Elastic properties and motion of dislocations

This expression can be generalized to an arbitrary dislocation line described by the vector I, and external stress described by the tensor a, to 

This force is evidently always perpendicular to the direction of the dislocation line I, and it is non-zero if there is a component of the stress tensor a parallel to the Burgers vector b, as in the example of the edge dislocation under shear stress r, shown in Fig. 10.4. 

The ease with which dislocations move, and the distortions they induce throughout the crystal, make them very important defects for mediating the mechanical response of solids. Dislocations are also important in terms of the electronic properties of solids. In semiconductors, dislocations induce states in the gap which act like traps for electrons or holes. When the dislocation line lies in a direction that produces a short circuit, its effect can be disastrous to the operation of the device. Of the many important effects of dislocations we will only discuss briefly their mobility and its relation to mechanical behavior, such as brittle or ductile response to external loading. For more involved treatments we refer the reader to the specialized books mentioned at the end of the chapter. 

Because dislocations induce long-range strain in crystals, and therefore respond to externally applied macroscopic stresses, they are typically described in the context of continuum elasticity theory. In this context, the atomic structure of the dislocation core does not enter directly. The basic concepts of elasticity theory are reviewed in Appendix E. 

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As a force is applied to the item through the die, the metal first becomes elastically strained and would return to its initial shape if the force were removed at this point. As the force increases, the metal s elastic limit is exceeded and plastic flow occurs via the motion of dislocations. Many of these dislocations become entangled and trapped within the plastically deformed material thus, plastic deformation produces crystals which are less perfect and contain internal stresses. These crystals are designated as cold-worked and have physical properties which differ from those of the undeformed metal. 

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