Why does paper cut through things so well?

Question

Paper is an extremely flexible material, at least when it is in sheet form. It will deform significantly according to the pressure applied and it is easy to fold.

Therefore, it's extremely counterintuitive that a sheet of paper could cut through human skin and probably through stiffer/harder materials, since when the skin applies a pressure on the paper, one would expect it to fold or bend. Yet it is easy to have a severe cut from paper, through both the epidermis and the dermis. How is that possible? Certainly the width of the sheet of paper plays a big role: the smaller it is, the sharper it is, but also the more flexible it becomes and the less it should sustain an applied pressure without folding up!

I can think of other materials such as thin plastic films and aluminium foils. My intuition tells me the plastic foil would not cut through skin but the aluminium foil would, although I am not sure since I did not try the experiment. If this hold true, what determines whether a material would be able to cut through skin? A hair for example, which is flexible and thinner than a paper sheet, is unable to cut through the skin. What makes paper stand out? What is so different that makes it a good cutter?

Maybe it has to do with its microscopic properties and that it contains many fibers, but I highly doubt it because the aluminium foil does not contain these and yet would probably also cut.

Somewhat related, a useful word for those who had slight shivers when reading this question and its answers: pulpuslacerataphobia. It seems somewhat "made-up" word (then again, all words are...), but Google gives several hits with it. Just think twice before going to the image search. — hyde, Sep 15 '18 at 10:32
When I first saw the title, it was "Why does paper cut so well?". I made a suggested edit of the title to "Why does paper cut skin so well?", since that was what the body of the question was about. That edit was ultimately rejected in favour of "Why does paper cut through things so well?", which is not so accurate as the question is still only about cutting skin (on fingers, etc.). If you want the question to be more general, you should edit the body to match the title. and probably through stiffer/harder materials means you're not sure / you haven't tried it. — CJ Dennis, Sep 16 '18 at 23:09
I just noticed an incorrect assumption: the smaller it is, the sharper it is, but also the more flexible it becomes. You'll find that the smaller something becomes, the harder / stiffer it becomes. A large piece of paper is more likely to bend than a small piece of paper. Unless you meant thinner, not smaller. — CJ Dennis, Sep 16 '18 at 23:16

Vincent Thacker · Accepted Answer · 2018-09-13T14:52:33.463

Paper, especially when freshly cut, might appear to have smooth edges, but in reality, its edges are serrated (i.e. having a jagged edge), making it more like a saw than a smooth blade. This enables the paper to tear through the skin fairly easily. The jagged edges greatly reduce contact area, and causes the pressure applied to be rather high. Thus, the skin can be easily punctured, and as the paper moves in a transverse direction, the jagged edge will tear the skin open.

Paper may bend easily, but it's very resistant to lateral compression (along its surface). Try squeezing a few sheets of paper in a direction parallel to its surface (preferably by placing them flat on a table and attempting to "compress" it laterally), and you will see what I mean. This is analogous to cutting skin with a metal saw versus a rubber one. The paper is more like a metal one in this case. Paper is rather stiff in short lengths, such as a single piece of paper jutting out from a stack (which is what causes cuts a lot of the time). Most of the time, holding a single large piece of paper and pressing it against your skin won't do much more than bend the paper, but holding it such that only a small length is exposed will make it much harder to bend. The normal force from your skin and the downward force form what is known as a torque couple. There is a certain threshold torque before the paper gives way and bends instead. A shorter length of paper will have a shorter lever arm, which greatly increases the tolerance of the misalignment of the two forces. Holding the paper at a longer length away decreases this threshold (i.e. you have to press down much more precisely over the contact point for the paper to not bend). This is also an important factor in determining whether the paper presses into your skin or simply bends.

Paper is made of cellulose short fibers/pulp, which are attached to each other through hydrogen bonding and possibly a finishing layer. When paper is bent or folded, fibers at the folding line separate and detach, making the paper much weaker. Even if we unfold the folded paper, those detached fibers do not re-attach to each other as before, so the folding line remains as a mechanically weak region and decreasing its stiffness. This is why freshly made, unfolded paper is also more likely to cause cuts.

Lastly, whether a piece of paper cuts skin easily, of course depends on its stiffness. This is why office paper is much more likely to cut you than toilet paper. The paper's density (mass per unit area), also known as grammage, has a direct influence on its stiffness.

This is indeed a good answer, but leaves several questions unanswered. For example, why can't I read this answer without my face twisting and hands clenching? — maxathousand, Sep 10 '18 at 13:28
@maxathousand Because it mentions paper cuts and toilet paper in the same sentence? — David Richerby, Sep 10 '18 at 14:04
And of course flexible things can cut quite well, for instance wire saws like these: https://en.wikipedia.org/wiki/Wire_saw or the more common ones used for camping. — jamesqf, Sep 10 '18 at 18:38
I'm not sure the fact that the edges are serrated is enough to ensure that paper cuts well. I think it would be nice if you edited your answer with Floris's information that the edges actually contain extra materials that are "hard" and so makes it easy to understand why paper cuts so well. Both of your answers are thus far complementing well each other's. — untreated_paramediensis_karnik, Sep 11 '18 at 18:44
@coniferous_smellerULPBG-W8ZgjR: What make the edges of paper serrated are the very fibers out of which the paper is made of - it has nothing fundamentally to do with filler particles (although they can enhance the sharpness). — Vincent Thacker, Sep 12 '18 at 14:09
Could you please edit your answer with this information explicitly written down? I would accept your answer. — untreated_paramediensis_karnik, Sep 14 '18 at 19:28
@coniferous_smellerULPBG-W8ZgjR: I have already said, the fibers are the main reason why the paper cuts. If you find that very important, I welcome you to edit this answer yourself. — Vincent Thacker, Sep 15 '18 at 00:38

score 57 · Answer 2 · answered Sep 10 '18 at 15:16

57

Paper is an extremely flexible material

This is true, but only in one direction at any given time. When you curve paper across a single axis it adds a massive amount of stiffness to the other axis. See SHUKHOV'S HYPERBOLOIDS and how this uses double curvature strengthening. It is best shown in this picture taken from the article.

My guess is that the majority of paper cuts will happen when there is some amount of curvature on the axis that is normal to the cutting edge of the paper. When the curvature is parallel to the cutting edge, the paper will simply bend more.

When paper is used as a disk cutter, as shown in this video provided by sammy gerbil, it is stiffened by centrifugal force from the very high angular speeds of the disk cutter.

So, in summary, paper is good at cutting because its material properties allow it to act stiff (in a given direction), as well as all of the other answers provided such as jagged edges/sawing effect.

answered Sep 10 '18 at 15:16

josh

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Also note blades of grass are often curved in the same way! – reve_etrange Sep 10 '18 at 23:29
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I think another way of putting this is that paper is inelastic (has a high modulus). You can bend a sheet of paper out of it's own plane, but you can't stretch or compress it in the direction of that plane. This is why you get the properties described in the article you cited. – Dave Tweed Sep 11 '18 at 18:32
@DaveTweed that's a nice info. Feel free to edit josh's answer. – untreated_paramediensis_karnik Sep 11 '18 at 18:40
sorry but your guess is wrong. the only thing that matters to the cutting effect is the speed and direction of the paper's motion relative the object it is cutting. – vulcan_ Sep 12 '18 at 17:18
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@vulcan_ while my guess could still be wrong, you reasoning doesn't seem to be correct as to why it could be wrong. There must be some force acting normal to the plane we are cutting. If there is no rigidity to the paper, it will simply bend instead of cut. This is why tissue paper doesn't cut and writing paper does. – josh Sep 13 '18 at 11:52
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I think this answer really complements user7777777's, and it's what I came here looking for. – Michael Ferguson Sep 14 '18 at 05:08
@josh There does not need to be any force normal to sheet doing the cutting .. in fact if there is a sideways force the bending moment will take the thin edge away from the cut as it starts to bend or even fold the paper. As for tissue paper .. its edge is not sharp enough to cut and is too pliable to stiffen the edge for long enough to make a cut so this is not the reason that tissue paper does not cut – vulcan_ Sep 16 '18 at 23:26
@vulcan_ I said normal to the plane we are cutting (i.e. your skin), not normal to the face of the paper. The whole concept of double curvature strengthening in this context is to mitigate against the bending/folding problem you have described. If there is something I can add to my answer to make it clearer, please let me know! – josh Sep 17 '18 at 08:52

score 28 · Answer 3 · answered Sep 10 '18 at 11:19

28

Paper contains filler particles. These are microscopic “knives” - see for example this picture (Precipitated Calcium Carbonate, from this paper)

When paper is freshly cut, such particles (CaCO3, TiO2, ...) are exposed on the edge. They act like any serrated blade, cutting and removing small amounts of material as you slide the edge along a surface (like your finger...). Many of these together can “eat” enough of your skin to make a cut.

answered Sep 10 '18 at 11:19

Floris

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Do you have a citation to show it's indeed these fillers that are responsible for the cutting? I don't know much about paper manufacture, but I'd think applications where appearance isn't as important, such as cardboard boxes, would have less filler. Yet some of the worst paper cuts I've had are from boxes. – Phil Frost Sep 10 '18 at 14:52
@PhilFrost - it's a fair point. I recall this from materials science lectures in the '80s - before lecture notes were posted online. If I can find something I will add it. The glue (binder) holding paper together also makes the fibers into an effective knife edge; and cardboard has a lot of binder... – Floris Sep 10 '18 at 16:49
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I like this answer because it's the only one so far that mention these extra materials on the edges of the sheet of paper. – untreated_paramediensis_karnik Sep 11 '18 at 18:41
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The materials your mention on the cut edges are from the clay or plastic used to finish some papers, they will not be present on most (cheaper) papers. The cutting effect of paper is more due to it being an extremely thing edge moving fast enough in the direction of the edge to slice through what it hits. – vulcan_ Sep 12 '18 at 17:16

score 16 · Answer 4 · answered Sep 10 '18 at 14:54

It's mostly the movement along the paper edge. It results in a sawing effect on your skin.

You can easily try to push on freshly cut paper (without moving along the edge), and it will be nearly impossible to cut yourself. As soon as you move along the edge(don't try this, or try on your own risk), the sawing effect will quickly cut you.

score 3 · Answer 5 · answered Sep 12 '18 at 18:47

There are some good answers here already, but there is also some misinformation. Paper as a material is essentially a fibre composite material .. compressed, felted, fibres bonded by glue, and possibly surface treated to enhance smoothness. It is a very thin sheet with a microscopic saw edge that when constrained against bending and in motion along the edges direction relative to another object can cut soft materials readily.

old paper will cut as readily as new and folding, curving, or any other structural configuration make no contribution to the paper cutting effect. the only thing that mattes is that the edge is thin and moving, relative to the thing being cut.

the extreme example of the paper cutting effect can be seen in this video https://www.youtube.com/watch?v=eLXHLRa37_g Mister Maker takes advantage of the stiffening effect of centrifugal force to use paper to slice and dice a variety of materials

Although it is also possible to cut yourself with old paper (well-stored paper changes its properties only very slowly over time), fresh paper does cut significantly better. In particular, bending paper multiple times in different directions softens it up and then it won't easily keep the edge against your skin anymore. Centrifugal force is a different matter and doesn't rely on stiffness, but this is completely different from every accidental papercuts. — leftaroundabout, Sep 13 '18 at 10:02

Why does paper cut through things so well?

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