One part heated in one end and cooled in the other

[drodrig]

Hi there,

Let's say I have a part (a bar) of a material (its properties are known).

Then I heat up the bar in one end and cool down the other end. So we will have a gradient of for example 50ºC.

If there are no constraints around this part (it can expand and shrink freely), how does this gradient stress the bar?

I mean, if I have a bar clamped in both ends and I heat it, this will general internal stresses.

Another way of asking the question is: will the gradient cause the part failure?

Thanks!
regards,

 

[ione]

If there are no restraints present, any stress will develop in the bar and if the procedure of heating/cooling is not cyclic (no thermal fatigue intended), neglecting creep phenomena under the only action of the bar’s weight, I can’t see any problem.

 

[drodrig]

Hi ione,
Thanks for the answer
And if it is cyclic?
How can I find when it fails?
cheers,

 

[EdStainless]

cyclic thermal fatigue is driven by the amount of expansion (TEC and heating) and the rate of temp change.
If the part is not constrained and the heating/cooling rates are rather slow then you will never thermal fatigue it.
If it is very high expansion material, with low yield strength, and you change temps rapidly over a side range, then you can induce failure.
And the symmetry is important. If the temp change cause a distortion then the stresses will be much higher and failure much more rapid.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[drodrig]

ahá,
Actually the changes are very slow.
So no problem
I have to make sure about the constraints (because the part is inside a box), but the temperatures are something like -25ºC and +60ºC, so it will shrink almost the same amount that it expands.
Thanks

 

[IRstuff]

Stress vs. strain is the usual way, isn't it?

However, unconstrained materials generally do not fail; just consider the grating on top of a gas stove with >800F at one end and near RT at the other. I've never seen any such grating fail

TTFN
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Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

 

[Compositepro]

And placing hot glass in cold water will shatter the glass.

Stresses are caused by strains. Temperature gradient causes strains. Rate of temperature change simply affects the magnitude of the temperature differential. It is the temperature differential and not the rate of temperature change that causes stress. In dynamic cases, where temperatures are changing, high thermal conductivity will reduce temperature differentials, and high heat capacity increases temperature. The ratio of conductivity to capacity is called thermal diffusivity.

Stress can be calculated from the stress strain curves and CTE (coefficient of thermal expansion) of the materials.

The case given in the original post, is a static case of constant temperature gradient, which makes calculation of the stresses much easier. If the stresses approach the yield strength or the tensile strength of the material then there will be problems.

 

[drodrig]

Hi Compositepro,

What you are saying contradicts what the other say.

So you say we have to apply these formulas:

http://www.fea-optimization.com/ETBX/hooke_help_files/Eqn26.gif

Since there is no reactions in the part (simplified case) the formula would be

strain = CTE*delta T

??

Then with this strain I calculate the stress (with the elastic limit) and I compare with the yield strength?

is this right?

thanks
regards,

 

[Compositepro]

You have to factor in the the distance over which the delta T occurs to get the temperature gradient.
Your rod will be larger in diameter on the hot end but it is still attached to the small end. This results in a shear strain, which can be resolved into tensile and compressive stresses by using the material modulus. Remember that the resulting stresses also affect the strains, so you have to iterate to the final solution.

 

[Compositepro]

I should add that it is highly unlikely that you will come close to "part failure". It's just that there will be internal stresses in the part, that most people would simple ignore.

 

[EdStainless]

When parts are heated or cooled faster than TC can keep temperatures uniform is when you get real trouble.
Over such a small temperature range and without constraints the strains will be very small.
Depending on how the part was made the initial residual stresses may be higher.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[drodrig]

Thank you all for the answers!

 

[chicopee]

I am not sure that you can compare glass to solid material since from what I remember from chemistry, ie, 1960's chemistry, glass is a supercool liquid.