Work hardening

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Work hardening, or strain hardening, is an increase in mechanical strength due to plastic deformation. In metallic solids, permanent change of shape is usually carried out on a microscopic scale by defects called dislocations which are created by stress and rearrange the material by moving through it. At low temperature, these defects do not anneal out of the material, but build up as the material is worked, interfering with one another's motion and thereby increasing strength and resulting in cold work. An example of work hardening happens when a piece of metal is bent back and forth. The point where it is bent becomes hot and then eventually breaks.

Any material with a reasonably high melting point can be strengthened in this fashion. It is often exploited to harden alloys that are not amenable to heat treatment, including low-carbon steel. Conversely, since the low melting point of Indium makes it immune to work hardening at room temperature, it can be used as a gasket material in high-vacuum systems.

Often, cold work is carried out by the same process that shapes the metal into its final form, including cold rolling (contrast hot rolling) and cold drawing. Techniques have also been designed to maintain the general shape of the workpiece during work hardening, including shot peening and constant channel angular pressing). A material's work hardenability can be predicted by analyzing a stress-strain curve, or studied in context by performing a hardness test before and after the proposed cold work process.

[edit] Mathematical descriptions

There are two common mathematical descriptions of the work hardening phenomenon. Hollomon's equation is a power law relationship between the stress and the amount of plastic strain ε_p. Ludwik's equation is similar but includes the yield stress σ_y

<math> \sigma = K \epsilon_p ^n \,\! </math> (Hollomon's)

<math> \sigma = \sigma_y + K \epsilon_p^n \,\! </math> (Ludwik's)

where K is the strength index and n is the strain hardening index.

If a material has been subjected to prior deformation (at low temperature) then the yield stress will be increased by a factor depending on the amount of prior plastic strain ε₀

<math> \sigma = \sigma_y + K (\epsilon_0 + \epsilon_p)^n \,\!</math>

The constant K is structure dependent and is influenced by processing while n is a material property normally lying in the range 0.2-0.5. The strain hardening index can be described by:

<math> n = \frac{d \log(\sigma)}{d \log(\epsilon)} = \frac{\epsilon}{\sigma}\frac{d \sigma}{d \epsilon} \,\!</math>

This equation can be evaluated from the slope of a log(σ) - log(ε) plot. Rearraging allows a determination of the rate of strain hardening at a given stress and strain

<math> \frac{d \sigma}{d \epsilon} = n \frac{\sigma}{\epsilon} \,\!</math>

ja:加工硬化