Strain fields and energies of grain boundary triple junctions

We compute the strain fields and the interactions between dislocations at the junctions of classical small-angle grain boundaries. It is shown that, in contrast with the results for infinite small-angle boundaries, there are always forces acting on the dislocations in the arrays that define the grain boundaries, and that there is also a long-range strain field and consequently an excess elastically stored energy associated with the triple junction (TJ). We explore the variations of the forces on the dislocations, and the excess stored energy of the TJ, with the dihedral angles formed by the grain boundaries and also with their misorientations. We find that the “equilibrium” dihedral angle based upon the Herring equation and the energies of the individual grain boundaries does not generally correspond to any kind of force or energy minimum. This relates to an unwarranted assumption in Herring’s original derivation, that no interactions occur between the grain boundaries that make up a TJ.