A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity
Résumé
A continuum mechanics model is introduced for a core and structure sensitive modeling of grain boundary mediated plasticity. It accounts for long range elastic strain and curvature incompatibilities due to the presence of dislocation and disclination densities. The coupled spatio-temporal evolution of the crystal defects is also accounted for by transport equations. Based on atomistic structures, copper tilt boundaries are modeled with periodic sequences of wedge disclination dipoles. Their self-relaxation by transport leads to grain boundary configurations with lower elastic energies, which are compared to molecular statics values. The characteristic internal length inherent to strain gradient elasticity, which relates the elastic energy weight of couple-stresses to that of stresses, is chosen to retrieve the elastic energy obtained by atomistic simulations. This length is found to be lower than interatomic distances. In agreement with atomistic modeling, couple-stress elasticity is thought to be relevant for the modeling of highly heterogeneous defect microstructures at atomic resolution scales only.