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12.2.4 Sharpness
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Defining
and Measuring Sharpness |
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Your sword or knife that's just lying
there is either sharp or blunt. So sharpness is a static property. Well, yes, but there are properties
closely related to sharpness that are more dynamic:
- Retaining (or loosing) sharpness while using the blade.
- Reconstituting sharpness after it was lost.
And now I have opened a rather large can of exceedingly squiggly worms! Let me
make one thing very clear right away: |
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No, I don't have that easy fail-proof
recipe for keeping your blades sharp
I have enough trouble to keep my
own blades (medium) sharp
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All I can give you is a little
"theory" of sharpness and retaining same. But that is not overly
helpful for sharpening a blade. It is a bit like playing the piano (or any
other musical instruments): Knowing all about the theory of musical notation
and how that transfers into hitting the right key the right way at the right
time, will not a piano player make. And the top players (who do certainly know
the theory) don't know exactly why they are somewhat better at it then the
second (still very good) tier of players.
Some top experts can sharpen your sword better than "normal" experts
but nobody knows what, exactly, they do differently. That's why sharpening a
blade by hand is still an art. Sharpening blades by machines is different. The
razor blades you buy are all extremely sharp (even so there are some
differences between brands) and come straight from a machine. |
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For reasons not all that clear to me,
the concept of sharpness did not receive much scientific attention until quite
recently. References 1 and 2 (freely available
in the Net) give examples of recent papers dedicated to the subject; their
literature lists will lead you on if you like scientific fights and heavy math.
What I learned from perusing some more publications is that there is no general
agreement on how to define and measure sharpness. Greatly simplified, two basic
ways of defining the sharpness of a given blade by a number are pursued:
- Sharpness relates to the geometry of the blade, in the most simple case it
relates to the inverse of the radius of
curvature of the edge.
- Sharpness relates to the performance of
the blade, e.g. how deep it cuts into a standard substrate for a given force
pushing it down.
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The picture below gives an idea of
how one could relate sharpness to the radius of
curvature of a blade: |
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Sharpness demands a small radius of curvature
at the blade edge |
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Sharpness sort of begins at a radius of
curvature of a few micrometers (µm). If you want "razor-sharp",
you need to do better: A radius of 0.01 µm (=10
nm) is a good number then. The limit, of course, is the size of an atom
(imagine the circle in the picture to be an atom), giving a radius of about
0.0001 µm or 0.1 nm. That would be a more than
10.000 fold improvement on sharpness relative to a 1 µm radius.
I'm not sure if anybody has made a length of blade "atomically"
sharp. But one-atom tips are common goods
in "scanning
tunneling microscopy" or STM. |
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But is it only the radius of curvature that determines
sharpness? Of course not, consider the next two pictures: |
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Blades with identical radius of curvature but
different shapes |
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Ideal and real edge |
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Not much needs to be said. The upper
picture shows blades with the same radius of curvature but different blade
geometries, Would they all be of identical perceived sharpness? Probably not - but it always
depends of what you have in mind. Cutting hairs close to the skin without
cutting the flesh certainly would profit from an optimized blade geometry like
the one on the left. A meat cleaver wouldn't do so well with this shape,
though.
A more severe problem, however, results from the fact that most likely the
geometry changes as you move along the
blade. The radius of curvatures will not be the same at every point, the edge
is not perfectly straight, and so on. My drawing skills cannot do justice to
that but you get the idea. Irregularities along the blade are probably not so
good for cutting straight into something by only pressing the blade down but
might give better results compared to the "ideal" blade if you start
"sawing". Saws do not have teeth just for looks, after all. |
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To conclude:
- The (average) radius of curvature of your blade is not a unique and precise measure of the sharpness of your blade. But
the trend is clear: A smaller radius of curvature will tend to increase the
sharpness.
- The (average) radius of curvature of your blade is not a convenient indication for the sharpness because it
is difficult to measure. Cut your blade and look at the cross-section in a
light microscope?
Won't work, you need far higher resolution than what a light microscope has to
offer. You need a (scanning) electron microscope!
Sharpness is nanoscience!
- Getting numbers for the radius of curvature thus is possible but not
convenient.
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Indeed, if you look for
high-magnification pictures of blade cross-sections in the Net, you won't find
many, if any - as long as you do not hit on the pages of "scienceofsharp". This
site features many excellent pictures that were taken in a "scanning electron
microscope" (SEM); here are a few: |
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Rather good edge (left), and a somewhat
crumbly one (right) |
Source (for all SEM pictures here): from
the
scienceofsharp web page
Whoever you are (the site doesn't reveal the maker), thanks a lot for sharing!
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About as sharp as it can get |
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It's not easy to obtain an edge like
that! Don't ask me how to do it! Consult the page I mentioned. |
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Retaining
Sharpness |
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It's difficult to produce a sharp
edge but it is impossible to retain a sharp edge if you use your blade
frequently. What causes an edge to blunt, and how does that happen in detail?
Rather tough questions, in particular the second one.
If you want answers to the detailed mechanisms of blunting, you need to look at
the blunted blade with a high-powered electron microscope once more. That's not
for everybody to do, and if you want pictures I must refer you to the the
scienceofsharp site once more.
Or even better, the article of our old acquaintance, John D.
Verhoeven
3) who has written an
extensive
article with many (SEM) pictures about the subject. |
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The first question is easier to
tackle - at least up to a point. All of us know one sure way of blunting a
blade: Use it on something harder than the edge of the blade. Hit a decent
stone with most blades and they are now definitely dull - if not fractured,
dent and bend |
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What happens is quite simple in
principle. During impact (slow or fast) stress builds up on the blade edge and
on the regions of the target that is hit by the edge. Hardness essentially
measures the stress needed to induce plastic deformation (the yield stress) or,
more loosely speaking, the onset of local cracking, and the softer material
will "give" first, deforming in some way and thus
blunting itself.
Here are a few pictures showing what could happen: |
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Razor edge dulled by pulling it
"sideways" over glass |
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No surprise here. We just bend the
edge by plastic deformation. This can be reversed to some extent by "stropping" because the sharp edge is still there. You
"only" need to bend it back. |
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Edge dulled by drawing it across the lip of a
glass beaker |
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Here we have a bit of bending but
mostly deformation by compression and "filing" or abrasion, resulting
in a blunt edge. Glass is just quite a bit harder than most steels and thus
acts as the file; the softer steel will be the filée |
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The hardness of a material is a
reasonable well defined property, I have
gone through
that. Below are some old examples: |
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Metals |
Vickers Hardness |
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Ceramics |
Vickers
Hardness |
Tin (Sn) |
5 |
Limestone |
250 |
Aluminum (Al) |
25 |
Magnesia (MgO) |
500 |
Gold (Au) |
35 |
Window glas |
550 |
Copper (Cu) |
40 |
Granite |
850 |
Pure iron (Fe) |
80 |
Quartz (SiO2) |
1200 |
Good tin bronze (Cu + 10% Sn) |
220 |
"China" (Mostly Al2O3) |
2500 |
Mild steel |
140 |
Tungstencarbide (WC) |
2500 |
Hardened steel (extreme) |
900 |
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Polymers |
Polypropylene |
7 |
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Polyvinylchloride (PVC) |
16 |
Polycarbonate |
14 |
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Epoxy |
45 |
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This table makes clear why our
ancient forebears were reluctant to embrace early iron technology, considering
that they had marvellous bronze blades that were generally superior to blades
made from wrought iron or mild steel. It also makes clear why case-hardening
the edge of a steel blade by
quenching makes
all the difference. You might end up with an edge that could, in principle, cut
glass or granite! However, the
first law of
economics still applies! You pay dearly because there are plenty of
problems, too:
- You need good and homogeneous carbon steel to start from.
- You can re-sharpen your edge only a few times (if at all) because you
quickly wear off the thin layer of hard martensite.
- Your edge is rather brittle and chips easily.
The Japanese
sword demonstrates what it takes to make the best out of extreme edge
hardening while not yet in possession of superior modern steel that was liquid
once and can be cast. |
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Now to the trickier points of
blunting a blade. All of us know that our kitchen knifes will eventually become
dull even if we never ever try to cut anything hard! One of the key words hear
is "wear" and with that you
open the door to hell. I'm not going through it. I'll just show two pictures
demonstrating what can happen: |
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Formerly sharp (and hard) knife blade after
cutting
about 7 m of heavy (but soft) cardboard |
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Razor edge after cutting a few cm of bond
paper |
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Paper is normally considered to be
much softer than hard steel. But "steter Tropfen höhlt den
Stein" (constant dripping wears the stone) as the Germans know, and the
wear of the steel cylinders of rotary presses (used, e.g. for your newspaper)
caused by their exposure to "soft" paper is a major issue in
technology. |
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If you want to know more than that,
you are best of by reading the article of Verhoeven and colleagues about
wear of steel
blades 4). Here is the abstract:
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A study is presented on the relative wear rates of
two carbon steels, a Damascus (wootz) steel
and a stainless steel, using the Cutlery and Allied Trades Research Association
(CATRA) of Sheffield England cutting test machine. The carbon steels and
stainless steel were heat treated to produce a fine array of carbides in a
martensite matrix. Tests were done at hardness values of HRC=41 and 61. At
HRC=61 the stainless steel had slightly superior cutting performance over the
carbon steels, while at HRC=41 the Damascus steel had slightly superior cutting
performance. |
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1) |
C: T. McCarhty, M.Hussey, and M.
D.Gilchrist: "On the sharpness of straight edge blades in cutting soft
solids: Part I - indentation experiments", Engineering Fracture Mechanics,
Vol 74 (2007) p. 2205 -2224
Available in the Net |
2) |
P. Stahle, A. Spagnoli, and M.
Terzano: "On the fracture process of cutting", Procedia Structural
Integrity, Vol. 3 (2017) P. 468 - 476 |
3) |
John D. Verhoeven: Experiments on
Knife Sharpening
Directly published in the Net |
4) |
John D. Verhoeven, Alfred H.
Pendray, Howard F. Clark: "Wear tests of steel knife blades"Wear, 265
(2008) pp 1093 1099 |
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© H. Föll (Iron, Steel and Swords script)