Size and boundary effects in discrete dislocation dynamics: coupling with continuum finite element

In this work, we develop a framework coupling continuum elasto-viscoplasticity with three-dimensional discrete dislocation dynamics (micro3d). The main problem is to carry out rigorous analyses to simulate the deformation of single crystal metals (fcc and bcc) of finite domains. While the overall macroscopic response of the crystal is based on the continuum theory, the constitutive response is determined by discrete dislocation dynamics analyses using micro3d. Size effects are investigated by considering two boundary value problems: (1) uniaxial loading of a single crystal cube, and (2) bending of a single crystal micro-beam. It is shown that boundary conditions and the size of the computational cell have significant effect on the results due to image stresses from free-boundaries. The investigation shows that surface effects cannot be ignored regardless of the cell size, and may result in errors as much as 10%. Preliminary results pertaining to dislocation structures under bending conditions are also given.