Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics

Constitutive rules are developed to include three-dimensional dislocation mechanisms, such as line tension and dynamic junction formation, within a two-dimensional dislocation dynamics formulation. Some of the junctions that form dynamically can operate as Frank–Read sources. Boundary value problems are 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 is used to analyse the plane strain tension of a single crystal. Calculations are carried out to strains of 3–8%, and the transition from stage I to II hardening is exhibited. The dependence of this transition and of the stage II hardening on constitutive parameters is explored. A variety of stress–strain responses are obtained and compared with available experimental results. The emergence of dislocation cells is seen and the structure of the cells is described.