the rifle barrel as a pressure vessel--the physics

[corncob]

Just for kicks, seeing as how school is out, I've been using the University's software to run some simple finite element analyses on a .308 rifle barrel. I'm seeing (as expected from thick-walled pressure vessel theory) the highest stresses near the inside wall--but the magnitude of these stresses is higher than I would expect, and I'm hoping someone out there in THR land might be able to shed some light on why our rifles aren't blowing up in our hands--or rather, what is missing from my analysis.

Specifically, using 62,000 psi as the internal pressure, I'm getting maximum von Mises stresses of around 130,000 psi. This seems awfully high to me--especially considering that the stress concentrations present at the corners of the rifling were not accounted for. And I'm assuming that fatigue is the real killer for rifle barrels--so what am I missing? I know that rifle barrels are usually 4140, 4340, or 416, but does anyone know about how it is heat treated? I was under the impression that barrel steel is not very hard. Is the load/unload cycle from a powder charge fast enough for strain-rate to be a factor? I understand that yield strength increases at very high strain rates, but I also understand that dynamic loads are much more destructive that static loads. I'm fuzzy on the specifics, though.

Can anyone explain the "proper" way to approach this?

 

[P95Carry]

I am an engineer - but an OLD engineer. I have to fly to books to remember a lot of the heavier stuff.

I wonder here tho what time frame you were using - over which to spread the pressure curve. Assuming the safety factor of say a 10 thou ''jump'' - allowing for absolute peak to start to fall before engaging rifling, then I'd be thinking that everything from then on becomes better and better distributed. Added to which if powder selection appropriate, there is burn long after that starting peak... further spreading the pressure curve.

Re hardness with barrels - the word needed is IMO ''tough'' - hardness = brittleness - whereas during pressure cycles there needs to be slight ''give'' or yield. I'd expect in good gun design that an average rule of x5 factor of safety is allowed for. I think strain rate is a factor but again - I am unsure without digging what time frame to allocate to the main period of interest.

I have no ''proper'' way to suggest here - I am waffling really and thinking out loud. Mete tho if he sees this will I am sure be able to add some useful metallurgical info.

BTW - afterthought - as the process here is very dynamic - even the bomb calorimeter has little place for energy calcs, being IIRC a totally contained system. I started thinking on that but discarded it.

 

[kaferhaus]

Varmint AL has a good animated finite analyisis graph on his site that he made.... He's a very accomplished engineer in that field

 

[AZ Jeff]

I think including the stress risers due to the rifling in your calculations would be in error. Peak pressures of 60K PSI only occur in the first few milliseconds after ignition, and at this point, the projectile probably has not even fully engaged the rifling.

In other words, your pressure vessel does not contain any of the rifled portion of the barrel when peak pressures are being seen.

Now as far as whether the von Mises stresses are reaching 130KSI.............I agree that sounds a bit high, but probably not TOTALLY out of the question.

Gun barrel steels are typically low in terms of heat treatment, the Rc20 or thereabouts, so the yield strengths are relatively low.

 

[bad LT]

The horror - this is bringing up bad memories of my last mechanics final

 

[rockstar.esq]

Not to sound like a dolt, but what is Von mises? I'm guessing it's some kind of stress running along the bore line. The other guys have suggested that you might have overlooked the chamber throat, which sounds reasonable to me since the mantra of all good reloaders is headspace, headspace, headspace!

 

[waterhouse]

Just out of curiosity which FEA program are you using?

 

[corncob]

...I'm not sure, but I think von Mises was the 15th apostle--you know, right after Newton and Bernoulli?...

I'm using ANSYS, by the way, and Varmint Al doesn't have anything on his page specifically relevant to barrels. Maybe I'll send him an email, though, as he seems to be the expert on stress due to dynamic loading. Judging by how much content he's got on his site, it looks like he might be willing to help.

As far as the time goes, look here:

http://www.armalite.com/library/techNotes/tnote48.htm

Now this is for a 5.56mm rifle, but if we take it as a "rule of thumb," then the pressure drops to about half of the max in about half a milisecond (rough, I know, but I'll leave the pressure-volume-burnrate-time relationship to someone smarter than myself). Integrating Newton twice, with a 150gr (~.01 kg) bullet, assuming pressure is nearly flat (which it isn't--we spend longer at low pressure at the beginning, which means the results we get with this math will be high), we get a distance of about a quarter of a meter, or 10 inches. Even if we are off by an order of magnitude, we still may have engaged the rifling. Something else must be going on here.

Even if we assume that the barrel spends most of its time pressurized to half of the max chamber pressure, we are still looking at a safety factor against yielding in the neighborhood of 2. Seems questionable to me considering that the rifling is most certainly going to cause stress concentrationsthen, and at the inside surface where the stress is already the highest. And yet, we don't see barrels bursting from fatigue cracks growing from the corners of the rifling after 10,000 rounds.

Taking the 5.56mm example directly with the plot on the Armalite site gives about 11 inches of bullet travel before the pressure drops to half.

Oh well, maybe someone will chime in with the answer and enlighten us poor sinners....

 

[SJG26]

ummmmmmmmmmmm.....carry the 3..................is there an 'R' in the month?? No----ok divide by Pi !

 

[boo586]

Hey corncob, are you using a 150 grain bullet in your check of the 5.56 mm NATO or is that a typo. Try using a 45 or 55 grain bullet in that 5.56 model and not a 150 grain bullet meant for your .308.

Boo586

 

[corncob]

I did use a 55 gr. bullet in the math--otherwise the travel would have been significantly shorter due to the slightly lower pressure and much smaller area.

 

[Art Eatman]

I ain't goin' back 40+ years to when I sorta knew how to do this kinda stuff...

BUT: To throw something else into the stewpot, I've seen curves of pressure vs. time for various powders. Very roughly, the peak pressure seems to occur at about one-fourth to one-third of the time of burning.

Caveat: This is NOT one-third of the barrel length; the bullet is accelerating rapidly and that first one-third of the burn time is in that first very few inches of barrel...

eclancy has better data, but I've always heard that the pressure at the gas port of a Garand is around 2,000 psi.

Lotsa stuff to play around with; the bullet's travel time is around 0.66 milliseconds, for a 24" barrel and 3,000 ft/sec MV.

, Art

 

[flashhole]

Does your model show the pressure moving as a wave-front in time or are you assuming the area of the case is engaging the barrel at the same pressure over the entire case area at the same time?

 

[corncob]

My model was completely static. I've heard that as a solid is "loaded" the stress moves through it like a pressure wave--but I don't know anything about how this works. I assume that it has to do with the solid's density, stiffness, etc. But, wouldn't this happen on a much faster time scale than the total time-at-pressure?