He said this didn’t match the predicted failure mode, but I don’t know if they took all the material properties into account.
Here’s a little primer on screw threads. There are two mating parts, internal (female) and external (male). To mate, they share a common profile. Simplistically the outermost diameter of the external thread is called the major diameter, and the innermost diameter of the internal thread is called the minor diameter. Note that a thread profile does not yield sharp V shapes, they are truncated for strength and clearance. The tips of the threads have ‘crest flats’, while the depths have ‘root flats’. The bump-to-bump width of one thread is called pitch, and the amount the thread travels in one full rotation is called lead (they’re the same in this case.)
Allowances are defined so that there’s enough clearance between parts to allow for assembly.
The strength of a thread under tension (pulling apart) is determined by the “length of engagement”, which is how deep the external thread is engaged with the internal thread. At some depth the thread is as strong as it’s going to get, and that’s called the minimum length of engagement. The calculation usually yields somewhere between 4.5 and 9 turns of the thread, but that’s only a rough average and depends on a lot of factors, including the material strength. Also note that big coarse threads are not necessarily stronger than shallow fine threads.
All other things being equal, internal threads are slightly stronger than the mating external threads, because the bulk of their material is nearer the major diameter. The major diameter’s circumference is larger than the minor diameter’s, and so each turn is longer and has more material than at the minor diameter, therefore more strength.
He’s adamant in claiming the cap was heat treated to a hardness of C-30. Case hardening treats the outer layer of the metal, giving it a very hard skin. This is normally done to prevent wear. It’s also valuable for cutting tools, which will keep a sharp edge much longer.
Case hardening is done by heating the metal to a certain temperature then rapidly quenching it. The outermost layer becomes very hard but brittle so the surface of the part is extremely resistant to wear; while leaving the inner core softer, more elastic and tougher so that it structurally absorbs shocks (critically important for this application.) If it helps, visualize it as a layer of really hard paint, 0.030 thick, extending beneath the surface of the original part.
And so his description is still weird to me. Case hardened parts are extremely difficult to machine, because the outer surface is as hard as the tools used to cut it. The normal way to thread a case hardened part is to cut the thread after it’s been heat treated. During the initial process of turning the part on the lathe, you’d normally turn the threaded portion of the part as a plain cylinder, leaving it larger than the major diameter of the thread (by adding twice the depth of the heat treatment), and then heat treat it. Afterwards you’d grind the turned diameter down to the major diameter, removing the entire case hardened layer from that area of the part. You’d then be able to cut or grind the thread in the untreated metal beneath. The threads would then have the strength of the untreated steel. And in that case, the heat treating is irrelevant because you’ve cut it away. So I don’t understand his emphasis on heat treating.
You can certainly cut the threads before heat treating, then heat treat the part, then finish the threads with a cleanup pass on a thread grinder. We used to do that for certain types of worm screws used in linear actuators, where the case hardened surface was needed to withstand the wear of decades of pushing loads. But it’s uncommon, and expensive. I suppose you could try to chase the threads with a die after heat treating, but that just seems like an efficient way to break a lot of dies, and would leave you with the weaker threads I mentioned above.
It’s also possible the breech was threaded after heat treating, but the cap was threaded before heat treating. Cutting internal threads is harder than cutting external threads, so they might have tapped the cap first, heat treated it, then run a die through it to clean it up. That could lead to an interesting mix of materials.
We can see from the third video that the cap threads did not fail; it was the threads on the breech that were sheared off near the minor diameter (the bottom of the V on an external thread.) Therefore the cap was stronger than the breech, as expected.
He said the threads didn’t match the predicted failure mode, but I think they did; they were sheared off just above the minor diameter of the breech threads. And he said the cap is made of 4140 steel, heat treated to C-30. I have to assume the barrel is also 4140 and also underwent the same heat treatment.
A 12 pitch thread has a lead of 0.083 inches. The root flat of a 1.5-12 UNF-2A thread is 0.0104. C-30 case hardening is 0.030 deep, leaving 0.013 inches of untreated metal per pitch at the root (actually less because of the 60 degree angle of the flank.) That leaves only about 15% of the material at the minor diameter untreated. It will be extremely hard but brittle, sapping it of the ductility needed to absorb hard shocks. A little higher than the minor diameter, but still below the pitch diameter, the case hardened layers would meet in the middle and become 100% of the material, with no untreated metal left for strength. That stress line would likely be the weakest path through the thread profile.
Now look at the shear line on those breech threads.
Finally, the length of engagement, which is not a calculation I performed here. I count 4 threads on the barrel, which seems close to the minimum; but that may have been ok for this application to meet its rated load. I simply don’t have enough info to know.
But if there’s any of the case hardened layer present in the thread profile, the ordinary computations based only on untreated 4140 might not have been sufficient.
And if the cap’s threads were hardened, but the breech’s threads weren’t, the sharp corners at the bottom of the Vs of the minor diameter of the cap might have acted like a sharp broaching tool and cut off the softer untreated metal of the breech threads. The more I think about this, the more likely I think is.
It does bother me the gun designer didn’t already have those calculations right in front of him from when he designed it. And given the (now apparent) variability of the ammunition loads, it seems that whatever he computed for length of engagement has nowhere near the safety margins needed for the task.
Disclaimer: I’m an engineer who wrote a thread form calculator for a precision grinding machine shop a very long time ago.
