Thanks for the tag,
@THEIS!
First off: I don’t know for certain and haven’t studied it specifically. As such I’m going to take a first principles approach. Also there’s a resource
here that passes the sniff test and will inform a couple of the answers.
1.
Powder fires are hot, and smokeless powder deflagrates (burns) but does not detonate (at the pressures we use it at). We then contain it in an expanding vessel, and since the internal pressure is a couple orders of magnitude higher than atmospheric, there will be some PV=nRT type contributions that raise the temperature higher. Plus, the powder burn rate depends on temperature, pressure, and geometry* - it doesn’t go off all at once, it’s still burning while the bullet travels some way down the barrel, and even once it’s finished burning the gas it produces is still expanding.
*This is why you don’t just do a 1-for-1 replacement with different powders when reloading - they’re optimized for different burn rates (through both geometry and flame retardant additives) and energy contents (higher or lower energy additives) and such.
In addition to the flame, there are other heat sources including the direct friction of the bullet sliding against the barrel, more heat from internal friction in the bullet as it is deformed by the rifling, and some heat from the expansion of the steel tube that we can approximate the barrel as. Finally, some combustion of the steel tube is technically possible with excess oxygen at those temperatures but I think that is negligible given the lack of rust in the barrel immediately after a gunshot.
The link I posted suggests that the heat going into the barrel is comparable to the kinetic energy going into the bullet, especially once we include friction.
Now, it’s important to note that we don’t just have a one-and-done flame when the bullet is lodged in the throat of the barrel. We can approximate the duration of the fire in the throat as the duration of the bullet in the barrel, which means we can back-calculate that we have an extremely high temperature for a fairly short duration (which should be obvious).
Given the inherent difficulty in monitoring temperatures directly at bullet timescales, I think it’s safe to say that the highest temperature is encountered slightly after the bullet has been engraved into the rifling, and will primarily affect the throat area of the barrel. Note that while the
gas temperature will start decreasing at this point, the
barrel temperature close to the bore will still be increasing because the gas is much hotter and the convective heat transfer from fast-moving hot gas to the steel barrel will be much faster than the (relatively poor) thermal conduction from the inside of the barrel to the outside, where we encounter convection to slow-moving gas that’s not much colder than the outside of the barrel and therefore not transferring much heat at our timescales.
Please also note that since this is a transient phenomenon, we will not see the
typical inverted half-paraboloid from a steady-state cylinder with internal heating source. Instead we will see a huge spike at the innermost surface that relatively slowly decays into such a half-paraboloid that itself is getting flatter as heat is removed. Side note: the barrelkuhl and other such widgets help because they turn the half-paraboloid temperature distribution into a full paraboloid for a given section of cylinder, and they don’t help much because the amount of air you can shove down a rifle barrel is pretty pathetic and air doesn’t have much volumetric heat capacity anyway.
In summary:
1. Likely cannot exceed that temperature (barring friction effects) and probably doesn’t (because transient phenomena with low heat relative to thermal mass of the barrel)
a. Definitely not.
2.
a. Total properties of the barrel, I’ve seen someone do full-auto dumps with an M16 and the gas tube melted shortly after the barrel was otherwise starting to glow a bit, after several hundred rounds at full cyclic rate. Bulk barrel steel structural properties don’t change until you’re pretty well on the way to the outer surface glowing, in part because geometry trumps elasticity every time, and the barrel surface - which is by definition the coldest part of a barrel in atmosphere with the barrel being shot regularly - has a massive contribution to total barrel stiffness.
Now, if we’re looking at the internal barrel temperature, we have a couple effects. Firstly, differential expansion within monolithic materials (like a barrel) induces stress cracking when taken beyond material limits. Second, material limits includes a fatigue element; at room temperature steels only survive about half as much load as theoretically possible from the stress-strain plot once the load is applied and removed a million or so times. As temperature goes up, fatigue behavior gets worse AND yield stress goes down in a compounding effect. Third, abrasion resistance also goes down (this is hardness plus micro scale toughness and really complicated to model, but happens to be something I’ve developed models for in other applications) as temperature goes up, and smokeless powder doesn’t burn completely clean so we are basically sandblasting the inside of the barrel after the bullet gets pushed through it (which also removes a few atoms here or there of material).
My assumption is that property change at the throat is measurable every shot, but structural property change of the bulk barrel itself requires more like one shot per minute per pound of barrel.
b. It will increase the rate at which you can fire without causing issues, because the bulk barrel will stay a lower temperature for longer at the same fire rate which helps wick heat from the throat through conduction, and you can keep the throat at the same temperature spike as you fire at a higher rate (transient phenomena on top of steady state) because the total heat rejection of the system scales with the area of the outer surface.
Alternatively, firing the same rate will on the whole keep temperatures lower and life longer because the increased cooling capability and increased thermal mass mean the heat gets wicked from the throat more effectively.
That said, I think it’s more a case of “same fire rate with twice as heavy a barrel means 110% barrel life”.
Please note that the gundrilled structured barrel approach is limited by the collective thermal conductance through the interstitial material between the holes or the free convection on the exterior surface, whichever is worse. I don’t see the long and relatively thin holes doing jack or shit for heat rejection into the air, but it may technically be measurable with lab equipment.
c. As mentioned above, yes, slightly. The throat still gets ridiculously hot relative to the rest of the barrel, but if the rest of the barrel stays cooler then the throat gets slightly less ridiculously hot, which means slightly less terrible thermal fatigue and abrasion resistance.
Answering the unasked question of “how do we get a barrel to last longer”? Some combination of improvements to the following without reducing the others.
1. High-temperature fatigue properties
2. High-temperature abrasion properties (chrome linings and nitride conversions do this but can make the fatigue cracking at the X/steel interface worse)
3. Higher thermal conductivities (transient spike lowered by conducting to the rest of the barrel)
4. Higher specific heat capacities (barrel stays cooler longer being the other half of the conduction equation from the bore to the bulk, but takes longer to cool back down)
I think the new material
@Frank Green has focuses on 1 and 2, and based on tooling comments I think the room temperature abrasion resistance and hardness are similar to 416R.
I would be very interested in something directionally along the lines of a rifled inconel sleeve (for high temperature properties) within a steel sleeve (because inconel structural properties are otherwise bad) within an aluminum extrusion (because steel thermal conductivities are terrible). I also know that such a barrel would be much more expensive than the life increase would justify.
pdf.sciencedirectassets.com 
