The inside diameter of the pressure interface in both a yoke and a DIN connection is about 0.5 inches, therefore the pressure area is about 0.196 inches square.
With a pressure of 3500 psi the pressure thrust is 687 pounds.
With a pressure of 5000 psi the pressure thrust is 982 pounds.
The minimum cross section area that I could measure on a 232 bar yoke is 0.125 inch square per side (two sides of 0.25in x 0.5 in). Therefore the maximum tensile stress on the yoke is only 3,927 psi (at 5000 psi).
Determining a worst case bending stress requires some very conservative assumptions since the geometry is intentionally design to minimize any bending (this is a good candidate for a Finite Element Analysis model, but I am not spending any more time in this issue). With some very conservative assumptions I come up with the worst case bending stress to be about 6,300 psi.
This stresses are well below the yield stress of annealed Naval Brass (25,000 psi), but most likely it should be compared to half-hard Naval Brass (yield strength = 53,000 psi). With this kind of loads alone it would never reach any fatigue failure of any kind.
The maximum elastic deflection I can calculate is about 0.0001 inches for the section in bending. The total cumulative deflection could easily be a few times that number.
And yes, all materials will flex under any load. In the elastic region, the deflection is proportional to the load, if the load is insignificant the deflection is insignificant. Any flexing that does not reach yield strength is defined as elastic flexing and the deflection will return when the load is removed.
The bottom line is that the modern heavy (232 bar) yoke attachments by design have a large safety factor even if used at 5000 psi (no surprises there, see note), and if they are not damaged, deformed in any way, and properly secure, they can handle any pressure encountered in Scuba diving.
DIN attachments do have the advantage of not having the yoke screw knob sticking out the back.
The 5 or 7 threads on any DIN fitting are barely loaded under any Scuba pressure (unless there is any sand grains trapped in the threads, but that is a different story).
BTW, Jimmer, if I recall correctly, the classical thread analysis that shows that the full strength of a screw can be carried by only 3 threads mostly applies to male and female threads using similar material Young’s modulus. This coincidentally does apply in this situation.
Unquestionably I have made mistakes. That is not because I am an engineer, but because I am human. One mistake that I have always avoided whenever possible is that of not listening and learning and learning from everyone around me. That will specially include all the technicians, mechanics, welders, fabricators, and other engineers both degreed and non-degreed engineers that I have had the luck to work with. And yes a few of the sharpest engineers I have had the pleasure to work with did not have a formal engineering education and many of the sharpest people I have ever met where technicians, etc.
In my engineering education one important point we were taught is that we only had the tools to keep learning…the learning never ends (this obviously applies to Scuba diving and live in general). Any day that I learn something new, it is a good day. Keeping an open mind is a good thing.
Added:
Note: This is a consumer item, if you don’t think a simple consumer item like this doesn’t have a huge safety factor, you are forgetting…this is America; if someone gets hurt, some will get sued. It would be very easy to calculate the structural safety factor on a yoke or DIN connection. I basically already did it.