Dislocation conservative motion

An edge dislocation is confined to move on its slip plane (conservative motion), and the slip due to the motion of the dislocation is also confined to the slip plane. Movement of a screw dislocation can capture on the plane where it started or else move to any other, parallel to the dislocation line (cross slip). If an edge dislocation were to move... 

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. 

Osmotic force Fosmonc resulting from non-conservative motion of dislocation (climb) and results in the production of intrinsic point defects. 

The non-conservative motion (or climb ) of a dislocation is indicated in a series of illustrations in Fig. 3.39 for positive and negative edge dislocations. 

Edge dislocations can glide only on the slip plane containing the Burgers vector of the dislocation. Such motion is called conservative motion. The extra partial plane of atoms (Figure 2) is normal to the... 

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 second major difficulty with the Peierls model is that it is elastic and therefore conservative (of energy). However, dislocation motion is nonconservative. As dislocations move they dissipate energy. It has been known for centuries that plastic deformation dissipates plastic work, and more recently observations of individual dislocations has shown that they move in a viscous (dissipative) fashion. 

Of particular interest in kinetics is the non-conservative dislocation motion (climb). The net force on a dislocation line in the climb direction (per unit length) consists of two parts Kei is the force due to elastic interactions (Peach-Koehler force), Kcbcm is the force due to the deviation from SE equilibrium in the dislocation-free bulk relative to the established equilibrium at the dislocation line. Sites of repeatable growth (kinks, jogs) allow fast equilibration at the dislocation. For example, if cv is the supersaturated concentration and c is the equilibrium concentration of vacancies, (in the sense of an osmotic pressure) is... 

If a crystal is exposed to stress in such a way that the strain is kept constant, the stress will decrease with time as shown in Figure 14-4. One concludes that stress relaxation has occurred. Conversely, strain does not remain constant under constant load. Time dependent (i.e., plastic) strain in stressed crystals is called creep. It was already mentioned that elastic strain due to the applied stress is usually less than 1%. Plastic strain definitely dominates beyond the elastic limit which, to a large extent, is due to dislocation formation and motion. Since the crystal lattice is conserved during this... 

We start with dislocations and describe both glissile (conservative) and climb (nonconservative) motion in Chapter 11. The motion of vapor/crystal interfaces and liquid/crystal interfaces is taken up in Chapter 12. Finally, the complex subject of the motion of crystal/crystal interfaces is treated in Chapter 13, including both glissile and nonconservative motion. 

The motion of a crystal/crystal interface is either conservative or nonconservative. As in the case of conservative dislocation glide, conservative interface motion occurs in the absence of a diffusion flux of any component of the system to or from the... 

Sharp boundaries of several different types can move conservatively by the glide of interfacial dislocations. In many cases, this type of motion occurs over wide ranges of temperature, including low temperatures where little thermal activation is available. 

The basic mechanisms by which various types of interfaces are able to move non-conservatively are now considered, followed by discussion of whether an interface that is moving nonconservatively is able to operate rapidly enough as a source to maintain all species essentially in local equilibrium at the interface. When local equilibrium is achieved, the kinetics of the interface motion is determined by the rate at which the atoms diffuse to or from the interface and not by the rate at which the flux is accommodated at the interface. The kinetics is then diffusion-limited. When the rate is limited by the rate of interface accommodation, it is source-limited. Note that the same concepts were applied in Section 11.4.1 to the ability of dislocations to act as sources during climb. 

The octahedral shear stress criterion has some appeal for materials that deform by dislocation motion In which the slip planes are randomly oriented. Dislocation motion Is dependent on the resolved shear stress In the plane of the dislocation and In Its direction of motion ( ). The stress required to initiate this motion is called the critical resolved shear stress. The octahedral shear stress might be viewed as the "root mean square" shear stress and hence an "average" of the shear stresses on these randomly oriented planes. It seems reasonable, therefore, to assume that slip would initiate when this stress reaches a critical value at least for polycrystal1ine metals. The role of dislocations on plastic deformation in polymers (even semicrystalline ones) has not been established. Nevertheless, slip is known to occur during polymer yielding and suggests the use of either the maximum shear stress or the octahedral shear stress criterion. The predictions of these two criteria are very close and never differ by more than 15%. The maximum shear stress criterion is always the more conservative of the two. 

Climb is nonconservative motion because vacancies and/or interstitials must be absorbed or emitted (their number is not conserved). When a jog moves, it can either glide or climb. The special point to remember is that the glide plane of a jog is not the same as the glide plane of the dislocation on which is sits. If we force a dislocation jog to move on a plane, which is not its glide plane, it must adsorb or emit point defects, but it can glide. Since it is charged, it carries a current when it glides. 

Previous Sect. 3.3.6 indicated that dislocation motion may be conservative (glide) and nonconservative (climb). For glide, the Burgers vector and dislocation must be in the same plane. Unlike edge dislocations (as indicated above), screw... 

Bulk-diflRision-assisted creep occurs in the processes listed above, namely in (b) climb (c) climb-assisted glide and (d) thermally-activated glide via cross-slip. All these are obviously associated with dislocation motion. High stress, below yield stress, causes creep by conservative dislocation motion, namely by dislocation glide within its slip plane. This readily occurs at high temperatures above 0.3 Tm for pure metals and at about 0.4 Tm for alloys, where the dependence on strain rate becomes quite strong. For ceramics, T > 0.4—0.5 T (K). A formulation used for such creep is ... 

Chen, S., Ertekin, E., Chrzan, D. C. (2010). Plasticity in carbon nanotubes Cooperative conservative dislocation motion. Phys. Rev. B 81,155417-8. 

However, long-range atomic transport is nevertheless required for the climb process because it is a non-conservative mode of dislocation motion. Depending on the direction of motion, either atoms or vacancies have to be moved to the dislocation-core region. 

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