Jon Chandler wrote:

> Wrong. 
> 
> Think about it this way.  Start with a sheet of metal.  Cut a disk out 
> of it.  The disk and the plate are the same material and the same 
> coefficient of expansion.  If you heat both pieces, the disk obviously 
> gets larger.....but it's still got to fit in the hole...so the hole must 
> get bigger!

This all assumes that both pieces of material are in their entirety at the 
same temperature so that no elastic deformation occurs. 

The question is what happens if the material that contains the hole is 
elastic -- which means that it can deform -- and the material that's 
farther away from the hole is at the original temperature (i.e. at the 
original size). 

I'm pretty sure that there will occur some elastic deformation, and so far 
nobody seems to have been able to really explain the nature of the elastic 
deformations and their effect on the hole size. 

Imagine a steel or iron cylinder (not cast iron, use more elastic iron), 20 
cm diameter and 20 cm long (increase as necessary to avoid breaking), and a 
hole of 1 cm diameter all the way through it along its axis. Now imagine 
you heat up the inside of the hole. I don't think this is as trivial as 
"all holes in materials with positive expansion coefficients expand when 
the material is heated up". I'm pretty sure there happens some elastic 
deformation of the material around the hole, and I don't think it's 
completely unreasonable for the hole to become smaller under certain 
conditions.

The expanding material has basically three ways of expanding: radially 
towards the outside (that would be the "hole gets bigger" way), axially 
(which may or may not increase the diameter of the hole, but probably not) 
and radially towards the inside. The latter two, and especially the latter, 
require some elastic deformation, whereas the first option requires that 
the material compresses (or breaks). Elastic deformation is not unheard of 
with steel or iron (again, I'm not talking about cast iron), and IMO more 
probable than compression. The outcome probably depends on the strength of 
the material around the hole (against breaking), the forces required for 
elastic deformation in the different directions and the force required for 
compression.

Gerhard

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