Particular slip planes

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

DISLOCATION. In crystallography, a type of lattice imperfection whose existence in metals is postulated in order to account for the phenomenon uf crystal growth and of slip, particularly for the low value of shear stress required lo initiate slip. One section of the crystal adjacent to the slip plane is assumed to contain one mure atomic plane that the section on the opposite side of the slip plane. Motion of the dislocation results in displacement of one of the sections with respect to another. 

Since the (0 0 1) is not a slip plane, the product dislocation is immobile, or sessile. It provides an obstacle to the movement of other dislocations passing down the (1 1 1)and(1 1 1) planes. This particular case is known as the Lomer lock. 

For many purposes, we will find that antiplane shear problems in which there is only one nonzero component of the displacement field are the most mathematically transparent. In the context of dislocations, this leads us to first undertake an analysis of the straight screw dislocation in which the slip direction is parallel to the dislocation line itself. In particular, we consider a dislocation along the X3-direction (i.e. = (001)) characterized by a displacement field Usixi, X2). The Burgers vector is of the form b = (0, 0, b). Our present aim is to deduce the equilibrium fields associated with such a dislocation which we seek by recourse to the Navier equations. For the situation of interest here, the Navier equations given in eqn (2.55) simplify to the Laplace equation (V ms = 0) in the unknown three-component of displacement. Our statement of equilibrium is supplemented by the boundary condition that for xi > 0, the jump in the displacement field be equal to the Burgers vector (i.e. Usixi, O" ") — M3(xi, 0 ) = b). Our notation usixi, 0+) means that the field M3 is to be evaluated just above the slip plane (i.e. X2 = e). 

Although there are a number of interesting features of this analysis, it also leaves us with serious concerns about the formulation of an elastic theory of the obstacle forces that impede dislocation motion. In particular, this analysis suggests that for an obstacle on the slip plane itself, there is no interaction with the dislocation. Despite this elastic perspective, it seems certain that core effects will amend this conclusion. 

It is useful if, first of all, we consider the motion of many dislocations on one slip plane (5,11). We shall see later (Section II,C,3) that a series of dislocation loops may glide freely (i.e., w e are referring to glissile dislocations) from a particular source, so that a continual supply of dislocations moves over the slip plane in question (see Fig. 16). A pileup of... 

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... 

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... 

Consider a single crystal being subjected to uniaxial tension or compression, as shown in Fig. 6.20. Clearly, the ease with which plastic deformation is activated will depend not only on the ease of dislocation glide for a particular slip system but also the shear stress acting on each system. This is similar to the problem discussed in Section 2.10 (Eq. (2.44)) though one should note the plane normal, the stress direction and the slip direction are not necessarily coplanar, (< +A)5 90°. In other words, slip may not occur in the direction of the maximum shear stress. The resolved shear stress acting on the slip plane in the slip direction is... 

Transition zones occur in many types of strata but are particularly common in sedimentary rocks. A transition zone occurs when some change in deposition causes a change in sedimentation. Different types of sediments compact at different rates. Discontinuities are abundant in the transition zones between distinct strata. For example, where ancient streambeds eroded the adjacent sediments, remnants of the stream channel disrupt the continuity of the normal roof beds, resulting in large slip planes. 

So far we have limited ourselves to solid, rigid particles, for which the interface and, in particular, the electrokinetic potential and the slip plane are well defined. We will briefly discuss two situations in which this hypothesis fails. The first one is the electrophoretic mobihty of charged hquid drops in an emulsion. Clearly, we cannot assume that the fluid velocity relative to the particle is zero at the separation between the drop surface and the liquid medium itself, as the motion of the latter will be transmitted to the drop, the viscosity of which is rjp. 

Virtually all observations of dislocation glide in bulk covalent crystals at stress levels above some modest threshold level on the order of 10 N/m reveal that the normal glide velocity on a particular slip system of a given material varies with resolved shear stress on the glide plane r es = o ijTi bi/b and absolute temperature T according to an Arrhenius relationship of the form... 

In single crystals, there are preferred planes where dislocations may propagate, referred to as slip planes. For a particular crystal system, the planes with the greatest atomic density will exhibit the most pronounced slip. For example, slip planes for bcc and fee crystals are 110 and 111, respectively other planes, along with those present in hep crystals, are listed in Table 2.9. Metals with bcc or fee lattices have significantly larger numbers of slip systems (planes/directions) relative to hep. For example, fee metals have 12 slip systems four unique 111 planes, each... 

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