I'm using an ax now that I braised when the head split. It's unique. I thought of tig welding it, but I don't know what kind of metal it is. They say finest Swedish steel. Filler rod? I'd like to have a Wetterling I can show off too.
Why it the heck would you even think of welding a forged and hardened piece of steel that you already paid someone else to do right the first time?
It looks to me like they forged it a little cold(brittle) in the area, hence the crack.
I would not stand for a $40 Estwing or Bahco axe having a defect like that, let alone an $80+ Wetterlings.
The best way to prevent more of this is in the future is to let them know it occured and make them replace it now.