Thermal expansion question ? 4

[Histogram]

Situation, if one has a 1 inch diameter x 6 inch long solid brass bar and a ¼ diameter hole was drilled in the center of the solid brass bar, now if the brass bar was heated to 1000 F would the ¼ hole expand or contract?

Thanks,
Dave

 

[vpl]

I'm assuming that the bar would be heated uniformly and that it would then remain at that temperature ...

Metals, in general, expand when heated. Therefore, without doing any detailed analsysis, I'd vote that the "hole" would contract.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[MintJulep]

With no other constraints, the hole gets bigger.

The question to ask yourself is "What would happen to the material that used to be in the hole?"

Or from a more practical perspective, when you want to assemble two parts with an interference fit what do you do? You heat up the part with the hole so that the hole gets bigger and fits over the part without the hole.

 

[corus]

If the hole was to get smaller, then presumably there must be a temperature at which the hole completely disappears, and a temperature above that at which the material around the hole also vanishes. A home made black hole? Me thinks not.

The hole expands.

corus

 

[ivymike]

the hole thing scales up. (pun intended)

that's why you can heat a washer and put it over a bar, then find that it won't come off when it's cool.

 

[Histogram]

Thanks to all for settling this debate.
Much appreciated,
Dave

 

[racookpe1978]

But, doesn't the reason a washer "expands" over the rod when heated is that the whole outside half of the "ring" of material of the washer expands radially "out" more than the "inside" half" of the ring expands radially "in"?

\\Thus, in this case - up to the point of melting "into" a copper hole - ain't no black hole here! - when heated, the rod expands = the OD gets bigger, the rod gets longer, and the hole thing inside the rod gets smaller.

 

[MintJulep]

Imagine if you will:

A circular disk with no hole. Heat it up. EVERY POINT ON THE DISK GETS FARTHER AWAY FROM THE CENTER.

Take the circular disk, cut out a hole (with an imaginary zero kerf). Heat up the resulting two pieces. The "slug" that became the hole gets bigger. The hole that the slug came from has to get bigger too. If the two pieces are left "co-axial" there will be no gap. Forming a hole is not some sort of mystical quantum process. It won't cause a discontinuity in the behavior of the material.

 

[25362]

Solid brasses have a published linear thermal expansion coefficient from 68 to 572[sup]o[/sup]F, [α], of about 11.3[×]10[sup]-6[/sup] F[sup]-1[/sup].

Assuming isotropy, every linear dimension expands in the same proportion upon heating causing the hole to expand too.

Again, assuming isotropy, the volume expansion coefficient [β] = 3[α].

 

[racookpe1978]

Ah, but good Sire Mint, doesn't the reason that all parts of the solid disk expand (radially) "out" (get bigger) is that the inward expansion pressure at all locations as the disk heats up get constantly opposed by outward pressure from the center.

If there is no "center" of the disk as in a hollowed disk, then there is no out opposing outward pressure, and so (a smaller) part of the ring DOES move inward. Its just that a smaller part of each hollow concentric ring is moving inward than is moving outward.

 

[MintJulep]

No.

 

[IRstuff]

It's not a "pressure" thing.

Imagine removing all but a narrow annulus next to the circumference of the hole. Apply temperature. Since the linear expansion along the circumference of the annulus is positive, the annulus must grow in diameter to accommodate the new circumference, so the hole grows. Look at the next annulus, same thing.

Note however, since its circumference is longer, the second annulus has a larger diameter growth relative to the width of this annulus, so there's no "push" from the outer parts of the washer.

Note also, that growth in width of the annulus from expansion is miniscule compared to the growth in diameter from the circumference increasing, so, again, nothing pushing to make the hole smaller.

TTFN

FAQ731-376

 

[Compositepro]

I am always amazed at how many engineers get this wrong. I've had this discussion at least four times in my career with engineers who are designing equipment. The answer to this question is taught in Physics 1A and is very fundamental to any understanding of the mechanical universe.
I strongly urge anyone who did not instantly know the correct answer to seriously think through the problem until it becomes obvious that the hole grows. Many real world problems involve exactly the principles discussed in this thread. By understanding how thermal expansion works in this simple example will make seemingly complex problems you encounter later in life become simple.