Dislocations elastic energy

The average value of A must be conserved over long distances to minimize both the elastic energy and the chemical (core) energy. Also, there will be little tendency for a dislocation line to remain in a single plane. It will tend to follow the plane of maximum shear stress. This is observed experimentally. 

Next, let us compile some quantitative relations which concern the stress field and the energy of dislocations. Using elastic continuum theory and disregarding the dislocation core, the elastic energy, diS, of a screw dislocation per unit length for isotropic crystals is found to be... 

Another quantity of interest is the velocity dependence of the energy of the dislocation. The energy density in the material around the dislocation, w, is the sum of the elastic strain-energy density and the kinetic-energy density,... 

Dislocation lines. The dilated region of an edge dislocation attracts the oversized Ag to reduce its and the Ag elastic energies. 

The effect of a dislocation line on dissolution nucleation has been attributed to the effect of their elastic strain energies on the chemical potential of the material nearby them (4). How ever this is a doubtful idea in both theory and practice. In theory the elastic energy of a screw dislocation line does not... 

This result may be borrowed for the continuous distribution imagined here once we recognize that the Burgers vector of each such infinitesimal dislocation is related to the local gradient in the slip distribution as is seen in fig. 8.27. Hence, the elastic energy due to all such dislocations is given by... 

We denote the stress field due to a single Volterra dislocation at position (x, y ) by olp x — x, y — y ). We also note that the original interpretation of the elastic energy release rate offered in section 2.4.4 can be reinterpreted in terms of the driving forces on the various dislocations making up the crack. Now that we have seen how the crack itself may be written in terms of dislocations, we turn to the question of how to think about such a crack when there are other dislocations in its vicinity. 

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