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Any material with a reasonably high Melting Point can be strengthened in this fashion. Alloys not amenable to Heat Treatment , including low-carbon Steel , are often work-hardened. Some materials cannot be work-hardened at normal ambient temperatures; for example Indium , which has a low melting point. This makes indium suitable for manufacturing Gasket s, which deform to fill gaps, for High-vacuum use. Work hardening is often produced by the same process that shapes the metal into its final form, including Cold Rolling (contrast Hot Rolling ) and '' Cold Drawing ''. Techniques have been designed to maintain the general shape of the workpiece during work hardening, including '' Shot Peening '' and '' Constant Channel Angular Press ing''. A material's work hardenability can be predicted by analyzing a Stress-strain Curve , or studied in context by performing Hardness tests before and after a process. Cold forming is a type of cold working that involves Forging operations, such as Extrusion , Drawing or Coining , performed at low temperatures. Cold working 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 working 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, and a decrease in Ductility . The effects of cold working may be reversed by Annealing the material at high temperatures where Recovery and Recrystallization reduce the dislocation density. THEORY Elastic and plastic deformation Work hardening occurs as a consequence of Plastic Deformation , as distinct from Elastic Deformation . The following discussion mostly applies to Metal s, especially Steel s, which are well studied. The Tensile Test is widely used to study deformation mechanisms. A material deforms elastically for small deforming up to a certain point, it will return to its original shape; stretch it too hard, and it will not. Elastic deformation stretches atomic bonds in the material away from their Equilibrium Radius Of Separation Of A Bond without applying enough energy to break the inter-atomic bond. Plastic deformation breaks atomic bonds. Before this happens, if the force is increased gradually, there is a permanent movement of Dislocations . Dislocations and lattice strain fields , Screw Dislocation ) The strained bonds around a dislocation are described with the terminology of lattice Strain Field s. 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 Field s 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. 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. ) 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, . 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. When a material under substantial and prolonged cavitation situation, the material also gets strain hardened. 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 εp. Ludwik's equation is similar but includes the yield stress σy : (Hollomon's) : (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 : 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: : This equation can be evaluated from the slope of a log(σ) - log(ε) plot. Rearranging allows a determination of the rate of strain hardening at a given stress and strain : SEE ALSO
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