well this is wordy but states it better than i could.
The USS SOUTH DAKOTA Class had a 12.2" (310 mm) Class 'A' belt laminated to about 2" (50.8 mm) of cement and 0.875" (22.2 mm) of STS bulkhead plating and inclined 19o from the vertical outboard (top overhanging bottom) to increase all possible impact angles. (The U.S. Navy made considerable use of homogeneous armor grade STS in its WWII battleships for the upper hull, major bulkheads and major decks -- a rather lavish design detail due to the higher cost of this metal.) This armor was recessed inboard on the third anti-torpedo bulkhead exactly like the later USS IOWA Class. There was a 1.25" (31.8 mm) vertical STS outer hull (increased to 1.5" (38 mm) in the IOWA) and a 0.5" (12.7 mm) mild steel or HTS second bulkhead plate spaced a few feet in front of the main belt. This added outer plating would only reduce the 38 cm projectile's striking velocity on the main belt by roughly 10 feet/second (3 m/sec), but it was (barely) thick enough to decap the German 38 cm projectile (), resulting in shatter when the projectile hits the face-hardened Class 'A' belt. [It should be noted that the South Dakota's outboard plating would certainly de-cap any projectiles under 16" (40.6cm). De-capping 16" projectiles is possible but not certain, and no larger projectile would usually be de-capped. The Iowa class' slightly thicker outer plating, however, would de-cap all projectiles up to 18.6" (47.3cm) in diameter.] A few projectile nose and upper body pieces penetrate at the HL, with their number increasing with increasing striking velocity until essentially all penetrate at the NL - the HL and NL are both drastically higher when shatter occurs. Also, unless the rare nose-only shatter occurs, shatter drastically reduces the projectile's explosive power and its further penetration ability. To deal with these, there was an upward extension of the last torpedo bulkhead spaced a few feet behind the main belt - 1" thick STS amidships and 1.5" around the magazines.
so the South Dakota armor would decap less than 16" and may decap 16" shells. Iowa would decap Yamatos' 18" shells. you would still get shell fragments at some ranges and at close ranges, the entire shell may go through but it would be damaged so as to not do catastrophic damage.
from this article. http://www.combinedfleet.com/okun_biz.htm a good source to start one's research.