How readily would modern warships be put back into service after sustaining damage?

Cite? The wiki page on the sinking of the Sheffield claims the superstructure was entirely of steel, and the Board of Inquiry reportdoes not mention aluminum as a contributing factor.

Sheffield was only hit once, but it was a major hit. The missile penetrated the hull, blowing a big hole, and triggered a major fire (it’s unclear if the warhead exploded, or simply the missile jet itself still had enough fuel to start the fire). As well, the location of the hit was important - it took out some of the water circulatory system, making it almost impossible to fight the fire. The British abandoned ship because it was doomed, even if it took a few days of burning and rough seas to sink it.

The ratio between the warhead and the ship isn’t that important - it’s where the hit occurs. Bismarck was heavily armoured, but was rendered almost unnavigable by one hit from a torpedo dropped by a little bi-plane(!). The torpedo hit the steering gear and essentially doomed Bismarck.

That is interesting to say the least. I was going on my memory of the news reports at the time the conflict was unfolding, and there was a lot of talk about an aluminium superstructure. That it should turn out to be wrong, and yet went uncorrected is interesting. It isn’t as if there wasn’t a huge amount of interest at the time from every quarter.

Generally, were WWII ships more resilient to getting hit by one shell than today’s warships are resilient to getting hit by one missile? I understand that the probability of hitting of one missile is usually much higher than one shell.
Shouldn’t the anti-air systems on a ship do well against a subsonic target like most anti-ship missiles?

I do agree that the modern equivalent of parrying (EW) seems to be more effective than the equivalent of blocking (CIWS)

Which WW2 ships?
Carriers had protection against bombs and torpedoes, some limited level of it against Naval gunfire. Cruisers were the same level.
Destroyers were floating tin cans with people in them and has protection consumate with that.
Battleships could and did absorb obsene amounts of punishment, from multiple vectors.

As for anti missile defence, the answer is, we don’t know. There has not been much actual combat, and kill probabilities remain mostly theoretical. The little there is, the Falklands, shows that AShM could be devastating.

If we look at WW2, then the Japanese Kamikaze (which were in essence anti ship missiles), had a hit rate of about 15%. Sunk about 40 ships and damaged 400.
Not a good ratio did any modern fleet.

Erroneous press reports about technicalities of weapons are hardly unusual. Indeed lots of press reports suggested an aluminum superstructure as a contributing factor in the Sheffield’s loss. But the ship didn’t have one. The assumption was probably made based on blame put on aluminum superstructure for the extent of damage to the US ‘cruiser’ (originally ‘frigate’ or ‘destroyer leader’) Belknap in a collision/fire in 1975.

More generally, modern ‘destroyer’ or ‘frigate’ type warships are probably less vulnerable than WWII ships with the same designations. The WWII ships, especially destroyers, were stuffed with steam machinery which was a maze of critical components. A single medium caliber shell hit to the machinery spaces was fairly likely to kill at least one of the two propulsion plants. The shell body or heavy nose fragments from it almost had to hit and sever some important pipe, cable etc. WWII destroyers were sometimes ‘mission killed’ even by .50 cal hits (though contrary to some claims at the time, no real destroyer is certain to have been sunk outright by machine gun fire).

Modern ‘DD-type’ ships have fundamentally simpler propulsion plants. They also often have non-metallic armor over critical locations (especially now as opposed to 1970’s or 80’s based on various incidents in that time period), though not continuous armor belts and decks like WWII and previous era armored ships. WWII destroyers generally had no armor of any kind, and only some of the larger ones (US Fletcher and Sumner/Gearing types for example) even had hull plating deliberately made thick enough to keep out heavy machine gun bullets and light shell fragments.

However, modern ‘destroyer’ type ships can be as large as some pretty well armored WWII cruisers. In that comparison the modern ship is thinner skinned.

OTOH in any comparison modern warships, at least those meeting NATO shock standards, are far more resistant to shock damage than WWII warships.

Separately from surviving damage and returning to base though, there’s the issue of repair and return to service. That does tend to take longer now, for a variety of reasons, but one big one is simply that major navies and their support infrastructure and national economies are not mobilized on a war footing like WWII. Particular components might take a long time to manufacture. But that was sometimes true even in WWII. Cases like temporarily repairing USS Yorktown in a few days after bomb damage at the Battle of Coral Sea so the ship could fight at Midway were not typical of full repair of more severe battle damage. At the other extreme the New Zealand cruiser Leander was hit by one (albeit big) Japanese torpedo at the Battle of Kolombangara in July 1943 and didn’t re-enter service till just after the war ended. A matter of priority also, warships damaged in post WWII incidents, and Leander, were not as critical to repair ASAP as Yorktown.

Which again speaks to yard capacity.
Was a factor post Jutland as well, the larger British ships were back in action in several weeks, while the Kriegsmarines vessels were out for months.

After striking the well-charted Wolf Rock in 2002 HMS *Nottingham * was towed to Newcastle, NSW for destoring and eventually bought back to England on a heavy lifting ship. There was some debate about whether it would have been cheaper to scrap the hull and bring forward another Type 42 from the mothball fleet as a replacement , but the modernisations it had recently had swung the balance. Repairs took a year.

Belfast was mined in the Firth of Forth in 1939 and repairs took three years (intermittent, as the dockyard put her aside for more urgent work from time to time)

HMS Sheffield was not properly configured to operate in a war zone such that when the fire main was breached, there was complete loss of fire fighting capacity.

There are protocols in place when operating in a likely hot zone, Sheffield was deficient in this regard.

Had she been operating in the correct manner at the time she would not have been destroyed by fire, however her operational capacity would have been seriously disrupted.

Other Royal Navy vessels were hit and sunk - but took a lot more damage, others took significant damage but were already on battle stations and remained operational.

There is a report out on some aspects of her sinking, however certain things have not been publicised even though they are well known.

Which is one of the relatively unknown issues the Navy has been struggling with in recent years. Public shipyards are greatly reduced over even the end of the Cold war and they are old. The lack of capacity is causing issues already. In late 2017 the Navy had 15 nuclear subs sitting idle because of maintenance backlogs. There’s just not currently spare capacity sitting available to deal with a surge of ships damaged in combat. We can’t even keep up with routine maintenance.

There are private shipyards that would offer capacity that’s not being used. Along with the security issues of using them, they aren’t set up to work on warship specific items. In an emergency that offers some prospects.

Not that we know of.