cliff you wrote an article/paper recently using this picture in it… would you mind posting it here? can’t find it but it was very helpful and well written.
Yes, and most people say the opposite. Here is why it is wrong :
These two crudely drawn triangles reflect a very low edge angle and a very high edge angle. Note the red lines represent the same thickness of a worn apex. The thickness of the apex is a very strong influence on the sharpness (it isn’t the only thing, but it is a heavy factor).
Which one do you think will happen sooner, which knife will reach the red line faster, the one on the left with the very low angle or the one on the right with the very high angle?
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Now there is where you might jump to “Hey, doesn’t this just say we should sharpen at zero degrees for ultimate performance - that is obviously wrong.”
Yes, this is true, the relationship in the above graph will not just continue beyond 13 dps in a straight line, at some point a very dramatic change will be made and the performance will decrease rapidly and at some further point the edge retention will fall to zero. This happens because at some point the micro-bevel will be so low that the apex is no longer strong and/or durable enough and it will just grossly deform/fracture. The trick then is to find the lowest angle this doesn’t happen as that give the optimal performance. This will depend on the steel, the material being cut and operator skill/experience.
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As a bit of math, the reason this happens is because the edge retention behavior in total has not only the affect I have noted in the above which is just a linear relationship it also includes step functions on strength and toughness. Step functions are particular functions because the basically do nothing until a certain limit is reached but at that point they can cause dramatic effects. The math is a bit wonky as step functions are written similar to this for the effect of angle on the stiffness of the edge which is related to it deforming to failure :
s(x) = (1 if x > Ao; 1/x^3 for X < Ao; 0 for x < Ac)
Thus the edge retention would be written as :
E(x) = l(x) * s(x)
Where l(x) is that linear equation and s(x) is the step function. This jibberish translates to :
-if the angle is above some angle (Ao) then the edge won't really deform/fracture significantly and just slowly wears, deforms and chips at a very small micro-level
-however if you go below that angle then the strength/toughness is no longer there to keep the micro-bevel stable and it will just deform/fracture beyond the apex, the entire micro-bevel will start to take damage and the blunting will be very rapid
-if you go beyond that point further and reach a critical angle, Ac, then the strength/toughness is so low that the micro-bevel will just crack of the first time you try to cut with it
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Now the math is a bit complicated and the language possibly foreign, but it is easy to understand as we see things like that every day. For example the life of tires on your car has a number of step functions. If you drive on the highway you get tire life which is a very slow process of small wear and little rips/tears. If you go off road at some point the rocks can be jagged enough that they will start to damage the tires beyond the normal tread wear. But if the rocks are not jagged enough this doesn't happen and you just see slow wear. If you hit a nail there is sudden and catastrophic failure.[/quote]
