# Thermal Expansion directions

1. Jan 6, 2006

### 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.

2. Jan 6, 2006

### 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.

3. Jan 7, 2006

### 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.

4. Jan 7, 2006

5. Jan 7, 2006

### Staff: Mentor

Yes. All linear dimensions scale in the same way.

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

6. Jan 7, 2006

### Clausius2

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).

7. Jan 7, 2006

8. Jan 7, 2006

### Astronuc

Staff Emeritus
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.

9. Jan 11, 2006

### Cyrus

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. Jan 11, 2006

### FredGarvin

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. Jan 11, 2006

### 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 $$\sigma_a =0$$.

12. Jan 12, 2006

### Gokul43201

Staff Emeritus
You have a contradiction there. If the structure is not the same in all directions, you do not have isotropicity.

13. Jan 12, 2006

### Cyrus

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