I've been impressed twice with UA's handling of damaged bags.

In LHR, they gave me a new replacement that they had in stock and let me keep the damaged one, too. In SFO, they also gave me a new replacement on the spot but they wanted to keep the damaged one. Had to transfer my stuff to the new one in the baggage claim area.

Both times, the damaged bags and the replacements were non-descript Samsonite hard-sided bags with wheels, so definitely not in the Hartmann class. Did not have to whine or beg either time and so I thought this was standard procedure. Based on other comments in this thread, apparently not ...

I second the Briggs & Riley recommendation. I had a soft-sided bag crushed (not by UA) and they repaired it at no charge.