BEM ANALYSIS OF GRAIN-BOUNDARY SLIDING IN POLYCRYSTALS

The paper presents a boundary element formulation of the stress analysis of an elastic polycrystal with viscous grain boundaries. The microstructure of the polycrystal is modelled as a periodic arrangement of hexagonal grains. Due to symmetry conditions the analysis can be restricted to a representative unit cell with special boundary conditions. These boundary conditions are derived in detail for an overall loading of the polycrystal by normal strains as well as by shear strains. Effective moduli are presented for a completely relaxed grain assemblage and they are compared to the outcome of several micromechanical theories. It is found that these theories cannot give an accurate description of the macroscopic behaviour of the crystal. Finally, an analysis of the stress relaxation of a crystal with nonlinear viscous grain boundaries is performed and the influence of the rate-sensitivity on the response is studied.