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
|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
|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
|The only difference between these
swords is Young's modulus. For wrought iron and bronze
|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 Fe3C). 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
| Other common mistakes often found in the
|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
|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.|
|1)||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)