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 11 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.