Analog dislocation

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. 

Fig. 9.10. The planking analogy of the screw dislocation. Imagine four planks resting side by side on a factory floor. It is much easier to slide them across the floor one at a time than all at the same time.

In general terms, as has already been mentioned, plastic deformation is a transport process analogous with electrical and thermal conductivity. These involve an entity to be transported, a carrier that does the transporting, and a rate of transport. In the case of electrical conductivity, charge is the transport entity, electrons (or holes) are the carriers, and the electron net velocities determine the rate. In the case of plastic deformation, displacement, b (cm) is the transport entity, dislocations are the carriers, N ( /cm2), and their velocities, v (cm/sec) determine the shear deformation rate, d8/dt. In two dimensions, the latter is given by the Orowan Equation ... 

Whereas in good-conducting doped or polymeric dyes ft-or -type conductivity can be explained without difficulty by analogy with inorganic semiconductors, the p- and -type photoconductivity in insulating (intrinsic) dye films cannot be explained in this manner. It is necessary to take into consideration the existence of defect states (lattice defects, dislocations, impurities etc.) distributed at different depths in the forbidden zone between valence and conduction band these defect states are able to trap electrons and holes, respectively, with different probability 10,11,88),... 

Fig. 7.151. Screw-thread spiral analogy to a screw dislocation.

Experiments demonstrate that along crystal imperfections such as dislocations, internal interfaces, and free surfaces, diffusion rates can be orders of magnitude faster than in crystals containing only point defects. These line and planar defects provide short-circuit diffusion paths, analogous to high-conductivity paths in electrical systems. Short-circuit diffusion paths can provide the dominant contribution to diffusion in a crystalline material under conditions described in this chapter. 

For a > 1, nucleation is barrierless—i.e., the transformation is controlled solely by growth kinetics. However, for a < 1, a barrier exists. The local minimum of AQ (r) at point A in the plot corresponds to a metastable cylinder of /3 of radius r0 forming along the dislocation line. (In a sense, this is analogous to the Cottrell atmosphere described in Section 3.5.2.) In Eq. 19.54, the metastable cylinder s radius is... 

The transition metal carbides do have a notable drawback relative to engineering applications low ductility at room temperature. Below 1070 K, these materials fail in a brittle manner, while above this temperature they become ductile and deform plastically on multiple slip systems much like fee (face-centered-cubic) metals. This transition from brittle to ductile behavior is analogous to that of bee (body-centered-cubic) metals such as iron, and arises from the combination of the bee metals strongly temperature-dependent yield stress (oy) and relatively temperature-insensitive fracture stress.1 Brittle fracture is promoted below the ductile-to-brittle transition temperature because the stress required to fracture is lower than that required to move dislocations, oy. The opposite is true, however, above the transition temperature. 

An important modification of this model was performed by Wakai.33 The main assumptions are that the solution and precipitation reactions take place at line defects as kinks in steps formed at the grain boundaries (Fig. 16.4), and the spacing between kinks is small enough for the step to be considered as an ideal source or sink of solute particles. Thus, the solution and precipitation of crystalline materials at these steps produces their movement, and consequently strain and strain rate will have an expression analogous to Orowan s equation for dislocation movement ... 

The first question to address is the definition of a defect in an amorphous material. In a crystal any departure from the perfect crystalline lattice is a defect, which could be a point defect, such as a vacancy or interstitial, an extended defect, such as a dislocation or stacking fault, or an impurity. A different definition is required in an amorphous material because there is no perfect lattice. The inevitable disorder of the random network is an integral part of the amorphous material and it is not helpful to think of this as a collection of many defects. By analogy with the crystal one can define a defect as a departure from the ideal amorphous network which is a continuous... 

---