Dislocation stress

Mathematically, the radial component of the dislocation stress may be written as ... 

One consequence of Equation 7.23 is that edge dislocations attract impurity atoms. Impurities (and intrinsic defects) are nearly always the wrong size for the site on which they lie. An oversized atom will be attracted to the tensile portion of the edge dislocation stress field while an undersized atom will be attracted to the compressive region. In other words, essentially all impurities will be attracted to edge dislocations. This is good when the impurities are detrimental but can be harmful when the impurities are intended dopant atoms. 

Actual crystal planes tend to be incomplete and imperfect in many ways. Nonequilibrium surface stresses may be relieved by surface imperfections such as overgrowths, incomplete planes, steps, and dislocations (see below) as illustrated in Fig. VII-5 [98, 99]. The distribution of such features depends on the past history of the material, including the presence of adsorbing impurities [100]. Finally, for sufficiently small crystals (1-10 nm in dimension), quantum-mechanical effects may alter various physical (e.g., optical) properties [101]. 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

At low temperatures, the surface mobiUty of the atoms is limited and the stmcture grows as tapered crystaUites from a limited number of nuclei. It is not a full density stmcture but contains longitudinal porosity on the order of a few tens of nm width between the tapered crystaUites. It also contains numerous dislocations with a high level of residual stress. Such a stmcture has also been caUed botryoidal and corresponds to Zone 1 in Figures 6 and . 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

The interface between the substrate and the fully developed film will be coherent if the conditions of epitaxy are met. If there is a small difference between the lattice parameter of the film material and the substrate, die interface is found to contain a number of equally spaced edge dislocations which tend to eliminate the stress effects arising from the difference in the atomic spacings (Figure 1.13). 

Dislocations are known to be responsible for die short-term plastic (nonelastic) properties of substances, which represents departure from die elastic behaviour described by Hooke s law. Their concentration determines, in part, not only dris immediate transport of planes of atoms drrough die solid at moderate temperatures, but also plays a decisive role in die behaviour of metals under long-term stress. In processes which occur slowly over a long period of time such as secondaiy creep, die dislocation distribution cannot be considered geometrically fixed widrin a solid because of die applied suess. 

In this study, the appearance and evolution sequence of planar slip bands, in addition to a dislocation cell structure with increasing e,, is identical to that observed in quasi-static studies of the effects of stress path changes on dislocation substructure development [27]. The substructure evolution in copper deformed quasi-statically is known to be influenced by changes in stress path [27]. Deforming a sample in tension at 90° orthogonal to the... 

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. 

Figure 7.3. Dislocation densities required to fit the precursor curves as a function of the initial quasi-static yield stress.

Figure 7.4. Dislocation density at the shock front as a function of shear stress on primary slip planes.

Dick et al. [29] present additional data on the <100) shock compression of LiF which further establishes a threshold shear stress of between 0.24 GPa and 0.30 GPa for nucleation of dislocations in the shock front. 

Flinn et al. [30] describes an experimental impact technique in which <100)-oriented LiF single crystals ( 8 ppm Mg) are loaded in a controlled manner and the multiplication of screw dislocations is measured. The peak shear stress in this relatively soft material is 0.01 GPa. For shear impulses exceeding approximately 40 dyne s/cm, dislocation multiplication is adequately described by the multiple-cross-glide mechanism [(7.24)] with m = l/bL = (2-4) X 10 m, in reasonable agreement with quasi-static measurement [2]. 

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