Case neck thickness and obturation

[Greener Jim]

As many will know, i have a habit of thinking outside the box, mainly just to work through something and see if it can be done.

Anyway, so i was working through one of these projects and i got thinking of case neck thickness.
When a cartridge is fired the case obturates, sealing the breech from gases that may attempt to go backwards towards the shooter. This is mainly done by the thinner neck section of the case.
Generally blackpowder cartridges were very thin and when the transition was made to cordite these cases (with cordite loads) stuck somewhat causing extraction issues in falling blocks and double rifles. The solution was thicker brass.

But how thick can you go before it stops obturating? Obviously pressure will have a huge impact on this but lets go to extremes here and say 3mm wall thickness and 30,000 psi.
Anyone know the formula i'd be best using and the values for cartridge brass?

 

[takbok]

For a quick calculation you could work out the hoop stress in the cartridge wall/neck. It's the first formula in the link below:

Pressure Vessel, Thin Wall Hoop and Longitudinal Stresses - Engineers Edge

Remember to use Pascals and metres for your units. This calculation is actually for thin walled pressure vessels as you'll see. Do a search online for the more involved thick wall pressure vessel calc if you're inclined to.

You can then use the stress value obtained to work out the deflection of the brass if you find the E value (Young's modulus for brass).

Change of length equals stress times length (circumferential length in your case)/E. Add this change of length to circumference and divide by pi to get diameter I will stretch to.

Very simplistic way but it's a start.

 

[bewsher500]

Not as straight forward as that though as anyone who has fired work hardened brass will attest. Your

It will also change as the various manufacturers use differing compounds in their brass

I personally use brass which from experience I believe is softer than others. I have no measurements to confirm this other than resistance to work hardening on sizing/firing cycles compared to other brands

The Young's Modulus will be different
I would propose that the elastic potential energy derived from Hooke's law might be relevant

you are looking for two things:
1) the case is elastic enough to expand
2) the pressure is enough to expand the neck PAST the point where it will spring back to original size

 

[Alantoo]

It will also change as the various manufacturers use differing compounds in their brass

Not even as straightforward as that!

Last week BillH on here sent me a paper he had found on the effect of temperature treatment during the manufacturing processes regarding grain size, strength and surface finish of 70:30 cartridge brass.

My non-engineer interpretation...the gist was that by only stress relieving between 250˚C and 350˚C rather than getting up to normal annealing temperatures of 450˚C to 680˚C the strength of the metal was increased...its ability to elongate jumped at these temperatures.

The alloy was the same in each case 70:30 cartridge brass used for its deep drawing properties...the temperature at which the elongation properties jumped varied only because of the previous cold rolling and heat treatments.

Arguably neck thickness has the least effect on obturation given the range of properties the alloy can have.

Alan