(Figured there was a factual answer, hence not in CS.)
In Lord of the Rings, Elendil’s broken sword, Narsil, is reforged for Aragorn. How practical is such a thing? Obviously, we can just say, “Elves did it,” and be done with it, but was reforging a sword whose blade was broken in half really a good idea? Would the sword be as strong as before, or would there always be an inherent weakness? For that matter, how did they join two pieces of steel in the days of blacksmithery? Or was the whole darn thing just melted down, and then poured back out, and hammered fresh?
When steel was rare it was not uncommon for a smith to forge weld a steel edge onto an iron axe head for example. Of course such doesn’t need to flex the way a sword blade does, the point is that forge welding essentially creates one piece of steel from two. It also heats a large area, so it does not create the localized stress that modern techniques do.
Blacksmiths generally don’t melt steel down. In fact I have never heard of one doing it. I have heard of blacksmiths selling off piles of worn-out horseshoes to foundries to be recast, but that might be anecdotal, if not made from whole cloth. However, the process of forge-welding iron and/or steel does involve heating the iron until the surface is liquid. Typically it goes like this: prepare the surfaces to be joined such that they are slightly convex. This is called scarfing. Once this is done, bring the piece to, say, orange heat and apply flux (typically borax). Return the iron(s) to the fire and heat carefully until the surface is liquid. Being able to judge this is difficult and is where we separate the rock stars from the groupies. I have to say that I am still a groupie at this point. If you leave the irons in the fire too long, it will start to burn. Anyway, remove the iron(s) from the fire and place them on opposing sides of the anvil so that they are hovering just above the anvil. Hit them lightly and they should stick together. Sometimes you don’t get a complete weld and you have to repeat the process. Then you need to dress the welded area (i.e. heat it and hammer it until it matches the surrounding metal).
I can’t answer the question of how common it was to weld up a broken sword, but it was generally cheaper to repair something that to make a new one in the old days.
1."but was reforging a sword whose blade was broken in half really a good idea? "
No.Reasons ensuing.
2.“Would the sword be as strong as before, or would there always be an inherent weakness?”
Sweeteviljesus gives a good description of forgewelding.Even a perfectly made hammer weld will be of different density than the adjacent HAZ (heat affected zone).Assuming subsequent annealing,then re-forging,then harden/tempering,the join area is DIFFERENT and thus doesn't share the rest of the blade's properties.The repair might be entirely suitable for usage though.
3.“Or was the whole darn thing just melted down, and then poured back out, and hammered fresh?”
Way beyond the PRACTICAL ability of the day (to this day ),lacking Elven (or Japanese ) powers.Though some smiths did smelt their own ore,melting large amounts of iron in a typical smithy would be laborious and time consuming.Smiths typically heat iron to solidus/liquidus phase,or below,called "heats" and given colour descriptors.Getting to white takes lotsa BTUs and oxygen,is too hot for most smithing,and is still below melting point.
The artists & craftsmen behind the LOTR movies were influenced by Japanese design when creating Elvish artifacts. The Houston Museum of Natural Science had the traveling exhibit of LOTR props & artworks a few years ago–it was quite a treat to see those wonderful things close up.
There have been several books on the esthetic & practical work behind the movies. Plus the additional features on the CD’s. So it’s evident that real weapon makers had some input.
And let’s remember Arthur Clarke’s statement: “Any sufficiently advanced technology is indistinguishable from magic.” The elves were really good!
They sure were. The ones entrusted to the reforging of Narsil were, we may reasonably assume, about as good as a high-class Japanese swordsmith would have been if he had devoted twenty lifetimes to the craft and been able to use magic into the bargain.
We have plenty of historical swords. It seems like re-forging would leave indelible evidence that experts could identify. And if it was cheaper and faster, it seems like it would have happened a lot. So…have we found any reforged swords?
One caveat I can think of is that, once swords were more decorative than necessary, people wouldn’t tend to save the ugly repaired swords and hand them down.