This is yet another topic which I often have to explain repeatedly, as people are usually either ignorant, misinformed or simply skeptical about it. So this time, the explanation comes with pictures and videos for ease of understanding.
So what is a citadel overpenetration?
Quite simply, it is when an AP shell overpenetrated the citadel, and exited through the other side of the ship. The reason for this is because the shell has plenty of penetration left and the fuze delay is too long or didn't even arm (if the armor was too thin). The result is an overpenetration ribbon and 10% shell damage.
To get a citadel hit with an AP shell it must actually detonate inside the citadel. So if it overpenetrated, it's not a citadel hit, so no citadel ribbon, even though the shell passed through the citadel.
But, "Aha!", someone might say, "I have anecdotal evidence that I overpenetrated a citadel and got a citadel hit!"
To which I might reply, "Can I see the replay?"
In most cases, people didn't really pay attention to their hit ribbons or misidentified their hits. But to be fair, occasionally it might be a bug (and I do have a few replays/screenshots of these). Usually it's the former, and can be explained.
To showcase a citadel overpenetration, I present to you the Kuma:
As you can see from the screenshot above (taken from the PT server using the new armor viewer), the Kuma's citadel is its whole midsection (except for the superstructure above it). The ship is narrow and its armor is relatively thin. If a shell penetrated it, it simply can't miss the citadel. A very suitable candidate for testing citadel overpen. All we have to do is shoot some AP shells into it at close range.
And here's a video of it, using Sims' 5" AP SC Mk38 shells at ranges of 0.5 km and 2.5 km respectively.
At 0.5 km, the AP shells have so much penetration and velocity left over that the shell simply went through the citadel. Result: Overpenetration ribbon.
At 2.5 km, the shells lost enough penetration and/or velocity that it didn't go right through the ship and detonated inside the citadel. Result: Citadel ribbon.
Note: the test was conducted using 5" AP shells, if you use battleship caliber shells they have a whole lot more penetration and retain velocity better due to their weight, so it could overpenetrate even from medium distances.
So how to avoid citadel overpens? Here are some options:
Shoot from further away so that shells lose velocity and/or penetration, or so that the shells would plunge down through the deck (not all ships can do this even at max range). Shoot below waterline so that the water slows the shells down (very tricky, and mostly relies on luck with dispersion). Shoot at the widest section of the citadel, or shoot at it at a slight angle; the more distance the shell has to travel after penetration, the more time it has to detonate before breaching the other side of the citadel. Shoot HE; only if shell caliber is big enough, and only if the citadel is directly behind first layer of armor (very few ships have this configuration). You can actually get citadel hits with HE shells this way. Works with bombs too if the citadel is directly beneath the deck (but does not give citadel ribbons).
Hopefully this information has been of use to those who took a few minutes time to read through the thread.
This thread does not address the argument of whether or not citadel overpens should be doing more than 10% shell damage. That is a suggestion/lobby thread that should be made separately from this one.