Frank-Read source

Although this sometimes occurs through the operation of Frank-Read sources it is not generally observed. What does generally occur is similar, but more complex. The process is called multiple-cross-glide, and was proposed by Koehler (1952). Its importance was hrst demonstrated experimentally by Johnston and Gilman (1959). In addition to its existence, they showed that the process produces copious dislocation dipoles which are responsible for deformation-hardening. 

Sir Frederick Charles Frank (1911-1998) received his Ph.D. in 1937 from Oxford University, followed by a postdoctoral position at the Kaiser Wilhelm Institut fiir Physik in Berlin. During World War II, Frank was involved with the British Chemical Defense Research Establishment, and because of his keen powers of observation and interpretation, he was later transferred to Scientific Intelligence at the British Air Ministry. In 1946, Frank joined the H. H. Wills Physics Laboratory at the University of Bristol under its director, Nevill Mott, who encouraged him to look into problems concerned with crystal growth and the plastic deformation of metallic crystals. A stream of successes followed, establishing his scientific fame, as evidenced by many eponyms the Frank-Read source, the Frank dislocation, Frank s rule, Frank-Kasper phases. His theoretical work has been the foundation of research by innumerable scientists from around the world. Frank was awarded the Order of the British Empire (OBE) Medal in 1946, elected a Fellow of the Royal Society (FRS) in 1954, and was knighted in 1977. 

Frank-Read Sources. It is well known that with increasing deformation, the density of dislocations increases. This effect is illustrated in fig. 8.40 in which the number of dislocations as a function of the strain is indicated schematically. The immediate conclusion from this observation is the fact that there are sources... 

Fig. 8.41. Frank-Read source as obtained using dislocation dynamics (adapted from Zbib et al. (1998)).

Moulin A., Condat M. and Kubin F. P, Simulation of Frank-Read Sources in Silicon, Acta Mat. 45, 2339 (1997). 

Fig. 17) onto an intersecting slip plane (see Fig. 23). After travelling a short distance on the new plane, that part of the dislocation may resume its motion on another plane of the original slip system. The segment XY, which has reached a third slip plane, can now act as a Frank-Read source and radiate new loops on their respective planes. In other words, through a process of cross glide, a dislocation line can make its own Frank-Read source.

Figure 6.11 A pinned segment of a dislocation undergoing bowing under the action of a shear stress. A dislocation loop forms as the bowing segments (X and Y) merge and the pinned segment returns. This mechanism allows dislocation multiplication and is known as a Frank-Read source.

Dislocation multiplication occurs when the dislocations are made to move during deformation. One possible multiplication mechanism is the Frank-Read source. Suppose that a dislocation is pinned at two points, which are a distance / apart, as shown in Figure 12.21a. Under the action of an applied stress the dislocation will bow out. The radius of curvature R is related to the applied shear stress. To. 

The Nabarro-Herring source is very similar to the Frank-Read source, but the dislocations move by climb instead of glide. 

The Hall-Petch relation (Eq. 14.8) indicates the effect of grain size, d, on the stress required to make the dislocation move in a polycrystalline sample. The origin of the relation is that the stress to operate a Frank-Read source increases as the size of the source decreases. If the grain size decreases, then the maximum size of the Frank-Read source also decreases. The result is the famous d relationship. 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

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