Effects of grain interaction on deformation in polycrystals

The deformations of a face-centered cubic polycrystal are simulated under idealized (plane strain compression) rolling conditions. A polycrystal is constructed using 1099 rhombic dodecahedron shaped crystals, each discretized with 48 tetrahedra elements. The rhombic dodecahedron is a 12-sided, space-filling polyhedron and serves as an idealized crystal geometry. The material behavior is specified at the level of a single crystal with rate dependent slip. The numerical formulation maintains compatibility and equilibrium in a weak sense using hybrid finite element methodology. The influence of the local neighborhood on crystal deformation is examined by conducting a series of numerical experiments on the same set of crystals. Each simulation uses a different spatial mapping of orientations to effectively alter the neighborhood of each crystal, allowing the dependence of deformation on crystal orientation to be examined. Comparisons are made to earlier results obtained with brick shaped crystals and to the results obtained with a second polycrystal consisting of 172 crystals with 576 elements in each rhombic dodecahedron. Coarse crystal discretizations are adequate for modeling bulk anisotropic properties, but a detailed investigation of local neighborhood effects require a finely discretized mesh that is better able to capture gradients in the deformation field.