The phase-field model for crystallographic slip, of Ortiz and Koslowski et al., was extended so as to treat to slip processes that required the activation of multiple slip systems. The resultant model was applied to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane was described by means of multiple integer-valued phase fields. It was shown that all of the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, could be written explicitly in terms of the multi-phase field. The model was used to determine the stable dislocation structures that would arise in an array of finite twist boundaries. These structures were found to consist of regular square, or hexagonal, dislocation networks which were separated by complex dislocation pile-ups over the intervening transition layers.

A Multi-Phase Field Model of Planar Dislocation Networks. M.Koslowski, M.Ortiz: Modelling and Simulation in Materials Science and Technology, 2004, 12[6], 1087-97