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Originally Posted by motan
The main strength parameter to increase (per weight unit) is the lateral stiffness and this is NOT a good idea because it reduces lateral flexibility and increase the chances of bending and breaking. A lot has been done in sword forging to achieve the exact opposite-more flexibility, like in katanas (very functional swords indeed).
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It's very easy to achieve more flexibility: just make the blade thinner. Thin enough, and the blade is very flexible and very difficult to break:
https://www.youtube.com/watch?v=eMAsCuDFSUI
(as long as the steel is resistant to metal fatigue). But too much flexibility reduces cutting and thrusting ability, since the blade will buckle instead of cutting/penetrating the target.
Stiffness is proportional to the thickness cubed, so the deflection of the blade by a given force is A/d^3, where d is the thickness, and A is some constant of proportionality. The strain (i.e., the proportional compression or elongation of the steel) is proportional to the deflection and the thickness, so deflection*B*d, where B is a constant of proportionality. The strain due to a given force is then A*B/d^2. If the strain exceeds the elastic limit, the blade will either break (at least crack, even if not completely break into two pieces) or take a set. Both things we wish to avoid. Note that a stiffer (i.e., thicker) blade reduces the strain - it's stronger, and less likely to break. It does not increase the chances of bending and breaking, but reduces them.
At this point, one should ask why, if this is the case, the thin very flexible blade doesn't break. The answer is that it's very difficult to apply a given force if the target gives with the force. Push on somebody hard - you can exert a lot of force. If they move away, you can't push that hard any more (without moving towards them). That's why the urumi survives. But if the blade wasn't able to get out of the way, you'd be able to press a small section of it into a tight kink without needing much force, and it would break or take a set. Since you probably don't have a urumi at hand, let alone one you're willing to destroy, you can try this with wire: compare the force you need to permanently bend thick wire vs thin wire (i.e., make the "blade" take a set). The thick wire needs more force; the thin wire needs to be bent further, but you can bend it further with less force.
The importance of stiffness for (a) supporting the blade against buckling while cutting, and (b) for strength explains why it common to see cutting-oriented swords with thin tips and thick bases. The last few inches near the tip can be about 1mm thick, while the base of the blade can be 10mm thick. A razor blade on a stiff 2.5 foot stick, rather than a 3 foot razor blade.