Internal Forces

[MechaWolf]

I have a thin ceramic tape formed into a disc (washer shape)- 0.2mm thick, external diameter 30mm, internal diameter 13mm. This works through a temperature range of 0 - 1000 degrees C. The change to the internal diameter through this temperature change is around 1.5mm. The material has a Youngs Modulus of 120GPa, Poisson's Ration 0.24, and Flexural Strength 320 MPa.

I am trying to understand the forces on internal diameter if these are held at 13mm and not permitted to change by 1.5mm, with the top and bottom also being clamped.

Anybody provide a formula?

The end result is to assess different materials as the internal component to see which one can withstand the forces applied from the ceramic tape. The internal materials will have a different co-efficient of expansion, and therefore there will be a interference.

Thanks

 

[drawoh]

MechaWolf,

If your internal diameter is held at 13mm, then the hoop stresses around the circumference are zero. First semester mechanics of materials. Just about the first thing they teach you after the professor's telephone and email.

Your clamping system to hold the thing at 13mm is absolutely significant and interesting now.

--
JHG

 

[MechaWolf]

Through the temperature range the internal part remains stable (whatever the material selected is going to be), however the external part although it can become smaller than dia.13mm, is will apply a force onto the internal part.

Is there anyway of assessing what this force may be without knowing the internal parts details?

Thanks

 

[drawoh]

MechaWolf,

Sorry, I am wrong. I was thinking only about stresses.

To keep the diameter constant at varying temperatures, you would have to apply force as some proportion of temperature. Either you have an intelligent clamp, or you have some material that is dimensionally stable through your temperature range.



--
JHG

 

[MechaWolf]

The material at the center will be dimensionally stable, but as yet unknown, therefore is there any way of knowing the forces acting on it?

Thanks

 

[drawoh]

MechaWolf,

If you assemble this thing at room temperature, 20[°]C, then it will expand 1.5mm when heated. A plug in the middle will not affect this unless you have an adhesive that works at 1000[°]C.

A dimensionally stable plug in the middle would reduce contraction if you assembled everything at 1000[°]C and cooled it to room temperature. Still, assuming that your plug has a CTE of zero, and that everything can withstand 1000[°]C, your final ID will be a function of the relative elastic moduli.

Your clamping is a complex problem that will massively affect your stresses.

--
JHG

 

[MintJulep]

The material at the center will be dimensionally stable, but as yet unknown[/quote}

Nothing is dimensionally stable over a 1,000 C temperature cycle.

 

[MechaWolf]

The parts will be assembled at 1000 degrees C and then cooled, it is the cooling where the two different CTE come in. The problem is that the ceramic in the middle does not have published strength data, and therefore I need to understand the forces acting on it and then generate tests on the different ceramics to proove they hold this force and beyond for a factor of safety.

Thanks