I don't think water channel erosion is a good analogy for cutting edge wear. Water weathers rocks in many ways. Most stream bed erosion comes from rocks and sand transported by the water scouring the banks. Another big effect is the solvent action of the water breaking apart soluable minerals that bind some rocks together. Then there is that ice expansion effect that cracks rocks apart. All these would be unusual mechanisms for edge wear.
A lot of materials will have dirt particles embedded in the structure. Quartz is pretty hard and a common soil contaminant. Abrasion that removes particles from the edge would depend on the hardness of the material that you are cutting and it's contaminants; however edge rolling is still the biggest dulling mechanism and primary to explain.
I think that you need to think in terms of forces against the edge. If you have a stiff material and on a microscopic level high spots push against the side of the edge unevenly there will be a tendency to push spots of the edge over sideways. The steel may have a higher elastic constant and yield strength, but sheer bulk can win out and lean over bits of the edge. The softer material will compress more than the steel, but you don't really notice. For example I can bend over a thin metal fence post with my much softer body. I lean my body more than the post leans and my palms compress more than the surface of the steel, but over it goes.
If everything were perfectly symmetrical and homogenous the edge would only roll due to pressure on the edge causing "column buckling". This would only happen if the edge is very thin. I would expect this to occur on a "wire edge" if it was standing straight up. Think of the edge like a sheet of paper. A solid slab of paper is tougher than the equivalent amount of wood, but when paper thin you can deflect it with something as soft as mashed potatoes. Pressing on the edge of a sheet of paper will cause it to bow. Continued pressure causes it to fold and not return to original shape.
This is why I try and finish my sharpening with some light strokes with a ceramic rod at a higher angle to try and cut off any wire edge. It's more involved than that, but you do want to minimise the edge burr if you want an edge that will last. Once an edge starts to roll the on-edge forces have an easier time to roll the edge further.
Back to the original question: Why do some materials dull a knife faster than others? I think that materials which are harder to compress (in local spots) will put more local bending pressures on the edge. Corregated cardboard may be weak as a structure, but the underlying paper fights being compressed or parted and can push back against an edge harder than bread or meat. Hemp fibers individually are hard to compress and have a high elastic modulus. Things like these dull knives more than you might think.
[This message has been edited by Jeff Clark (edited 21 June 1999).]
[This message has been edited by Jeff Clark (edited 22 June 1999).]
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