Is hardening equivalent with reducing the ductility of a metal and improving the yield strength of it?
[Physics] Does hardening reduce the ductility of a metal
material-sciencemetals
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Work hardening does not cause things to break, but in fact will cause them to resist further plastic deformation increasing their strength. Wires bent back and forth may eventually break due to fatigue. The material at the edge is compressed and stretched resulting in fatigue. How much cyclic stress there is determines how many cycles the material can last its fatigue limit.
From that article:
If the stress on the wire at the edge is below the endurance limit then the wire could be bent back and forth indefinitely. One way to reduce stress and allow for more flexible wires is to use braided wires. This works by reducing the cross section of each strand and thus reducing the amount of strain required to produce a certain bend radius.
Of course, if by fiddle with and bend you mean deform past the elastic limit so that there is a kink, then you are inherently exceeding the yield stress every cycle and micro cracks will propagate very quickly. If this is what you'd like to due to your cords and would like a cord to survive this treatment, I would design such a cord with thin braided wires that were surrounded by a self-healing polymer. This would allow you to plastically deform the cord and have the cord heal itself.
As for metals that can recover from being yielded there are shape-memory alloys, though I think they would be cost prohibitive.
It's important to distinguish between two very different regimes when considering the stress-strain behavior of metals: (1) The elastic regime and (2) the plastically deforming regime. When relatively small stresses are applied to metals, they tend to behave elastically. If you apply a stress it bends a little, and if you then remove the stress it goes back to its original position. Elastic properties of metals depend on the elemental composition of the metal, but they tend to be insensitive to the microstructural details of the metal. Things like dislocations (produced by work hardening a metal) or fine precipitates (which can be produced by age hardening the metal) don't affect the elastic properties of metals like the Young's modulus much since they tend to be a relatively small volume fraction of the overall volume of the metal.
So the question is really why do these microstructural details become so important when the metal starts to plastically strain? When the stress on a metal becomes large enough to plastically stain it, we enter into a very different regime in which the material is undergoing large deformation which is enabled by the movement of dislocations through it. When this starts to happen, then all those little microstructural details in the metal such as grain boundaries, pre-existing dislocations, and fine precipitates become very important because they all act to block the smooth flow of dislocations through the metal. As a result, more stress has to be applied to the metal in order to overcome the dislocation barriers and make the metal plastically flow. That's why work-hardening and precipitation hardening (i.e., "age hardening") are so effective at increasing the yield strength, which is a measure of the stress required in order to make the metal plastically deform.
Bottom Line:
Elastic Properties (e.g., Young's modulus, Bulk modulus, Poisson's ratio) depend on the elemental composition of a metal but are insensitive to the microstructural details of a metal.
Plastic Properties (e.g., Yield strength, tensile strength, elongation at maximum yield) are sensitive to the microstructural details of a metal (e.g., grain boundaries, pre-existing dislocation bundles, fine precipitates) because these microstructural features can block the movement of dislocations through a metal which enable the metal to plastically deform.
Best Answer
From Wikipedia:
Link to original reference: Hardening Metal
Ductility is reduced after hardening, but you don't say which metal or alloy you have in mind and, because of the varying crystal structure, it's a property that varies with the metal.
Again from Wiki:
Yield Strength Factors From Wikipedia