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A sharper knife can puncture a surface with less force than a dull knife, presumably because a sharp knife has greater pressure than a dull knife for the same force.

I suspect that pressure alone isn't what we need for puncturing; e.g. if I apply the same pressure as the knife uniformly over a large area, I might not puncture the surface. Presumably I need some sort of minimum tension in the surface for it to tear after deforming under the pressure, or something like that, but I'm not sure what. How would you build a simple model for puncturing?

For a specific example, just imagine puncturing the leather on a couch, I guess.

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  • $\begingroup$ Doesn't seem like there's any simple answer in general. I don't know of any engineering property of materials which is a good proxy for "resistance to puncturing". Puncturing/penetration all depends on the specifics of not just the knife blade and the material it is made of, but also the specifics of the target material. Seems like you're basically asking about the properties of a good penetrator versus a good armor, and that's a complicated subject with a long history. $\endgroup$ – user93237 Sep 14 '17 at 19:53
  • $\begingroup$ far from being able to provide an answer, I do think this would be closely related with the issue of fissure formation and their propagation - which is as far as I know a highly complicated field without an accepted theory that explains all kinds of phenomena $\endgroup$ – Sanya Sep 14 '17 at 20:32
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Essentially, with sharper edges, you have to "perturb" less of the material.

A sharper edge can pierce better not only because of the increased pressure, but also because it can penetrate between mesoscopic features of the surface (fibers, layers, etc.).

Also, a sharper edge has to "push aside" less material and dislocate fewer crystal layers in order to penetrate the surface.

You should definitely check the answers to How does a knife cut things at the atomic level? for much more information.

I also wonder if it's perhaps also possible that a sharper edge leads in some cases to a smaller radius of the dent produced on the surface, which would imply higher local stress.

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