Not to Break and Not Bend
It is thought that the process of creation of Katana has been developed basically in order to achieve three conflicting natures, 'Not to break, not bend, and sharply cut' simultaneously. In the modern metallurgy, 'not break and not bend' is called 'compatibility of strength and tenacity' and improvement research of structural material has still being done night and day. Because saving trouble even a little makes this compatibility balance lost.
Not to Break and Sharply Cut
Also, 'sharply cut' and 'not break' are difficult to be compatible. This has been realized by having so-called functionally-gradated structure that the cutting edge is hard, and the hardness is gradually decreased to the core, which makes compressive residual stress generate at the cutting edge. The explanation above is a case showing that the ideal condition is realized in the whole blade, so in fact, invisible defects can make a sword easily broken. However, a Katana in the ideal condition is called 'the world's strongest cutting tool,' and with reason. The sharpness of Katana are stated everywhere. As a notable example, 'Kabuto-wari (helmet splitting)' with Katana by the Dotanuki group led by Kenkichi SAKAKIBARA is famous. With best pieces of katana, if you drop one sheet of paper on it, it will be cut by its weight.
Katana is specialized for 'Cut Off'
katanaA Katana is not really light if you compare in the blade length, because its handle is longer than other swords. However, among the swords for double-handed use, it is one of the lightest ones. A Katana is originally suitable to 'cut off.' However, it is necessary to slide and pull when cutting so that the direction of force is added at a right angle against the object to cut, because the sword itself is light. With the same reason, when sharpening a sword to 'cut and kill,' it is sharpened in the direction to slide like a kitchen knife (similar in the way to handle double-edged sword). Tracing the history, from the Kofun period to the Nara period, when swords became separated between ceremonial use and actual use, 'Keito Tachi' and 'Kurozukuri-no Tachi' were only for 'cutting off.' In the Heian period, 'Kogarasu' adopted 'Kissaki moroha-zukuri (double edged tip style)' to be suitable also to 'stab,' but later, Tachi and Uchigatana didn't adopt Kissaki moroha-zukuri and had a curve to be suitable to 'cut' by wristing.
Values and Roles of Katana
It is quite an abnormal situation when people fight risking their lives, not just in battle, and they need to have a special determination. In such time, it is no wonder that 'the very soul of the samurai' of Katana, the mental and religious value as sacred treasures and the artistic value are needed as realistic force, in a way. There exist a lot of swords made during the war-torn period that are engraved with names of Shinto and Buddhist deities the owners believed in or with mantra, which interestingly reflects warriors' naked feelings. From the engineering aspect, in the periods when the theory of metallic crystal or phase transition was not resolved, sword craftsmen kept making an effort and achieved cutting tools that were excellent scientifically as well, which attracts much interest even now. This is because engineering control in the black box style is realized by accumulating and transmitting lots of meta-information including apparent change, texture, and smell that are not theorized or verbalized. In fact we don't interpret people's expression by fine and strict definition, but have an advanced ability to 'read the mind,' and especially since the Japanese are excellent in this ability, attempts to use Japanese manufacturing as an engineering system has begun in recent years.