Work hardening

Although oxide crystals exhibit a variety of work-hardening behavior, only three systems will be discussed in this section, namely MgO, spinel, and sapphire. 

As explained above, dislocations are obstacles for other dislocations. The more dislocations there are in a metal, the higher is its yield strength. Dislocation sources, like the Frank-Read source or others described in section 6.2.8, create new dislocations during plastic deformation and serve to increase the dislocation density. This hardens the material, a process called work hardening, strain 

Work hardening is the reason why the flow curve of metals increases in the plastic regime (see chapter 3). If the material is unloaded after plastic deformation, the stress-strain curve follows a line parallel to the elastic line. If the load is raised again, the yield strength has increased and the stress-strain curve follows the same line as on unloading. The strain until the material starts to neck or fracture is reduced the material has lost ductility. 

The influence of the dislocation density on the strength of a metal can be estimated Consider a dislocation line moving through an array of dislocations perpendicular to it as sketched in figure 6.34. Let the distance between the dislocation obstacles be 2A. If the dislocations were insurmountable, they would have to be by-passed with the Orowan mechanism. As they can be cut instead, the necessary stress is smaller than the Orowan stress. This results in Tout = kd Gbj2X, with fed 0.1... 0.2. 

The spacing between the dislocation lines is determined by the dislocation density g. If we simply assume all dislocations to be parallel and arrayed in a regular way, each penetration point in a plane perpendicular to the dislocation occupies an area of 2A-2A. The dislocation density is the number of penetration points per unit area i.e., /g = 1/2A. Inserting this into the equation given above, we get 

The strength of a material can thus be increased by simply deforming it plastically. This is used during rolling or wire drawing. Table 6.4 shows 

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The Brinell test range is limited, by the capabUity of the hardened steel baU indenters used, to HBN 444. This range can be extended upward to HBN 500 by using special cold work-hardened steel baUs and to as high as HBN 627 by using special tungsten carbide bads. 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Collapse and Bursting Pressure. If the pressure is sufficiently large to push the plastic—elastic boundary to the outer surface of the cylinder so that the fibers at that surface yield, then there is nothing to restrain the wad, and the cylinder is said to codapse. With an ideal material which does not work harden the codapse pressure, P, sometimes caded the full plastic flow pressure, the full overstrain pressure or the full thickness yield pressure, would be the bursting pressure of the cylinder. It is given by equation 10 when thus... 

Little error is introduced using the idealized stress—strain diagram (Eig. 4a) to estimate the stresses and strains in partiady plastic cylinders since many steels used in the constmction of pressure vessels have a flat top to their stress—strain curve in the region where the plastic strain is relatively smad. However, this is not tme for large deformations, particularly if the material work hardens, when the pressure can usuady be increased above that corresponding to the codapse pressure before the cylinder bursts. 

Properties. Table 1 hsts many of the physical, thermal, mechanical, and electrical properties of indium. The highly plastic nature of indium, which is its most notable feature, results from deformation from mechanical twinning. Indium retains this plasticity at cryogenic temperatures. Indium does not work-harden, can endure considerable deformation through compression, cold-welds easily, and has a distinctive cry on bending as does tin. 

Fig. 8. Microhardness profile across interfaces of two types of explosion clads that show widely divergent response resulting from the inherent cold-work hardening characteristics where Q represents the 3.2-mm type 304L stainless/28.6-mm, A 516-70 control (before cladding) ( ) = clad + flat ...

The hardness on the basal plane of the cobalt depends on the orientation and extends between 70 and 250 HK. Cobalt is used in high temperature alloys of the superaHoy type because of its resistance to loss of properties when heated to faidy high temperatures. Cobalt also has good work-hardening characteristics, which contribute to the interest in its use in wear alloys. 

Mechanical Properties. An advantage of the two corrosion-resistant alloys is that they may be strengthened considerably by cold working. MP35N alloy is iatended for use ia the work-hardened or work-hardened and aged condition, and the manufacturers have suppHed considerable data concerning the mechanical properties of the alloy at different levels of cold work. Some of these data are given ia Table 8. 

The several wrought alloys of commercial importance span the range of 1.0 to 10 wt % tin and are mosdy used in work hardened tempers. These... 

For welded construction with work-hardened grades, use the stresses for annealed material for welded construction with precipitation-hardened grades, use the special allowable stresses for welded constrnction given in die tables. 

Fabrication Expanding the tube into the tube sheet reduces the tube wall thickness and work-hardens the metal. The induced stresses can lead to stress corrosion. Differential expansion between tubes and shell in fixed-tube-sheet exchangers can develop stresses, which lead to stress corrosion. 

When austenitic stainless-steel tubes are used for corrosion resistance, a close fit between the tube and the tube hole is recommended in order to minimize work hardening and the resulting loss of corrosion resistance. 

More uniform results may be expected if a substantial layer of metal is removed from the specimens to ehminate variations in condition of the original metaUic surface. This can be done by chemical treatment (pickling), electrolytic removal, or grinding with a coarse abrasive paper or cloth, such as No. 50, using care not to work-harden the surface. At least 2.5 X 10 mm (0.0001 in) or 1.5 to 2.3 mg/cm (10 to 15 mg/iu") should be removed. If clad alloy specimens are to be used, specif attention must be given to ensure that excessive metal is not removed. After final preparation of the specimen surface, the speci-... 

Austenitic stainless steels are the most corrosion-resistant of the three groups. These steels contain 16 to 26 percent chromium and 6 to 22 percent nickel. Carbon is kept low (0.08 percent maximum) to minimize carbide precipitation. These alloys can be work-hardened, but heat treatment will not cause hardening. Tensile strength in the annealed condition is about 585 MPa (85,000 Ibf/in"), but workhardening can increase this to 2,000 MPa (300,000 Ibf/in"). Austenitic stainless steels are tough and ducdile. 

Gray and Follansbee [44] quasi-statically tested OFE copper samples that had been shock loaded to 10 GPa and pulse durations of 0.1 fis, 1 /rs, and 2 fus. The quasi-static stress-strain curves are shown in Fig. 7.10 with the response of annealed starting copper included for comparison. The yield strength of shock-loaded copper is observed to increase with pulse duration, as the work-hardening rate is seen to systematically decrease. 

Bai [48] presents a linear stability analysis of plastic shear deformation. This involves the relationship between competing effects of work hardening, thermal softening, and thermal conduction. If the flow stress is given by Tq, and work hardening and thermal softening in the initial state are represented... 

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