What, in physics, is sharpness?

August 3, 2011 9:25 PM

What, in terms of physics, does it mean for something to be sharp? What exactly is it about the arrangement of matter that gives it this property, and what makes it more or less so?
posted by shivohum to Science & Nature (10 answers total)

From what I recall from a materials course I took back in 1997... sharpness in materials centers around the material's ability to maintain its form with a minimal external lattice structure. What this means is, with a substance like glass, one can make something super sharp principally because you can thin a sheet down to a single molecule thick. With that thin a structure, one then gets the added benefit of being able to slide between the gaps in a different structure and segment the bonds of the secondary substance.

So by having glass one molecule thick on one edge, yet being dense enough from both the side and back, you could have a ridiculously thin - yet useful - blade. Glass incidentally is one of very few lab substances that can make that nearly perfect lattice structure.

That's all I remember...
posted by Nanukthedog at 9:45 PM on August 3, 2011 [2 favorites]

I believe it's a matter of force divided by area, accounting for material strength. When you hit something with a blunt object, the mass of the object is distributed across the surface area that comes into contact with the target. But if you use a sharpened blade, the leading edge is much smaller in comparison, so the force is concentrated enough to do acute physical damage. The size and strength is important, too -- a razor blade (or a sheet of paper) can slice your skin, but it can't cut down a tree.

Here's an interesting PDF that goes into some more detail: "Sharpness and Bluntness: Absolute or Relative?" from the book The Science and Engineering of Cutting (this Google Books preview shows more, albeit with skipped pages).
posted by Rhaomi at 10:02 PM on August 3, 2011 [3 favorites]

Glass incidentally is one of very few lab substances that can make that nearly perfect lattice structure.

Um. No. Glass has no lattice structure whatsoever. Actually, the lack of a crystal structure is one of the defining characteristics for determining what is a glass and what isn't.

Coincidentally, from a physics perspective, glasses have more in common with liquids than they do with most solids. (Glass is not a liquid, but I'm not going to fault those who believe that myth, because the similarities are pretty darn convincing, and the distinction ultimately comes down to a technicality. Also, don't believe anything you hear about cathedral windows...)

I studied Physics and Materials Science at an undergraduate level, and never encountered any technical use of the word "sharpness." I have no idea if there actually is one, but Google doesn't seem to suggest that there is.

On the other hand, you could use an object's hardness alongside details about its surface geometry (ie. how thin it is, or the radius of curvature for a given edge) to create a de-facto definition of "sharpness." Or at least, that's how I'd do it.
posted by schmod at 10:06 PM on August 3, 2011

Generally when you talk about how sharp something is you're talking about how well it can take and hold an edge, i.e. taper down in a wedge shape as narrow as possible. As the tool is used, due to all the force being concentrated in that small area, the wedge shape tends to become blunted, deformed, or even nicked away -- the material is so thin that it easily wears. So generally you want your metal to have a high hardness to resist this deformation, but hardness also generally means the metal is no longer tough, i.e. it will fracture instead of bending, and that's no good either. You can reduce the hardness a little bit to get toughness, but then the edge dulls faster. There are various compromises and workarounds that have been invented. One is case-hardening, whereby you harden the outer layer of the metal only, leaving the bulk substrate more tempered. This gives the edge a flexible backbone to absorb stress while still maintaining the hard shell to help prevent dulling.
posted by Rhomboid at 10:13 PM on August 3, 2011 [1 favorite]

Sharpness is simply having a very fine edge. As Rhaomi says, it is about multiplying force onto a very small area. A sharp thing splits apart the thing it is cutting, like a wedge. And as schmod says, it is ultimately about geometry.

But another aspect of sharpness is the microscopic irregularity in the edge. If you take a knife and press it onto a tomato, it won't go through. But if you move it while pressing (slicing), it goes through instantly. That's because at some level, all sharp things look like a saw.

The materials science stuff is more about how long something can remain sharp.
posted by gjc at 5:46 AM on August 4, 2011

Tomatoes only resist blunt knives. I worked in a vegetarian kitchen as a kitchen hand, and while slicing helps, pressure was enough to get through the skins.
posted by titanium_geek at 6:52 AM on August 4, 2011

Sorry hit post too soon- I meant to add that we had kick butt knives compared to the home kitchen. my favourite was the meat cleaver for pumpkins.
posted by titanium_geek at 6:55 AM on August 4, 2011

The concept of "sharpness" includes a lot of qualities that many people confuse, some chemical, some geometric. For instance, the iconic Ginsu knife was not, in fact, truly sharp. Neither is a hacksaw. Instead, the serrations make it easy to tear chunks away from the object being cut. Naturally, these serrated knives rely on lots of side-to-side motion. All they need to maintain their "sharpness" is a relatively strong steel (and they cannot be re-sharpened when dull).

Now, if you look at something that is truly sharp, take a diamond knife that is used to slice unbelievably thin samples for electron microscopes. It combines both the hardest substance known with a very fine edge as Rhomboid and gjc discuss, allowing the force of the entire blade to come down on a vanishingly small area. The limit, as mentioned by Nanukthedog, is a single row of atoms.

Most materials are not strong enough to resist being worn away the way diamond does, though. That's what material hardness means, and it is an important component of maintaining true sharpness over time. Then there's the ability of a material to be worn away during sharpening without breaking. A ceramic knife is extremely hard, and therefore can be manufactured with a very fine edge. However, you can't re-sharpen it because it would break. The various types of steel (including differences in manufacturing like forging, stamping, tempering) used in kitchen knives are a tradeoff between hardness (keeps a fine edge but takes more force to sharpen), flexibility (can resist the strains of use and sharpening), and other qualities like ability to resist rusting and staining. Interestingly, most kitchen knives are not sharp from the manufacturer, and even professional knife sharpeners often will not actually sharpen them. The angle of the edge of the knife is about the same as that of an axe, 40 degrees in total. See this discussion of knife angles to see why Japanese knives are manufactured with a sharper edge, for instance.
posted by wnissen at 7:13 AM on August 4, 2011 [1 favorite]

Obsidian is one of the sharpest substances known.

The inhibition of atomic diffusion through this highly viscous and polymerized lava explains the lack of crystal growth. Because of this lack of crystal structure, obsidian blade edges can reach almost molecular thinness, leading to its ancient use as projectile points and blades, and its modern use as surgical scalpel blades.

I recently watched an anthropologist giving a lecture about obsidian and its use by ancient peoples, and as he was fracturing this material and describing its extreme sharpness, blood started to drip profusely from his hand onto the floor. He had cut himself without even feeling it. And he was being careful.
posted by weapons-grade pandemonium at 7:14 AM on August 4, 2011

any kind of foam (like foam rubber) will dull a blade very quickly...it's the surfaces of things that take the most toll on a blade (and foams have lots of little bubble surfaces)...due to surface tension.
oiling a blade lightly before use will keep it sharp longer...
posted by sexyrobot at 9:59 AM on August 4, 2011