Dislocation dynamics example

As noted above, one interesting application of these ideas is to the motion of a dislocation through an array of obstacles. An alternative treatment of the field due to the disorder is to construct a particular realization of the random field by writing random forces at a series of nodes and using the finite element method to interpolate between these nodes. An example of this strategy is illustrated in fig. 12.27. With this random field in place we can then proceed to exploit the type of line tension dislocation dynamics described above in order to examine the response of a dislocation in this random field in the presence of an increasing stress. A series of snapshots in the presence of such a loading history is assembled in fig. 12.28. 

In this chapter we discuss the computational implementation of the dynamical theory of diffraction Takagi-Taupin theory, the solution for grids and thin layers, HRXRD simulation, deviation parameters, strategies, effect of strain, dislocation and defect arrays. We then give a number of examples of simulations. 

The EAM and MEAM potentials once determined from electronics principles calculations [178] have been used to reproduce physical properties of many metals, defects, and impurities. For example, EAM molecular statics, molecular dynamics, and Monte Carlo simulations were performed on hydrogen embrittlement effects on dislocation motion and plasticity [46,179-181]. These potentials have been used to analyze plasticity [74,144,145,148-150,182,183], cracks and fracture [117,184], and fatigue [119, 120, 185, 186]. 

Thus, because of these empirical correlations, it may be possible, at least in principle, to estimate quantitatively the stress, temperature, and perhaps the strain-rate of a naturally deformed rock from measurements of dislocation density, subgrain size, and dynamically recrystallized grain size, together with Burgers vector determinations. However, these estimates will be questionable unless certain conditions are fulfilled. Some of the more important of these conditions will now be discussed before considering specific examples of the application of microstructural observations to tectonic problems. 

Jogs are formed by climb. They are favorable sites for the absorption and emission of point defects. In thermal equilibrium, the atoms at jog sites are in dynamic equilibrium and arrive and leave the jog at equal rates. If there is an increase in vacancies, for example, in the vicinity of a dislocation line above the thermal equilibrium value, the probability of atomic exchange at a jog with a vacancy increases, climb occurs and the extra plane (defining the dislocation line) shrinks. Therefore, excess vacancies promote the process of climb. Similarly, an excess of interstitial atoms adds atoms to the existing jog, which causes it to grow. In summary, when atoms are removed from an extra plane, the crystal collapses... 

Ftg. lOJ Localized anodic (A) and cathodic (C) zones on the same metal surface covered by an electrolyte. This is a snapshot of a dynamic situation the anodic and cathodic zones may change in shape, size and position. The zones may arise due to differences in, for example, constituent phases, stress levels, thermal history, surface coatings and imperfection levels (such as grain boundaries, dislocations, kink sites, etc). These features tend to become anodic. 

---