A mesoscopic theory of dislocation and disclination fields for grain boundary-mediated crystal plasticity

Abstract

A coarse-grained extension of a recent nanoscale elasto-plastic model of polar dislocation and disclination density fields is developed to model grain boundary-mediated plasticity in polycrystals. At a small resolution length scale, the polar dislocation/disclination densities render continuously the discontinuities of the elastic displacements/rotations across grain boundaries. When the resolution length scale increases, the net polarities of a crystal defect ensemble decrease, perhaps to the point where no strain/curvature incompatibility is left in the body. The defect densities are then labeled “statistical”. However both polar and statistical dislocation/disclination densities contribute to plastic flow, and a coarse-grained mesoscopic plastic curvature rate needs to be defined. In addition, whereas it is overlooked at nanoscale where grain boundaries are seen as continua, tangential continuity of the elastic/plastic curvature/strain rates across grain boundaries needs to be considered at mesoscale, because the latter are seen as singular discontinuity interfaces. It induces long-range, grain-to-grain, elastic/plastic interactions across interfaces. The mesoscale model allow preserving the essential features of the lower scale approach. In particular, it is shown that it allows accounting for such plastic deformation mechanisms as grain boundary migration and grain boundary misorientation variation by disclination motion and concurrent dislocation nucleation, when plasticity by dislocation glide is unavailable. Accumulation of polar defect densities in the vicinity of the grain boundaries and triple lines, leading to long-range inter-granular activation of slip and grain size effects, are also predicted by the model.