I can calculate the compression and tension, but don't know how they add.
The 10 mm pistol cartridge has a primer pocket ~.208 and an extractor
The makes the primer pocket walls thickness = [ .338-.208"]/2= .065" thick
Neglecting the primer thickness and the time delay of the flash hole,
the thin wall hoop stress of the primer pocket wall is then
S [tension] = P [chamber pressure] .208/[ .338-.208"] = 1.6 P
The inside diameter of the case mouth is .408".
Neglecting case to chamber friction, the bolt thrust is then:
F [bolt thrust] = P [chamber pressure] pi A [inside case area] squared =
P pi [.408"/2] [.408"/2] = .13P
The stress on the primer pocket walls is then
S [compression] = F [bolt thrust] /A [ longitudinal cross sectional area
of walls] = .13P/ [pi [ .408/2] [ .408/2] - pi[ .208/2][ .208/2]] = 1.34 P
The 10 mm cartridge is rated for 37.5 kpsi chamber pressure so:
primer pocket wall tension = 1.6 P = 1.6 37.5 kpsi = 60 kpsi
primer pocket wall compression = 1.3 P = 1.3 37.5 kpsi = 50 kpsi
There must be a way for 60 kpsi tension and 50 kpsi compression at 90
degrees from each other to be added and compared to the yield point of
A simple way to look at it would be force vectors. Assuming the forces
are at 90 degrees, applying the pythagorean theorum, squareroot(60 *60 +
50 * 50) = 78 ksi.
I confess however, that I was not able to fully follow your explanation
without a diagram, so I may have missed the boat. It is possible that
you could have different forces dominant in different parts of the
cartidge. Since the cartridge is fully enclosed by the chamber, it is
not clear to me why the yield strength even matters, the cartridge can't
yield because it has nowhere to go.
It would seem that these calculations would be covered somewhere in the
massive literature available with respect to guns and ammunition, and I
would use a sample calculation from the literature over any theortical
model that you or I could dream up, which might or might not be valid.
that will destroy the society. It is Darwinian.
Thanks for the response.
The primers fall out when the primer pocket grows a little in diameter.
It is a real problem, and I chose one of the worst case cartridges.
Here is a picture of some primers falling out:
Here is another:
Can you see how the cartridge has a narrow ring near the base?
The is the extractor groove.
The primer pocket is inside of that, so the brass is thin there.
It's called Mohr's Circle, but it's been 30+ years since I've even thought about
one, much less did any figuring about it.
You trying to make us oldtimers (Alzheimers) feel bad?
Clark Magnus> I can calculate the compression and tension, but don't know how they add. >
that will destroy the society. It is Darwinian.
Yes, there are indeed different forces in play in the cartridge though
the pressure cycle, and different places receive varying amounts of
pressure during the cycle. The neck/shoulder may be subject to
decreasing pressures as the primer pocket may still be subject to the
Typically, the weak spot of most cartridges is indeed the primer
pocket, as the primer is only pressed in, and brass flow may open the
hole the primer is pressed into, allowing gas to escape to the outside
of the case, past the primer itself. This is generically called
"blowing out the primer pocket". Standard pressure testing of this
phenomenon shows that in most rifle cartridge cases, this starts
showing up (in modern cartridges) somewhere in the area of
62,000-70,000 PSI. In this range also, is where the primer cup itself,
may be perforated by internal gas pressure in the very small area that
is not supported..IE the firing pin hole in the face of the
bolt/slide/etc. Higher pressures may actually blow out the web of the
cartridge, pierce the primer, and damage the weapon AND the shooter by
the sudden and overpowering injection of uncontrolled hot gases into
the action of the weapon. Most modern rifles are designed to vent this
gas in safe directions, away from the shooters face. Much higher
pressures, in a weapon perhaps already damaged, may sheer the bolt
locking lugs, and turn the bolt into a high speed projectile rear
This is generally only of interest to the mortician, whom has to
repair the damage to the face and skull, after the medical examiner
has removed the bolt from the shooters skull, during the autopsy.
A well known gun writer appears to have been the victim of metal
fatigue, a year or so ago, when he was found on the firing line, while
testing some hand loaded ammunition in a vintage Mauser rifle. Big
hole in his face, with the bolt stuck through his skull.
The above of course, assumes that the case be of the "mostly
supported" type most often associated with rimless bolt actions, and
most, but not all rimmed cartridge/action combinations. Revolvers are
generally fully supported by the cylinder and the frame. Where the
problem may show up most often, is in self loaders..ie semi-automatic
pistols, most notably the Glock, where a rather frightening amount of
actual cartridge case is left unsupported, above the magazine at the
bottom rear of the barrel. Glocks, fired with hot hand loads, often
exhibit "guppy bellies" in fired cartridge cases. When such brass is
reloaded several times, and work hardening has done its damage, the
cartridge case may blow out (downwards actually), and blow the
magazine out of the weapon, often shearing off the magazine catch and
depositing the magazine rather forcefully on the shooters right foot
(assuming a decent Weaver stance and right handedness), while in
addition, occasionally causing a quantity of fecal material to be
deposited in the shooters trousers.
"At the core of liberalism is the spoiled child -
miserable, as all spoiled children are, unsatisfied,
demanding, ill-disciplined, despotic and useless.
Liberalism is a philosphy of sniveling brats." -- P.J. O'Rourke