The Edge Dislocation

We have now succeeded in identifying the deformations induced by a screw dislocation, and have also found a generic formula for the fields due to an arbitrary dislocation. Our present task is to return to the edge dislocation for the purposes of completeness and because this solution will make its way into our future analysis. This is particularly evident in the case of isotropic linear elasticity where we will find that even for dislocations of mixed character, their geometries may be thought of as a superposition of pure edge and pure screw dislocations. 

Recall from our discussion in chap. 2 that the solution of elasticity problems of the two-dimensional variety presented by the edge dislocation is often amenable to a treatment in terms of the Airy stress function. Consultation of Hirth and Lothe (1992), for example, reveals a well-defined prescription for determining the Airy stress function. The outcome of this analysis is the recogiution that the stresses in the case of an edge dislocation are given by 

Earlier we made the promise that the energy stored in the elastic fields had a generic logarithmic character, regardless of the type of the dislocation. To compute the elastic strain energy associated with the edge dislocation we use eqn (8.16). In the context of the stress fields given above, 

The integrand is determined by computing the tractions on the slip plane using the stresses for the edge dislocation described above, and as claimed, the structure of the energy is exactly the same as that found earlier for the screw dislocation. 

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One type of dislocation is the edge dislocation, illustrated in Fig. VII-7. We imagine that the upper half of the crystal is pushed relative to the lower half, and the sequence shown is that of successive positions of the dislocation. An extra plane, marked as full circles, moves through the crystal until it emerges at the left. The process is much like moving a rug by pushing a crease in it. 

Assume the edge dislocation density to be divided into positive and negative populations, N+ and N, moving only on slip planes at 45° (maximum shear stress) to the planar shock front. For a dislocation multiplication (annihilation) rate M, show that conservation of dislocations requires that... 

In making the edge dislocation of Fig. 9.3 we could, after making the cut, have displaced the lower part of the crystal under the upper part in a direction parallel to the bottom of the cut, instead of normal to it. Figure 9.7 shows the result it, too, is a dislocation, called a screw dislocation (because it converts the planes of atoms into a helical surface, or screw). Like an edge dislocation, it produces plastic strain when it... 

The edge dislocation on the 011 plane is again widely spread on the glide plane w = 2.9 6) and moves with similar ease. In contrast, the edge dislocation on the 001 plane is more compact w = 1.8 6) and significantly more difficult to move (see table 1). Mixed dislocations on the 011 plane have somewhat higher Peierls stresses than either edge or screw dislocations. 

Comparing to the previous atomistic studies of (110) dislocations in NiAl [7, 6], there are differences in many details but all studies clearly show that the edge dislocations are limiting the mobility. 

The simplest type of line defect is the edge dislocation, which consists of an extra half plane of atoms in the crystal, as illustrated schematically in Fig. 20.30a edge dislocations are often denoted by 1 if the extra half plane ab is above the plane sp, or by T if it is below. 

The edge dislocations bounding the dislocation loops just described cannot glide, but nevertheless the loop can grow by the continued collection of vacancies or interstitials. This method of movement of an edge dislocation, which allows edge... 

Low-angle tilt boundaries are the most easily visualized. Two regions of crystal separated by a slight misorientation can be drawn as a set of interlocking steps (Fig. 3.21a)- The edge dislocations coincide with the steps. The separate parts can be linked to make the edge dislocation array clearer (Fig. 3.21b). In the situation in which the misorientation between the two parts of the crystal is 0, the distance between the steps A and C is given by twice the dislocation separation, 2d, where... 

Dislocations. Screw dislocations are the most important defects when crystal growth is considered, since they produce steps on the crystal surface. These steps are crystal growth sites. Another type of dislocation of interest for metal deposition is the edge dislocation. Screw and edge dislocations are shown in Figure 3.4. 

The second type of line defect, the screw dislocation, occurs when the Burger s vector is parallel to the dislocation line (OC in Figure 1.33). This type of defect is called a screw dislocation because the atomic structure that results is similar to a screw. The Burger s vector for a screw dislocation is constructed in the same fashion as with the edge dislocation. When a line defect has both an edge and screw dislocation... 

The primary consideration we are missing is that of crystal imperfections. Recall from Section 1.1.4 that virtually all crystals contain some concentration of defects. In particular, the presence of dislocations causes the actual critical shear stress to be much smaller than that predicted by Eq. (5.17). Recall also that there are three primary types of dislocations edge, screw, and mixed. Althongh all three types of dislocations can propagate through a crystal and result in plastic deformation, we concentrate here on the most common and conceptually most simple of the dislocations, the edge dislocation. 

Figure 3.8. Explanation of dislocations in relation to glide. The solid arrow, b, corresponds to the Burgers vector of the dislocation. SV is the screw dislocation, WE is the edge dislocation, and VW is a mixed dislocation. The shaded area represents a glide plane.

The edge dislocation moves easily on its glide plane perpendicular to s under the influence of a shearing force. This force is well below the theoretical shear strength of a perfect crystal since not all of the atoms of a glide plane perform their slip at... 

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

A dislocation is characterized by its Burgers vector. An atom-to-atom circuit that would close in a perfect crystal will fail to close if it is drawn around a dislocation. The closure failure is the Burgers vector of the dislocation. This is illustrated in Figure 5.6. The edge dislocation (middle) is perpendicular to its Burgers vector and the screw dislocation (right) is parallel to its Burgers vector. 

Figure 10.8. The two extreme types of dislocations. In the edge dislocation (a), the Burgers vector is perpendicular to the dislocation line. In the screw dislocation (b), the Burgers vector is parallel to the dislocation line.

F re 5.26 Edge dislocation (a) and screw dislocation (b) in crystals with a simple cubic lattice. The symbol (-L) denotes the edge dislocation. The lattice atoms involved in a Burgers circuit construction are denoted as ( ). 

From atomistic aspects, a metal can be considered as a fixed lattice of positive ions permeated by a gas of free electrons [1], Positive ions are the atomic cores, while the electrons are the valence electrons. Since there are about 1022 atoms in 1 cm3 of a metal, one can expect that some atoms are not exactly in their right place. Thus, one can expect that a real lattice will contain defects (imperfections). The most common defects are point defects (e.g. a vacancy, an interstitial) and dislocations (e.g. the edge dislocation, screw dislocation) [2]. 

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