Synopsis:
This is something I wrote some years ago about cartridge case 
walls "welding" to chamber walls.  Of course, case walls 
don't really weld to chamber walls.  The pressure inside a 
case will normally be high enough so that it expands the case 
until it touches the chamber wall (that's how a case seals or 
"obturates").  Any pressure in excess of that pressure causes 
a contact pressure between the case walls and the chamber 
walls.  This excess pressure (times the area over which it 
works), then, provides the normal force which figures into 
the equation for frictional force: 
frictional force = coefficient of friction times normal force.  
If this frictional force exceeds the force trying to 
extract the cartridge (extraction force due to that same 
pressure acting on the case head through the area of the 
largest inside diameter of the case), then the case will do 
one of two things: sit there and not put any force on the 
breech block, or the extraction force will be high enough to 
stretch the case into contact with the breech block and then 
start to put force on the breech block.

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coeff's. of friction from CRC
steel on brass
.11 castor oil
.13 long-chain fat acid
.19 min oil
.35 clean

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> From: John Bercovitz (bercov@bevb.bev.lbl.gov)
> Subject: Re: Colt GM dynamics - conclusion 
> Newsgroups: rec.guns
> Date: 1990-09-19 13:14:42 PST 

     Chris Luchini's article in which he mentioned cartridge  
cases 'welding' to chambers intrigued me.  We all know it 
happens or else we'd never see case stretching.  But we also 
know that some cartridge cases, like that of the 45 ACP, 
don't stretch.  So what's the difference?  I think I've come 
up with a possible answer and I'd like to run it past you 
folks for comment.
     In short I propose that some cases have enough body 
surface area to grip the chamber walls and some don't.  Since 
we already know that a 270 will exhibit case stretching if 
you set its shoulder back, let's look at some lower-pressure 
cartridges:

30-30:
     The body of a 30-30 averages about 0.4" diameter and is 
about 1.5" in length.  A fired cartridge shows that the case 
expands from about 0.3" forward of the case head on to the 
case mouth.  This leaves 1.2" for gripping the chamber (I'm 
ignoring the shoulder and neck).  The area of this surface is 
(pi)*D*L= 1.5 in^2.  So the force resisting axial motion of 
the case in the chamber when propellant pressure is high is: 

Faxr = (coefficient of friction) * (1.5 in^2) * (pressure of the propellant) 

     The inside diameter of the case at its largest point is 
about 0.35" so the area on which the pressure acts is: 
(pi/4)*0.35^2 = 0.096 in^2 

Axial force on the interior of the case head is then: 

Fax = (pressure of the propellant)*( 0.096 in^2) 

I think we'll all agree that if the force on the case head 
trying to extract the case from the chamber (Fax) is larger 
than the gripping force of the case body (Faxr), the case 
will move (unless the case stretches or the head separates).  
Since the pressure of the propellant is the same on the case 
head and in the case body, and Fax = Faxr to see some 
incipient motion, it is fair to combine the two equations 
above and find:  

(coefficient of friction)= (0.096 in^2)/( 1.5 in^2) = 0.064

So as long as the coefficient of friction of the 30-30 case 
in its chamber is greater than 0.064, the case will 'weld' to 
the chamber.  Note that it would be unusual for the 
coefficient of brass against steel to be quite so low; 
therefore the 30-30 case must be a 'welder'.
     Hey - here's a crazy and dangerous thought: to fireform 
cases, why not reduce the powder charge to 2/3 so as to 
reduce the pressure to about 1/2  and then put a thin layer 
of high pressure grease on the case?  It might lower the 
coefficient of friction enough to prevent case stretching.  
But I digress.

45 ACP:
     The same process applies mutatis mutandis to the 45 ACP: 
Pressure ring is 0.4 forward of case head leaving 0.49" for 
grip length; outside diameter is about 0.48 for a grip area 
of about 0.74 in^2.  Cross sectional area of the internal 
diameter of 0.45" is 0.159 in^2.  So minimum coefficient of 
friction for case welding is: 0.159 / 0.74 = 0.21.  Since it 
would be unusual for a smooth chamber to have that high of a 
coefficient of friction against a brass case, the 45 ACP must 
be a 'slipper' rather than a 'welder'.  All bets are off if 
you have a rough chamber; then you have gross deformation of 
the brass into grooves which, in the case of really decent 
rubber tires against asphalt, can give a pseudo-coefficient 
of friction higher than one.

     Be assured that I checked a few other things such as 
what pressure it takes to expand the case walls into contact 
with the chamber (low - about 7000 psi for the 30-30 and 
about 2700 psi for the 45 ACP) and what pressure it would 
take to stretch a 30-30 case in a rough, overlong chamber 
(about 30,000 psi give or take).

JHBercovitz@lbl.gov

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The case is already in motion and gas is escaping when the 
case's walls contact the chamber's walls.  Only way around 
that would be if the case were thinner in its middle than at 
its ends.  Then the middle could expand before the case opens 
up enough to let go of the bullet.  Also, in the case of a 
bottle-necked cartridge, the case wall is thin as a fraction 
of its inside diameter in the large part of the case but 
pretty thick as a fraction of its diameter around the bullet.  
So in that instance, the case body very likely expands into 
contact before the bullet is released.

Since the case is already in motion and gas is escaping, the 
coefficient of friction between the case and chamber walls is 
greatly reduced: no static friction and the propellant gasses 
serve as a lubricant.  And for the reason given above, such 
would not be the situation with a bottle-necked case.

How far forward from the face of the case head do cartridges 
expand into contact with the chamber walls?  (What is the 
distance to the bright "expansion ring"?)  Obviously there is 
some head expansion even where the case does not contact the 
chamber; that's the principle of the case head expansion 
method of measuring safe chamber pressures.  However, only 
case wall area in contact with the chamber walls generates 
friction.  Also, only the area normally in contact with the 
chamber walls needs to be supported by the chamber walls; the 
rest of the area is normally unsupported and can be 
unsupported as the case is in ejecting itself in a blowback 
weapon.