Dislocations interactions

If two identically oriented edge dislocations are parallel and lie almost on top of each other, the tensile stress field of one overlaps with the compressive stress field of the other. This is energetically favourable, so the dislocations attract and, in the ideal case, finally stop if one is exactly on top of the other. If several dislocations are arranged in this way, the crystal regions on both sides of the dislocation lines are tilted (figure 6.18). This is called a low-angle grain boundary. 

It can be seen from figure 6.7 that the edge dislocation shown will repel another, identically oriented, dislocation when it is positioned in regions I, IV, V, or VIII. In the other regions, the dislocation is attracted. In both cases, dislocation movement may be hampered, depending on the direction of movement. If the dislocations repel each other, this is obvious because energy is needed to overcome the barrier. If they attract, the released energy 

For oppositely oriented dislocations, the attractive and repulsive regions are exactly reversed. Similar considerations are also valid for screw dislocations. 

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An analogy to sHp dislocation is the movement of a caterpillar where a hump started at one end moves toward the other end until the entire caterpillar moves forward. Another analogy is the displacement of a mg by forming a hump at one end and moving it toward the other end. Strain hardening occurs because the dislocation density increases from about 10 dislocations/cm to as high as 10 /cm. This makes dislocation motion more difficult because dislocations interact with each other and become entangled. SHp tends to occur on more closely packed planes in close-packed directions. 

Thus, in simple metals, interactions between dislocations rather than interactions between atoms, are most important. The hardnesses of metals depend on deformation hardening (dislocation interactions) rather than individual mobilities. The elastic resistance to shear plays a dominant role because it is directly involved with dislocation mobility. 

How Steps from a Pair of Screw Dislocations Interact... 

Dislocations interact and tend to order if they can move. Consider the arrangement shown in Figure 3-6a. This is called an edge dislocation tilt boundary. It is seen that the number of lattice planes terminating at the boundary is n - (2/6)-sin 0/2, from which the (mean) spacing between the dislocations is found to be... 

The stress fields of edge dislocations interact with other edge dislocations. The systems energy is lowered if they are aligned so that the compressive field of one... 

Edge and screw dislocations are abrupt changes in the regular ordering of atoms along an axis in the crystal (Figure 2.29). These line defects are introduced during the crystallization process, and may not always be detrimental. As we will see in Chapter 3, it is the dislocation interactions within a metal that are responsible for... 

Figure 5 represents a typical evolution of the dislocation pattern during the deformation. The simulation was performed in a 20 mm diameter crystal, with 2 initial basal planes activated (one system in each plane) at the beginning of the deformation. It clearly appears that the double cross-slip mechanism propagates the plasticity in many other basal planes. One can also notice the asymmetry in the plane expansion due to the dislocation interactions. 

Dislocation-Dislocation Interactions and Work Hardening In addition to the chemical mechanisms for hardeiung described above, there are intrinsic mechanisms that accompany the increase in dislocation density with increasing strain. Recall fig. 8.40 in which it was shown that the density of dislocations increases continuously with increasing plastic strain. Attendant with this increasing dislocation density is a hardening effeet. An example of the type... 

Fig. 12.26. Results of mesoscopic dislocation dynamics simulation of dislocation interactions in a strained epitaxial layer (adapted from Schwarz and LeGoues (1997)). The network shown in the figure results from the interaction of dislocations on parallel glide planes.

Numerical calculations of dislocation pair interactions have been carried out for systems of particles with / [89] and LJ [90] potentials. For the potential, Fisher et al. [89] find that the elastic dislocation interaction potential is accurate for dislocation separations as small as 3 lattice spacings, while Joos and Duesbery [90] find that separations of 30 lattice spacings are necessary to reach the asymptotic elastic limit. The adequacy of the continuum elastic approximation in describing the short-range interactions between defects is thus still something of an open question, and may depend on the range of the interparticle potential. 

The particular merit of transmission electron microscopy is that the three-dimensional arrangements of dislocations can often be observed and that the identity, i.e., the slip plane and Burgers vector, can be determined. Dislocation interaction and movements may also be observed directly. However, one serious limitation devolves upon the fact that thin sections have to be used, which means that the arrangement of dislocations and their mutual interaction may be influenced by the sample size. In addition, rather small and unrepresentative samples have to be used and, most inconvenient of all for those interested in... 

This enables us to calculate dislocation interactions but it must be borne in mind that the theory is not strictly valid for distances of the order of the core radius. 

After the various dislocation interactions, the stress needed for further plastic deformation will depend on the mean free dislocation length L. The dislocation density should be proportional to ML and thus Eq. (6.22) can be used to estimate the shear stress needed to overcome the obstacles, i.e.. 

Is the dislocation interacting with other dislocations, or with other lattice defects ... 

FIGURE 14.13 An extrinsic dislocation interacting with a low-angle 001 twist GB in spinel. Note how all the dislocations are changed by the Interaction as seen in the enlarged inset. 

Dislocation interactions, other than orthogonal, have not been reported to date. 

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