The increasing application of plane-strain testing at the (sub-) micron length scale of materials that comprise elastically anisotropic cubic crystals has motivated the development of an anisotropic two-dimensional discrete dislocation plasticity method. The method relied upon the observation that plane-strain plastic deformation of cubic crystals was possible in specific orientations when described in terms of edge dislocations on three effective slip systems. The displacement and stress fields of such dislocations in an unbounded anisotropic crystal were recapitulated, and modified constitutive rules were proposed for the discrete dislocation dynamics of anisotropic single crystals. Subsequently, to handle polycrystalline problems, an idea of O’Day and Curtin (2004) was followed: each grain was treated as a plastic domain, and superposition was used to determine the overall response. This method allows for a computationally efficient analysis of micro-scale size effects. As an application, free-standing thin copper films under plane-strain tension were studied. Firstly, the computational framework was validated for the special case of isotropic thin films modelled by means of a standard two-dimensional discrete dislocation plasticity method. Next, predictions of size dependent plastic behavior in anisotropic columnar-grained thin films with varying thickness/grain size were compared with the isotropic results.

Plane-Strain Discrete Dislocation Plasticity Incorporating Anisotropic Elasticity. S.S.Shishvan, S.Mohammadi, M.Rahimian, E.Van der Giessen: International Journal of Solids and Structures, 2011, 48[2], 374-87