1872-H Quarter. A/V Or Plug Metal?

There is no real A/V 1872h 25cents. It is a misnomer.
What we call A/V for these are merely fortuitous die chips.
There are two different dies with these chips.
One has a doubled N in Canada. The other, like yours, has a prominent die crack from the truncation of the bust to the rim.
Yours is a very late die state coin, on earlier struck examples the chip is smaller and more resembles an A.
There are 1880h 25cents with a true A/V similar to the 1872h 50cents A/V

That's correct...it is not a true A/V...

but I dont think the other names "die break V, Bar V" will ever catch on.

I've wrestled with this issue for my book, I think I'll go with the name "A/V"