Grain boundary and triple junction energies in crystalline media: A disclination based approach

A disclination-based framework is used to quantify the effect of rotational incompatibility on internal stresses and excess energies in crystalline media in the presence of symmetric tilt boundaries and triple junctions. Also, a new theoretical model for triple junctions, based on the balance of rotational incompatibility at surfaces of discontinuity is introduced. The systems internal energies are obtained first by considering solely the Cauchy stress and elastic strain relationship and then by considering a more general Cosserat-type elastic response, involving couple-stresses and elastic curvature. Comparison between the two models in face centered cubic systems yields quantification of the contribution of rotational defects to internal energy. The work reveals that the curvature and its work conjugate provide for a significant part of the elastic strain energy of symmetric tilt boundaries. In the case of triple junctions, due to screening, such contribution is found to fluctuate significantly. The model is used to exhibit the evolution of the energy of triple junctions built solely from symmetric tilt boundaries as a function of their degrees of freedom. It reveals significant departure from Herrings relationship.