Work hardening

From Wikipedia, the free encyclopedia

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 decreased ductility.

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, work hardening 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.

Cold forming is a type of cold work that involves forging operations, such as extrusion, drawing or coining, that are performed at low temperatures. Cold work may also refer to the process through which a material is given this quality. Such deformation increases the concentration of dislocations which may subsequently form low-angle grain boundaries surrounding sub-grains. Cold work generally results in a higher yield strength as a result of the increased number of dislocations and the Hall-Petch effect of the sub-grains. However, there is a simultaneous decrease in the ductility. The effects of cold working may be removed by annealing the material at high temperatures where recovery and recrystallization reduce the dislocation density.

1 Theory
2 Mathematical descriptions
3 See also

[edit] Theory

[edit] Elastic and plastic deformation

Work hardening occurs as a consequence of plastic deformation. A discussion of elastic deformation and plastic deformation must first be made. The discussion mostly involves metals, especially steels, which are well studied. The tensile test is a popular method to study deformation mechanisms.

Elastic deformation is deforming a material only slightly with a minimum-smoothly-applied force. This only slightly stretches atomic bonds in the material away from their equilibrium radius of separation of a bond, while not applying so much energy as to break the inter-atomic bond completely. The deformation is recoverable. Plastic deformation is the act of deforming a material past its elastic limit. Atomic bonds break which, in smooth-controlled conditions, is accompanied first by permanent movement of dislocations.

[edit] Dislocations and lattice strain fields

We define dislocations as irregularities in a crystal structure. They are surrounded by relatively strained bonds than in the regular crystal lattice. This is why these bonds break first in plastic deformation. The next step is the reformation of these bonds with alternate nearby atoms: to leave atoms unbonded altogether would be severely energetically unfavored. The end result is an alternate, but lower energy conformation within the applied strain. Dislocations are a "negative-entity" in that they do not exist: they are merely defects in the host medium which does exist. As such, the material itself does not move much. To a much greater extent visible "motion" is movement in a bonding pattern of largely stationary atoms. (Please see for further discussion: edge dislocation, screw dislocation)

The strained bonds around a dislocation are described with the terminology of lattice strain fields. For example, there are compressively strained bonds directly next to an edge dislocation and tensilely strained bonds beyond the end of an edge dislocation. These form compressive strain fields and tensile strain fields respectively. Strain fields are like electric fields in some ways. Dislocations both form their own strain fields and are affected by the fields from other dislocations. In short, opposite fields attract and like fields repulse.

The visible (macroscopic) results of plastic deformation are the result of microscopic dislocation motion. Such as the stretching of a steel rod in a tensile tester.

[edit] Increase of dislocations and work hardening

Increase in the number of dislocations is a quantification of work hardening. Plastic deformation occurs as a consequence of work being done on a material; energy is added to the material. In addition, the energy is almost always applied fast enough and in large enough magnitude to not only move existing dislocations, but also to produce a great number of new dislocations by jarring or working the material sufficiently enough.

Yield strength is increased in a cold-worked material. Using lattice strain fields, it can be shown that an environment filled with dislocations will hinder the movement of any one dislocation. Because dislocation motion is hindered, plastic deformation cannot occur at normal stresses. Upon application of stresses just beyond the yield strength of the non-cold-worked material, a cold-worked material will continue to deform using the only mechanism available: elastic deformation. The regular scheme of stretching or compressing of electrical bonds (without dislocation motion) continues to occur, and the modulus of elasticity is unchanged. Eventually the stress is great enough to overcome the strain-field interactions and plastic deformation resumes.

However, ductility of a work-hardened material is decreased. Ductility is the extent to which a material can undergo plastic deformation, that is, it is how far a material can be plastically deformed before fracture. A cold-worked material is, in effect, a normal material that has already been extended through part of its allowed plastic deformation. If dislocation motion and plastic deformation have been hindered enough by dislocation accumulation, and stretching of electronic bonds and elastic deformation have reached their limit, a third mode of deformation occurs: fracture.

[edit] Example

For an extreme example, in a tensile test a bar of steel is strained to just before the distance at which it usually fractures. The load is released smoothly and the material relieves some of its strain by decreasing in length. The decrease in length is called the elastic recovery, and the end result is a work-hardened steel bar. The fraction of length recovered (length recovered/original length) is equal to the yield-stress divided by the modulus of elasticity(Here we discuss true stress in order to account for the drastic decrease in diameter in this tensile test.) The length recovered after removing a load from a material just before it breaks is equal to the length recovered after removing a load just before it enters plastic deformation.

The work-hardened steel bar has a large enough number of dislocations that the strain field interaction prevents all plastic deformation. Subsequent deformation requires a stress that varies linearly with the strain observed, the slope of the graph of stress vs. strain is the modulus of elasticity, as usual.

The work-hardened steel bar fractures when the applied stress exceeds the usual fracture stress and the strain exceeds usual fracture strain. This may be considered to be the elastic limit and the yield stress is now equal to the fracture stress, which is of course, much higher than a non-work-hardened-steel yield stress.

The amount of plastic deformation possible is zero, which is obviously less than the amount of plastic deformation possible for a non-work-hardened material. Thus, the ductility of the cold-worked bar is drastically reduced.

[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

$\sigma = K \epsilon_p ^n \,\!$ (Hollomon's)

$\sigma = \sigma_y + K \epsilon_p^n \,\!$ (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

$\sigma = \sigma_y + K (\epsilon_0 + \epsilon_p)^n \,\!$

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:

$n = \frac{d \log(\sigma)}{d \log(\epsilon)} = \frac{\epsilon}{\sigma}\frac{d \sigma}{d \epsilon} \,\!$

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

$\frac{d \sigma}{d \epsilon} = n \frac{\sigma}{\epsilon} \,\!$