Constitutive rules were developed to include 3-dimensional dislocation mechanisms, such as line tension and dynamic junction formation, within a 2-dimensional dislocation dynamics formulation. Some of the junctions that form dynamically could operate as Frank-Read sources. Boundary value problems were solved by using superposition to represent the solution in terms of the infinite medium fields for discrete dislocations and non-singular complementary fields that enforce the boundary conditions. This framework was used to analyze the plane strain tension of a single crystal. Calculations were carried out to strains of 3 to 8%, and the transition from stage-I to II hardening was exhibited. The dependence of this transition and of the stage-II hardening on constitutive parameters was explored. A variety of stress–strain responses were obtained and compared with available experimental results. The emergence of dislocation cells was seen and the structure of the cells was described.

Incorporating Three-Dimensional Mechanisms into Two-Dimensional Dislocation Dynamics. A.A.Benzerga, Y.Bréchet, A.Needleman, E.Van der Giessen: Modelling and Simulation in Materials Science and Technology, 2004, 12[1], 159-96