe]

Sure, but all are derived from the same linear expansion formula.

Yeah, I see I'm barking up the wrong tree to think that might have any signifigance here.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp2.html#c1

 

[Astronuc]

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.

 

[Cyrus]

As $$\alpha=\frac{1}{L_o}\frac{\partial L}{\partial T}$$ is relative to the initial length $$L_o$$, 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.

 

[FredGarvin]

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...

 

[Cyrus]

and my take home mid term, to mention a few. Thats exactly the problem I had in mind. Shrink fit of two tubes, where $$\sigma_a =0$$.

 

[Gokul43201]

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.

 

[Cyrus]

Sorry, I should have put the word *if* in there, good catch.