Dislocation strain energy

When metals are deformed plastically at room temperature the dislocation density goes up enormously (to =10 m ). Each dislocation has a strain energy of about Gb /2 per unit length and the total dislocation strain energy in a cubic metre of deformed metal is about 2 MJ, equiva-lent to 15 J mol k When cold worked metals are heated to about 0.6T new strain-free grains nucleate and grow to consume all the cold-worked metal. This is called - for obvious reasons - recrystallisation. Metals are much softer when they have been recrystallised (or "annealed"). And provided metals are annealed often enough they can be deformed almost indefinitely. 

Pit formation. If we consider a dissolution nucleus at a screw dislocation intersecting the surface which consists of a cylindrical hole of radius r, one atom layer deep (a), then the free energy of formation of this nucleus will be composed of a volume energy, surface energy, and elastic strain energy term, respectively, as follows ... 

He and Hutchinson (1989) considered a crack approaching an interface as a continuous distribution of dislocations along a semi-infinite half space. The effect of mismatch in elastic properties on the ratio of the strain energy release rates, Gi/Gj, is related to two non-dimensional parameters, the elastic parameters of Dundurs, a and /f (Dundurs, 1968) ... 

Annealing in metals can first lead to stress relaxation in which stored internal strain energy due to plastic deformation is relieved by thermally activated dislocation motion (see Figure 5.18). Because there is enhanced atomic mobility at elevated temperatures, dislocation density can decrease during the recovery process. At still higher temperatures, a process known as recrystallization is possible, in which a new set of... 

Since screw and edge components of a mixed dislocation have no common stress components, one can add the respective strain energies in order to obtain the line energy of a mixed dislocation. The strain and stress fields of a screw dislocation (in direction 5) are respectively... 

Boundaries between solids transmit shear stress, particularly if they are coherent or semicoherent. Therefore, the strain energy density near boundaries changes over the course of solid state reactions. Misfit dislocation networks connected with moving boundaries also change with time. They alter the transport properties at and near the interface. Even if we neglect all this, boundaries between heterogeneous phases are sites of a discontinuous structural change, which may occur cooperatively or by individual thermally activated steps. 

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,... 

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