  A novel continuum theory of incoherent interfaces with triple junctions is
applied to study three-dimensional coupled grain boundary (GB) motion in
polycrystalline materials. The kinetic relations for grain dynamics, relative
sliding and migration of the boundary, and junction evolution are developed. In
doing so a vectorial form of the geometric coupling factor, which relates the
tangential motion at the GB to the migration, is also obtained. Diffusion along
the GBs and the junctions is allowed so as to prevent nucleation of voids and
overlapping of material near the GBs. The coupled dynamics has been studied in
detail for two bicrystalline and one tricrystalline arrangements. The first
bicrystal consists of two rectangular grains separated by a GB, while the
second is composed of a spherical grain embedded inside a larger grain. The
tricrystal has an arbitrary shaped grain embedded inside a much larger
bicrystal made of two rectangular grains. In all these cases, analytical
solutions are obtained wherever possible while emphasizing the role of various
kinetic coefficients during the coupled motion.
