Mesoscopic Dislocation Dynamics

Kinematics of Lines. The first order of business is the characterization of the dislocation lines themselves without reference to the forces that result in dislocation motion. In principle, each and every dislocation line can be characterized through a parameterization of the form 

As noted above, one of the key outcomes of carrying out the discretization of dislocation lines into a series of segments is that the various integrals used to compute displacements, strains, stresses and interaction energies are replaced by sums over the nodal degrees of freedom. On the other hand, as with any numerical approximation scheme, we must assess the errors that are an inheritance of that numerical scheme. One particularly useful setting within which to effect such assessments is in the context of simple planar loop geometries for which there 

The final feature of the dislocation dynamics method that must be introduced so as to give such methods the possibility of examining real boundary value problems in plastic deformation is the treatment of boundary conditions. In particular, if we wish to consider the application of displacement and traction boundary conditions on finite bodies, the fields of the relevant dislocations are no longer the simple infinite body Volterra fields that have been the workhorse of our discussions throughout this book. To confront the situation presented by finite bodies, a useful scheme described in Lubarda et al. (1993) as well as van der Giessen and Needleman (1995) is to use the finite element method to solve for the amendments to the Volterra fields that need to be considered in a finite body. Denote the Volterra fields for an infinite body as In this case the fields of interest are given by 

Line Tension Dislocation Dynamics. Though our discussion above has given a generic feel for the dislocation dynamics strategy and has emphasized the full treatment of interactions between different segments, a watered down version of 

We begin by stating the problem in continuous form in which the kinematics of the line is described in terms of the parameterization x(x). The formulation is then founded upon a variational statement of the form 

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Fig. 12.26. Results of mesoscopic dislocation dynamics simulation of dislocation interactions in a strained epitaxial layer (adapted from Schwarz and LeGoues (1997)). The network shown in the figure results from the interaction of dislocations on parallel glide planes.

Mesoscopic computer simulations [27] of the 3-D dislocation dynamics of fatigue hardening reveal that dipoles forming in one half-cycle unzip during the next, unless stabilized to form EDLs via annihilation. This... 

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