... what is cutting?

[hardheart]

It seems like a really dumb question. But I mean how is cutting different from, say, breaking? A knife cuts because the edge is very thin, which focuses the pressure on a small area. Well, with more pressure over a larger area, you can still separate material. I dunno, like a dull and damaged lawnmower blade still 'cutting' the grass. This question partially comes from some thinking about how a knife can cut through a bulletproof vest. Is it just that the contact area of a bullet is just so large in comparison to an edge, that despite the large amount of force driving it it still can't generate the same pressure as a blade?

 

[rlcanon]

Just to complicate the issue, there are different modes of cutting with a blade. Chopping, slicing, and shearing for starters. I'm also interesed if there are any technical documents that describe what happens at a micro level when various common materials are cut with a blade.

 

[Cliff Stamp]

But I mean how is cutting different from, say, breaking? A knife cuts because the edge is very thin, which focuses the pressure on a small area. Well, with more pressure over a larger area, you can still separate material.

Yes, if you were for example to move a knife fast enough you could cut through a 2x4 with the spine. You can see the results of this by looking at impacts of objects in high winds. Generally the defination is that cutting means that there is minimal gross deformation/damage to the material around the point it is severed. Thus you chopped through a piece of rope with a knife and smashed it with a hammer as there is far more damage to the rope with the hammer. But yes, if you look at the rope under high magnification it is smashed by the knife edge as the actual edge of a knife, even the sharpnest one is massively large compared to the scale of the microscopic nature of materials. Essentially materials have some tensile point or compression limit and once they pass this they will tear/fracture, if the contact area is really low then this pressure can be exceeded with a lot force. Since the force is low this means minimal distortion on the object as a whole and thus a "cut" is made.

-Cliff

 

[VegasNick]

Isn't the knife breaking the bond between molecules or maybe even seperating the atoms of molecules?

 

[rlcanon]

Isn't the knife breaking the bond between molecules or maybe even seperating the atoms of molecules?

I think that's the way a Hattori Hanso sword works...

 

[kel_aa]

Isn't the knife breaking the bond between molecules or maybe even seperating the atoms of molecules?

In the way that say a line of people holding hands is the struture (you being the atoms in the case of metals or molecules in the case of organics, and your hands being the bonds), and an extra-wide dumptruck driving toward you is the edge knife edge. I think you can imagine the rest.

 

[HoB]

Very good analogy Kel_aa, just imagine your extra wide dumptruck about a mile wide .

 

[Cliff Stamp]

In the way that say a line of people holding hands is the struture (you being the atoms in the case of metals or molecules in the case of organics, and your hands being the bonds), and an extra-wide dumptruck driving toward you is the edge knife edge.

It is more like a line of ants getting hit by a 747. Edges are about 10^-6 m, atoms are 10^-10. Yes the bonds are broken, the bonds are broken if you drop a piece of concrete on the floor, however a knife edge isn't cutting through individual bonds.

-Cliff

 

[kel_aa]

Edges are about 10^-6 m

Is that the best you can do, Cliff?
Thanks for correcting me on the scales.

 

[erdvark]

Edges are about 10^-6 m

I'm curious about this number, where did it come from? i always figured it should be around this size since light is on the order of 500 nm or 0.5^-6 m so anything much larger would be a few wavelengths and make a specular reflection, which would mean that the edge was dull. I know from experience that i can see light reflecting off a 20 um wire, i wonder how much smaller it can get before it's invisible?
Also it seems like this discussion on cutting as a separation of bonds implies that the material being cut is flexible enough to move away immediately after the edge, like meat. In the case of stiffer materials like wood being cut along the grain, it can break ahead of the edge if the blade is thick enough, viz. the book on sharpening.

 

[puukkoman]

Now I'm scared to cut anything... What if I split an atom???

 

[Cliff Stamp]

Is that the best you can do, Cliff?

Generally I like to stop about there, when you go much finer you can induce chemical reactions with the edge cutting through electron clouds and that can be bothersome. Though it is handy to have in a survival situation as you can carve water out of still air, carve some sodium out of salt to make a fire and so forth.

I'm curious about this number, where did it come from?

Magnification of edges, specifically Verhoeven did it in the most detail and the finest he achieved was 0.1 to 1 micron. When edges are fairly blunt, to the point they lose fine cutting ability, they are generally above 10 microns thick and highly distorted laterally.

Also it seems like this discussion on cutting as a separation of bonds implies that the material being cut is flexible enough to move away immediately after the edge, like meat. In the case of stiffer materials like wood being cut along the grain, it can break ahead of the edge if the blade is thick enough, viz. the book on sharpening.

Yes, that is a good point, you can induce splitting in some materials and the edge generally just starts a cut.

-Cliff

 

[erdvark]

Magnification of edges, specifically Verhoeven did it in the most detail and the finest he achieved was 0.1 to 1 micron. When edges are fairly blunt, to the point they lose fine cutting ability, they are generally above 10 microns thick and highly distorted laterally.

Optical magnification? Then we are back to the light problem, optical microscopes have a few hundred nm resolution. Ok, got his paper, nevermind he used a SEM to look at the blades.

Ok, so here's another question. If you polish a metal surface enough, the friction will increase since more surface is in contact, eventually you get cold welding of metal on metal but usually only in a vacuum. So is there some optimal amount of smoothness or polish on a knife blade beyond which friction increases? Would a highly polished blade have higher drag cutting meat than one that is conventionally ground or versus a kullenshliffed granton slicer? Hmm, this is more a function of blade surface smoothness than edge smoothness, which is the point of sharpening. I suppose also that blade friction is highly material dependent, cheese will stick to just about any blade...

 

[Cliff Stamp]

There are limits to the steel finish dependent on the nature of the steel, specifically the grain size and the carbide size. Consider that some steels have large aggregated carbides which can be of the order of 10 microns in size. Trying to hone to a ignificantly finer polish would just tear out the carbides as there would be no steel to hold them under the force of the abrasive. This is why if you go to very low angles the edge actually starts to degrade beyond a certain polish on coarse steels. You can even see this under very low magnification, 10x is enough to notice the effect on very coarse steels.

Finish polish has been studied in detail on wood, Lee gives references to it in his book, noting specifically how the orientation of the grind lines make a difference, having a much lower drag if they are parallel to the line of action of the cutting versus perpendicular to it which is fairly straightforward. In terms of working polish, it is near impossible to keep a very high finish on a knife because they are degraded immediately in use. A mirror polish quickly turns in a rough satin one after cutting cardboard for example. There is obviously an effect of friction, however it is usually really insignificant compared to gross geometry issues.

-Cliff

 

[erdvark]

Mmm, ok it won't stay polished.. But then i was thinking about this later, this friction is an effect of the blade friction, not the edge. So if it's all about the edge, i wonder how well a monomolecular filament blade would work, like you read about in sci-fi? It would be a blade of molecular thickness with no relief angle and no drag on the blade. Practically, they seem impossible since if cutting is in effect breaking the molecular bonds of the material i don't see how you wouldn't break the bonds in the filament itself, they would be on the same order.

 

[kel_aa]

When you go below the marsenite structure, doesn't the material end up behaving like basic mild steel with huge aggregates embedded in it?

Very fine tips are not unheard of. For instance, the tip of an atomic force probe is on the atomic radii scale, I believe.

The molecular monofilament cutting tool is a little far-fetched. The closest thing we have are carbon nanotubes?

 

[Cliff Stamp]

So if it's all about the edge, i wonder how well a monomolecular filament blade would work, like you read about in sci-fi?

These type of cutting edges exist, not in the mono-sense, but the general principles are well known. For example a commonly used cheese knife is just a very thin piece of wire. Here since the main forces which oppose a blade are on the flats and not on the edge, the "knife" doesn't need to be sharp, just very thin. Many types of rotary weed cutters use the same principles, no actual blade, just an edge which is usually some type of synthetic cord.

Practically, they seem impossible since if cutting is in effect breaking the molecular bonds of the material i don't see how you wouldn't break the bonds in the filament itself, they would be on the same order.

They are stronger than those in the material being cut. You don't need to go all the way to mono, even a strand which is 100-1000 times thicker would still be "sharper" than steel knives. You would just want an extremely high tensile strength. You can make a "knife" like this by using something like Spiderwire stretched tightly across a coping saw, very thin fishing line will cut through human flesh very easily for example and it is insanely strong for its thickness.

When you go below the marsenite structure, doesn't the material end up behaving like basic mild steel with huge aggregates embedded in it?

This perspective is actually really rare, most people just assume the same gross principles apply to the edge as to the bulk steel, but very different things happen to steels when they are a micron thick and it would seem obvious that cm sized sample gross properties might miss some of the details.

Edges really can't go under the martensite BCT structure (currently anyway) however they can readily go under the size of the primary carbides. This is why for example guys like Johnston found the coarse steels like D2 didn't have good edge retention or sharpness at low angles, this was verified directly recently by Landes who confirmed it is a carbide issue.

You can also find for example that the edges on even very hard knives will plastically deform readily when they are thin because the strain is very low under a given angle of flex due to the extreme cross section. This would not be obvious if you tried to bend a piece of it a cm thick.

-Cliff

 

[redstead]

:jerkit: Pertaining to knives, I would say: using focused energy to separate solid material with relative precision. <-- I'm going to copywrite that .
Thus sharp edges cut, saws cut, lasers cut, water jets cut...may I dare say shaped charges "cut" through tank armor. That last one may be moving into the figurative sense (e.g. cutting through defenses), but I think it's still pretty close.

 

[erdvark]

Well, this question is kind of non-trivial. To say that it is using focused energy to separate solid material is a functional definition, but not a physical one. What actually happens when you cut something?

In your examples, a saw cuts by removing material, but it does this by cutting a little chip with a sharp tooth, a laser does this by directly converting the material to vapor. In the case of a shaped charge, a high speed jet of metal cuts through armor in probably the same way as a water jet, which i'm not clear on the mechanism.

Maybe a definition could be: A blade cutting a soft material separates the material without removal by applying pressure greater than the tensile strength of the material at a sharp edge. This is different than breaking, as refered to in the OP, because in breaking the force is applied over large areas and the material will separate at the weakest plane of cleavage.

For a concrete example, in thread cutting sharpness tests, i could break the thread by pulling on it until i exceed the tensile strength. If i push a blade onto the thread, does the edge press on the thread until the strength is exceeded, at which point it is cut? This would seem to make sense as a sharper blade requires less force to cut a thread which implies that it has a smaller area to push on the thread.
It's also encouraging that the units work out. Tensile strength is in force, but there is the cross-sectional area of the thread, so force/area = pressure. The blade is applied with some force, again over some area of contact, again pressure.
Hmm, now need some actual numbers....

 

[Cliff Stamp]

On the light thread I use, on a tensile break the area is circular so 10^-8, the thread is about 1/10 of a mm. Under a cut the area is basically width of thread (smeared out flat) * edge thickness. With edges from 0.1 to 1 micron, you would predict sharp blades would cut at about 1/10 to 1/100 the force of a tensile break. Experimentally, the thread breaks at ~kg, sharp blades are ~100 grams and exceptional ones approach 10 grams. Details can be seen in the reviews.

-Cliff