In the phase field model of dislocations, the short-range, non-linear core–core interactions were characterized through the crystalline energy and the gradient energy. The approximations to these energies, used in previous phase field models, were extended and generalized here in order to account for dislocation reactions leading to network formation. In order to characterize dislocation activities involving all slip planes, it was suggested that the crystalline energy was a function of a general plastic strain tensor produced by arbitrary linear combinations of simple shears associated with each slip system. For the four {111} slip planes in a face-centered cubic crystal, a particular form of such a crystalline energy was formulated by simple linear superposition of the interplanar potential of each individual slip plane. A more detail and general form of the gradient energy was derived from the consideration of the total Burgers vector dependence of dislocation line energy. Examples of applications were presented for interactions between two dislocation loops expanding on either a single slip plane or two intersecting slip planes, as well as for more complex reactions taking place in dislocation networks. It was shown that the generalized expressions were able to handle self-consistently reactions among dislocations of all slip systems in accord with Frank’s rule. These extensions were necessary steps toward advanced applications of the phase field method to dislocation substructure formation and coarsening.

Phase Field Model of Dislocation Networks. C.Shen, Y.Wang: Acta Materialia, 2003, 51[9], 2595-610