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12.2.4 Sharpness |
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Defining and Measuring
Sharpness |
 |
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: |
| | 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 | |
|
 | 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. |
 | 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.
|
|  | The picture below gives an idea of how one
could relate sharpness to the radius of curvature of a
blade: |
| |  | Sharpness
demands a small radius of curvature at the blade edge | |
|  |
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. |
 | But
is it only the radius of curvature that determines sharpness?
Of course not, consider the next two pictures: |
| |  | Blades with identical radius of curvature
but different shapes | |
| |  | Ideal and real edge
| |
|
 |
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. |
 | 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.
|
|  |
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: |
| | |
| |
 | 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!
| |
|
|  | About as sharp as it can get | |
|  | It's not easy to obtain an edge like that! Don't ask me how to do it! Consult
the page I mentioned. |
|
Retaining Sharpness |
 | 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. |
 | 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 |
|  |
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: |
| |  |
Razor edge dulled by pulling it "sideways"
over glass | |
|  | 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. |
| |
 | Edge dulled by drawing
it across the lip of a glass beaker | |
|  | 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 |
| The hardness of a material is a reasonable
well defined property, I have gone
through that. Below are some old examples: |
| Metals | Vickers Hardness |
| 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 | |
| Polymers |
Polypropylene | 7 | |
Polyvinylchloride (PVC) | 16 | Polycarbonate |
14 | | Epoxy | 45 |
|
|
 |
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. |
 | 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: |
|
|
 | Formerly sharp (and hard) knife blade after cutting about 7 m of
heavy (but soft) cardboard | |
| |  | Razor edge after cutting a
few cm of bond paper | |
|  | 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. |
 | 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: . |
| | 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. | |
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)