Glass vacuum chamber minimum thickness

[Marcelo Rodrigues]

Hello!
I am designing a vacuum chamber made of a vertical glass cylinder free of contact from any other structure, except by the top and bottom where aluminum disks seal the device.
Temperature is the same inside and outside.

I found on several books the following formula for the hoop stress:

s = p * r / t
s = stress
p = pressure
r = cylinder radius
t = wall thickness
They say the formula is the same for external or internal pressure.
But I assume the strength for internal pressure is tensile and for external pressure is compressive.

Glass compressive strength is 10^9 Pa.
The diference of the pressure inside and outside is 10^5 Pa.
Cylinder radius is 0.15 m

So...
10^9 = 10^5 * 0.15 / t
t = 1.5 x 10^-5 m

This doesn't make any sense. This pressure from outside the cylinder would break the glass.
What is wrong here?

Please, does anyone have any reference on calculating a "brittle material thin-walled cylinder subject to external pressure", even better if glass specifically.

Von Mises is not applicable since glass is a brittle material.

Any help would be highly appreciated. ;-)

 

[cjl]

Well, one thing to check is buckling as well. I don't know the buckling load for a thin walled cylinder off the top of my head, but given how thin that result is, I suspect it'll be your limiting factor.

 

[Nidum]

It does not even have to be fully developed buckling - any distortion which puts bending loads into the glass can be dangerous .

Design in any case should not be based on the maximum compressive strength of the glass - allowable stress for thickness calculations should be very much less than the maximum .

 

[256bits]

Glass compressive strength is 10^9 Pa.

Where did that figure pop up from?

Are you sure that the number of defects in the glass you are using is low enough that the glass will have a good probability of not failing below that stress level?

 

[Marcelo Rodrigues]

cjl, yes indeed. In another forum, an engineer warned the problem is buckling, not stress. Probably this is the reason for those unlikely numbers I got.

Nidum, by my readings so far, the glass will have an elastic distortion and suddenly will break (no plastic phase). So you are right about being far away from the limit, but some distortion will happen anyway.

256bits, I got this number from suppliers like below. Some books also show similar values for compression.
http://www.saint-gobain-sekurit.com/glossary/glass-properties

Yesterday I found two references that use different formula. The thickness I found was now 2.7mm for:
E = 7 E +10 Pa
Pk = 1 E +5 Pa
u = 0.2
d = 0.3

The references are:
- Process Equipment Design - Lloyd E. Brownell, Edwin H. Young. John Wiley & Sons, Inc. (Chapter 8)
This paper makes a lot of sense too, since the project is using a brittle cylinder under external pressure.
- http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5603796&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D5603796 - Shinichi Takagawa, University of Tokyo - IEEE 2010.

I hope I am on the right track now.

Thank you for all the comments!

 

[256bits]

Please, does anyone have any reference on calculating a "brittle material thin-walled cylinder subject to external pressure", even better if glass specifically.

Why thin walled?
You don't even yet have a t/r ratio to justify thin walled.

You also have an axial load if the glass cylinder is also taking up that load.

Successive loading/unloading may have a fatigue effect.
Then again, even under a continuous load, the glass can suddenly fail. Glass doesn't work harden, or go plastic, as metals do for example.
Temperature of use?
Any water in contact with the glass?

An guestimate allowable stress of 10^7 or 10^6 could be a starting point, and work around that for a thickness.
The better glass you obtain ( more free of defects ) the higher the working stress can be.
I don't think there is any way to give you a thickness figure since there is no way to know what type of glass you will be using and from what manufacturing method it came from.

 

[Nidum]

Finding out what wall thicknesses are conventionally used in this application would be a good place to start .

 

[Mech_Engineer]

Calculating strength in glass structures is a complex subject. Breaking strength has to do with any potential surface defects present, and the material's "fracture toughness," especially when looking at tensile forces. A rule of thumb I've used in the past is to keep any tensile stresses in the glass part (like a lens for example) to less than 1 ksi (about 6.9 MPa), so tensile stresses typically have to be pretty low in a glass part. This rule of thumb comes from typical scratch sizes on an optical lens and the probability of fracture at that stress level.

Here is a solid white paper that details some of the complexity around glass strength analysis:
http://fp.optics.arizona.edu/optomech/student reports/tutorials/SalaminTutorial1.pdf

The strength of glass can be theoretically estimated on the basis of breaking atomic bonds [Stansworth 1950, p. 75], and this gives about 10^6 psi. This far exceeds the measured strength, and the discrepancy is due to the presence of small flaws within the glass. Stress concentrates at the edges of the cracks, and while fracture may occur where the atomic-scale local stress is 10^6 psi, the average stress in the bulk of the glass may be more like 10^4 psi.

 

[Marcelo Rodrigues]

256bits,
Thin walled because (for sure) the t/r ratio will be <0.1. I need a point to start.
Axial load is present but its stress is also compressive and lower than hoop stress.
I am not considering fatigue yet. But intend to do later. I am trying to keep the problem as simple as possible at this moment.
Steady ambient temperature (~25C). No water contact.
Good manufacturers inform the Young's modulus, poisson ratio, compressive strength, etc, so using this info I assume it is possible to calculate the thickness.
My problem is find the right mathematical method to calculate that.

Nidum,
I agree and have been checking the commercial chambers thickness. They are between 6 and 10mm by what I found so far.
Considering my first calculations gave me 2.7mm, a security factor of 4 would result in 10.8mm, so I think the method from the above sources are not so far.

Mech_Engineer,
Thank you for the article. I will read it.

Thank you guys for the comments!

All the best!

 

[256bits]

Calculating strength in glass structures is a complex subject. Breaking strength has to do with any potential surface defects present, and the material's "fracture toughness," especially when looking at tensile forces. A rule of thumb I've used in the past is to keep any tensile stresses in the glass part (like a lens for example) to less than 1 ksi (about 6.9 MPa), so tensile stresses typically have to be pretty low in a glass part. This rule of thumb comes from typical scratch sizes on an optical lens and the probability of fracture at that stress level.

Here is a solid white paper that details some of the complexity around glass strength analysis:
http://fp.optics.arizona.edu/optomech/student reports/tutorials/SalaminTutorial1.pdf

What about increasing the strength of the glass through mechanical or chemical means as a recommendation for the OP?

 

[Mech_Engineer]

It's my understanding that precipitation treatments or heat tempering can improve glass strength in a couple of ways:

• Tempering can create residual compression stresses on the surface of the glass, reducing tensile stresses under bending loads. This effectively increases the glass's strength because the inherent compression force must be negated before the critical tensile strength is reached (common in cooking glassware and car windows).
• Precipitation treatments can increase the glass's fracture toughness, meaning it can in some instances tolerate larger surface scratch sizes before fracturing (I think Corning's Gorilla Glass is an example of this method).

Another article which covers some "rules of thumb" for glass strength calculation, see pages 12-13 of this PDF: http://www.optimaxsi.com/wp-content...ions-and-Rules-of-Thumb-for-Optomechanics.pdf. This includes the conservative "1 ksi" rule of thumb which covers many useful optical glasses used in imaging systems, but might not be as relevant for a pressurized beaker...

Still, if your stresses are all compression you may be able to tolerate much higher stresses before failure, possibly up to 50 ksi. In this case, you'll have to carefully balance your risk aversion with both buckling concerns and avoiding tensile stresses.

 

[Mech_Engineer]

Corning makes a series of "bell jars" which are designed for vacuum experiments, have you considered purchasing one of their off-the-shelf solutions?

PYREX® 140mm Diameter Bell Jar with Top Knob and Ground Flange (Product #6885-140)

At very least, you may be able to inspect these off-the-shelf products to see what their wall thicknesses are and how they might compare to your design plans. How are you hoping to have this custom design fabricated?

 

[Marcelo Rodrigues]

Mech_Engineer,

Thank you very much for all the links and ideas! I appreciate that.
Yes, I considered buying a bell jar for vacuum, but the equipment I am designing would have penetrations points on the top and bottom. So the device will be a glass cylinder with ends closed by aluminum thick disks. Through them I intend to pass electrical current and signals for sensors and other stuff. It is possible to use a bell jar, but the design will be much better using a glass cylinder.

Anyway, as you mentioned, the commercial vacuum bell jar are, at least, a good reference for my design. So I definitely will check them.

Thanks, man!

All the best!