I'm now reading a paper on J.R.R. Tolkien's use of myths and legends as inspiration for his book. It's called The Influence of Legends and Myths on J.R.R. Tolkien's Works by Jitka Cernochova. Not very exiting but it's really good! It's a rather long teaser, but science needs time and space you know!
The theme of broken and reforged swords also appears in the Volsungsaga. The swords usually break after the death of their owners and could only be reforged for the use of their succesors who faced a challenging task. In the Volsungsaga, Odin broke Sugmund's sword and in obedience to Sigmund's last wish, the fragments ofthe sword, like those of Narsil in The Lord of the Rings, were preserved.