One of the PCs in my group is trying to go through every locked door in a dungeon with his acid breath weapon. They're supposed to find the key or lock pick it open, but the player wanted to just melt every door. Does the acid count as corrosive to metals? Or just flesh?
TL:DR - Even if acid does "melt" metal, it may not open a locked door
Although not a direct answer to the question, it strikes me that in this situation whether the acid is capable of melting metal or not is irrelevant.
Consider the term "melt". Acid does not really melt things: it corrodes/dissolves them from the surface downward, with the acid losing potency as it goes, since it's reacting with the substrate to form an inert product. Powerful acid is an effective weapon because skin is thin and is essential to the body. Dissolving the surface of it down to the flesh is agonizing and debilitating.
Now think about applying the same logic to metal armour. It's thicker than skin, and so will take longer to dissolve. It also has a greater chance of rendering the whole volume of acid inert before it eats through to the other side.
Now apply the same logic again to a lock. The visible portion of a medieval level lock on a door is a chunky bit of metal. To actually damage the internal mechanism you've got to eat through that outer casing. That's likely to require a lot of acid.
Furthermore, trying to dissolve a lock from the outside of a door isn't an easy task even if you do have enough acid. If you apply it to the visible lock and it does corrode through the outer plate, all you'll likely achieve is to damage the internal mechanism so much that you'll never open the door, even with a key. To open the door you need to corrode the bolt itself which, if you think about it, has almost no surface area accessible in a locked door.
In short, you would seem to have plenty of options to discourage this sort of behaviour should you wish to do so, regardless of whether you and your players agree that the breath weapon can corrode metal. The first time your players find themselves stuck because they can't now open a locked door they tried to corrode even once they do have the key will probably also be the last.
The 5e SRD says about Objects:
...given enough time and the right tools, characters can destroy any destructible object.
So, is acid breath "the right tool" for destroying a metal lock, or a wooden/metal/stone door?
Objects and Damage Types: Objects are immune to poison and psychic damage. You might decide that some damage types are more effective against a particular object or substance than others. For example, bludgeoning damage works well for smashing things but not for cutting through rope or leather. Paper or cloth objects might be vulnerable to fire and lightning damage. A pick can chip away stone but can’t effectively cut down a tree. As always, use your best judgment.
It doesn't say they're immune, and it doesn't say they're vulnerable. In the end, it falls to DM judgement.
If you decide it is able to be destroyed, the Objects page gives the stats for objects' Armor Class:
Substance AC Cloth, paper, rope 11 Crystal, glass, ice 13 Wood, bone 15 Stone 17 Iron, steel 19 Mithral 21 Adamantine 23
and Hit Points:
Size Fragile Resilient Tiny (bottle, lock) 2 (1d4) 5 (2d4) Small (chest, lute) 3 (1d6) 10 (3d6) Medium (barrel, chandelier) 4 (1d8) 18 (4d8) Large (cart, 10-ft.-by-10-ft. window) 5 (1d10) 27 (5d10)
eg, an iron lock: AC 19; HP 2-5 (1d4-2d4)
But even then, he can't use it on every door, unless your party takes a lot of rests. From the 5e SRD:
After you use your breath weapon, you can’t use it again until you complete a short or long rest.
And, destroying the lock or door may have unfortunate consequences. Maybe a trap will trigger. Maybe you'll want to re-lock the door later - easy if you've used the key, impossible if you've melted it.
Not all Acid Damage corrodes metal
If you take a look at the most infamous creatures that deal Acid damage, Oozes, you'll see that the Monster Manual is specific on what kind of oozes can corrode metal. Two kinds of ooze, namely the Gelatinous Cube and the Ochre Jelly, though they deal Acid damage, do not corrode metal.
In the case of a Dragonborn's Breath Weapon, they are modeled after a Dragon's Breath Weapon, and both Copper and Black Dragons lack the ability to melt metal objects.
No, a Dragonborn's breath weapon cannot be used to melt anything other than flesh simply because the game doesn't say so.
The dragonborn's Breath Weapon racial trait explains how it works:
When you use your breath weapon, each creature in the area of the exhalation must make a saving throw, the type of which is determined by your draconic ancestry. The DC for this saving throw equals 8 + your Constitution modifier + your proficiency bonus. A creature takes 2d6 damage on a failed save, and half as much damage on a successful one. The damage increases to 3d6 at 6th level, 4d6 at 11th level, and 5d6 at 16th level.
Target choices for spells and other game features are deliberate. If a dragonborn's breath weapon was intended to affect objects, it would say so. Note that this is also consistent with the breath weapons on the stat blocks for dragons.
Each acid reacts differently to each metal. Copper reacts with practically everything. Chrome and aluminum resist most acids unless there is electricity. Platinum and palladium react very slowly with HN and HCl. Gold can only be dissolved by agua regia...
Some metals will dissolve instantly, others sit and bubble for a long time.
Piranha will dissolve steal, but it is probably going to explode when it hits the floor with sulphuric fumes...
Not sure about brass.
Make the locks out of other metals...
(source: work with acids and metals.)