Two-dimensional dislocation dynamics simulations under fully periodic boundary conditions were employed to study the relation between microstructure and strength of a material. The material was modeled as an elastic continuum that contains a defect microstructure consisting of a preexisting dislocation population, dislocation sources, and grain boundaries. The mechanical response of such a material was tested by uniaxially loading it up to a certain stress and allowing it to relax until the strain rate falls below a threshold. The total plastic strain obtained for a certain stress level yields the quasi-static stress–strain curve of the material. Besides assuming Frank–Read-like dislocation sources, an investigation was also made of the influence of a pre-existing dislocation density on the flow stress of the model material. The results showed that, despite its inherent simplifications, the Two-dimensional dislocation dynamics model yielded material behavior that was consistent with the classical theories of Taylor and Hall–Petch. Consequently, if set up in a proper way, these models were suited to study plastic deformation of polycrystalline materials.

A Two-Dimensional Dislocation Dynamics Model of the Plastic Deformation of Polycrystalline Metals. N.Ahmed, A.Hartmaier: Journal of the Mechanics and Physics of Solids, 2010, 58[12], 2054-64