Change in the size of a hole in a constrained metal when heated

[tommd]

TL;DR

Size of hole in a constrained metal when heated.

I have seen many discussions on the topic of whether a hole in a metal will get larger or get smaller when the metal is heated. And the conclusion is the hole will get larger. My question is if the metal is constrained so the outside dimension of the metal cannot expand, what happens to the hole in the center.

Example: a one quarter inch thick disk, two inches in diameter with a one inch hole in the center. The metal is heated. The two inch disk is not allowed to expand or get thicker. What happens to the dimensions of the one inch hole?
Thanks,
Tom

 

[berkeman]

I have seen many discussions on the topic of whether a hole in a metal will get larger or get smaller when the metal is heated. And the conclusion is the hole will get larger.

To help this discussion about the constrained edge case, can you let us know what your understanding is for why the hole gets larger when the unconstrained plate gets heated? Does that offer any clues about the constrained case?

 

[pines-demon]

TL;DR Summary: Size of hole in a constrained metal when heated.

I have seen many discussions on the topic of whether a hole in a metal will get larger or get smaller when the metal is heated. And the conclusion is the hole will get larger. My question is if the metal is constrained so the outside dimension of the metal cannot expand, what happens to the hole in the center.

Example: a one quarter inch thick disk, two inches in diameter with a one inch hole in the center. The metal is heated. The two inch disk is not allowed to expand or get thicker. What happens to the dimensions of the one inch hole?
Thanks,
Tom

In PF you are required to show that you have done some effort before getting any help. There is a lot of information on this on books, in PF and any other physics websites that you can look up easily. What exactly you do not get?

While you look for it, here is the ('s Gravesande's) experiment in real life:

 

[tommd]

Sure- I understand that when heated, the molecules will move farther apart. Sometimes, one tends to think that since there is a hole, that leaves "room" for the molecules to mover farther from each other by filling into the empty hole. But one way to see that that does not happen would be to ask the same question off what happens to the inner perimeter molecules at that same spot if the hole material were not removed, and in that case we would all say them move outward, thus expanding.
So I am imagining the same thing will occur here if the external dimensions are restrained. The molecules will still try to expand outward, even trying to make the hole bigger. With the external dimension restrained, I do not know if no expanding will occur, or if something else happens.
And along these lines, what does happen to a material in this situation?

 

[tommd]

In PF you are required to show that you have done some effort before getting any help. There is a lot of information on this on books, in PF and any other physics websites that you can look up easily. What exactly you do not get?

While you look for it, here is the ('s Gravesande's) experiment in real life:

Thank you for the reply and video. Unfortunately, I only know English and so only saw the visuals, and I believe my OP indicates that I do understand that heating a hole makes it larger and thus cooling one makes it smaller. The video, at least from the visuals, does not address what happens when constrained. All my internet searches also did not come up with anything about a constrained heating.
Tom

 

[A.T.]

My question is if the metal is constrained so the outside dimension of the metal cannot expand, what happens to the hole in the center.

The unconstrained case is easy because if the material expands uniformly, while trying to preserve the shape (angles / length ratios), than is just like geometric scaling-up.

But the constrained case is hard to predict, because you can have material failure, buckling, etc. It might depend on the exact shape and material properties.

 

[snorkack]

May I offer comparison of experiments to reflect on?
1) Heat a ring while stopping it from expanding, as in your OP
vs:
2.1) Heat the ring while free to expand in any direction, then as a separate step:
2.2) Compress the outside of the hot ring until its outer size matches the original outer size while cold.
Should the size, shape and stress distribution in the ring be the same after step 1) as after step 2.2), or different?

 

[Baluncore]

Assume elastic deformation of the sample, without plastic changes or yield.

When the unconstrained sample is heated, the hole diameter will increase proportionally.

As the constraint force is linearly "self-applied" from zero, by the thermal expansion, the hole diameter will increase, but not by as much as in the unconstrained sample.

If the same maximum constraint force was applied to a cold sample, the hole diameter would be reduced by the external elastic compression.

 

[tommd]

May I offer comparison of experiments to reflect on?
1) Heat a ring while stopping it from expanding, as in your OP
vs:
2.1) Heat the ring while free to expand in any direction, then as a separate step:
2.2) Compress the outside of the hot ring until its outer size matches the original outer size while cold.
Should the size, shape and stress distribution in the ring be the same after step 1) as after step 2.2), or different?

I would think after step 2.2, the hole would either be the same six or slightly larger, it not smaller.

 

[tommd]

As the constraint force is linearly "self-applied" from zero, by the thermal expansion, the hole diameter will increase, but not by as much as in the unconstrained sample.

So you are clearly saying the hole will not get smaller.
And I believe everyone else is also. Thank you, that is what I was thinking but wanted some assurance from others with more knowledge than I on the topic.
Tom