My wedding ring is tungsten; my wife and I decided to go with, shall we say, non-standard metals for our wedding bands to keep the costs down. I got her the usual gold/diamond sort of ring for engagement. We figured we could always get platinum or gold rings later.
I've found that I really love it, and now we may not replace mine at all. It's hilariously heavy and has a nice brushed finish.
You can easily shatter it with a vice grip or locking wrench, and with the rise of tungsten wedding bands EMTs and hospitals are more and more equipped for this.
Vice grips would probably be your best bet because they allow you to adjust the diameter they grip at fairly precisely hopefully avoiding further injury to your finger (such as: embedded tungsten fragments).
I've found that I really love it, and now we may not replace mine at all. It's hilariously heavy and has a nice brushed finish.