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305:. As the material is work hardened it becomes increasingly saturated with new dislocations, and more dislocations are prevented from nucleating (a resistance to dislocation-formation develops). This resistance to dislocation-formation manifests itself as a resistance to plastic deformation; hence, the observed strengthening.
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As shown in Figure 1 and the equation above, work hardening has a half root dependency on the number of dislocations. The material exhibits high strength if there are either high levels of dislocations (greater than 10 dislocations per m) or no dislocations. A moderate number of dislocations (between
696:
For an extreme example, in a tensile test a bar of steel is strained to just before the length 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 result is a
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Work hardening is a consequence of plastic deformation, a permanent change in shape. This is distinct from elastic deformation, which is reversible. Most materials do not exhibit only one or the other, but rather a combination of the two. The following discussion mostly applies to metals, especially
324:
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
412:
In materials science parlance, dislocations are defined as line defects in a material's crystal structure. The bonds surrounding the dislocation are already elastically strained by the defect compared to the bonds between the constituents of the regular crystal lattice. Therefore, these bonds break
1182:
as work progresses. If work continues beyond a certain hardness the metal will tend to fracture when worked and so it may be re-annealed periodically as shaping continues. Annealing is stopped when the workpiece is near its final desired shape, and so the final product will have a desired strength
171:, is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation. This characteristic is what sets ductile materials apart from brittle materials. Work hardening may be desirable, undesirable, or inconsequential, depending on the application.
397:
Elastic deformation stretches the bonds between atoms away from their equilibrium radius of separation, without applying enough energy to break the inter-atomic bonds. Plastic deformation, on the other hand, breaks inter-atomic bonds, and therefore involves the rearrangement of atoms in a solid
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is widely used to study deformation mechanisms. This is because under compression, most materials will experience trivial (lattice mismatch) and non-trivial (buckling) events before plastic deformation or fracture occur. Hence the intermediate processes that occur to the material under uniaxial
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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 (brittle) material that has already been extended through part of its allowed plastic deformation. If
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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
477:. 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
420:
fields. For example, there are compressively strained bonds directly next to an edge dislocation and strained in tension bonds beyond the end of an edge dislocation. These form compressive strain fields and tensile strain fields, respectively. Strain fields are analogous to
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within the material culminating in a lattice rearrangement as the dislocations propagate through the lattice. At normal temperatures the dislocations are not annihilated by annealing. Instead, the dislocations accumulate, interact with one another, and serve as
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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.
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steels, which are well studied. Work hardening occurs most notably for ductile materials such as metals. Ductility is the ability of a material to undergo plastic deformations before fracture (for example, bending a steel rod until it finally breaks).
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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.
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in certain ways. Specifically, the strain fields of dislocations obey similar laws of attraction and repulsion; in order to reduce overall strain, compressive strains are attracted to tensile strains, and vice versa.
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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
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The amount of plastic deformation possible is zero, which is less than the amount of plastic deformation possible for a non-work-hardened material. Thus, the ductility of the cold-worked bar is reduced.
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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
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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
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Items made from aluminum and its alloys must be carefully designed to minimize or evenly distribute flexure, which can lead to work hardening and, in turn, stress cracking, possibly causing
386:, which is also known as the yield stress. At that point, the material is permanently deformed and fails to return to its original shape when the force is removed. This phenomenon is called
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Before work hardening, the lattice of the material exhibits a regular, nearly defect-free pattern (almost no dislocations). The defect-free lattice can be created or restored at any time by
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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:
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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:
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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
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up to a certain point, it will return to its original shape, but once it is stretched beyond the elastic limit, it will remain deformed and won't return to its original state.
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In metallic crystals, this is a reversible process and is usually carried out on a microscopic scale by defects called dislocations, which are created by fluctuations in local
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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
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Much gold jewelry is produced by casting, with little or no cold working; which, depending on the alloy grade, may leave the metal relatively soft and bendable. However, a
1226:. For this reason modern aluminum aircraft will have an imposed working lifetime (dependent upon the type of loads encountered), after which the aircraft must be retired.
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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:
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inadvertently work-harden the workpiece surface, causing damage to the cutter during the later passes. Certain alloys are more prone to this than others;
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Copper was the first metal in common use for tools and containers since it is one of the few metals available in non-oxidized form, not requiring the
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dislocation motion. For example, the stretching of a steel rod in a tensile tester is accommodated through dislocation motion on the atomic scale.
1245:"Automated Calculation of Strain Hardening Parameters from Tensile Stress vs. Strain Data for Low Carbon Steel Exhibiting Yield Point Elongation"
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Integration of
Mechanics into Materials Science Research: A Guide for Material Researchers in Analytical, Computational and Experimental Methods
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a great number of new dislocations by jarring or working the material sufficiently enough. New dislocations are generated in proximity to a
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state it may then be hammered, stretched and otherwise formed, progressing toward the desired final shape but becoming harder and less
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is an important engineering material, used in many applications. Steel may be work hardened by deformation at low temperature, called
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1174:. Copper is easily softened by heating and then cooling (it does not harden by quenching, e.g., quenching in cool water). In this
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is unchanged. Eventually the stress is great enough to overcome the strain-field interactions and plastic deformation resumes.
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Increase in the number of dislocations is a quantification of work hardening. Plastic deformation occurs as a consequence of
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1058:{\displaystyle n={\frac {d\log(\sigma )}{d\log(\epsilon )}}={\frac {\epsilon }{\sigma }}{\frac {d\sigma }{d\epsilon }}\,\!}
190:, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at low temperatures, such as
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decrease in ductility. The effects of cold working may be reversed by annealing the material at high temperatures where
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Van Melick, H. G. H.; Govaert, L. E.; Meijer, H. E. H. (2003), "On the origin of strain hardening in glassy polymers",
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exploits these properties of copper, enabling the construction of durable jewelry articles and sculptures (such as the
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showing typical work hardening plastic behavior of materials in uniaxial compression. For work hardening materials the
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compression before the incidence of plastic deformation make the compressive test fraught with difficulties.
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The yield stress of an ordered material has a half-root dependency on the number of dislocations present.
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may intentionally use work hardening to strengthen wearable objects that are exposed to stress, such as
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or cold forming processes. They are characterized by shaping the workpiece at a temperature below its
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that intentionally induce plastic deformation to exact a shape change. These processes are known as
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194:, however others can be strengthened only via work hardening, such as pure copper and aluminum.
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observed, the slope of the graph of stress vs. strain is the modulus of elasticity, as usual.
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as well as several polymers can be strengthened in this fashion. Alloys not amenable to
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or obstacles that significantly impede their motion. This leads to an increase in the
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Swenson, C. A. (1955), "Properties of Indium and
Thallium at low temperatures",
1119:{\displaystyle {\frac {d\sigma }{d\epsilon }}=n{\frac {\sigma }{\epsilon }}\,\!}
277:. Applications include the heading of bolts and cap screws and the finishing of
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is the intrinsic strength of the material with low dislocation density and
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950:{\displaystyle \sigma =\sigma _{y}+K(\epsilon _{0}+\epsilon _{p})^{n}\,\!}
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281:. In cold forming, metal is formed at high speed and high pressure using
261:. Cold forming techniques are usually classified into four major groups:
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Substantial and prolonged cavitation can also produce strain hardening.
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Scales, M.; Kornuta, J.A.; Switzner, N.; Veloo, P. (December 1, 2023).
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A material generally deforms elastically under the influence of small
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The strained bonds around a dislocation are characterized by lattice
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1148:. Typically, an increase in cold work results in a decrease in the
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139:. The strain can be decomposed into a recoverable elastic strain (
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10 and 10 dislocations per m) typically results in low strength.
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of the material. Many non-brittle metals with a reasonably high
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627:{\displaystyle \tau =\tau _{0}+G\alpha b\rho _{\perp }^{1/2}\ }
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An example of desirable work hardening is that which occurs in
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808:. Ludwik's equation is similar but includes the yield stress:
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at relatively lower stresses, leading to plastic deformation.
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dies. The cold working of the metal increases the hardness,
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is dependent on the shear modulus, G, the magnitude of the
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860:{\displaystyle \sigma =\sigma _{y}+K\epsilon _{p}^{n}\,\!}
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Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003),
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of the material and a subsequent decrease in ductility.
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and recrystallization reduce the dislocation density.
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tend to exhibit a lower strain hardening exponent .
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Strengthening a material through plastic deformation
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202:An example of undesirable work hardening is during
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222:machining strategies that take it into account.
178:movements and dislocation generation within the
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1459:Hollomon, J.R. (1945). "Tensile deformation".
775:{\displaystyle \sigma =K\epsilon _{p}^{n}\,\!}
378:. This behavior in materials is described by
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225:For metal objects designed to flex, such as
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111:Learn how and when to remove this message
1484:Materials and Processes in Manufacturing
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1379:"Cold Forming and Cold Heading Process"
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402:Dislocations and lattice strain fields
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174:This strengthening occurs because of
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1391:Cheng, Y. T.; Cheng, C. M. (1998),
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533:, b, and the dislocation density,
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344:tests before and after a process.
153:). The stress at initial yield is
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1366:Degarmo, Black & Kohser 2003
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501:Quantification of work hardening
336:can be predicted by analyzing a
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127:A phenomenological uniaxial
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241:Intentional work hardening
198:Undesirable work hardening
135:increases with increasing
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657:{\displaystyle \tau _{0}}
354:Deformation (engineering)
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1354:Smith & Hashemi 2006
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293:, and tensile strength.
257:temperature, usually at
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1486:(9th ed.), Wiley,
1432:Prawoto, Yunan (2013).
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62: –
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56:Find sources:
50:
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34:This article
32:
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1540:Metalworking
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1476:Bibliography
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133:yield stress
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43:Please help
38:verification
35:
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699:true stress
527:dislocation
435:microscopic
431:macroscopic
408:Dislocation
392:coil spring
380:Hooke's Law
212:superalloys
176:dislocation
1524:Categories
1467:: 268–277.
1230:References
398:material.
283:tool steel
71:newspapers
1269:1747-1567
1110:ϵ
1107:σ
1093:ϵ
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842:ϵ
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757:ϵ
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672:α
646:τ
604:⊥
600:ρ
593:α
578:τ
571:τ
546:⊥
542:ρ
513:τ
494:Ductility
490:ductility
488:However,
450:Figure 1:
303:annealing
263:squeezing
204:machining
1217:Aluminum
1186:repoussé
1176:annealed
1168:smelting
475:stresses
342:hardness
327:recovery
275:shearing
218:require
214:such as
1408:Bibcode
1330:Bibcode
1296:Polymer
1206:jeweler
1180:ductile
804:is the
692:Example
525:, of a
463:produce
287:carbide
271:drawing
267:bending
227:springs
216:Inconel
85:scholar
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1170:of an
1161:Copper
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637:where
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297:Theory
273:, and
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208:cutter
192:indium
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1396:(PDF)
1210:rings
1142:Steel
1136:Steel
92:JSTOR
78:books
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1488:ISBN
1440:ISBN
1265:ISSN
1198:Gold
458:work
362:The
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