Physics
The ability of a blade to cut arises from the concentration of the force applied to the blade onto a very small area, resulting in a high pressure on the matter to be penetrated.
A serrated blade (a blade which has many small "teeth") takes this further as each individual tooth concentrates the force on a smaller area which helps cut through denser materials. A jagged knife can cut through objects solely with a sliding motion with little pushing force, this is useful, for example, in bread knives. Some bladed weapons (and tools) have curved blades.
As a rule the blade must be made of a substance which is harder than (or as hard as) the material it is intended to cut. If this is not the case the blade will either be unable to cut (as it absorbs all the energy and is damaged) or will wear away very quickly (if it is hard enough to transfer enough of the energy to damage the material). The material must also be tough enough to last (e.g. glass is very hard but it shatters easily and thus is not very effective as a material for a blade).
Heat treatments, which increase hardness for better edge-holding, reduce the material's toughness. A balance must be found between the sharpness and how well it can last. Methods that can circumvent this include differential hardening. This gives an edge that can hold its sharpness and a body that is tough.
Read more about this topic: Bladed
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