The Motion of Dislocations

The force opposing the motion of a dislocation is balanced by the force encouraging its motion. Thus, in a first approximation, there is no net force on the dislocation and the motive stress required is zero. Nevertheless, the small force actually required to move a dislocation has been explained by Peierls-Nabarro. Peierls-Nabarro stress , as it became known, is given as  

w is the width of the dislocation defined in Fig. 3.26 (Sect. 3.3.2), written 

The width of the dislocation, Eq. (3.23), defines the magnitude of the Peierls-Nabarro stress and is a measure of the degree of distortion that has occurred due to dislocation. It is basically the distance over which the dislocation causes disreg-istry thus, it is the magnitude of the displacement of the atoms from their perfect-crystal positions. As indicated in Sect. 3.3.2, when w is several atomic spacings, a dislocation is considered to be wide if it is on the order of one or two atomic spacings, it is narrow. 

we understand why the stress to move a dislocation is not zero. Though the Peirels-Nabaro equation indicates the low stress required for dislocation motion, it is not accurate, since the structure at the core of the dislocation and the changes in energy during slip are not known. 

To briefly review, the dislocation motion described above largely explains, for example, why FCC metals can be ductile, as long as some obstacle does not retard 

---

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

Materials with a high yield stress tend to go through the ductile to brittle transition at higher temperatures. This property has led to the assumption that true brittle fracture, unlike ductile fracture, is not accompanied by the motion of dislocations. The validity of this assumption is sometimes confirmed by the appearance of brittle fractures, which show essentially no ductility. 

The plastic deformation patterns can be revealed by etch-pit and/or X-ray scattering studies of indentations in crystals. These show that the deformation around indentations (in crystals) consists of heterogeneous rosettes which are qualitatively different from the homogeneous deformation fields expected from the deformation of a continuum (Chaudhri, 2004). This is, of course, because plastic deformation itself is (a) an atomically heterogeneous process mediated by the motion of dislocations and (b) mesoscopically heterogeneous because dislocation motion occurs in bands of plastic shear (Figure 2.2). In other words, plastic deformation is discontinuous at not one, but two, levels of the states of aggregation in solids. It is by no means continuous. And, it is by no means time independent it is a flow process. 

Plastic deformation is mediated at the atomic level by the motion of dislocations. These are not particles. They are lines. As they move, they lengthen (i.e., they are not conserved). Therefore their total length increases exponentially. This leads to heterogeneous shear bands and shear instability. 

A key feature of the motion of dislocation lines is that the motion is rarely concerted. One consequence is that the lines tend not to be straight, or smoothly curved. They contain perturbations ranging from small curvatures to cusps, and kinks. In covalent crystals where there are distinct bonds between the top... 

Surface layers interfere with the motion of dislocations near surfaces. Among other effects, this causes local strain-hardening, creating a harder surface region which thickens with further deformation, and eventually affects an entire specimen. A specific way in which this happens is through curving... 

It was discovered by Al shits et al. (1987) that static magnetic fields of order 0.5T affect the motion of dislocations in NaCl crystals. This is not an intrinsic effect but is associated with impurities and/or radiation induced localized defects. Also, magnetic field effects have been observed in semiconductor crystals such as Si (Ossipyan et al., 2004). 

Correlated plastic deformation in polymers is very evident in the necking of polymeric rods or filaments. This is one form of inhomogeneous deformation. Experiments with Nylon filaments, for example, have shown that necks in them behave quite similarly to the Lueders bands observed in steel (Dey, 1967). This strongly suggests that plastic deformation in Nylon is associated with the motion of dislocations. 

In Chapter 4, Corbett deals with specific defect centers in semiconductors. He points out that H aids the motion of dislocations in Si, which can lead to enbrittlement. Throughout this chapter, Corbett raises many questions that need further exploration. For example Is oxygen involved in processes that are attributed to hydrogen Does H play a role in defect formation ... 

The various topics are generally introduced in order of increasing complexity. The text starts with diffusion, a description of the elementary manner in which atoms and molecules move around in solids and liquids. Next, the progressively more complex problems of describing the motion of dislocations and interfaces are addressed. Finally, treatments of still more complex kinetic phenomena—such as morphological evolution and phase transformations—are given, based to a large extent on topics treated in the earlier parts of the text. 

Adsorption of surfactants can reduce the strength of materials by blocking the motion of dislocations... 

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. 

Slip from the motion of dislocations (linear defects in the crystal structure)... 

An explanation of the tendency for crystalline solids to deform plastically at stresses that are so much smaller than the calculated critical resolved shear stress was first given in 1934 independently by Taylor, Oro-wan, and Polanyi. They introduced the concept of the dislocation into physics and showed that the motion of dislocations is responsible for the deformation of metals and other crystalline solids. At low temperatures, where atomic diffusion is low, dislocations move almost exclusively by slip. 

From a mechanistic perspective, what transpires in the context of all of these strengthening mechanisms when viewed from the microstructural level is the creation of obstacles to dislocation motion. These obstacles provide an additional resisting force above and beyond the intrinsic lattice friction (i.e. Peierls stress) and are revealed macroscopically through a larger flow stress than would be observed in the absence of such mechanisms. Our aim in this section is to examine how such disorder offers obstacles to the motion of dislocations, to review the phenomenology of particular mechanisms, and then to uncover the ways in which they can be understood on the basis of dislocation theory. 

Conceptual Overview of the Motion of Dislocations Through a Field of... 

For coarse-grained metals, dislocation movement and twinning are well known primary deformation mechanisms. Ultrafine, equiaxed grains with high-angle grain boundaries impede the motion of dislocations and... 

These features suggest the following picture for the deformation of this type of steel at very low temperature the stress produces a deformation due to the motion of dislocations (effect visible by electron microscopy). These motions induce a transitory phase e in the lattice, and this e phase rapidly evolves toward the a phase. The martensitic a phase is therefore only a secondary phenomenon bound to the dislocation motion and a simple function of the strain associated with this motion. 

To this point, the motion of dislocations on slip planes in particular slip directions has been discussed. The factors that control the choice of these slip systems have not, however, been clearly identified, particularly with respect to crystal structure. It was established earlier (Eq. (6.3)) that the easiest slip process should be one that involves the smallest (unit) displacement on planes that are most... 

The creep of materials can also occur solely by diffusion, i.e., without the motion of dislocations. Consider a crystal under the action of a combination of tensile and compressive stresses, as shown in Fig. 7.4. The action of these stresses will be to respectively increase and decrease the equilibrium number of vacancies in the vicinity of the boundaries. (The boundaries are acting as sources or sinks for the vacancies.) Thus, if the temperature is high enough to allow significant vacancy diffusion, vacancies will move from boundaries under tension to those under compression. There will, of course, be a counter flow of atoms. As shown in Fig. 7.4, this mass flow gives rise to a permanent strain in the crystal. For lattice diffusion, this mechanism is known as Nabarro-Herring creep. The analysis showed that the creep rate e is given by... 

Hardness as resistance of a material against penetration of another body marks a decisive material characteristic. The hardness of important construction materials can be influenced or selectively set by special hardening processes. Hardening is based upon different principles, e.g., the formation of martensite in steels as a result of thermal treatment For nonferrous metals, precipitatiOTi hardening plays an important role. Alloying elements are deposited by a multilevel thermal process. Their phase boundaries and size influence the increase of hardness and stability decisively. This attribute improvement is based upon the hindrance of the motion of dislocation (Bargel and Schulze 1988). 

---