Dislocation velocities

This phenomena has been attributed to the very high strain rates associated with shock loading and the subsonic restriction on dislocation velocity requiring the generation and storage of a larger dislocation density during the shock process than for quasi-static processes [1], [2], [12],... 

Kumar and Clifton [31] have shock loaded <100)-oriented LiF single crystals of high purity. The peak longitudinal stress is approximately 0.3 GPa. Estimates of dislocation velocity are in agreement with those of Flinn et al. [30] when extrapolated to the appropriate shear stress. From measurement of precursor decay, inferred dislocation densities are found to be two to three times larger than the dislocation densities in the recovered samples. 

Dislocation motion in the clear region between obstacles is determined by the viscous drag coefficient B [2]. The relationship between the applied shear stress and dislocation velocity is... 

Combination of effects of thermal activation and viscous drag then gives for an average dislocation velocity... 

Koehler attributed the cross-gliding to thermal activation, but it was found experimentally that it increases with dislocation velocity, which is inconsistent with thermal activation, so Gilman (1997) proposed that it is associated with flutter of screw dislocations caused by phonon buffeting. 

An equation that describes the dependence of dislocation velocity, v on the applied shear stress, x is ... 

W. G. Johnston and J. J. Gilman, Dislocation Velocities, Dislocation Densities, and Plastic Flow in Lithium Fluoride Crystals, Jour. Appl. Phys., 30,129 (1959). 

J. R. Patel, Electronic Effects on Dislocation Velocities in Heavily Doped Silicon, ... 

Intrinsic resistance to dislocation motion can be measured in either of two ways direct measurements of individual dislocation velocities (Vreeland and Jassby, 1973) or by measurements of internal friction (Granato, 1968). In both cases, for pure simple metals there is little or no static barrier to motion. As a result of viscosity there is dynamic resistance, but the viscous drag coefficient is very small (10" to 10" Poise). This is only 0.1 to 1 percent of the viscosity of water (at STP) and about 1 percent of the viscosity of liquid metals at their... 

In the study of the nucleation and propagation of dislocations (Figure 10.11) from scratches in a geometry designed to produce slip on non-basal planes, edge dislocations were found to glide on non-basal planes, but screw dislocations were completely immobile except in the basal plane. Detailed measurements of the dislocation velocities using stress pulse techniques showed that... 

Dislocations move when they are exposed to a stress field. At stresses lower than the critical shear stress, the conservative motion is quasi-viscous and is based on thermal activation that overcomes the obstacles which tend to pin the individual dislocations. At very high stresses, > t7crit, the dislocation velocity is limited by the (transverse) sound velocity. Damping processes are collisions with lattice phonons. 

Drag Effects. Dislocations gliding in real crystals encounter dissipative frictional forces which oppose their motion. These frictional forces generally limit the dislocation velocity to values well below the relativistic range. Such drag forces originate from a variety of sources and are difficult to analyze quantitatively. 

Any lateral displacement of the segment will be small compared to its length and the drag force can be taken as viscous (i.e., proportional to the dislocation velocity). 

Drag force, Bv, where B is the drag coefficient and v is the dislocation velocity. Peierls stress Fpeierb. 

In materials with high dislocation mobility such as copper, dislocation patterns proceed through the rapid motion of dislocations in a very small volume of the specimen [36]. Under high strain rate deformation conditions, it is expected that the dislocations move at subsonic speed or even as fast as the shear wave velocity. The random motion of dislocations on their slip planes causes random changes not only in the local dislocation densities, but also in the dislocation velocities. 

In order to overcome the difficulty that thermal processes cannot support the plastic wave due to a shock or severe impact, it has been suggested that dislocation motion occurs by quantum tunneling [15,16], The dislocation velocity, v(i, U), can be written as... 

The dislocation velocity, once the stress cr is large enough to cause motion, can be assumed to follow a law of the form... 

Silicon at 900 °C and germanium at 500 °C both show very pronounced yield points, when the initial dislocation density is low, and these correspond very closely in shape and position to those found for ice. Since a pronounced yield point is associated in the theory with a small value of the exponent m in the dislocation velocity relation (8.43), it is satisfying that direct observation of dislocation motion in these materials (Chaudhuri et al. 1962) gives m from 1-3 to i 9 in close similarity to the value m 1 found by Higashi Sakai (19616) for ice or the value between i 5 and 2 5 deduced from macroscopic experiments. These values are in... 

The onset of yielding is not always as smooth as that depicted in Fig. 6.21 and it can be accompanied by a stress drop (strain softening). In some cases, the drop occurs over a range of strain whereas, in the other cases, it is instantaneous. The former behavior occurs when yielding is associated with a rapid increase in the dislocation density. This allows the dislocation velocity to drop (Eq. (6.16)) and, hence, yielding can continue at a lower stress. A sharper yield drop is usually associated with dislocations being pinned by impurity atmospheres and, once the dislocations escape, yielding continues at a lower stress. 

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