  The microstructure of polycrystalline materials consists of networks of grain
boundaries (GBs) and triple junctions (TJs), along which three GBs meet. The
evolution of such microstructures may be driven by surface tension
(capillarity), applied stresses, or other means that lead to a jump in chemical
potential across the GBs. Here, we develop a model for the concurrent evolution
of the GB/TJ network based upon the microscopic mechanism of motion; the motion
of line defects (disconnections) in the GB that have both dislocation and step
character. The evolution involves thermally-activated disconnection
formation/annihilation and migration of multiple disconnections modes/types. We
propose this crystallography-respecting continuum model for the disconnection
mechanism of GB/TJ dynamics derived with a variational approach based on the
principle of maximum energy dissipation. The resultant TJ dynamics is reduced
to an optimization problem with constraints that account for local
microstructure geometry, conservation of Burgers vectors, and thermal-kinetic
limitations on disconnection fluxes. We present analysis of and numerical
simulations based upon our model to demonstrate the dependence of the GB and TJ
mobilities and the TJ drag effect on the disconnection properties, and compare
the predictions with molecular dynamics and experimental observations.
