One part heated in one end and cooled in the other
One part heated in one end and cooled in the other
(OP)
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,
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,





RE: One part heated in one end and cooled in the other
RE: One part heated in one end and cooled in the other
Thanks for the answer
And if it is cyclic?
How can I find when it fails?
cheers,
RE: One part heated in one end and cooled in the other
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
RE: One part heated in one end and cooled in the other
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
RE: One part heated in one end and cooled in the other
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

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
Of course I can. I can do anything. I can do absolutely anything. I'm an expert!
RE: One part heated in one end and cooled in the other
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.
RE: One part heated in one end and cooled in the other
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_fi...
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,
RE: One part heated in one end and cooled in the other
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.
RE: One part heated in one end and cooled in the other
RE: One part heated in one end and cooled in the other
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
RE: One part heated in one end and cooled in the other
RE: One part heated in one end and cooled in the other