12.2.5 Sword Types and Static Properties
|Comparison of "Ideal" Swords - Bending Within the Elastic Limit
|Let's perform a classical elastic bending
experiment with completely different kinds of swords that are, however, completely identical in their geometry.
Same blade length, same cross-section, same tapering etc. Let's look at the following list
|Let's start by assuming that all those swords are made from homogeneous
and uniform materials, not containing any large defects or inclusions. In other words, we have perfect or ideal
swords from a material point of view.
|We know that for a given force acting
on the blades as shown above once more, the amount of bending or maximum deflection
(given by the distance zmax) increases
|The only difference between these swords is Young's modulus. For wrought iron
and bronze we have
|You should now be a bit confused since neither bronze nor wrought iron are well-defined materials. Do I mean 90% Cu / 10% Sn bronze? Arsenic bronze? Wrought iron with almost no carbon or with 0.2 % carbon? Those are different materials after all.
|That is perfectly true. Nevertheless, Young's modulus for all those different copper or iron alloys, summarily addressed as bronze or wrought iron, is about the same. Differences are at most in the 10 % region and that is negligible for what we are doing here. I have emphasized that before and I have given the scientific reasons for that. In essence, Young's modulus is a property resulting from the bonding between atoms and as long as most atoms are of one kind, it is much the same. It doesn't depend much on what kinds of other atoms are mixed in as along as there are only a few percent.
|Now let's include swords No. 3 - 6 in our comparison. They are made from very
different kinds of steel or from several kinds in some composite construction. Nevertheless,
their bending behavior in the experiment above is not noticeably different from the wrought steel sword. That's because
Young's modulus of all (low-alloyed) steels is about the same for the reasons given. The large majority of bonds is still
found between iron atoms.
However, in some of the steels we now may have a lot of cementite, (iron carbide, Fe3C). Doesn't that make a difference?
|Yes, it does. Young's modulus of a composite material with large
percentages of other atoms will be some kind of average of the individual moduli of the constituents. I have shown you how
to calculate this.
Wootz steel for example, can be seen as a composite of ferrite (=iron) and cementite (=iron carbide Fe3 C). However, as it happens, Young's modulus of cementite, around 200 GPa, is not much different from that of iron around 210 GPa. You don't have to believe me, in reference 1 I give you one serious source plus the abstract of that paper. So no matter how you average, you end up around the value of iron.
Of course, if you look closely you will find some differences. But here we don't care about differences of 10 % or so. We simply commit to memory:
|I know that this contradicts a large amount of what has been written about "elastic"
properties of composite swords. Pattern-welded swords are almost
always described as a combination of a hard but brittle steel with a soft but elastic one, giving you hard and elastic as
a result. Wrong on three counts:
| Other common mistakes often found in the literature are:
|A sword might be pronounced to be more elastic for example if you can bend it to a larger
degree than some other sword before something unpleasant happens.
That leads us to the second point we want to look at here: How do those still ideal swords compare if I increase the force in the bending experiment to a value where "something" happens?
|Comparison of "Ideal" Swords - Bending Beyond the Elastic Limit
|So what happens if you bend until something
happens? What will happen? For the first three swords the answer is simple. All of them are ductile and therefore all of
them will deform plastically as soon as their yield stress is reached. This will first take place in the outer layers as
described before as soon as a critical force
is reached on the bending experiment. Then the stress
in the outer layers exceeds the yield stress of the material. It is not too difficult to calculate the stress in a
bending experiment from the force but it is no longer straight-forward as in a tensile test experiment.
If you keep increasing the force beyond the critical level, the plastic deformation spreads into the interior because deeper and deeper parts experience the yield stress. In the "neutral line (or plane) in the center, the stress is (ideally) always zero.
Since yield stress is (more or less) just another word for hardness, and hardness depends not just on the chemical nature of the material but also very much on its internal structure, only general statements about the behavior of our swords can be made.
|The first general statement is easy: As soon as parts of your blade deformed plastically,
it will not "snap back" to being perfectly straight after you release the force. The permanent bending effect,
however, may be small for reasons considered below.
Bearing this in mind, we now look cursorily at our examples form above:
|In the case of swords No. 4 and 5 we are looking at properties of composite swords.
They are by definition "inhomogeneous" if still ideal swords. In other word, we have a composite of at least two
steels with quite different behaves concerning plastic deformation and fracture, even
so they have the same Young's module and thus behave identical as long as only elastic deformation
is concerned. But each steel of the composite construction is still perfectly homogeneous as we assume here.
|We can't avoid any more to look a bit more closely on how an (ideal!) composite material performs in a classic tensile test or bending experiment. I will do that in the next subchapter.
|A. P. Miodownik: "Young's modulus for carbides of 3d elements (with particular
reference to Fe3C)", Journal Materials Science and Technology Volume 10, 1994 - Issue 3; Published online:
19 Jul 2013
Absract:The Young's modulus of transition metal carbides has been calculated from their assessed thermal properties to explain why the modulus of steels and white cast irons can be only marginally altered by changes in composition or heat treatment . It is shown that the modulus of cementite (200 GN m-2) is virtually identical to the value calculated for pure ferrite (215 GN m-2). The predicted systematic variation for the modulus both with structure and position in the periodic table rationalises previous isolated experimental observations and confirms that the MC carbides of the group IV elements should have the most powerful strengthening effect in a matrix of their parent metal.
© H. Föll (Iron, Steel and Swords script)