Long-range stresses associated with boundaries in deformed materials

The deviation from a perfect low energy dislocation structure (LEDS) for the boundaries in deformed polycrystals is described. For polycrystals with approximately equiaxed grains it is argued that the existence of the grain boundaries introduces a population of geometrically necessary dislocations around the boundaries, a population which, because of the long-range stresses associated, does not represent a perfect LEDS, but the deviation is moderate. For polycrystals with flat grains and for polycrystals with the grains subdivided into flat bands the geometrically necessary dislocations may remain in the (grain or band) boundaries, but they still represent a certain, moderate deviation from LEDS. A distinction is made between two contributions from the geometrically necessary dislocations to hardening: conservative hardening which is associated with long-range stresses and frictional hardening which is associated with the dislocation density.