I tried using the durtanium brackets artifact and it said "You cannot use that here" or something. Now the artifact is gone, and I see no difference on my ship. What's the deal?

Might've been a bug. Try logging out of Facebook, clear your cache, then log back in. If there's still no change, and the Brackets definitely aren't in your artifacts list, contact the admin.

I've used a few Brackets myself, so I know they work. They increase your hull strength by 10 points. It's not visibly much, especially if you've already got a lot of hull, so it's easy to miss the effect. I's still worth it though.

Or 13 if your profession is fixer.