...If I may, I would like to differentiate between bending and flexing. Bending implies a permanent set is left even when the blade is released. Flexing indicates the blade returned to straight when released.
With that out of the way, the outside of the bend needs sufficient ductility to stretch without cracking. However, if only flexing is happening, no ductility is required. I have flexed blades as hard as 66 HRc to 90 degrees a dozen times with no effect on the blade. I have also bent them and after straightening, there was no noticeable difference. Heat treatment plays a role in toughness, ductility, and bending. As long as a blade is only being flexed, the only thing heat treatment determines is when bending starts. Cross sectional geometry and blade length affect flexing.
You might as well keep the vocabulary lesson going and use the terms
elastic and
plastic deformation here and get into Stress/Strain curves.
me2 surely knows all this but I will throw in my hat to explain quickly and others can clarify if desired:
"Flex" as used above describes "elastic deformation" - this is bending that is recoverable once the applied force (stress) is removed, i.e. the thing bent returns (springs back) to its original state.
"Bend" as used above is a casual use as one might employ in the phrase, "takes a bend", i.e. it permanently deforms or does NOT return (spring back) to its original state when the applied force (stress) is removed.
Hardness is the ability to withstand plastic (permanent) deformation. In the rockwell test, the material experience a compression force over a small area and the ease of indentation (a form of plastic deformation) is a direct measurement of the material hardness. Now 66 Rc is pretty hard for a steel blade, and yet it can be
"flexed" to 90' and return to true precisely because
hardness is
resistance to permanent deformation - that is why it can return to true, it is very resistant to "taking a bend". But if you are wondering how it can then be flexed in the first place, understand that
flexibility of a given material (i.e. the ease with which it can be bent at all) or rather
stiffness (i.e. resistance to bending) is in cubic proportion to its
thickness (cross-sectional geometry mentioned by me2 above). In other words, if you have two identical materials but one is
2x thicker than the other, then the thick piece will require
8x the force to be bent to the same degree as the thinner piece. A thin sheet of glass can also be bent to some degree and will return to its original form when the bending-force is removed. Understanding this, that stiffness/flexibility is largely determined by thickness, is important as a preliminary to understanding "fragility" or "brittleness" vs ductility in different materials. If
me2 had tried to bend a blade twice as thick, he would have required either more force or more leverage (to achieve the force, that is what his point about
blade length entails), and without a very long blade to distribute the stress via curvature, he might easily have fractured it at the greater thickness.
So
elastic deformation (flexing) is what happens when a blade is flexed and returns to true... But what happens if you apply more force, bend the blade even further until... what? Eventually it "takes a bend" or becomes permanently deformed - this is the material's "elastic limit" or "yield point". HERE is where you begin to consider "ductility" in the material -
how much stress can it take, how much can it bend, before it breaks/fractures altogether? A "brittle" material, like glass, will deform very little before it fractures, whereas a ductile material will deform and NOT fracture (not yet anyway). In the context of a knife blade or rather the knife edge, a ductile edge will roll or squash whereas a less ductile or more "brittle" edge will chip. The two terms are "relative" - one edge is brittle
relative to the other, being "more brittle" does not make it "weaker" but only indicates that it will chip sooner after reaching its elastic limit whereas the more ductile edge will take more permanent deformation before experiencing a fracture. We often speak of this resistance to fracture as "toughness". Note that an edge LACKING "toughness" (i.e. "brittle") may actually be the "stronger" edge - "brittle" does not mean "weak".
But if "brittleness" does not imply "weakness", then what IS weakness? A "weak" edge is one that permanently deforms (i.e. ceases to be an edge at all) at a
lower level of stress than a "strong" edge. Consider that the ductile edge, the one that resists chipping by bending instead, may begin bending under relatively low stress, whereas the more brittle edge may only flex or may remain entirely true at the same level of stress and require much more force/stress to incur damage - in such a case, the latter is the "stronger" edge.
Strength (in a blade edge) is the ability to hold your shape against the stresses involved in cutting, i.e. resistance to "flex", "bending", and finally fracture.
Just remember that resistance to "flex" can be accounted for largely through
thickness so a very ductile or a very brittle edge can be made stronger through an increase in thickness. The problem with that is that it is in direct opposition to the mechanical advantage of the edge to make a
cut so a balance must be struck between
edge strength and
mechanical advantage. By using a
harder material (i.e. one that is more resistant to deformation), we can make an edge thinner (to increase mechanical advantage) without sacrificing edge strength.
However it is again important to note that "strength" is not defined by how brittle or ductile a blade is, only by how resistant to deformation it is, i.e. it is defined relative to the stress involved. So what about "
toughness"? Above "ductility" is defined as the ability to take a bend (or just deform) rather than fracture once the elastic limit is exceeded - this can be the same thing as "toughness".
me2's distinction regarding the rate of applied stress (impact vs slow-load) can also come into play for how one wishes to define/distinguish these. Again, it is key that "toughness" ONLY comes into play
once the elastic limit is reached - before then, you are still talking about strength. So if we take two blades, one that deforms while the other holds its shape (having not reached its elastic limit), we might say colloquially that the second blade is "tougher" but it is really only
stronger - until it begins to take a bend, you won't get to see how tough it really is
That's a wall of text, so I'll stop typing there.
