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Mythbusters tackled this one once; they tested a variety of swords, with the swing speed and force matching that of an expert swordsman, and found that no authentic pre-20th century hand-forged blades broke, and only one low-quality factory-made sword snapped, and that was at the base, not at the point of contact. IIRC.
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If the question is can a piece of metal cut another piece of metal in half I say the answer is definitely yes. Under the right circmstances you can cut through a sword with a piece of wood.Whether it's possible for a particular sword to cut through another depends on specifics. I have no doubt that in actual history almost no one would have intentionally have cut a sword in half in battle. I do know swords broke fairly frequently (depending on the technology used) but just where they were likely to break I don't know.