Uh... you're shooting armor-piercing at destroyers? By choice, and not just to clear your gun barrels so you can load high explosive?
No. Just no.
Destroyers (the Khabarovsk aside) have no armor. None. There's no armor to pierce, let alone a citadel to penetrate. You will get overpenetrations with destroyer-caliber guns on destroyers, let alone anything bigger.
It doesn't have anything to do with tier. It has to do with how much armor you have to pierce, what the angle on target is, whether or not your guns are large enough to overmatch the armor of a target (this generally applies to battleship guns only), and your shells' velocity and penetration (the Des Moines, for example, has poor shell velocity but high armor penetration on its AP). Compare the two tier 6 Russian cruisers, for example -- the Budyonny has up to 140mm of armor to pierce, while the Molotov only has 70mm at best. And they're the same nationality, same class, and same tier. And one has double the armor of the other.
Tiers do not imply increasing armor (the Cleveland is tougher than the Pensacola, for example). You have to know what your weapons can do, and what you're shooting at, and where to shoot that target for maximum effect.
And use high explosive on destroyers for crying out loud.
AP works very well on DD"s if used correctly, if you catch a DD angled 45 degrees or more, the shell will go through enough of the destroyer to count as a penetration and in BB's that counts to 3-5k damage per hit which is easily 2-3x more than HE will do. Yes, for new players HE is better, but if you don't practice with AP you will never get better or understand the practice