Mobile dislocations

Calculations of this type are carried out for fee, bcc, rock salt, and hep crystal structures and applied to precursor decay in single-crystal copper, tungsten, NaCl, and LiF [17]. The calculations show that the initial mobile dislocation densities necessary to obtain the measured rapid precursor decay in all cases are two or three orders of magnitude greater than initially present in the crystals. Herrmann et al. [18] show how dislocation multiplication combined with nonlinear elastic response can give some explanation for this effect. 

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

Meir and Clifton [12] study shocked <100) LiF (high purity) with peak longitudinal stress amplitudes 0.5 GPa. A series of experiments is reported in which surface damage is gradually eliminated. They find that, while at low-impact velocities the dislocations in subgrain boundaries are immobile and do not affect the dislocation concentration in their vicinity, at high-impact velocities ( 0.1 km/s) dislocations emitted from subgrain boundaries appear to account for most of the mobile dislocations. 

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-... 

From the early work of Taylor [63T01] connecting dislocation behavior to observed viscoplastic shock-compression response, numerous studies have attempted to relate conventional dislocation dynamics models to experimental observations. Theory and observations consistently require unusually large numbers of mobile dislocations. Although qualitatively descriptive, progress to date on dislocation models has not proven to provide quantitative descriptions to the observations in metals. 

Using average values, the density of mobile dislocations, N which increases with the deformation, may be written ... 

The non-monotonous dependence of surface layer microhardness on deformation degree results from different mechanisms of nitrogen diffusion in deformed material. In our point of view, under the deformations of 3-8 and 20-30 % the greatest number of mobile dislocations, capable to provide the additional transfer of nitrogen interstitial atoms with Cottrell s atmospheres by the dislocation-dynamic mechanism [6-8], can be formed. 

The maximum rise of number of mobile dislocations in the deformed materials occurs in the range of 10-20 % [9, 10]. Such processes influence on kinetic of phase formation that results in the accelerated growth of s- and y-nitrides and in increase of microhardness of the surface diffusion layers. 

When all the SE s of a solid with non-hydrostatic (deviatoric) stresses are immobile, no chemical potential of the solid exists, although transport between differently stressed surfaces takes place provided external transport paths are available. Attention should be given to crystals with immobile SE s which contain an (equilibrium) network of mobile dislocations. In these crystals, no bulk diffusion takes place although there may be gradients of the chemical free energy density and, in multicomponent systems, composition gradients (e.g., Cottrell atmospheres [A.H. Cottrell (1953)]). 

The yield point, work-hardening, and recovery. The yield stress, whether in a creep or a constant strain-rate experiment, is determined by the onset of dislocation mobility, usually glide. The subsequent deformation depends on the density mobile dislocations and their speed v. Provided the dislocations are distributed reasonably homogeneously in the specimen, the deformation is described by the Orowan equation... 

In a constant strain-rate experiment, the rapid multiplication of dislocations following the yield point can produce more mobile dislocations than are necessary to maintain the imposed strain-rate and consequently the stress drops. The deformation will continue at a constant stress provided any decrease in u is compensated by an increase in iom, or vice versa. However, in general, the stress rises with increasing strain. The slope (dajdt) of the stress-strain curve is determined by the competition between two dislocation processes namely, work-hardening and recovery, which we now consider briefly. 

The initial density of mobile dislocations is at least five orders of magnitude less than that required to initiate deformation in the Griggs (1974) microdynamical calculations (McLaren, Fitz Gerald, and Gerretsen 1989). 

Investigation of the deformation relief occurring on the surface of samples additionally subjected to by 15% strain after different number of compression steps have shown that plateau on the initial portion of strain curves is result of strain localization (Fig. 2a) in macro shear bands (MSB). Its appearance is result of scattering some dislocation boundaries onto individual dislocations (Baushinger effect) and formation of avalanche of mobile dislocations (Fig. 2b). So, in this case yield of titanium is controlled by substructure that, probably, leads to weak dependence of yield stress on strain. Macrobands formed at the beginning of the cycle of loading remain until the end of loading. So, plastic flow of titanium is localized. 

The theory of heat generation by mobile dislocations was given by Eshelby and Pratt [73] in terms of the temperature rise AT produced by the movement of n dislocations at a velocity F in a medium of thermal diffusivity a. Two cases were considered, one in which the mean spacing of the dislocations X is much smaller than A = 2a/F, and that for which X A. The final expressions have the form... 

Table 16.1 Comparison of distances between dislocations in sub-boundaries X and average distances zq between jogs in mobile dislocations.

The sub-boundaries that have been formed seem to be sources of slipping dislocations. The process of generation of mobile dislocations by sub-boundaries is readily affected by the applied stress. The TEM technique allows one to observe the beginning of a dislocation emission. The creation of dislocations occurs as if the sub-boundary blows the dislocations loops. These loops broaden gradually and... 

Some dislocations, which are observed in specimen after high-temperature deformation, are not associated in sub-boundaries. They are located inside subgrains. Bends and kinks at these dislocations attract one s attention. They give an impression that certain points of mobile dislocations are pinned up. 

We compared the average distances 1 between sub-boundary dislocations, determined with the X-ray method, and the spacings Zq between jogs in mobile dislocations measured with the aid of electron microscopy. We revealed that the two values are close to each other. The data of comparison are shown in Table 16.1. 

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