A disclination-based approach for mesoscopic statistical modeling of grain subdivision in niobium

A mesoscopic statistical model for orientation fragmentation is presented and applied to a niobium polycrystal under uniaxial compression at room temperature. It is proposed that re-orientation bands nucleate at grain boundaries as a consequence of mismatch stresses and strains resulting from prior intersections of slip bands with these boundaries. In this view, the elementary process responsible for slip patterning also governs re-orientation banding. The model assumes that this elementary process be superjog formation in the bulk with subsequent flip-over of edge dislocations. Balance equations are formulated for the evolution of the densities of forest edge and screw dislocations, slip band edge and screw dislocations, and propagating and immobilized partial disclination dipoles. Microstructural parameters as well as work-hardening contributions can be predicted in reasonable agreement with experiment. The mismatch stress contribution to work-hardening is predicted to saturate, while a barrier contribution related to the newly formed re-orientation band boundaries may become decisive at large strains.