Thermal expansion of aluminum disc

[jklops686]

I have an aluminum disc that is 15in in diameter and about 1in thick. I am going to put it in a 400°F oven and I need to know how much the diameter will expand.

One of the engineers I work with(i'm an intern) is using what I found to be the linear expansion equation (ΔL/Li=αΔT)...so Length change = Original length x alpha(coefficient) x delta T. He's using 15in as the original length. I don't see how this can be accurate because it's a disc that is pretty thick. The calculation comes out to .03. Does this mean .03 in all directions? How do we take the thickness into account? What if the disc was 1ft thick? Should I use volume expansion to be more accurate?

Thanks

 

[Simon Bridge]

Using the formula, you'll see that the change in length depends on the initial length as well as the change in temperature, so the disk won't change by 0.03 inches in every direction.

How would you go about using the coefficient of volume expansion for this problem?

 

[jklops686]

ΔL/Li=3αΔT Then something

 

[Chestermiller]

If the disk is not constrained, then it expands linearly in all directions by the same percentage. If you want to find the change in volume, then you use ΔV/V_i=3αΔT. Notice that the coefficient of volume expansion is equal to 3 times the coefficient of linear expansion.

Chet

 

[jklops686]

That makes sense. I was thinking that when i stared at it for a minuet today. Thanks

 

[jklops686]

But what if the disc is constrained, like 500lbs on top of it?

 

[Chestermiller]

But what if the disc is constrained, like 500lbs on top of it?

As long as the force is constant, it would have no bearing on the thermal expansion, and the expansion would still be the same in all directions. Therefore, the 500 lb would not be considered a constraint. The kind of constraint I am referring to is if the material is prevented from fully expanding in a certain direction (i.e., constraint on the deformation, not on the loading). For example, consider a case where the material is not allowed to extend in a certain direction (i.e., zero strain). Under these circumstances, if the material were heated, the stress in the constrained direction would have to increase. The best way to understand this is to examine the 3D tensorial version of Hooke's law, in which thermal expansion is included. The easiest version to work with is where the strains are expressed in terms of the stresses.

Chet

 

[sophiecentaur]

That makes sense. I was thinking that when i stared at it for a minuet today. Thanks

Interval for a stately 17th Century dance. Some typos introduce a whole new atmosphere of sophistication to the hurly burly of Physics. I wish there were more like this.

 

[jklops686]

This is why I love physics forums.