Hoop stress in solid disc from thermal contraction

[elrohir00]

Hi,

I have been looking at hoop stresses and the information I have found hasn't been all that useful to me as I am having a hard time converting the thermal contraction of a system into a pressure for the equation (stress=a+b/r^2). This is the thick walled hoop equation

The disc is a few microns of copper on 0.7mm silica and from the thermal contraction the disc bends from Stoney's equation. The discs are solid (no hole) and have a radius of 40mm.

as the disc is solid b=0 so we only have a which is apparently the pressure. As all of the stresses are coming from thermal contraction I'm not sure if it will all cancel out.

the radius of the copper contracts by 0.1304mm and the silica contract by 0.0032mm if its required.

Thanks for your time

 

[Studiot]

hello, elrohir.

Are you describing a composite disc where a complete layer of copper is bonded to a complete layer of silica, like a part sandwich?

So that if the composite disk is flat and cools the copper will contract more than the silica, pulling the disc into a cup shape?

Or have I misunderstood?

 

[elrohir00]

yes the copper is stuck onto the silica. At room temperature the disc is flat to a few nanometres and when its cooled it makes a cup/bowl shape and the edges lift by around 1 mm

 

[Studiot]

http://www.iasmirt.org/SMiRT16/B1834.PDF

I think its also in Timoshenko "Theory of Plates and Shells"

 

[elrohir00]

Thats looking right on the money. I will give it a read through and see what i can extract

Thanks studiot for a quick response

 

[Studiot]

go well